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An Inventive Method for Eco-Efficient Operation of Home Energy Management Systems

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A demand response (DR) based home energy management systems (HEMS) synergies with renewable energy sources (RESs) and energy storage systems (ESSs). In this work, a three-step simulation based posteriori method is proposed to develop a scheme for eco-efficient operation of HEMS. The proposed method provides the trade-off between the net cost of energy ( C E n e t ) and the time-based discomfort ( T B D ) due to shifting of home appliances (HAs). At step-1, primary trade-offs for C E n e t , T B D and minimal emissions T E M i s s are generated through a heuristic method. This method takes into account photovoltaic availability, the state of charge, the related rates for the storage system, mixed shifting of HAs, inclining block rates, the sharing-based parallel operation of power sources, and selling of the renewable energy to the utility. The search has been driven through multi-objective genetic algorithm and Pareto based optimization. A filtration mechanism (based on the trends exhibited by T E M i s s in consideration of C E n e t and T B D ) is devised to harness the trade-offs with minimal emissions. At step-2, a constraint filter based on the average value of T E M i s s is used to filter out the trade-offs with extremely high values of T E M i s s . At step-3, another constraint filter (made up of an average surface fit for T E M i s s ) is applied to screen out the trade-offs with marginally high values of T E M i s s . The surface fit is developed using polynomial models for regression based on the least sum of squared errors. The selected solutions are classified for critical trade-off analysis to enable the consumer choice for the best options. Furthermore, simulations validate our proposed method in terms of aforementioned objectives.
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energies
Article
An Inventive Method for Eco-Efficient Operation of
Home Energy Management Systems
Bilal Hussain , Nadeem Javaid , Qadeer Ul Hasan , Sakeena Javaid, Asif Khan and
Shahzad A. Malik
Department of Computer Science, COMSATS University Islamabad, Islamabad 44000, Pakistan;
bilal_hussain@yahoo.com (B.H.); qadeer.hasan@comsats.edu.pk (Q.U.H.); sakeenajavaid@gmail.com (S.J.);
akbarech@gmail.com (A.K.); smalik@comsats.edu.pk (S.A.M.)
*Correspondence: nadeemjavaidqau@gmail.com or nadeemjavaid@comsats.edu.pk; Tel.: +92-300-579-2728
Received: 21 August 2018; Accepted: 29 October 2018; Published: 8 November 2018


Abstract:
A demand response (DR) based home energy management systems (HEMS) synergies
with renewable energy sources (RESs) and energy storage systems (ESSs). In this work, a three-step
simulation based posteriori method is proposed to develop a scheme for eco-efficient operation of
HEMS. The proposed method provides the trade-off between the net cost of energy (
CEnet
) and
the time-based discomfort (
TBD
) due to shifting of home appliances (HAs). At step-1, primary
trade-offs for
CEnet
,
TBD
and minimal emissions
TE Miss
are generated through a heuristic method.
This method takes into account photovoltaic availability, the state of charge, the related rates for the
storage system, mixed shifting of HAs, inclining block rates, the sharing-based parallel operation
of power sources, and selling of the renewable energy to the utility. The search has been driven
through multi-objective genetic algorithm and Pareto based optimization. A filtration mechanism
(based on the trends exhibited by
TE Miss
in consideration of
CEnet
and
TBD
) is devised to harness
the trade-offs with minimal emissions. At step-2, a constraint filter based on the average value of
TE Miss
is used to filter out the trade-offs with extremely high values of
TE Miss
. At step-3, another
constraint filter (made up of an average surface fit for
TE Miss
) is applied to screen out the trade-offs
with marginally high values of
TE Miss
. The surface fit is developed using polynomial models for
regression based on the least sum of squared errors. The selected solutions are classified for critical
trade-off analysis to enable the consumer choice for the best options. Furthermore, simulations
validate our proposed method in terms of aforementioned objectives.
Keywords:
eco-efficient home energy management, dispatch of renewables and energy storage
systems, load-shedding-compensating dispatchable generators, optimization using surface fitting
techniques, multi-objective genetic algorithm, Pareto optimization
1. Introduction
From the previous decades, the energy requirement has grown to a critical level; however,
the generation units have not been maintained at a sufficient rate to manage this increasing demand.
The balance between demand and generation is a vital requirement for stable power system operation.
The problem to maintain this balance has conventionally been addressed in the past; utilities have
upgraded their centralized generation units and transmission capabilities through some supply side
management methodologies. However, during the previous decade, demand-side management
(DSM) has become a substituent scheme to manage the increasing requirement of energy which
focuses on the consumer side. The home energy management system (HEMS) is used to implement
DSM in a home. Major approaches for HEMS operation include price-based demand response (DR),
and DR synergized with renewable energy sources (RESs) and energy storage systems (ESSs) optimal
Energies 2018,11, 3091; doi:10.3390/en11113091 www.mdpi.com/journal/energies
Energies 2018,11, 3091 2 of 40
dispatch (DRSREOD) [
1
]. The DR-based HEMS operation schedules the consumer ’s loads by shifting
them towards the off-peak periods. Such scheduling benefits the consumer with a minimized cost
of energy (
CE
) based on the acceptable value of time-based discomfort (
TBD
) [
2
,
3
]. The utility,
on the other side, is benefited with a reduced cost of generation through a smoother demand profile.
The DRSREOD-based HEMS operation schedules the load in coordination with the optimal dispatch of
the power grid, renewable energy sources (RESs) and energy storage systems (ESSs). The operation of
such HEMS introduces additional benefits by minimizing the electricity cost, minimizing high demands
and permanent demands, increasing total cost minimization and empowering the selling of the extra
power to the utility [
4
11
]. The aforementioned HEMSs are modeled to optimize the objectives
comprising the net
CE
(
CEnet
), consumer discomfort/inconvenience, and peak and permanent
demands. The abbreviations and nomenclature are given in Tables 1and 2, respectively.
Table 1. Abbreviations.
AS
Advanced scheduling/advanced
scheduled ASCF Average-surface-based
constraint filter
AVCF Average-value-based constraint
filter DAP Day-ahead pricing
DG Dispatchable generator DR Demand response
DRSREOD DR synergized with RESs and
ESS optimal dispatch DRSREODLDG DRSREOD integrated with load
shedding-compensating DG
DS Delayed scheduling/delayed
scheduled EM Energy management
ESS Energy storage system EVH Electric vehicle
GA Genetic algorithm HA Home appliance
HEMS Home energy management
system LDG Load shedding-compensating
DG
LSD Load shedding MGD Micro-grid
MILP Mixed integer linear
programming MOGA Multi-objective GA
MS
Mixed scheduled (includes SHAs
with AS and DS) NSHA Non-shiftable home appliance
PO Pareto optimization POS Pareto-optimal set
PV Photovoltaic energy RES Renewable energy source
RTP Real-time pricing SB Storage battery
SHA Shiftable home appliance ToU Time-of-use pricing
WSMD Weighted sum method WTB Wind turbine
PAR Peak-to-average ratio EFTs Emission factors
Furthermore, a general architecture of DRSREODLDG-based HEMS is shown in Figure 1.
The main components of such a system include home appliances (HAs), RESs, an ESS, an LDG,
the HEM controller (HEMC) and the smart meter (SM) with the local communication for home area
network. The SM is used for bidirectional interaction in order to exchange the electricity bill and
power consumption data between users and power grid. The HEMC embeds whole computational
intelligence which is sufficient for the proposed optimum HEMS operations.
Energies 2018,11, 3091 3 of 40
Remote
control
Internet RESs
U
¡
lity company
Smart meter
LDG
Figure 1.
Architecture for demand response synergized with renewable energy sources and energy
storage systems optimal dispatch integrated with load shedding-compensating dispatchable generator
based home energy management system for a smart home [10].
Furthermore, the rampant rise in green house gas (GHG) emissions, the consequent climate
changes and the related environmental issues have raised serious concerns over the quality of the
life on the earth. In order to mitigate the serious environmental issues, various proposals have
been discussed for GHG emissions at the highest international forums to confine them. The Kyoto
protocol of United Nations Framework Convention on climate change has been mutually signed by
192 countries all over the world which proposes a reduction in GHG emissions through selling of
emission commodities [
12
]. Such a trading sets penalties and quantitative limitations on emissions
by polluters that may include utilities, independent microgrid (MGD) operators, and the prosumers
having fossil fuel based generation deployed with DRSREODLDG-based HEMSs.
The aforementioned scenario has incentivized utilities to reduce not only the cost of generation of
energy; however, also the supply-side emissions making use of RESs installed for DRSREOD-based
HEMS. The research on HEMS now seems to focus on reducing the GHG emissions along with the
other well-known objectives for
CE
,
TBD
, etc. In [
13
], a scheme for DR-based HEMS is presented.
Non-critical house loads are shifted towards low demand periods for minimizing the daily bill of
the generation-side and the supply-side emissions. It is validated that implementation of the DR
program effectively reduces the cost of generation on the supply-side; however, the emission on
this side is reduced only when peak demand is met by high emission fuels based peaking plants.
The DRSREOD-based HEMS, on the other hand, through an optimal operation of HEMS devices,
can easily be used for reducing the supply-side emissions along with the reductions in the
CEnet
for
the consumer and cost of generation for the utility. In [
14
], the authors present a scheme for optimal
scheduling of shiftable home appliances (SHAs) integrated with the optimal dispatch of an RES and an
storage battery (SB). The objectives include reductions in
CEnet
, temperature based discomfort, peak
load, and the GHG emissions. The supply-side emissions are computed using GHG emission factors
(EFTs) for the energy mix adopted at different times of the day. The supply-side emissions are reduced
through an optimal operation of local RESs and SBs during high emission times.
Furthermore, fossil fuel based DGs are integrated into MGDs to improve the self-healing structure
and the flexibilty of the power supply. In [
15
], an operational scheme is developed for a stand-alone
HEMS operation using PSO. The scheme is based on load shifting of SHAs, an optimal dispatch of a
wind turbine (WTB), a DG, and an SB. The DG is operated at the rated power in order to improve its
efficiency and to reduce emissions. The power from the grid, however, is not included in the modeling.
Energies 2018,11, 3091 4 of 40
In [
16
], an optimal dispatch scheme for a PV unit, a WTB, an ESS, a DG, and the power grid to supply
a fixed load profile in an MGD is computed using GA. Constraints for ESS charge/discharge rates,
generator start/stop and supply capacity are taken into account. Net emission for the power supplied
by the grid and local DGs are computed.
Table 2. Nomenclature.
BVector for numbering SHAs CE Electricity bill from the utility
CEMiss Cost of emissions paid by the utility to
prosumer for his sold renewable energy CEnet Net cost of energy to be paid by
the consumer
EFT GHG emission factor EMiss Vector of GHG emissions from
the LDG
ENslot Vector of the ending slots of the SHAs’
operating time intervals IBR Inclining block rate
Iterat Number of iterations KNumber of SHAs
LoT Vector of lengths of SHAs
operating times NNumber of slots in the scheduling
horizon
Ng_mx Maximum number of generations for
the GA Pa Vector of per slot power of SHAs
Pch Vector of SB charging power values Pch_mx Maximum SB charge rate
Pdl Vector of power dissipated in a dummy
load during LSD Pds Vector of SB discharging power
values
Pds_mx Maximum SB discharge rate PE Vector of the electricity price from
the grid
PE f Vector of the feed-in tariff PE g Levelized cost of energy from
the LDG
Pgd Vector of the power from the grid Pgds Power grid status
Pgn Vector of the power supplied by
the LDG Ppv Vector of the power from the PV
Pschd Vector of the scheduled load Psold Vector of the energy sold to the grid
SoC Vector of states of charge SoC(init)Initial SoC at the start of the
scheduling horizon
SoC_mn Minimum SoC limit SoC_mx Maximum SoC limit
SSE Sum of the squared error terms in
regression STslot Vector of the starting slots of the
SHAs’ operating time intervals
Sty p Vector of scheduling types for SHAs TBD Average time-based discomfort due
to shifting of AS and DS type HAs
TE Miss Total GHG emissions during the
scheduling horizon
TE Miss_
Resid_avg
Residual below the average value of
TEMiss used as reference for
filtration of solutions in step-2
Furthermore, fossil-based LDGs are integrated into DRSREOD-based HEMSs to supply the load
during load shedding (LSD) hours. Such a LDG adds a vital benefit of uninterrupted supply of power
to DRSREOD-based HEMS. An algorithm for optimal sizing of LDG for DRSREODLDG-based HEMS
was proposed in our recent research [
11
]. The proposed sizing was based on the trade-off analysis
for the parameters including
CE
,
TBD
and size of LDG. An uninterrupted supply of power through
the integration of LDG was ensured; however, the operational schemes for HEMS were remained to
Energies 2018,11, 3091 5 of 40
be analyzed for the emissions released during the LDG operations. To implement an eco-efficient
operation of DRSREODLDG-based HEMS, optimal trade-offs between
CEnet
,
TBD
and minimal GHG
emissions
(TE Miss)
need to be computed. This research introduces a method to harness a diversified
set of solutions to decision vector
Tst
and the related trade-offs for
CEnet
,
TBD
and minimal
TE Miss
for an eco-efficient HEMS operation.
The proposed method for an eco-efficient operation of DRSREODLDG-based HEMS is based on
a three-step approach. In step-1, a set of primary solutions in terms of
Tst
and the related trade-offs
for
CEnet
,
TBD
and minimal
TE Miss
are generated using Algorithm 1. The algorithm is based on
a heuristic derived from our previous studies on HEMS in [
11
]. The proposed heuristic takes into
account PV availability, the state of charge, the related rates for the storage system and the similar
functionality of the sources. To achieve maximum reduction in
CEnet
, SHAs are modeled for mixed
scheduled (MS) as already validated in [
11
]. This research formulates the trade-off parameters for:
CEnet
to include the cost of energy purchased from the grid, cost of energy sold to the grid and the cost
of energy supplied by the LDG;
TE Miss
to include the energy supplied by the LDG during LSD hours,
EFT
based on the calorific value of the fuel, the consumption efficiency of the LDG and the related
emission factors for GHGs; and
TBD
to include the delay in the starting times of delay scheduling (DS)
type and advanced completion of the job of advanced scheduling (AS) type for HAs. The trade-off
solutions obtained in step-1 are analyzed for
TE Miss
as related to the trade-offs between
CEnet
and
TBD as shown in Figure 2.
R² = 0.8501
R² = 0.0111
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Figure 2. Un-even trends for T EMiss as related to CEnet and TBD.
The plot in Figure 2reveals a highly un-even relation between
TE Miss
and the related parameters
for
CEnet
and
TBD
. This un-even trend for
TE Miss
is exploited to screen out/exclude a set of trade-offs
with larger values of
TE Miss
using a constraint filtration mechanism as presented in Algorithm 2
(step-2 and step-3). In step-2, an average value based constraint filter (AVCF) for
TE Miss
is developed
and applied to filter out the trade-offs with extremely high values of
TE Miss
. In step-3, average
surface fits for
TE Miss
are developed in terms of
CEnet
and
TBD
using polynomial based regression.
The most suitable polynomial is selected after cross-validation of 25 number of polynomial model that
fits on their capabilities in order to reduce
TE Miss
and
TBD
, and to maximize the number of diverse
trade-offs for
CEnet
and
TBD
. The average surface fit based constraint filter (ASCF) with the selected
polynomial formulation is applied to screen out the trade-offs with even marginally higher values of
Energies 2018,11, 3091 6 of 40
TE Miss
. The solutions for an eco-efficient HEMS operation are thus achieved including diversified
trade-offs for CEnet,TBD and minimal TEMiss. Followings are the novelties of this research:
An innovative method is proposed to harness diversified trade-offs between
CEnet
,
TBD
and
minimal TE Miss for an eco-efficient operation of DRSREODLDG-based HEMS.
Trade-offs for such HEMS have rarely been computed by combining a multi-objective genetic
algorithm or Pareto optimization (MOGA/PO) based heuristic and regression based constraint
filtration. The polynomial model fit for regression is based on its capabilities to reduce the
trade-off parameters for eco-efficient HEMS operation.
Most of the authors use the weighted sum method (WSMD) to handle multi-objectivity for similar
problems. This research presents a diverse set of trade-offs that are critically analyzed to enable
the consumer choosing the best option.
Trends exhibited by the trade-off parameters are analyzed based on vital factors affecting these
parameters, e.g., loss of unused energy from the PV unit.
The proposed method validated to minimize the emissions from a local LDG for a
DRSREODLDG-based HEMS; however, it is easily extendable to reduce the supply-side emissions
as well.
The organization of the paper is as follows: Section 2describes the related work whereas the
system model is elaborated in Section 3. The problem formulation for eco-efficient operation of
DRSREODLDG-based HEMS and the techniques used to solve this problem are presented in Section 4.
The proposed Algorithm 1to generate primary trade-offs for optimal HEMS operations, and Algorithm
2to harness eco-efficient trade-offs through a constraint filtration mechanism are presented in Section 5.
In Section 6, simulations are presented to demonstrate the validity of Algorithm 1to generate schemes
for DRSREODLDG-based HEMS operation in terms of
Tst
and the primary trade-offs between
CEnet
,
TBD
and
TE Miss
. The trends exhibited by the primary trade-offs are analyzed in detail and the bases
for the selection of constraint filters including AVCF and ASCF are validated. Further simulations are
presented to demonstrate the validity of Algorithm 2to harness eco-efficient trade-off solutions using
the optimal constraint filters. Conclusions and future work are discussed in Section 7.
2. Related Work
With the installation of smart grid technologies enabling DSM, a widespread deployment of DR-
and DRSREOD-based HEMSs has been carried out throughout the world in the past few years [
17
,
18
].
The report
in [
17
] has given an overview and boost to the RESs by forming policies among various contries.
In [18], the current phase of Paris agreement has focused on developing a global approach, which limits
the GHG emissions of all countries. In recent years, authors have presented various models and methods
for the optimal operation of such systems [
2
8
]. The objectives for optimal HEMS operation include
minimizing
CE
,
TBD
, peak-to-average ratio
(PAR)
and peak/permanent demands [
19
21
].
In [19]
,
the authors
have used different priorities to derive user comfort. Khan et al. [
20
] have used three different
appliances to minimize
CE
,
TBD
, and
PAR
. Meta-heuristics approaches including optimal stopping rule
are used as optimization schemes. Similarly, the authors in [
21
] have applied meta-heuristics approaches
along with a hybrid approach to minimize
CE
. Furthermore, utilities owning energy deficient power
networks in developing countries are subjecting their users for LSD to maintain energy demand and
supply. In such power networks, consumers deploy a LSD-compensating DG in DRSREOD-based HEMS
for ensuring the reliable distribution of the energy [
11
]. The aforementioned objectives for optimal HEMS
operation have been achieved using optimization techniques like linear programming (LP), mixed integer
LP (MILP), advanced heuristics, etc.
Additionally, the issue regarding serious environmental concerns over the use of fossil fuels has
been raised at international forums consistently in the past few decades. Recently, worldwide consensus
has been reached to reduce the GHG emissions by selling them as commodities [
12
]. Such trading
sets quantitative limitations on the emissions made by polluters that may include utilities, independent
Energies 2018,11, 3091 7 of 40
MGD operators and the prosumers having local fossil fuel based generations. The present scenario
based on the polluter pays principle has incentivized utilities to reduce not only the generation cost;
however, the supply-side emissions as well while making use of the RESs installed for DRSREOD-based
HEMSs [
14
,
22
,
23
]. Furthermore, MGD operators having RESs, ESSs and DGs also include
TEMiss
as an
objective in the optimal dispatch scheme for their systems [
15
,
16
,
24
]. Furthermore, in energy-deficient
power networks, DRSREODLDG-based HEMSs having LSD-compensating DGs are used to ensure an
uninterrupted supply of power during LSD hours [
11
]. The operation of LDG in such HEMSs, however,
does accompany the release of emissions, which needs to be minimized.
The related work includes the recent research on models and methods to achieve important
objectives for DR and DRSREOD-based HEMSs including reductions in
TE Miss
(supply-side),
CEnet
,
and
TBD
; for MGDs including reductions in
TE Miss
and
CEnet
; and for DRSREODLDG-based HEMS
including reductions in
TE Miss
(local),
CEnet
and
TBD
. The recent research related to the proposed
method for an eco-efficient operation of DRSREODLDG-based HEMS is summarized in Tables 3and 4.
Table 3. Related work of proposed method for eco-efficient DRSREODLDG-based HEMS operation.
Tariff + HEMS
Devices Objectives Salient Features of the HEMS Achievements Limitations Optimization
Method
ToU + SHAs [2]CE and TBD
Horizon divided into 4 windows;
HAs classified in terms of occupancy,
activity and delay tolerance are
operated in designated windows;
Objectives for CE and T BD are
combined through the WSMD for
user comfort
Gain of 0.185 for
user comfort,
compared with
0.149 for
unscheduled
loads
Fixed windows
limit user
convenience;
TE Miss not
included
Particle swarm
optimization
(PSO)
ToU/IBR +SHAs
+EVH [3]
CE, peak load
and satisfaction
Optimized scheduling for SHAs and
charging/discharging of EVHs;
Preferred periods for NSHAs; CE
and interruption cost for SHAs are
combined using the WSMD
CE reduced by
22% through
optimal SHAs
scheduling
TE Miss not
included CPLEX solver
RTP+SHAs + PV [4]
CE and
frustration due
to time shifting
Prosumer-based HEMS; Predicted
demand; Delayed/advanced
scheduling; HAs clustered for
operation in three time windows;
Frustration and CE combined using
the WSMD; Penalty cost to consumer
for not providing PV to utility
CE reduced by
11% for DR and
further through
sale of PV energy
Start/end limits
not modeled, that
affects
convenience;
SB/TE Miss not
included
linear
programming
(LP)
ToU/IBR +SHAs
+Elastic +PV [5]
CE,T BD and
PAR
Evaluation of HEMS algorithms
based on GA, BPSO and ant colony
optimization (ACO); Fixed HAs,
SHAs, and elastic HAs;
Knapsack-based formulation;
CE
and
TBD combined using the WSMD
GA-based
algorithm
outperforms
BPSO and ACO
for
CE
,
TBD
, and
PAR
SB may be
included with PV
to reduce TBD;
TE Miss not
included
GA, Binary
PSO (BPSO),
and ACO
ToU + SHAs +
Curtailable + Fixed +
PV + SB [6]
CE and peak
demand
Priority-based resource scheduling;
Maximized PV usage; SB used after
PV; SHAs operation based on
real-time priority adjustment
CE reduced by
15.96% and sold
units/day are 90
Nos.
TBD and
TE Miss not
included
Heuristic based
on resource
priorities
DAP + PV + SB +
EVH [7]CE
EVH scheduling integrated with
SB/EVH/PV power utilization;
Difference between CE and cost of
energy sold minimized; SB charged
from PV/utility for low demand
periods and discharged during peak
periods; Penalty function adjusts
priority of PV, SB, and EVHs to sell
energy
CE reduced by
65% by shifting
EVHs towards
off-peak periods
and selling PV,
ESS, and EVH
energy
SHAs scheduling
and objectives for
TBD and
TE Miss not
included
MILP/CPLEX
solver
RTP/LMP + SHAs +
Curtailable + PV +
SB [8]
CE
DR for aggregated homes; Locational
marginal price-based HA shifting
and AC temperature control; PV/SB
integrated to supply loads based on
PV, SoC,Pds_m x and Pch_mx
CE reduced by
9.5% for DR and
by 28.6% for
DRSREOD for
1000 homes
TBD and
TE Miss not
included
LP
ToU/IBR + Fixed +
SHAs + PV +
SB+LDG [11]
CE,T BD and
LDG size
Sizing of an LDG based on DR based
forward/reverse load shifting of
SHAs integrated with an optimal
dispatch based on parallel operation
of RESs, SB, and LDG; LDG operates
during LSD in collaboration with
RES and SB
Trade-offs
provided for
optimal sizing of
LSD-compensating
DGs with
CE
and
TBD
Trade-off
solutions for
CEnet,TB D and
TE Miss not
computed
MOGA/PO
based heuristic
Note: The abbreviations used in table are defined in Table 1.
Energies 2018,11, 3091 8 of 40
2.1. Emissions Reduction Using DR-Based HEMSs
Most of the research on DR-based HEMS has focused on objectives like
CE
,
PAR
, peak load
and discomfort [
2
,
3
]. Such systems have limited capabilities to play a role in the reduction of GHG
emissions. In [
13
], a scheme for DR based HEMS is presented. Non-critical house loads are shifted
towards off-peak hours to minimize the daily cost of generation and emissions for the supply-side.
It is validated that implementation of DR program effectively reduces the cost of generation on the
supply-side; however, the emissions on this side are reduced only when peak demand is met by
peaking plants based on high emission fuels like coal, diesel, etc.
Table 4. Related work.
DAP/ToU +
SHAs [13]
CE and
TE Miss
DR-based scheduling of noncritical loads
to minimize daily cost of generation and
the supply-side emission for the utility
CE reduced by
3.7% and
TE Miss
by 20%
The emission is
reduced only if
peaking plants
are fossil fuel
based
Heuristic/stochastic
programming
ToU + SHAs
+ PV + EVH
+ ESS [14]
CE, thermal
discomfort,
total/peak,
load and
TE Miss
DR-based scheduling of SHAs integrated
with the optimal dispatch of RES, SB, and
the power grid; TE Miss computed using
emission coefficients for the energy mix
adopted by utility; DRSREOD reduces
supply-side TE Miss by supplying load
during high emission hours
CE reduced by
28% at a
discomfort of
41.7%
Trade-off
solutions for CE,
TBD and
TE Miss not
available to
consumer
MILP
RTP + SHAs
+ WTB + DG
+ SB [15]
Generation
Cost, DG
efficiency
and TE Miss
An algorithm for an optimal HEMS
operation for HES including WTB, DG,
and SB; PSO is compared with sequential
quadratic programming (SQP)
PSO is 90 times
faster; DG at
rated power
improves
efficiency and
reduces TEMiss
Computing of
TE Miss,T BD
and the grid
power not
included
LP/PSO and
SQP
ToU + Fixed
+ PV + WTB
+ FC + ESS +
DGs [16]
Operating
cost, TE Miss
and RES
usage
Algorithm for optimal dispatch of PV,
WTB, ESS, and main grid in a MGD;
Constraints for ESS charge/discharge,
DGs start/stop, emissions and supply
capacity considered; TE Miss computed
using emission factors for grid, power
supplied from local plants and ESS
Model validated
for varied load
for different
seasons
Load shifting not
considered while
computing
dispatch for
power sources
GA
TOU/RTP +
thermostat +
SHAs + PV
+ SB [22]
CE,
consumption,
TE Miss, and
peak
demand
Shifting of major HVAC loads integrated
with PV, SB and power grid dispatch;
HEMS operation based on user
preferences, home occupancy, day ahead
emissions and climate forecasts; Net
emission cost includes carbon footprint
of customer from grid electricity usage
minus emission reduction by injecting
emission free PV energy
CE reduced by
20% and peak
load reduced by
50%
Diversified
trade-off
solutions based
on CE,T BD and
TE Miss not
available to
consumer
MILP/GLPK
Solver
DAP + PV +
SB [23]
Welfare for
consumers
and the
utility, and
privacy for
the consumer
An algorithm to maximize a sum of
benefits to consumers and the utility;
Emission mitigation through CEMiss
based trading; Utility profited by
reducing his carbons purchasing energy
from the local RES and the SB during
high emission hours; Welfare includes
benefits due to consumption-based
satisfaction and reduced electricity cost
to the consumer, and reduced peak load,
generation cost and emissions to
the utility
A welfare
function
proposed to
integrate optimal
objectives;
Dynamic selling
and buy-back
tariff proposed
Diversified
trade-off
solutions based
on CE,T BD and
TE Miss are not
available to the
consumer
Lagrange
multipliers
used to
introduce
scalability and
privacy
Note: The abbreviations used in table are defined in Table 1.
2.2. Emissions Reduction Using DRSREOD-Based HEMSs
Most of the models for DRSREOD-based HEMS presented in the recent past are based on optimal
scheduling of SHAs integrated with the optimal dispatch of RESs and ESSs. HEMS problems for
these models have been solved to reduce
CE
and discomfort for the consumer, and to minimize
peak load/PAR and cost of generation for the utility [
4
8
]. Recently, in the context of worldwide
concerns over GHG emissions, authors have focused on the reduction in emission as an objective
Energies 2018,11, 3091 9 of 40
for DRSREOD-based HEMS. In [
14
], authors proposed a scheme for optimal scheduling of SHAs
integrated with the optimal dispatch of RES, SB, and the utility. Major goals include reductions in
CEnet
, temperature based discomfort, peak load, and the supply-side emissions. Such emissions are
computed using emission coefficients for the energy mix adopted by the utility during various times
of the day. An optimal dispatch of local RESs and SBs results in the reduction of net supply-side
emissions by supplying the load during high emission hours. MILP has been used to solve the model.
In [
22
], an operating mechanism of major HAs including heating and cooling appliances integrated
with the optimal dispatch of PV and SB is presented. The algorithm for real-time HEMS operation is
based on user preferences, home occupancy, day ahead emissions and climate forecasts. The objectives
for reduction in
CE
, electric consumption,
TE Miss
, and the peak demand are formulated. The net cost
of emission includes carbon footprint of the customer from the grid electricity usage minus carbon
reduction from injecting emission-free electricity from RES. In [
23
], a prosumer based algorithm is
presented to maximize the sum of benefits to the consumer and the utility. The emission trading has
been considered as a mean of mitigating this commodity. The utility is profited by reducing his carbon
footprints while purchasing energy from locally installed RESs and ESSs during high emission times.
The fitness function maximizes the welfare including consumption-based satisfaction and monetary
benefits from RESs and ESSs to consumers and benefits of the reduced peak load, generating cost and
emissions to the utility. A dynamic selling with dynamic buy-back pricing scheme is also proposed
to implement the model. For scalability and user privacy, the problem is solved using Lagrange
multipliers. The objectives in all of the above research are combined using the WSMD.
2.3. Emissions Reduction in MGDs
In MGDs, RESs and ESSs are integrated with DGs to enhance the quality and the reliability
of the power supply. In [
15
], a solution for DRSREOD-based HEMS operations for a stand-alone
home including WTB, DG, and SB is computed using PSO. The local fossil fueled DG is operated
at rated power for an improved efficiency and reduced emissions. A separate objective function for
emissions; however, is not included. An optimal dispatch for an MGD is computed in [
16
] using
GA. Additional constraints for ESS charge/discharge rates, DG start/stop and supply capacity are
considered. Total emission is computed using emission factors for the grid, power supplied from the
local DG and the ESS. The model does not include load shifting while computing the dispatch for
power sources. A method to compute an optimal dispatch of RESs and DGs for a MGD is presented
in [
24
]. The dispatch is based on costs of energy from WTB, PV and DG,
EMiss
and
CE
from/to main
grid for a fixed load profile. The WTB and the PV are the preferred sources. The SB is discharged
based on its SoC if local RESs are not able to meet the demand; else, the load is supplied through the
economic dispatch of the DG, fuel cell (FC), SB and the grid. Non-critical loads are disconnected when
local sources are insufficient. The DG is operated at rated power to minimize
EMiss
. DR based load
shifting is not included.
2.4. Emissions Reduction in DRSREODLDG-Based HEMS
Energy-deficient power supply networks in developing countries are based on the compromises
for the consumers to LSD in order to maintain the equilibrium between demand and generation of
energy [
10
,
11
]. While a number of consumers in developing countries are participating in DSM making
use of DRSREOD-based HEMSs, LSD-compensating DGs are deployed in such HEMSs for ensuring the
uninterrupted supply of electricity. An algorithm for optimum sizing of an LDG for DRSREOD-based
HEMS was presented in our recent research [
11
]; however, such a DG does introduce emissions when
operated during LSD hours. Based on the recent scenario for quantitative restrictions on carbon
emissions, research on the optimized operation of DRSREODLDG-based HEMS focusing reduction
in
TE Miss
looks pertinent. A simulation-based posteriori method for an eco-efficient operation of
DRSREODLDG-based HEMS takes into account the trade-offs between
CEnet
,
TBD
, and minimal
TE Mmiss
is proposed. A three-step approach is followed. At step-1, primary trade-off solutions
Energies 2018,11, 3091 10 of 40
for
CEnet
,
TBD
, and
TE Mmiss
are generated using a heuristic proposed for an optimal operation of
DRSREODLDG-based HEMS. The heuristic, which uses MOGA/PO to search optimal trade-offs, is
detailed in Algorithm 1. At step-2, an AVCF is used to filter out the trade-offs with extremely high
values of
TE Miss
, whereas an ASCF is used to screen out the trade-offs with marginally high values
of
TE Miss
at step-3. The ASCF was developed using advanced regression techniques. The filtration
mechanism including AVCF and ASCF used to harness eco-efficient trade-off solutions for
CEnet
,
TBD, and minimal T EMmiss is detailed in Algorithm 2.
3. System Model
The architecture for DRSREODLDG-based HEMS is shown in Figure 1. The major components
of such HEMSs include home appliances, renewable energy sources, an energy storage system,
an LSD-compensating DG, a HEMS controller, a local communication network, and a smart meter for
bidirectional interation between users and the power grid. The proposed optimal operation for such
HEMS are based on DR synergized with the optimal dispatch scheme for RESs, ESSs and an LDG.
The operating scheme takes into account the MS of SHAs, their combined corresponding functions
of the PV unit, the SB and the utility, and the energy sold to the grid based on the parametric values
of power vector from PV
(Ppv)
, vectors of the state of charge
(SoC)
, the maximum charge/discharge
rates, and the tariff scheme. PV unit is the preferred source that is responsible for suppling the power
to the scheduled appliances. The surplus PV energy is saved into the SB for utilizing the power during
peak hours and it is sold to the utility for a monetary benefit. During the LSD hours, if SB is full and
there is no energy demand than the excess energy from the PV unit is dissipated in a dummy load [
9
].
The mentioned energy (shown by
Pdl
) represents a loss of the PV energy that could not be sold due to
the unavailability of the main grid. The LDG is used for supplying the load in high demand periods
which is contributing similar to PV unit and the SB to prevent the electricity blackouts. The operation
of the LDG in such systems ensures an uninterrupted supply of power; however, such operation of
the LDG accompanies the release of GHGs emissions as well. The problem for DRSREODLDG-based
HEMS operation has been formulated as multi-objective-optimization (MOO) to minimize
CEnet
,
TBD, and T EMiss.
Furthermore, according to [
10
], 31% and 21% energy is consumed in industrial and residential
sectors, respectively. However, in this paper, we consider only residential area for implementation of
our proposed scheme. Because our proposed schemes are based on load scheduling from ON-peak to
OFF-peak hours, it is not possible in industrial or agriculture sectors to reduce electricity cost via load
shifting due to production problems. Therefore, we consider only residential area for implementations.
Moreover, there are a lack of sources in developing countries, so the energy management system is a
huge opportunity for these countries.
A three-step simulation based posteriori method is proposed to provide trade-off solutions for
an eco-efficient operation of DRSREODLDG-based HEMS. The method makes use of Algorithm 1
and Algorithm 2to harness eco-efficient schemes for HEMS operation in terms of
Tst
and the related
trade-offs for
CEnet
,
TBD
, and minimal
TE Miss
. At step-1, primary trade-off solutions for
CEnet
,
TBD
, and
TE Miss
are generated making use of Algorithm 1. Algorithm 1is based on a MOGA/PO
based heuristic proposed in this work. At step-2, the primary trade-off solutions are passed through
an AVCF to filter out the trade-offs with extremely high and above average values of
TE Miss
. The
filtrate is then passed through an ASCF to screen out the trade-offs with even the marginally higher
values of
TE Miss
at step-3. The proposed filtration mechanism comprising AVCF and ASCF is detailed
in Algorithm 2. The simulations to validate the method for harnessing the desired trade-offs for
eco-efficient operation of DRSREODLDG-based HEMS are presented in Section 6.
Major components of the proposed model for DRSREODLDG-based HEMS are presented below.
Energies 2018,11, 3091 11 of 40
3.1. Parameters for Scheduling
A scheduling resolution of 10 min. slot has been adopted. To formulate the HEMS operations,
total time is sub-divided into 144 slots. While scheduling, each SHA is executed in the specific horizon
for a specified number of slots. The proposed model for HEMS operation is dependant on a dynamic
electric pricing signal, i.e., an IBR pricing signal, the PV panel, the SB, and the LDG. The control
parameters for HEMS components are described in Section 4on problem formulation.
3.2. HAs
Motivated from the literature [
21
,
25
], the HAs are classified into non-shiftable home appliances
(NSHAs) and SHAs. NSHA, e.g., electric lamps, and fans, are working on required time slots and can
not be opted for scheduling. SHAs are assumed to be scheduled towards the low demand hours and
the PV harnessing hours for optimized HEMS operation. To achieve a maximized reduction in the cost
of energy, shiftable appliances are modeled as AS and DS. Such classification enables more reduction
in the cost of energy making use of enhanced flexibility in the appliances shifting and an increased
direct usage of the PV energy from the PV unit [
11
]. AS and DS type SHAs with the user prioritize
settings and the NSHAs along with their forecasted load, used in the simulation section are described
in Tables 5and 6.
Table 5. Shiftable home appliances and scheduling specifications.
SHA Power (kWh) LoT (slots) Start/End (slots)
Air Conditioner 1 (Reversible) 1 18 01–36 (DS)
Air Conditioner 2 (Reversible) 1 9 37–54 (DS)
Air Conditioner 3 (Reversible) 1 9 103–120 (DS)
Air Conditioner 4 (Reversible) 1 12 121–144 (DS)
Dishwasher 1 0.6 3 49–102 (DS)
Dishwasher 2 0.6 3 127–144 (DS)
Electric Geyser 1 0.8 6 01–36 (DS)
Rice Cooker/Oven 1 (Manual) 0.4 3 73–81 (DS)
Computer/Laptop (Manual) 0.1 6 114–144 (DS)
Washing Machine 0.7 9 93–123 (AS)
Water Pump 0.7 3 37–117 (AS)
Electric Geyser 2 0.8 6 55–121 (AS)
Rice Cooker/Oven 2 (Manual) 0.4 3 100–117 (AS)
Iron (Manual) 0.6 3 55–117 (AS)
Table 6. Non-shiftable home appliances considered for scheduling.
NSHAs Power (kWh) Start/End (slots)
01 Light + 02 Fans + 01 Refrigerator 0.2 01–36
02 Lights + 02 Fans + 01 Refrigerator 0.25 37–54
01 Lights + 02 Fans + 01 Refrigerator 0.2 55–78
02 Lights + 02 Fans + 01 Refrigerator 0.25 79–108
03 Lights + 03 Fans + 01 Refrigerator + 01 TV 0.3 109–114
04 Lights + 03 Fans + 01 Refrigerator + 01 TV 0.35 115–144
The proposed method is generic in nature and is equally applicable to DRSREODLDG-based
HEMS based on time-of-use pricing and Day-ahead pricing schemes. A 2-step ToU pricing tariff with
respective IBR values and threshold power demand are used in simulations in Section 6.
Energies 2018,11, 3091 12 of 40
3.3. RESs
Solar irradiation data as measured by the Pakistan Engineering Council in Islamabad has been
applied for the simulations to validate the proposed system [
11
]. It is possible to sell the surplus
energy produced from the RESs [
26
]. The PV system is used in the simulations and its parameters’
configurations are given in Table 7. The energy generation profile of PV unit is displayed in
Figure 3
.
The electricity bill of generations from local RESs has not been included in the model and such
installations have been considered as a module of the current system [11].
Time Slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Ppv (kWh)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 3. Profile for photovoltaic energy.
Table 7. Photovoltaic system specifications.
Parameter Value
Total capacity 5 kW
Rating of each panel 250 W
Number of panels and panel area 20, 32 m2
Efficiency of PV panels 15%
3.4. ESS
The SB and the inverter are important parts of the proposed DRSREODLDG-based HEMS.
These components along with their specifications are given in Table 8. Net loss for the SB is initially
supposed up to 20%; otherwise, it is considered for charging.
Table 8. SB and inverter specifications.
Parameter Value
Inverter rating 5 kW
Inverter efficiency 70%
SB Ah 600 Ah
SB voltage 48 V
SB capacity 4.8 kWh/slot
SB charge rate 0.48 kWh/slot
SB discharge rate 0.32 kWh/slot
Minimum SoC 30%
Maximum SoC 95%
SB efficiency 80%
Energies 2018,11, 3091 13 of 40
3.5. LDG
The consumers perform optimally sizing the LDGs according to their deficient load as [
27
].
The specifications of the LDG to cope with the LSD are used in the simulation of proposed model as
given in Table 9. The emission factor is computed as per Equation (8) using the pertinent data given
in [
28
,
29
]. The cost of energy for the LDG is according to the levelized cost of energy for such units
given in [30].
Table 9. Load shedding-compensating dispatchable generator specifications.
Parameter Value
LDG rating 1 kVA
Power factor 0.8
Emission factor 1.6 Lbs./kWh
Levelized cost of generation for the LDG 17 Cents/kWh
4. Formulating DRSREODLDG-Based HEMS Problem and the Related Optimization Techniques
The contents of this section are inherently divided into two parts: (1) the problem formulation for
HEMS optimization to generate optimal schedules of SHAs in terms of
Tst
and the primary trade-offs
for CEnet,TBD and TEMiss along with the proposed techniques.
The problem to generate the primary trade-offs for
CEnet
,
TBD
and
TE Miss
is computed using
the following input values:
B= [1, 2, .., b, .., k]= SHAs used for scheduling,
T= [1, 2, 3, .., n, .., N]= Slot numbers defined for the scheduling horizon,
Pa = [Pa1,Pa2, .., Pak]= Power ratings of the SHAs rer-slot,
LoT = [LoT1,LoT2, .., LoTk]= SHAs having different lengths of operation time,
STslot = [STslot1,STslot2, .., STslotk]= SHAs starting slots,
ENslot = [ENslot1,E Nslot2, .., E Nslotk]= SHAs Ending slots,
PE = [PE1,PE2, .., PEN]= ToU pricing tariff values in Cents/kWh,
IBR = [IBR1,IBR2, .., IBRN]=IBR factors for power more than PT,
Tst = [Tst1,Tst2, .., Tstk]= Each SHA’s decision vector for start time.
The problems for HEMS are formulated to compute the power requirement for whole of the
scheduling horizon. With
Tst
as the decision vector, HEMS problem for the scheduling vector
Pschd_sh
is treated as MILP and computed using the following Equations.:
Pschd_sh =
N
n=1
k
b=1
X(b,n), (1)
where X(b,n)for the bth SHA is computed based on the following terms,
X(b,n) = (Pa(b):f o r Tst(b) + LoT(b)>nTst(b),
0 : f or Tst(b)>nTst(b) + LoT(b).
The load vector
Pload_nsh
for NSHAs is added to
Pschd_sh
to calculate the final scheduled load
vector (Pschd)using Equation (2):
Pschd =Pschd_sh +Pload_nsh. (2)
The problem is solved using a MOGA/PO based heuristic proposed in Algorithm 1to obtain a
decision vector,
Tst
, which optimizes the outcomes for trade-offs parameters by fulfilling the required
constraints.
Energies 2018,11, 3091 14 of 40
4.1. Objectives for DRSREODLDG-Based HEMS Problems
The main objective for DRSREODLDG-based HEMS optimization is to achieve the optimal
trade-offs between the
CEnet
,
TBD
and
TE Miss
. To obtain the above-mentioned trade-offs,
the problem for HEMS is formulated using SHA schedules by calculating
Pschd
paralelly, synergizing
the scheduling with RES, ESS, LDG and power grid dispatch for N time intervals over a specified
scheduling horizon. The LDG is integrated in the dispatch only for the LSD intervals to supply
the load in collaboration with the PV unit and SB. The heuristic presented in Algorithm 1
computes the corresponding vectors for
Pgd
,
Pgn
, and
Psold
that are used to compute the objective
functions/trade-off parameters.
4.1.1. Reduction of CEnet
The CEnet is computed using the Equation (5):
Minimize
N
n=1
(Pgd ×PE +Pgn ×PEg Psold ×P E f ). (3)
Here,
Pgd
and
PE
are the power purchased from the main grid and its price in Cents/kWh.
The terms
Psold
and
PE f
are the energy sold to the utility by the consumer and its feed-in price in
Cents/kWh, respectively. Pgn and PEg are the energy supplied from the LDG and its levelized price
in Cents/kWh, respectively. A factor
Psold ×CEMiss
can be excluded from
CEnet
as a reward for
reducing the supply-side emissions through the PV energy sold to the utility.
4.1.2. Minimization of TBD for the Consumer
We consider user discomfort in terms of average waiting time (TBD) of appliances. It simply
means how much time a user will wait to switch ON any appliance. Moreover, the maximum average
waiting time means maximum user discomfort and vice versa. For instance, if the average waiting
time of all appliances is four hours, then user discomfort will increase by 0.4 because the user feels
discomfort to wait. Moreover, in the case of unscheduled electricity consumption, users do not wait to
turn ON their appliances. Electricity user can use any appliance at any time, so their waiting time is 0
and the user’s comfort is maximum (no discomfort). The TBD formulation is given below:
TBD(D) =
k1
b=1
((Tst STslot)/,
(ENslot LoT STslot +1))/k1,
(4)
where
STslot
and
ENslot
indicate the users’ time bounds flexibility for representing the starting and
ending boundaries for SHAs working.
LoT
is a vector which is comprised of total length of operation
time for eacg SHA for completing its execution.
Tst
is also a decision vector which consists of starting
intervals of all SHAs, whereas k1is the number of SHAs designated as DS.
When the corresponding SHA starts its execution at
STslot
, the
TBD(D)
uses its initial value as
0, i.e., the start of the execution time is assigned from the users. When
Tst(b)
is equal to
ENslot(b)
LoT(b)
+ 1, it obtains its maximum value at 1, i.e., late starting time for the SHA results in finishing of
the task at the late alloted time
ENslot(b)
. The boundaries for the selection of
Tst
should be considered
feasibly which are calculated with the help of the next Equation:
Lb =STslot and Ub =ENslot LoT +1. (5)
Energies 2018,11, 3091 15 of 40
Due to the advanced completion of the jobs of AS type SHAs denoted by
TBD(A)
, the average
TBD
is computed. It is calculated by taking the average of the normalized advance-completion times
of all gadgets. This value is computed using the next equation:
TBD(A) =
k2
b=1
((ENslot Tst LoT +1)/
ENslot LoT
STslot +1))/k2,
(6)
whereas, k2denotes the number of SHAs for AS type.
When the corresponding SHA completes its execution at
ENslot(b)
,
TBD(A)
takes its initial value
as 0, for example, when
Tst(b) + LoT(b)
-1 is equal to
ENslot(b)
. When
Tst(b)
is equal to
STslot(b)
,
it gets its maximum value as 1, for example, using the finishing time of the appliance which is calculated
with STslot(b) + LoT(b)-1.
There are muitple appliances and some of them are categorized as AS and others are categorized
as AS in MS. For minimizing the average
TBD
for total
k
appliances in MS mode, the objective function
is defined as below:
Minimize(TBD(D) + TBD(A)). (7)
For a scheduling flexibility and better reduction in
CEnet
,
TBD
based on MS of SHAs as per
Equation (7) has been opted for this model.
4.1.3. Reduction of TE Miss
Equation (8) computes the emissions’ minimization ratio, i.e.,
TE Miss
, from which the LDG
is formulated:
Minimize
N
n=1
(Pgn ×EFT). (8)
Here,
EFT
is the carbon emission factor (kg/kWh) and
Pgn
is the vector for the energy supplied
by the LDG in kWh during the LSD hours [
13
,
16
]. A value of 1.6 Lbs./kWh has been used for
EFT
for
the LDG as per the data available in [28,29].
4.2. Techniques to Solve DRSREODLDG-Based HEMS Optimization Problems
The HEMS optimization is considered as a combinatorial optimization problem. Multiple HEMS
problems are nonlinear, non-convex constrained, multi-dimensional in nature and they have a variety
of the solutions available in literature. To solve these problems, both conventional and advanced
heuristic optimization techniques are used.
4.3. Techniques to Handle Multi-Objectivity in HEMS Optimization
Multiple HEMS optimization problems faced in existing scenarios are multi-objective optimization
(MOO); however, these problems have conflicting objectives. Minimization of
CEnet
is considered
as a major aim in most existing studies on HEMS, while minimizing
TBD
is another significant aim
in the consumer perspective. After the serious concerns over the environmental issues, the role of
DRSREOD-based HEMS to reduce the emissions due to the local as well as due to the centralized
generation by the utility has recently started to be investigated. Various methods have been used in
the recent research to take into account important trade-offs between
CEnet
,
TBD
and
TE Miss
. The
most widely used approach is the WSMD [
12
,
13
,
15
,
18
20
]. This is an a priori technique that converts
MOO into single-objective optimization (SOO) in order to achieve one solution. These techniques do
not give the feasible relations among the objectives to allow the consumer to choose among specific
preferences. The methods may miss a number of good solutions for a specific user regardless of their
preference standards. Analysis of the trade-offs among the above-mentioned aims is considered very
Energies 2018,11, 3091 16 of 40
pertinent, which enables consumers in decison-making from the set of the diverse set of optimized
outcomes. The posteriori method known as Pareto-based multi-objective optimization is dependent on
the Pareto dominance idea, which provides the diverse set of possible solutions for multiple objectives.
The concept of MOO problems for a HEMS using decision vector
Tst
and
m
objectives
for Pareto-based optimization is computed as: minimizing the objective vector
F(Tst) =
[F1(Tst)
,
F2(Tst)
, ..,
Fm(Tst)]
, following the mentioned constraints. When
Tst1
is better than
Tst2
in any
one of the given objectives and is not considered worse in any other than the solution
Tst1
, which is said
to dominate another
Tst2
. The Pareto-optimal set is composed of the set of non-dominated solutions.
The recently introduced MOGA includes features to implement Pareto optimization. Pareto-optimal
sets providing optimal trade-offs between
CEnet
,
TBD
and
TE Miss
for a DRSREODLDG-based HEMS
have been calculated in this work by using MOGA and the Pareto optimization features as described
in Algorithm 1. One hundred of these aforementioned trade-offs computed through MOGA/PO based
heuristic are processed to enhance eco-efficiency making use of a constrained filtration mechanism as
discussed in Sections 4.4 and 4.5.
4.4. Constrained Filtration of Trade-Offs to HEMS Optimization
The trade-off solutions achieved for a multi-objective optimization problem can be passed through
an adequately designed filtration mechanism in order to apply a constraint on any one or more of
the specified trade-offs. Such filtration mechanism enables harnessing the trade-offs with enhanced
efficiency. In this research, a filtration mechanism has been proposed to screen out the trade-offs with
larger values of
TE Miss
as related to the trade-offs for
CEnet
and
TBD
. This mechanism comprises of
an AVCF and an ASCF. AVCF makes use of an average value of the trade-off parameter
TE Miss
to
filter out the trade-offs with above average and extremely high values of
TE Miss
. While ASCF takes
into account an average surface fit for
TE Miss
in terms of
CEnet
and
TBD
to screen out the trade-offs
with higher values of
TE Miss
. ASCF has been developed using polynomial based regression technique
elaborated in Section 4.5. The formulation for AVCF and ASCF and their application to harness
eco-efficient trade-off solutions are presented in Section 4.
4.5. Regression Based Surface Fitting Techniques to Develop ASCF
Regression models are used to establish a relation between the dependent and the independent
variables in a set of data (
zi
,
xi
,
yi
). In order to develop a surface for the variable
z
in terms of variables
x
and
y
, a regression model is fit to the set of input data. Major models for surface fitting include
interpolant, lowess, and polynomial. A polynomial surface fit model has been used in this research for
its flexibility in application to the input data. For polynomial surfaces, a general model is designated
as Poly(
kl
), where
k
is the degree in
x
and
l
is the degree in
y
. The degree of
x
in each term will be less
than or equal to
k
, and the degree of
y
in each term will be less than or equal to
l
. The maximum for
the sum of
k
and
l
is
m
. The degree of the polynomial is the maximum of the values of
k
and
l
. A linear
regression model (LRM) for
i
number of observations for the independent variables (
xi
,
yi
) defines a
curved surface for the dependent variable
zi
in a 3D-space. The LRM for the surface in terms of an
order-mpolynomial may be represented as:
zi=
k
f=1
l
g=1
A(k,l)×xk×yl+ui, (9)
where 0 k+1m.
zi
is called a dependent variable or regressand, and
xi
and
yi
are called independent variable
or regressors. The first term in Equation (9) is deterministic and represents the conditional mean of
zi
based on the given values of
xi
and
yi
. The second term
ui
, called the error term, is random in
nature. The term is added or subtracted from the first term to realize the actual data.
A(k
,
l)
are called
regression coefficients (RCs). In LRMs, they are assumed to be fixed numbers. The term linear in
Energies 2018,11, 3091 17 of 40
LRM refers to the linearity of the RCs. The fitting of a model is based on the estimates for the RCs.
The estimation is carried out based on the minimization of the least squares of the error term called a
least square method. Based on Equation (9),
ui
is the difference between the actual value of
zi
and the
one obtained through the regression. For an optimal linear coefficient (LC) for surface fitting, the sum
of the squared error term (SSE) to be minimized is given as follows:
SSE =
i
e=1
ui2= (zi
k
f=1
l
g=1
A(k,l)×xk×yl)
2
. (10)
As
ui
is a function of RCs, the minimum value of the
SSE
may be computed by taking partial
derivatives of the same with respect to each of the RCs and equating the expression to zero. Based on
the estimated a(
k
,
l
), a sample model
zis
is formulated and the error term is also known as residuals,
which is computed as
ei=zizis
. The regression coefficients
a(k
,
l)
are the estimators of
A(k
,
l)
and
ei
is the estimator of the error term
ui
. The numerical values taken by an estimator are called estimates.
The least-squares solution to the problem is a vector
a(k
,
l)
, which estimates the unknown vector of
coefficients
A(k
,
l)
. In present research,
SSE
has been used to estimate the model fit for an average
surface for
TE Miss
in terms of
CEnet
and
TBD
. It is assumed that the observed data is of equal quality
and thus has constant variance; however, the fit might be unduly influenced by the data of poor
quality. Methods like weighted-least-squares regression are applied to reduce the influence of the low
quality data on estimating the model fits [
31
,
32
]. In present research, the use of AVCF to screen out the
trade-offs with extremely high values of
TE Miss
inherently improves the data quality for the model fit
for ASCF.
The model fit in this research is based on minimization of
SSE
that may be improved using
methods like minimization of root mean square error and root mean square error of approximation.
However, the improved well-fitting is of minimal value, if it is not based on the ideas from a theory
validation point of view and in such cases an extensive cross-validation is required [
33
]. Accordingly,
various polynomial models fit, 25 in number, have been examined for their capabilities to reduce the
average value of trade-off parameters for
TE Miss
and the number of diverse trade-offs available for
CEnet and TBD after the application of filtration mechanism.
5. Algorithms for Eco-Efficient Trade-Offs for DRSREODLDG-Based HEMS
A three-step approach has been used to achieve eco-efficient trade-off solutions for
DRSREODLDG-based HEMS. In step-1, schemes for optimal HEMS operation and the related trade-offs
for
TE Miss
,
CEnet
, and
TBD
are computed using Algorithm 1. The trade-off solutions thus obtained
are passed through a filtration mechanism to harness the ones with bare minimum
TE Miss
in terms of
CEnet
and
TBD
using Algorithm 2. The filtration mechanism is completed in two stages designated as
step-2 and step-3. In step-2, an AVCF for
TE Miss
is developed and applied to the primary trade-offs
to filter out the ones with extremely high and above average values of
TE Miss
. The remaining
trade-offs are then passed to step-3 to screen out the trade-offs with even the marginally higher values
of
TE Miss
. In step-3, an ASCF is used to filter out the trade-offs with
TE Miss
parameters residing
above the average surface fit for
TE Miss
. Eco-efficient solutions including bare minimum
TE Miss
and diversified trade-offs for
CEnet
and
TBD
are thus achieved for DRSREODLDG-based HEMS
operation. The followings algorithms have been proposed to harness the eco-efficient tradeoff solutions
for DRSREODLDG-based HEMS:
Algorithm 1to generate primary tradeoffs for DRSREODLDG-based HEMS (Step-1).
Algorithm 2for filtration mechanism to harness eco-efficient tradeoffs for DRSREODLDG-based
HEMS (Step-2 and step-3).
The algorithms are presented in the following subsections.
Energies 2018,11, 3091 18 of 40
Algorithm 1:
Algorithm to generate operating schemes and the primary tradeoffs for
drsreodldg-based hems (step-1).
Input:PE,P E f ,PEg,I BR,TP,EFT,Pa,Sty p,STslot,ENslot,LoT,Pload_nsh,Pgds,
SoC(init),SoC_mx,SoC_mn,Pch_mx,Pds_mx,Ppv
Output: Optimal tradeoffs for T EMiss,CEnet and TBD with Tst for SHAs
1: Initialize input parameters
2: Call MOGA
3: Initialize Tst within bounds STslot and ENslot-LoT+1
4: for Iterat = 1: Ng_mx
5: if Iterat >1
6: Generate new Tst populations within bounds using GA operations
7: end
—-Computing Pschd vector for DR-based scheduling—–
8: Tend = Tst+LoT-1
9: for i = 1:k
10: for j = 1:N
11: if (jTst(i)&&jTend(i))
12: Power_matrix(i,j) = Pa(i)
13: else
14: Power_matrix(i,j) = 0
15: end
16: end
17: end
18: Pschd = sum(Power_matrix)+ Pload_nsh
—–Computing dispatch for the PV system, SB, grid and the LDG—–
19: for j = 1:N
20: Pres(j) = Ppv(j)-Pschd(j)
——-Dispatch when PV energy >Pschd——-
21: case (Ppv(j)>Pschd(j)) do
22: if SoC(j)SoC_mx
23: if Pgds(j) == 0
24: Pdl = Pres(j)
25: else
26: Psold(j) = Pres(j)
27: end
28: SoC(j+1) = SoC(j)
29: else
30: Pch(j) = min(Pch_mx,Pres(j),SoC_mx-SoC(j))
31: if Pch(j)6=Pres(j)
32: if Pgds(j) == 0
33: Pdl = Pres(j)-Pch(j)
34: else
35: Psold(j) = Pres(j)-Pch(j)
36: end
37: end
38: SoC(j+1) = SoC(j)+0.8* Pch(j)
39: end
40: endcase
——-Dispatch when PV energy Pschd——-
41: case (Ppv(j)Pschd(j)) do
42: if (SoC(j)SoC_mn) |((SoC(j)>SoC_mn) && (PE(j)price_set))
43: if Pgds(j) == 1
44: Pgd(j) = -Pres(j)
45: else
Energies 2018,11, 3091 19 of 40
Algorithm 1: Cont.
46: Pgn(j) = -Pres(j)
47: end
48: SoC(j+1) = SoC(j)
49: elseif ((SoC(j)>SoC_mn) & & (PE(j)>price_set))
50: Pds(j) = min(Pds_mx,-Pres(j),SoC(j)-SoC_mn)
51: if Pds(j) == Pds_mx
52: Pload_d(j) = Pschd(j)-Ppv(j)- pds_mx
53: elseif Pds(j) == (SoC(j)-SoC_mn)
54: Pload_d(j) = Pschd(j)-Ppv(j)-(SoC(j)-SoC_mn)
55: end
56: if Pgds(j) == 0
57: Pgn = Pload_d(j)
58: Pload_d(j) = 0
59: end
60: SoC(j+1) = SoC(j)-Pds(j)
61: end
62: endcase
63: Pgd(j) = Pgd(j)+Pload_d(j)
——-Computing tariffs with I BR———
64: if Pgd(j)>TP
65: PE(j) = IBR ×PE(j)
66: end
67: end
—–Computing fitness function forTEMiss—–
68:TE Miss = EFT ×sum(Pgn)
—–Computing fitness functions for CEnet—–
69: CEnet = sum(PE ×Pgd)+sum(PEg ×Pgn)-sum(PEf ×Psold)
—–Computing fitness function for TBD—–
70: for a = 1:k
71: if Styp = DS
72:TBD(D)(a) = (Tst(a)-STslot(a))/
(ENslot(a)-LoT(a)-STslot(a)+1)
73: else
74:TBD(A)(a) = (ENslot(a)-Tst(a)-LoT(a)+1)/
(ENslot(a)-LoT(a)-STslot(a)+1)
75: end
76: end
77: Compute TBD = (sum(TBD(D))+sum(TBD(A)))/k
78: end
79: Exit MOGA; return results as TEMiss,
CEnet and TBD tradeoffs and
corresponding Tst
80: Goto Algorithm 2 to harness eco-efficient tradeoff solutions
Energies 2018,11, 3091 20 of 40
Algorithm 2:
Algorithm for filtration mechanism to harness eco-efficient tradeoffs for
drsreodldg-based hems (step-2 and step-3).
Input: Tradeoffs from algorithm 1 for CEnet,TBD and T EMiss
Output: Eco-efficient tradeoff solutions for CEnet,TBD and minimal TEMiss
—–Step-2: Filtration of tradeoff solutions using AVCF for TEMiss—–
1: Do
—–Computing average value of TEMiss—–
2: TEMiss_avg = Average (TEMiss)
—–Computing residuals for TEMiss w.r.t TEMiss_avg —–
3: TEMiss_Resid_avg = Average (TEMiss)- TEMiss
—–Filtration based on average value of TEMiss—–
4: Filter out/ Exclude solutions with negative TEMiss_Resid_avg
5: Collect the remaining solutions for refined filtration in step-3
6: End do
—–Step-3: Refined filtration of tradeoffs based on average surface of T EMiss—–
7: Do
8: Tabulate CEnet, TBD and TEMiss
—–Computing average surface for TEMiss—–
9: Generate an average surface using polynomial option (Ploy41)
—–Computing residuals for TEMiss w.r.t average polynomial surface—–
10: TEMiss_Resid_avgs = TEMiss on surface - Actual value of TEMiss
—–Filtration based on average surface of TEMiss —–
11: Filter out tradeoffs with negative TEMiss_Resid_avgs
12: Collect the remaining tradeoffs as eco-efficient tradeoff solutions
13: End do
5.1. Algorithm 1to Generate Operating Schemes and the Primary Tradeoffs for DRSREODLDG-Based HEMS
(Step-1)
This algorithm computes a set of primary tradeoff solutions for optimized HEMS operation based
on MS of SHAs synergized with the optimal dispatch of the PV system, the SB, the grid, and an
LDG. The LDG supplies the load only during LSD hours in coordination with the PV unit and the
SB. Tradeoffs for
CEnet
,
TBD
, and
TE Miss
are based on the underlying scheme for HEMS operation.
At the start
, vector
Tst
for SHAs is generated that is followed by the production of
Pschd
vector.
The PV
system is regarded as the preferred source to directly supply
Pschd
. The dispatch planning is mainly
based on the excess PV energy in each slot denoted by
Pres
which is the arithmetic difference between
Ppv
and
Pschd
. Two main cases arise with regard to the relative values of these two quantities and in
each case,
SoC
, the maximum charge/discharge rates, the grid status and the power from the LDG
play major roles in the dispatch. In the first case, where excess PV energy is available, as shown on
line 21, the energy is stored in the SB if
SoC
is less than its maximum value; otherwise, it is sold to
the grid. However, during LSD hours, the excess energy that would be sold to the grid is instead
supplied to a dummy load as shown on line 24. The SB charging state depends on the condition given
on
line 30
. If a value other than
Pres
is computed, it indicates that either the maximum charge rate or
the limiting value of
SoC
is restricting the complete storage of the excess PV energy in the SB. Hence,
any excess energy left after charging the SB is sold to the grid, as shown on line 35. However, during
LSD hours, the excess energy that would have been sold to the grid is instead supplied to a dummy
load, as shown on line-33. In the second case, in which
Ppv
is less than or equal to
Pschd
, as shown
on line 41, the PV energy is insufficient to completely supply the load. The residual energy, in this
case, will be supplied from the grid if
SoC
is less than or equal to its minimum limit or from the SB
otherwise. Moreover, the SB will still also not be discharged if cheap energy is available from the grid
as given on line 42. However, during LSD hours, the LDG will supply the load in place of the grid, as
shown on line 46. SB shall supply the load only during peak hours when the cost of energy is greater
than a maximum price limit. The discharging state of the SB depends on the condition given on line 50.
Energies 2018,11, 3091 21 of 40
If the minimum computed value is equal to the maximum discharge rate or to the residual capacity of
the SB before discharging to the minimum
SoC
, then one of these constraints is restricting the ability to
supply the full load from the SB, and the remaining load must be supplied from the grid, as shown
on lines 52 and 54. However, during LSD hour, the LDG will supply the remaining load in place of
the grid as shown on line 57. For each slot in the scheduling horizon, one of the above two cases
will hold, the vectors
Ppv
,
Pgd
,
Pds
, and
Pgn
will be computed for dispatch accordingly. Similarly,
the loads
for each slot is computed for
Pschd
,
Pch
,
Pdl
, and
Psold
.
TE Miss
is computed (applying
EFT
)
for the net generation from LDG as shown on line 68.
CEnet
is computed by arithmetically adding
CE
(
applying PE/I BR
), cost of generation from LDG (applying
PEg
) and cost of energy sold to the grid
(applying
PE f
) as shown on line 69. The
TBD
values are computed on line 77 after adding
TBD(A)
and
TBD(D)
on lines 72 and 74. The values for the mentioned objective functions are computed for
each MOGA iteration. The algorithm provides Pareto optimal sets comprising one hundred operating
schemes for HEMS in terms of Tst and the related tradeoffs for CEnet,TBD and TE Miss.
5.2. Algorithm 2for Filtration Mechanism to Harness Eco-Efficient Trade-Offs for DRSREODLDG-Based
HEMS (Step-2 and Step-3)
The algorithm completes the filtration process in two steps as stated below:
Step-2: An AVCF based on the average value of
TE Miss
is developed taking into account all of
the primary trade-offs generated through Algorithm 1as shown on line-2. The residuals for
TE Miss
(
TE Miss_Resid_avg
) for each solution are then computed as given on line-3. A trade-off solution with
the value of
TE Miss_Resid_avg
less than 0 indicates an above average value for
TE Miss
, and all such
trade-offs are filtered out at the step shown on line-4. The trade-off solutions with average (or less
than average)
TE Miss
values are collected and forwarded to step-3 for further processing as shown
on line-5.
Step-3: An ASCF based on the average surface fit (using polynomial-based regression) is
developed making use of the trade-off solutions forwarded from step-2 as shown on line-9.
The residuals
for
TE Miss
(
TE Miss_Resid_avgs
) for each solution are then computed by taking the
difference between the
TE Miss
and the average surface fit of
TE Miss
computed in terms of
CEnet
and
TBD
as shown on line-10. A trade-off solution with the value of
TE Miss_Resid_avgs
less than
0 indicates the
TE Miss
value greater than the respective value on the average surface fit, and all
such trade-offs are filtered out at a step shown on line-11. The remaining trade-off solutions with the
TE Miss
values equal to (or less than) the respective values on the average surface fit are selected and
declared final eco-efficient trade-offs for DRSREODLDG-based HEMS operation as shown on line-12.
6. Simulations for DRSREODLDG-Based HEMS Operation and the Filtration Mechanism to
Harness Eco-Efficient Trade-Off Solutions
The simulations are conducted using MATLAB 2015 and are reported in Section 6.1 based on
Algorithm 1. These results show the validity of MOGA/PO based heuristic for DRSREODLDG-based
HEMS to compute operational schemes for SHAs in terms of vector
Tst
and the primary trade-offs
for
CEnet
,
TBD
and
TE Miss
. The results of simulations enable analyzing the trends exhibited by the
trade-off parameters taking into consideration vital factors affecting these parameters. The critical
analysis of the primary trade-offs enabled designing a filtration mechanism to extract desired set
of eco-efficient trade-off solutions with minimal
TE Miss
. The simulations reported in Section 6.2
are based on Algorithm 2. They demonstrated the validity of the filtration mechanism to harness
eco-efficient trade-offs. Regression based polynomial formulations and the procedure to finalize the
model fits for the proposed mechanism are also elaborated in Section 6.2. Simulations have been
conducted for the following:
-
DRSREODLDG-based HEMS operation to compute primary trade-offs for HEMS ( based on
Algorithm 1/step-1).
Energies 2018,11, 3091 22 of 40
-
Application of filtration mechanism to harness eco-efficient trade-offs for HEMS (based on
Algorithm 2/step-2 and step-3).
6.1. Simulations for DRSREODLDG-Based HEMS Operation to Compute Primary Trade-Offs Using
Algorithm 1
Simulations were performed to validate DRSREODLDG-based HEMS operation using
Algorithm 1. Operating schemes for SHAs in terms of
Tst
and the primary trade-offs were computed.
The trends exhibited by the trade-off parameters were analyzed. Critical analysis for validating
the relation between the trade-off parameter:
TE Miss
and the trade-offs for
CEnet
,
TBD
, enabled
designing a filtration mechanism required to harness the desired eco-efficient trade-off solutions with
minimal TE Miss from a large set of primary trade-offs.
For the simulations, the 2-stage ToU pricing tariff with an IBR value of 1.4 are considered.
This comprises of hourly price of 15 Cents/kWh during the peak hours from 7:00 p.m. to 11:00 p.m.
(slot numbers 115–138) hours and a hourly price of 9 Cents/kWh for the whole day, as displayed in
Figure 4. The
IBR
factor threshold is considered as the power demand of 2.4 kW. A feed-in tariff,
PE f
,
valued at 0.7 times of PE was considered for the PV energy sold to the grid.
Time Slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Tariff (cents/kWh)
0
2
4
6
8
10
12
14
16
18
20
Figure 4. Two-stage time-of-use tariff scheme.
The software and hardware technologies used in simulations have included the followings items:
Machine: Core i7-4790 CPU @3.6 GHz with 16 GB of RAM.
Platform: MATLAB 2015a.
Optimization tool: MOGA/PO with the following parameters,
Population size: 100,
Population type: Double vector,
Generation size: 1400,
Crossover fraction: 0.8,
Elite count: 0.05 x population size,
Pareto fraction: 1.
The primary trade-offs for
CEnet
,
TBD
and
TE Miss
, generated through simulation for an optimal
DRSREODLDG-based HEMS operation, are presented in Table 10. Due to space limitation, the related
Tst
vector is not shown in this table (however, it is presented with the final eco-efficient trade-offs
in Table 13). The primary trade-offs are graphically shown in Figure 5. The trends exhibited by the
trade-off parameters and the relationship between them has been analyzed to approach a filtration
Energies 2018,11, 3091 23 of 40
mechanism that enables harnessing trade-offs with diversified options for
CEnet
,
TBD
and minimal
value of TEMiss.
Table 10. Primary trade-offs for DRSREODLDG-BASED HEMS using Algorithm 1(Step-1).
Sr.No. CEnet
(Cents) TBD T EM iss
(Lbs.)
TEMiss
_Resid
_avg
Pdl
(kWh) Sr.No. CEnet
(Cents) TBD T EM iss
(Lbs.)
TEmiss
_Resid
_avg
Pdl
(kWh)
152.87 0.17 0.67 0.11 1.87 51 36.65 0.28 0.56 0.22 1.06
252.87 0.17 0.67 0.11 1.87 52 36.34 0.28 0.7 0.08 0.91
351.74 0.17 0.67 0.11 1.87 53 36.18 0.31 1.27 0.49 0.59
451.74 0.18 0.67 0.11 1.87 54 36.18 0.31 1.27 0.49 0.59
551.02 0.17 0.75 0.03 1.79 55 35.82 0.28 0.73 0.05 0.99
651.02 0.17 0.75 0.03 1.79 56 35.56 0.29 0.57 0.22 0.94
750.39 0.17 0.81 0.03 1.69 57 35.13 0.3 0.6 0.18 0.86
850.3 0.18 0.67 0.11 1.71 58 35.03 0.3 0.57 0.22 0.86
949.5 0.17 0.84 0.06 1.58 59 33.9 0.32 0.57 0.22 0.84
10 48.78 0.18 0.8 0.02 1.55 60 33.86 0.33 0.64 0.14 0.74
11 48.78 0.18 0.8 0.02 1.55 61 33.85 0.31 0.92 0.14 0.57
12 48 0.18 0.75 0.03 1.63 62 33.68 0.34 0.56 0.22 0.81
13 47.51 0.19 0.81 0.03 1.38 63 33.67 0.29 0.65 0.13 0.63
14 47.51 0.19 0.81 0.03 1.38 64 33.02 0.59 0.57 0.21 0.27
15 46.77 0.18 0.85 0.07 1.45 65 32.98 0.33 1.11 0.33 0.33
16 45.81 0.19 0.57 0.21 1.61 66 32.96 0.36 0.56 0.22 0.62
17 45.72 0.19 0.99 0.21 1.24 67 32.67 0.34 0.56 0.22 0.7
18 45.18 0.18 0.6 0.18 1.66 68 32.57 0.47 0.56 0.22 0.73
19 45.01 0.19 0.56 0.22 1.9 69 32.37 0.33 0.65 0.13 0.51
20 44.62 0.2 0.6 0.18 1.5 70 32.24 0.33 0.7 0.08 0.54
21 44.36 0.2 1.36 0.58 1.24 71 32.01 0.35 1.23 0.45 0.17
22 44.08 0.19 0.88 0.1 1.31 72 32.01 0.35 1.23 0.45 0.17
23 43.96 0.22 1.55 0.77 1.09 73 31.99 0.35 1.2 0.42 0.17
24 43.96 0.22 1.55 0.77 1.09 74 31.92 0.51 0.56 0.22 0.63
25 43.8 0.2 0.74 0.04 1.49 75 31.88 0.43 0.65 0.13 0.59
26 43.74 0.2 1.15 0.37 1.24 76 31.76 0.57 0.62 0.17 0.27
27 43.57 0.2 0.56 0.22 1.74 77 31.76 0.57 0.62 0.17 0.27
28 43.45 0.19 1.18 0.39 1.24 78 31.45 0.35 0.7 0.08 0.42
29 43.27 0.24 0.56 0.22 1.34 79 31.27 0.52 0.56 0.22 0.53
30 43.07 0.22 0.79 0.01 1.26 80 31.15 0.35 0.9 0.12 0.32
31 42.73 0.2 0.99 0.21 1.09 81 30.82 0.32 0.73 0.05 0.34
32 41.9 0.2 0.68 0.1 1.43 82 30.49 0.35 0.7 0.08 0.32
33 41.33 0.21 0.57 0.21 1.46 83 30.34 0.4 0.7 0.08 0.25
34 41.15 0.22 0.8 0.02 1.24 84 30.3 0.36 0.73 0.05 0.29
35 40.92 0.23 0.56 0.22 1.58 85 30.15 0.43 1.09 0.31 0.03
36 40.87 0.22 0.66 0.13 1.4 86 30.02 0.53 0.56 0.22 0.33
37 40.69 0.22 0.74 0.04 1.32 87 29.65 0.37 0.7 0.08 0.14
38 40.43 0.27 0.64 0.14 1.01 88 29.65 0.37 0.7 0.08 0.14
39 40.31 0.21 0.66 0.13 1.25 89 29.03 0.36 0.73 0.05 0.21
40 40.06 0.26 1.41 0.63 0.84 90 28.77 0.37 0.73 0.05 0.22
41 40.06 0.26 1.41 0.63 0.84 91 28.75 0.37 0.85 0.07 0.09
42 39.22 0.23 1.03 0.25 0.96 92 27.98 0.38 0.73 0.05 0.04
43 38.94 0.25 0.68 0.1 1.28 93 27.87 0.44 0.85 0.07 0.01
44 38.69 0.24 0.74 0.04 1.18 94 27.87 0.44 0.85 0.07 0.01
45 38.47 0.23 0.85 0.07 0.88 95 27.36 0.46 0.65 0.13 0.11
46 38.11 0.24 1.03 0.25 0.84 96 26.98 0.41 0.73 0.05 0.04
47 37.88 0.25 0.6 0.18 1.21 97 26.98 0.49 0.73 0.05 0.04
48 37.56 0.26 0.56 0.22 1.11 98 26.8 0.45 0.65 0.13 0.11
49 36.89 0.32 0.56 0.22 1.28 99 26.66 0.51 0.73 0.05 0.04
50 36.66 0.27 0.6 0.18 1.16 100 26.22 0.48 0.65 0.13 0.11
Energies 2018,11, 3091 24 of 40
50
CEnet (Cents)
45
40
35
30
0.2
0.3
TBD
0.4
0.5
0.6
0.8
1
1.2
1.4
0.4
1.6
TEMiss (Lbs.)
Step-1 Solutions Generation:
Primary solutions generated
through algorithm-1
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Figure 5.
Primary trade-off solutions with un-even surface for
TE Miss
generated through Algorithm 1.
Refer to Table 10, each trade-off solution is related to a unique
Tst
. The decision vector
Tst
is
generated through the MOGA based on the vectors
STslot
and
ENslot
. The vector
Tst
for each of the
solution corresponds to a unique demand profile,
Pschd
. To supply this demand, a dispatch scheme
for energy sources and ESS based on the parameters
Ppv
,
Pgd
,
Pgn
,
Pch
, and
Pds
is computed through
the heuristic proposed in Algorithm 1. Preferably, the load is supplied from the PV unit. The extra
energy from the PV unit is stored in the SB after supplying the load. The SB is discharged to supply
the load during the peak hours for making use of the stored energy. The LDG supplies the load in
coordination with the SB during LSD hours only. The excess PV energy is sold to the grid. This is
designated as
Psold
after supplying the load and charging the SB. However, during the LSD hours, the
excess energy from the PV ought to be dissipated into the dummy load viz. designated as
Pdl
.
The PV
,
SB, and the charger system are considered a part of the existing infrastructure and their cost is not
included in computation.
The trade-off parameter
CEnet
is based on the dispatch from various sources to supply the
scheduled load and the energy sold to the utility according to Equation (3). The rates for energies
including
PE
,
PE f
and
PEg
in different slots play vital role in the computation of
CEnet
. The loss of
the harnessed PV energy due to the unavailability of the grid, given by
Pdl
, is another important factor
affecting the value of
CEnet
. The parameter
TE Miss
primarily depends on the energy supplied by
the LDG,
Pgn
, during LSD hours. The
EFT
for the LDG is also important while evaluating
TE Miss
.
The
TBD
is based on the time shift of SHAs from their preferred times of operation and is computed
using Equation (7). The relationships between the trade-off parameters for the primary trade-off
solutions are graphically presented in Figures 2and 6.
Energies 2018,11, 3091 25 of 40
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
52.87
51.02
48.78
45.81
44.36
43.74
42.73
40.87
40.06
38.11
36.65
35.56
33.85
32.96
32.01
31.76
30.82
30.02
28.75
26.98
TEmiss (Lbs.), TBD
CEnet (Cents)
TBD TEmiss
Figure 6. Relations among primary trade-offs for CEnet, TBD and TEMiss using Algorithm 1.
The trends exhibited by the trade-off parameters comprising
CEnet
,
TBD
and
TE Miss
are
analyzed in subsections below. The primary trade-offs with extreme values of the parameters have
especially been investigated.
6.1.1. Trends for CEnet
The objective to minimize the CEnet is mainly based on the following factors:
1.
Maximized usage of the PV energy to supply the load directly: This avoids the loss of energy in
the SB due to storage/re-use of the PV energy while supplying the load (a net loss of 20% has
been assumed for the SB). The energy thus saved enables to reduce the demand from the grid
and the LDG which ultimately results in a reduced value of CEnet.
2.
Maximized usage of the stored PV energy to supply the load during the peak hours: This reduces
the energy to be supplied from the grid during the peak hours as well as from the LDG during
the peak LSD hours, which results in a reduced value of CEnet.
3.
Selling of the extra PV energy to the utility: A direct usage of the energy from the PV unit is better
than selling it to the utility as
PE f
is generally lesser than the
PE
(
PE f
is assumed as 70% of the
PE
). However, it is beneficial to sell the PV energy to the utility, if a surplus of it is available
after supplying
Pschd
and the charging load. The above-mentioned factors enable reducing the
CEnet
parameter through an optimal use of the PV energy based on the
PE
,
PE f
,
PEg
and the SB
efficiency. Other factors to reduce CEnet parameter include the followings:
4.
Load shifting towards the off-peak hours: The load left after being supplied from the PV and
the SB unit should have been shifted towards off-peak hours. This shifting minimizes the
CEnet
based on the tariff PE.
5.
Load to be supplied by the LDG during LSD hours: The algorithm enables supply of the energy
from the LDG during LSD hours. If more load is shifted towards LSD hours, LDG is required to
supply that load in coordination with the PV/SB at a higher cost of energy (
PEg
), which results
in an increased value of CEnet.
6.
Loss of the harnessed PV energy: The dummy load
Pdl
has been identified as a factor of vital
importance for reducing
CEnet
. Figure 7reveals a direct relationship between the
CEnet
and the
Pdl
. The
Pdl
needs to be minimized to achieve an optimal value of
CEnet
. A larger
Pdl
indicates
Energies 2018,11, 3091 26 of 40
a loss of the PV energy due to lesser shifting of the load (including charging of the SB) towards
the LSD hours having the harnessed PV that results in a larger CEnet.
= 0.8904
0.00
0.50
1.00
1.50
2.00
2.50
0.00 10.00 20.00 30.00 40.00 50.00
60.00
Pdl (kWh)
CEnet (Cents)
Pdl Linear (Pdl)
Figure 7. Relation between CEnet and Pdl for DRSREODLDG-based HEMS.
To investigate the variations in
CEnet
parameter based on the above-mentioned six factors,
solution-1 and solution-100 with the maximum and the minimum values of
CEnet
are analyzed as
case studies. The analysis is based on the related HEMS operation including the power profiles for
the loads and the dispatch scheme for the power sources and the SB. Solution-1 shows a
CEnet
value
of 52.87 Cents, the largest of all solutions. This largest value of
CEnet
may be analyzed based on the
above-mentioned factors by focusing on the power profiles for this solution shown in Figure 8.
Time slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Power (kW/ slot), EMiss (Lbs.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pschd
Ppv
Pgrid
Pdis
Pchg
Psold
Pdl
SOC of SB(%)
Pgdstatus
EMiss
Figure 8. Power and emission profiles for DRSREODLDG-based HEMS operation for solution-1.
First, a very small portion of the load (Pschd) has been supplied directly from the PV energy that is
available from time slot no. 37. Some of the available PV energy has been used to charge the SB while
Energies 2018,11, 3091 27 of 40
most of the PV energy is sold to the utility at cheap rates (
PE f
equals 70% of
PE
). A part of the load,
instead of being supplied directly from the PV unit, is shifted towards the off-peak slots and supplied
from the grid at the off-peak time rate. This load thus has been supplied at a net 30% increased cost of the
energy as compared to the cost of energy sold to the grid. Second, a load larger than the capacity of the
SB is shifted towards the peak-time slots. An average load of 0.21 kWh is thus supplied from the grid
during peak time slot nos. 132–134. The
CEnet
could be reduced if the load exceeding the capacity of the
SB was shifted towards off-peak time. Third, a net load of 0.348 kWh has been supplied from the LDG
during LSD based slot nos. 139–144 at a rate of
PEg
(
viz. higher than PE
). This load is based on NSHAs
only and it can not be shifted. However, the LDG also supplies a load of 0.068 kWh during slot no. 102
that may be shifted towards the grid/PV to reduce the
CEnet
. Fourth, the least of part of the the load has
been shifted within the PV harnessed LSD hours starting from slot
nos. 61 and 97
. Under this scenario,
1.87 kWh of the PV energy has been lost/dumped during slot nos. 63–66 and slot nos. 97–101. More load
could be shifted towards the mentioned slots to minimize the loss of the harnessed energy from the PV
and thus to reduce the
CEnet
. In brief,
a load
shifting resulted in a non-optimal use of the PV energy, a
very large value of the
Pdl
and other aforementioned factors resulted in the largest value of
CEnet
for
this solution. Solution-100, on the other hand, exhibits the lowest
CEnet
value of 26.22 Cents that is again
based on the aforementioned factors. The lowest value of
CEnet
may again be analyzed by focusing on
the corresponding power profiles for the solution as shown in Figure 9.
Time slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Power (kW/ slot), EMiss (Lbs.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pschd
Ppv
Pgrid
Pdis
Pchg
Psold
Pdl
SOC of SB(%)
Pgdstatus
EMiss
Figure 9. Power and emission profiles for DRSREODLDG-based HEMS operation for solution-100.
First, a larger portion of the load (
Pschd
), as compared to solution-1, has been supplied directly
from the PV that is available from time slot no. 37. The harnessed PV energy has been used to charge
the SB as well as to supply the maximum of the load, while a smaller value of the PV energy is
sold to the utility at cheap rates. Second, the remaining load viz. smaller as compared to solution-1
has been shifted towards the peak time slots so that the SB is able to supply most of the said load.
Accordingly, an average load of 0.189 kWh is left to be supplied by the grid during the peak time slot
nos. 135–137, which is smaller as compared to the same load in solution-1. Third, the LDG supplies
a total energy of 0.054 kWh during slot nos. 100–101, which is smaller as compared to the same
parameter in solution-1. Fourth, most of the load has been shifted towards the PV harnessed LSD
hours and hence
Pdl
exhibits a minimal value 0.11 kWh. In brief, a load shifting enabling an optimal
use of the PV energy minimized the value of
Pdl
and other aforementioned factors resulted in the
lowest
CEnet
for this solution. Similarly, the solutions with an intermediate value of
CEnet
may also
be validated by focusing the same above-mentioned factors affecting CEnet.
Energies 2018,11, 3091 28 of 40
6.1.2. Trends for TBD
The value of
TBD
is based on the total time shifts of the SHAs from the preferred times (
STslot
or
ENslot
based on type of scheduling) provided by the consumers. It depends on the decision vector
Tst
and computed using Equation (7) through Algorithm 1. The simulations reveal an exponential
relation between the
CEnet
and
TBD
as shown in Figure 10. The
TBD
increases exponentially while
reducing the
CEnet
. The relationship between the
CEnet
and
TBD
is very important in the context of
the consumer’s welfare. The optimal solutions provide diverse choices to the consumer for trade-offs
between
CEnet
and
TBD
. However, it has been observed that
CEnet
cannot be reduced beyond a
specific value after the
TBD
reaches a knee-point value. A knee-point value of 0.48 for
TBD
may be
realized from Figure 10.
= 0.8501
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
20.00 25.00 30.00 35.00 40.00 45.00 50.00
55.00
TBD
CEnet (Cents)
TBD Expon. (TBD)
Figure 10. Relation between CEnet and TBD for a DRSREODLDG-based HEMS.
On the other hand, the relation between the
TBD
and
TE Miss
for DRSREODLDG-based HEMS
is highly un-even as shown in Figure 11. Such relations are not possible to be defined using
standard techniques.
= 0.0351
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0.00 0.10 0.20 0.30 0.40 0.50 0.60
0.70
TEMiss (Lbs.)
TBD
TEMiss Linear (TEMiss)
Figure 11. Relation between TBD and T EMiss for a DRSREODLDG-based HEMS.
Energies 2018,11, 3091 29 of 40
6.1.3. Trends for TEMiss
The variation in
TE Miss
is analyzed based on the primary trade-offs presented in the
Figure 6/Table 10. Figure 6exhibits an extremely uneven variations in
TE Miss
as related to
CEnet
(and
TBD
), especially around the center of the data. The solution-23 with the largest, solution-27 with
the smallest and solution-73 with moderate values of TEMiss are analyzed as case studies.
Solution-23 exhibits a
TE Miss
value of 1.55 Lbs., the largest of all solutions. The value of
TE Miss
parameter depends on the profile for
Pgn
parameter. The profile for this solution is analyzed by
focusing on the power/emission profiles shown in Figure 12. The value of
TE Miss
mainly depends on
the operation of the LDG during four number of LSD hours discussed as follows. The loads shifted in
the first LSD hour (starting at slot no. 61) and in the third LSD hours (the peak time hour starting at
slot no. 121) are completely supplied by the PV and the SB, respectively. Thus, in actuality, the LDG
has to operate only during the second LSD hour (starting at slot no. 97) and during the fourth LSD
hour (starting at slot no. 139) to supply the shifted load as neither the grid nor the SB is available to
supply within these hours. During the fourth LSD hour, a fixed load made up of NSHAs is supplied
by the LDG completely. As no other source is available to supply during this hour, the fixed load has
been supplied by the LDG in all scenarios. Focusing the second LSD hour, PV is available to supply
the shifted load; however, the demand exceeding the energy harnessed from the PV (named excess
demand) is only supplied through the LDG. This excess demand to be supplied by the LDG during
the second LSD hour combined with the fixed demand in the fourth LSD hour, in fact, determines the
net value of
TE Miss
. A maximum shifting of the excess demand out of the second LSD hour results in
the minimization of the
TE Miss
. For solution-23, a maximum excess demand supplied through the
LDG during the second LSD hour resulted in a maximum
TE Miss
value of 1.55 Lb. for this solution.
The
CEnet
parameter in this scenario assumes a near average value of 43.96 Cents that is based on the
combined effect of the related parameters’ values including: a PV energy loss of 1.09 kW; a supply
of an average load of 0.2 kWh through the grid during peak time slot nos. 132–134; and a maximum
supply of 0.98 kWh of energy from the LDG at a higher cost of value (PEg).
Time slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Power (kW/ slot), EMiss (Lbs.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pschd
Ppv
Pgrid
Pdis
Pchg
Psold
Pdl
SOC of SB(%)
Pgdstatus
EMiss
Figure 12. Power and emission profiles for DRSREODLDG-based HEMS operation for solution-23.
Solution-27 exhibits a
TE Miss
value of 0.56 Lbs, the lowest in all solutions and the power profiles
shown in Figure 13. The minimum value of
TE Miss
in this scenario is because of zero loading of LDG
during the second LSD hour. On the other hand, the
CEnet
parameter shows a near average value
of 43.57 Cents that is very similar to the
CEnet
value in solution-23. The value is again based on the
combined effect of the related parameters’ values including: a PV energy loss of 1.75 kW; supply of an
Energies 2018,11, 3091 30 of 40
average load of 0.23 kW by the grid during the peak time slot nos. 132–134; and a minimum supply of
0.35 kWh of energy from the LDG at a higher cost, PEg.
Time slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Power (kW/ slot), EMiss (Lbs.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pschd
Ppv
Pgrid
Pdis
Pchg
Psold
Pdl
SOC of SB(%)
Pgdstatus
EMiss
Figure 13. Power and emission profiles for DRSREODLDG-based HEMS operation for solution-27.
Solution-73 shows a moderate
TE Miss
value of 1.20 Lbs. corresponding to the power profiles
shown in Figure 14. The excess load during the second LSD hour has not been completely shifted
out of this hour and so the same has been supplied through the LDG. The
TE Miss
for this solution,
therefore, is higher as compared to its value for solution-27. A much lower
CEnet
of value 31.99 Cents
as compared to the value of
CEnet
in solution-27 is based on a more efficient shifting of the load and a
smaller value of Pdl in solution-73.
Time slots
0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
Power (kW/ slot), EMiss (Lbs.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pschd
Ppv
Pgrid
Pdis
Pchg
Psold
Pdl
SOC of SB(%)
Pgdstatus
EMiss
Figure 14. Power and emission profiles for DRSREODLDG-based HEMS operation for solution-73.
6.1.4. Critical Analysis for TE Miss and Trade-Offs for CEnet and TEMiss
The relation between
TE Miss
parameter and the trade-offs for
CEnet
and
TBD
is analyzed based
on the primary trade-offs (sorted on
CEnet
), presented in Table 10. The trade-offs are graphically
shown in Figure 15. Based on the variations in
TE Miss
, the data may be divided into three classes.
Energies 2018,11, 3091 31 of 40
Class-1, including solution nos. 01–20 at the beginning of the data, class-2, including solution nos.
21–73 around the center of the data, and class-3, including solution nos. 74–100 at the end of the data.
Class-1 is characterized by the trade-offs with minimal values of
TE Miss
combined with maximal
values of
CEnet
; and class-3 by the trade-offs with minimal values of both of the
TE Miss
and
CEnet
parameters. Whereas class-2 around the middle section of the data, including more than 50% of the
trade-offs, exhibits a highly un-even/irregular trend for
TE Miss
as related to the trade-offs for
CEnet
and
TBD
, it includes an un-even distribution of the data with the minimal, average as well as extremely
high values of the
TE Miss
. Such trends indicate the presence of numerous solutions with comparable
values of the trade-offs for
CEnet
and
TBD
, however with large variations in the related values for
TE Miss
. Solutions-23 and 27, graphically shown as points A and B respectively in Figure 15, are an
example of such large variation in the
TE Miss
parameter. For comparable values of (43.96, 0.22) and
(43.57, 0.2) for
CEnet
and
TDB
, the solutions exhibit extremely varied values of 1.55 Lbs. (maximum
of all solutions) and 0.56 Lbs. (minimum of all solutions) for TE Miss.
A
B
D
C
R² = 0.8501
R² = 0.0111
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
20.00 25.00 30.00 35.00 40.00 45.00 50.00
55.00
TEMiss (Lbs.), TBD
CEnet (Cents)
TBD TEMiss Expon. (TBD) Linear (TEMiss)
Figure 15.
Variations in total GHG emissions during the scheduling horizon
TE Miss
with the related
trade-offs for net cost of energy CEnet and time-based discomfort TBD.
Solution-69 and solution-72 shown as points C and D are another example of similar large
variations in
TE Miss
. For comparable values of (32.37, 0.33) and (32.01, 0.35) for
CEnet
and
TDB
,
the solutions show largely varied respective values of 0.65 Lbs. and 1.23 Lbs. for TEMiss.
Figure 15 reveals a large number of data points especially in class-2 exhibiting large variations
in
TE Miss
with very small corresponding variation in the respective trade-off values of
CEnet
and
TBD
. The finding regarding the existence of a large number of multiple comparable trade-offs for
CEnet
and
TBD
with extremely varied values of
TE Miss
in the primary trade-offs was exploited to
design a mechanism to harness eco-efficient trade-offs for DRSREODLDG-based HEMS operation.
A filtration mechanism was proposed to screen out the trade-offs with larger values of
TE Miss
in order
to harness eco-efficient trade-offs with minimal
TE Miss
and a set of diverse trade-offs for
CEnet
and
TBD
. The proposed mechanism, based on an average value constraint filter and an average surface
based constraint filter, is presented in Algorithm 2.
Energies 2018,11, 3091 32 of 40
6.1.5. Simulation for Filtration Using AVCF (Step-2)
This step includes the formulation and application of a constraint filter based on the average
value of
TE Miss
for the primary trade-off solutions presented in Table 10. In the following are the
software and hardware tools used to demonstrate the solution space, and to formulate and apply the
filter to validate the AVCF based filtration:
Machine: Core i7-4790 CPU @3.6 GHz with 16 GB of RAM,
Platform: MATLAB 2015a,
Regression model = Linear interpolation,
Interpolation surface model = linearinterp,
Method = Linear least square,
Normalize = off,
Robust = off,
AVCF formulation and application:
TE Miss_Resid_avg =average(TE Miss)T EMiss,
Exclude = TEMiss_Resid_avg <0,
Where
TE Miss_Resid_avg
is the decision element for the filter. The exclude option provided
with the surface fitting function can be used to screen out the trade-offs based on the formulation
of the decision element. As per the formulation for
TE Miss_Resid_avg
, a trade-off solution with
a negative value of the decision element
TE Miss_Resid_avg
indicates the above average value for
TE Miss
. The application of AVCF thus screens out the trade-offs with extremely high as well as
above the average values of
TE Miss
. The function of the AVCF to screen out the un-desired trade-offs
with larger values of
TE Miss
are graphically shown in Figure 16. The selected solutions after the
application of the AVCF are presented in Table 11.
50
CEnet (Cents)
45
40
35
30
0.2
0.3
TBD
0.4
0.5
0.8
1
1.2
1.4
1.6
0.4
0.6
TEMiss (Lbs.)
Step-2 Avg. Filteration:
Selected solutions
(with below avg. TEMiss).
Filtered out/ excluded solutions
(with above avg. TEMiss)
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Figure 16. Application of AVCF to screen out the trade-offs with larger TEMiss values.
6.1.6. Simulation for Filtration Using ASCF (Step-3)
This step includes the formulation and application of a constraint filter based on the average
surface fit for
TE Miss
. The average surface fit for
TE Miss
in terms of
CEnet
and
TBD
is generated
Energies 2018,11, 3091 33 of 40
using polynomial based regression for the trade-offs achieved after the application of AVCF presented
in Table 11. What follows are the software and hardware tools used to develop the surface fit and to
formulate and apply the filter to validate the AVCF based filtration:
Machine: Core i7-4790 CPU @3.6 GHz with 16 GB of RAM,
Platform: MATLAB 2015a,
Regression model = Polynomial,
Polynomial surface model = Poly41,
Method = Linear least square,
Normalize = off,
Robust = off,
ASCF formulation and application,
average_sur f a ce_f it = sfit( CEnet ,TBD),
TE Miss_Resid_avgs =average_sur f a ce_f it T EMiss,
Exclude = TEMiss_Resid_avgs <0,
Where
average_sur f a ce_f it
is the value of emission obtained through the average surface fit
based polynomial for the respective
CEnet
and
TBD
trade-off. In addition,
TE Miss_Resid_avgs
is
the decision element for the filter. The exclude option provided with the surface fit function has
been used to screen out the trade-offs based on the formulation of the decision element. As per the
formulation for
TE Miss_Resid_avgs
in this research, a trade-off solution with a negative value of the
decision element
TE Miss_Resid_avg
indicates the average surface fit for
TE Miss
. The application of
ASCF thus screened out the trade-offs with higher values of
TE Miss
lying above the average surface
fit for TEMiss.
Table 11. Trade-offs achieved after applying AVCF based on Algorithm 2(Step-2).
Sr.
No.
CEnet
(Cents) TBD T EM iss
(Lbs.)
TE Miss_
Resid
_avg s
Pdl
(kWh)
Sr.
No.
CEnet
(Cents) TBD T EM iss
(Lbs.)
TE miss_
Resid
_avg s
Pdl
(kWh)
152.87 0.17 0.67 0.02 1.87 34 35.03 0.3 0.57 0.06 0.86
252.87 0.17 0.67 0.02 1.87 35 33.9 0.32 0.57 0.07 0.84
351.74 0.17 0.67 0.02 1.87 36 33.86 0.33 0.64 0.01 0.74
451.74 0.18 0.67 0.00 1.87 37 33.68 0.34 0.56 0.07 0.81
551.02 0.17 0.75 0.06 1.79 38 33.67 0.29 0.65 0.00 0.63
651.02 0.17 0.75 0.06 1.79 39 33.02 0.59 0.57 0.04 0.27
750.3 0.18 0.67 0.00 1.71 40 32.96 0.36 0.56 0.07 0.62
848 0.18 0.75 0.08 1.63 41 32.67 0.34 0.56 0.09 0.7
945.81 0.19 0.57 0.08 1.61 42 32.57 0.47 0.56 0.04 0.73
10 45.18 0.18 0.6 0.07 1.66 43 32.37 0.33 0.65 0.01 0.51
11 45.01 0.19 0.56 0.09 1.9 44 32.24 0.33 0.7 0.04 0.54
12 44.62 0.2 0.6 0.04 1.5 45 31.92 0.51 0.56 0.03 0.63
13 43.8 0.2 0.74 0.10 1.49 46 31.88 0.43 0.65 0.02 0.59
14 43.57 0.2 0.56 0.08 1.74 47 31.76 0.57 0.62 0.05 0.27
15 43.27 0.24 0.56 0.03 1.34 48 31.76 0.57 0.62 0.05 0.27
16 41.9 0.2 0.68 0.04 1.43 49 31.45 0.35 0.7 0.03 0.42
17 41.33 0.21 0.57 0.06 1.46 50 31.27 0.52 0.56 0.04 0.53
18 40.92 0.23 0.56 0.05 1.58 51 30.82 0.32 0.73 0.04 0.34
19 40.87 0.22 0.66 0.04 1.4 52 30.49 0.35 0.7 0.02 0.32
20 40.69 0.22 0.74 0.12 1.32 53 30.34 0.4 0.7 0.03 0.25
21 40.43 0.27 0.64 0.06 1.01 54 30.3 0.36 0.73 0.05 0.29
22 40.31 0.21 0.66 0.03 1.25 55 30.02 0.53 0.56 0.06 0.33
23 38.94 0.25 0.68 0.07 1.28 56 29.65 0.37 0.7 0.01 0.14
24 38.69 0.24 0.74 0.12 1.18 57 29.65 0.37 0.7 0.01 0.14
25 37.88 0.25 0.6 0.02 1.21 58 29.03 0.36 0.73 0.02 0.21
26 37.56 0.26 0.56 0.06 1.11 59 28.77 0.37 0.73 0.02 0.22
27 36.89 0.32 0.56 0.03 1.28 60 27.98 0.38 0.73 0.01 0.04
28 36.66 0.27 0.6 0.02 1.16 61 27.36 0.46 0.65 0.04 0.11
29 36.65 0.28 0.56 0.06 1.06 62 26.98 0.41 0.73 0.00 0.04
30 36.34 0.28 0.7 0.08 0.91 63 26.98 0.49 0.73 0.05 0.04
31 35.82 0.28 0.73 0.10 0.99 64 26.8 0.45 0.65 0.06 0.11
32 35.56 0.29 0.57 0.05 0.94 65 26.66 0.51 0.73 0.06 0.04
33 35.13 0.3 0.6 0.03 0.86 66 26.22 0.48 0.65 0.05 0.11
Energies 2018,11, 3091 34 of 40
6.2. Simulations for Filtration Mechanism to Harness Eco-Efficient Trade-Offs Using Algorithm 2
The simulation for filtration mechanism is based on Algorithm 2. The mechanism completes its
task in two steps as follows:
Application of an AVCF to the primary trade-offs to filter out the the trade-offs with extremely
high and above average values of TEMiss (step-2),
Application of an ASCF to the filtrate of step-2 to filter out the trade-offs with marginally higher
values of TEMiss (step-3).
Various polynomial model fit options were coupled with the ASCF. The best model fit for the
polynomials was achieved after comparison of the actual trade-offs for DRSREODLDG-based HEMS
problem exhibited by various polynomial models ranging from Poly11 to Poly55. The trade-off
solutions harnessed through each polynomial based ASCF were analyzed for the average value of
TE Miss
and the number of diverse trade-offs harnessed for
CEnet
and
TBD
. Poly11 based ASCF
achieved the minimum average
TE Miss
value of 0.58 Lbs.; however, the filter harnessed the least
number of trade-off solutions that did not include the desired solutions like ones with
CEnet
value
below 30 Cents. Poly12 based ASCF, on the other hand, included the trade-offs with minimal
CEnet
value less than 30 Cents; however, on the other hand, it lacked the diversification due to a lesser
number of trade-off solutions. The options with the average
TE Miss
value equal or less than 0.59 were
focused and poly41 was selected based on the lesser average values for
TE Miss
and
TBD
(0.59 Lbs.
and 0.3) and more diverse solutions for trade-offs between
CEnet/TBD
. In this way, the model fit is
based on an optimal set of the performance trade-offs for DRSREODLDG-based HEMS problems [
33
].
A summary comparing the performance of polynomial based ASCFs is given in Table 12 below.
Table 12. A comparison of performance parameters for polynomial based ASCF.
Regression Model No. of Trade-Offs
Harnessed
Average
CEnet (Cents) Average TBD Average
TEM iss (Lbs.) SSE R2
Poly11 29 37.01 0.31 0.58 0.28 0.05
Poly12 29 36.98 0.31 0.58 0.21 0.31
Poly13 32 37.48 0.31 0.6 0.18 0.41
Poly14 31 37.66 0.31 0.59 0.17 0.42
Poly15 33 38.49 0.3 0.6 0.17 0.44
Poly21 34 38.41 0.3 0.6 0.19 0.35
Poly22 35 37.46 0.31 0.6 0.17 0.42
Poly23 35 37.46 0.31 0.6 0.17 0.42
Poly24 35 37.01 0.31 0.6 0.17 0.42
Poly25 34 36.95 0.31 0.61 0.16 0.48
Poly31 32 37.62 0.31 0.59 0.19 0.37
Poly32 36 37.82 0.31 0.6 0.17 0.43
Poly33 37 37.52 0.3 0.61 0.17 0.43
Poly34 35 37.67 0.3 0.61 0.16 0.47
Poly35 35 37.51 0.3 0.61 0.13 0.55
Poly41 33 38.01 0.3 0.59 0.19 0.37
Poly42 33 38.47 0.3 0.6 0.17 0.44
Poly43 32 37.56 0.3 0.6 0.16 0.45
Poly44 33 37.57 0.3 0.6 0.16 0.47
Poly45 33 36.59 0.31 0.61 0.13 0.55
Poly51 33 37.67 0.31 0.6 0.18 0.4
Poly52 35 35.78 0.32 0.61 0.15 0.51
Poly53 37 35.6 0.33 0.61 0.14 0.53
Poly54 34 36.32 0.31 0.61 0.13 0.56
Poly55 35 36.16 0.31 0.62 0.13 0.56
Energies 2018,11, 3091 35 of 40
The proposed polynomial model, poly41, for ASCF is based on the following formulation:
z(x,y) = p00 +p10 ×x+p01 ×y+p20 ×x2+p11 ×x×y+p30 ×x3+p21 ×x2×y+p40 ×x4+p31 ×x3×y.(11)
The proposed polynomial model is based on the coefficients (with 95% confidence bounds)
as follows:
p00 = 5.48 (41.39, 52.35),
p10 =0.3234 (4.894, 4.248),
p01 =9.079 (77.88, 59.73),
p20 = 0.00699 (0.1564, 0.1704),
p11 = 0.6176 (5.337, 6.572),
p30 =4.498 ×105(0.002571, 0.002482),
p21 =0.013 (0.1842, 0.1582),
p40 =1.359 ×108(1.426 ×105, 1.423 ×105),
p31 = 6.749 ×105(0.001563, 0.001698).
The eco-efficient solutions harnessed after the application of Poly41 surface filter are
graphically shown in Figure 17. The final set of trade-off solutions for eco-efficient operation of
DRSREODLDG-based HEMS are tabulated as Table 13.
Table 13. Eco-efficient solutions for DRSREODLDG-BASED HEMS using Algorithm 2(Step-3).
CEnet
(Cents) TBD T EM iss
(Lbs.)
Pdl
(kWh) Ts1Ts2Ts3Ts4Ts5Ts6Ts7Ts8Ts9Ts10 Ts11 Ts12 Ts13 Ts14
52.87 0.17 0.67 1.87 6 39
104 123
60
128
4 73
119
107 108 102 114 95
52.87 0.17 0.67 1.87 6 39
104 123
61
128
5 73
119
107 108 102 114 95
51.74 0.17 0.67 1.87 6 39
104 123
60
128
5 73
119
107 107 102 114 95
50.3 0.18 0.67 1.71 6 40
104 123
61
128
5 73
119
107 107 102 114 95
45.81 0.19 0.57 1.61 5 40
104 123
60
128
4 73
119
107 107 93 114 94
45.18 0.18 0.6 1.66 5 39
104 123
60
128
4 73
119
107 106 94 114 94
45.01 0.19 0.56 1.9 6 39
104 123
60
128
5 73
119
107 105 92 114 94
44.62 0.2 0.6 1.5 5 40
104 123
60
128
5 73
119
105 107 94 114 94
43.57 0.2 0.56 1.74 5 40
104 123
61
128
5 73
120
107 104 92 114 94
43.27 0.24 0.56 1.34 5 40
105 123
60
128
5 73
119
107 107 63 113 94
41.33 0.21 0.57 1.46 6 41
104 123
60
129
5 73
119
107 104 93 114 94
40.92 0.23 0.56 1.58 5 42
104 124
60
129
6 73
119
106 104 90 114 93
37.88 0.25 0.6 1.21 5 42
105 123
60
129
6 74
119
106 103 94 113 90
37.56 0.26 0.56 1.11 5 40
104 123
60
128
5 74
120
104 105 62 112 95
36.89 0.32 0.56 1.28 5 42
104 123
62
132
5 75
122
105 91 78 108 97
36.66 0.27 0.6 1.16 5 42
104 123
62
130
6 74
120
106 98 91 110 95
36.65 0.28 0.56 1.06 5 41
104 123
60
129
5 74
120
103 103 62 112 93
35.56 0.29 0.57 0.94 5 42
105 123
60
129
7 74
118
105 97 86 114 64
35.13 0.3 0.6 0.86 5 42
105 123
62
130
7 74
120
104 98 64 114 94
35.03 0.3 0.57 0.86 5 40
105 124
60
129
7 74
117
104 97 62 111 89
33.9 0.32 0.57 0.84 5 42
105 123
62
130
7 74
120
103 97 64 110 94
33.68 0.34 0.56 0.81 5 42
105 123
60
130
7 74
119
103 95 62 110 76
33.67 0.29 0.65 0.63 5 42
104 123
60
130
5 74
120
104 99 62 113 90
32.96 0.36 0.56 0.62 5 41
104 124
60
132
7 75
121
104 64 62 110 95
32.67 0.34 0.56 0.7 5 43
105 123
62
130
8 74
121
103 96 63 109 93
32.57 0.47 0.56 0.73 6 44
105 124
75
132
8 76
120
103 84 62 106 63
32.37 0.33 0.65 0.51 5 42
105 124
60
131
5 74
119
103 99 61 112 82
31.92 0.51 0.56 0.63 6 44
106 124
78
133
11 76
121
103 78 61 105 62
31.27 0.52 0.56 0.53 6 44
105 124
95
135
11 75
120
103 80 61 104 62
30.02 0.53 0.56 0.33 7 44
104 124
81
135
12 77
130
103 63 61 104 98
27.36 0.46 0.65 0.11 3 41
105 125
58
133
8 74
117
93 61 60 104 61
26.8 0.45 0.65 0.11 5 44
105 125
58
134
10 74
119
93 61 61 107 94
26.22 0.48 0.65 0.11 6 44
105 124
59
135
7 74
117
93 85 61 103 61
Energies 2018,11, 3091 36 of 40
TBD
0.4
0.2
50
45
CEnet (Cents)
40
35
30
1
0.5
0
-0.5
TEMiss (Lbs.)
Step-3 Avg. Surface Filteration:
Selected eco-efficient solutions
(under avg. surface for TEMiss).
Filtered out/ excluded solutions
(above avg. surface for TEMiss).
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Figure 17.
Eco-efficient solutions selected using average surface filtration based on Algorithm 2(Step-3).
6.3. Critical Trade-Off Analysis of Solutions for Eco-Efficient DRSREODLDG-Based HEMS Operation
The final trade-off solutions for eco-efficient HEMS operation harnessed through Algorithms 1and 2
are analyzed in this section for percentage reduction in
CEnet
,
TBD
, and
TEMiss
. The values of
CEnet
,
TBD
and
TEMiss
obtained without using the proposed method are 68.32 Cents, zero and
1.354 Lbs.
,
respectively, and the same have been used as base values in this analysis. For critical trade-off analysis
(CTA), the finalized trade-offs are classified for percentage reduction in
CEnet
,
TBD
and
TEMiss
as
presented in Table 14. In the following are the main features of the proposed classification:
Class-I: The percentage in
CEnet
ranges from 22.61 to 36.23, with the corresponding discomfort
levels from 17% to 20%. The comfort-conscious consumers are likely to opt this class due to minimal
TBD
and a reasonable reduction in
CEnet
. Maximal reduction in
TE Miss
ranging from 50.53% to
58.58% ensures eco-efficiency.
Class-II: The percentage reduction in
CEnet
ranges from 36.67 to 52.18 with the corresponding
discomfort levels from 21% to 36%. The reduction in
TE Miss
ranges from 51.72% to 58.58%. With the
double-tailed polynomial trend for
TE Miss
as shown in Figure 18, the class lies in the minimal range
for emission. The class exhibits the best trade-off solutions taking into account
CEnet
, discomfort and
TE Miss
. Most of the consumers are likely to choose this class for a fairly high welfare in terms of
CEnet
and the discomfort for the consumer with bottom minimal
TE Miss
. The class is regarded as the
best for eco-efficiency.
Class-III: The percentage reduction in
CEnet
ranges from 52.33 to 61.63 with the corresponding
discomfort levels from 33% to 53%. Users who belong to this class have an increase in cost reduction
up to 61.63% (largest for all classes) followed by high user discomfort level of 53% (largest for all
classes). Users can choose this class for getting the large possible reduction in
CEnet
. The maximal
reduction in
TE Miss
ranging from 50.53% to 58.58% for this class ensures eco-efficiency. Furthermore,
the last three solutions in this class offer the maximum reduction in
CEnet
reaching up to 61.63% with
a relatively low level of discomfort of value down to 45% as compared to the other members of this
class. The consumers satisfied with these typical operating schemes may avail the maximum welfare
through the largest reduction in CEnet at a relatively low level of discomfort.
Energies 2018,11, 3091 37 of 40
Table 14. Critical trade-off analysis for eco-efficient DRSREODLDG-BASED HEMS operation.
Classes CEnet
(Cents)
Reduction
in CEnet (%)
Range
(%) TBD Range
(%)
TE Miss
(Lbs.)
Reduction
in TE Miss (%)
Range
(%)
I
52.87 22.61
22.61–36.23
0.17
17–20
0.67 50.53
50.53–58.58
52.87 22.61 0.17 0.67 50.53
51.74 24.26 0.17 0.67 50.53
50.30 26.38 0.18 0.67 50.53
45.81 32.95 0.19 0.57 58.11
45.18 33.87 0.18 0.60 55.74
45.01 34.12 0.19 0.56 58.58
44.62 34.70 0.20 0.60 55.74
43.57 36.23 0.20 0.56 58.58
II
43.27 36.67
36.67–52.18
0.24
21–36
0.56 58.58
51.72–58.58
41.33 39.50 0.21 0.57 58.11
40.92 40.11 0.23 0.56 58.58
37.88 44.56 0.25 0.60 55.74
37.56 45.02 0.26 0.56 58.58
36.89 46.00 0.32 0.56 58.58
36.66 46.33 0.27 0.60 55.90
36.65 46.36 0.28 0.56 58.58
35.56 47.95 0.29 0.57 58.19
35.13 48.58 0.30 0.60 55.90
35.03 48.73 0.30 0.57 58.19
33.90 50.38 0.32 0.57 58.19
33.68 50.70 0.34 0.56 58.58
33.67 50.71 0.29 0.65 51.72
32.96 51.75 0.36 0.56 58.58
32.67 52.18 0.34 0.56 58.58
III
32.57 52.33
52.33–61.63
0.47
33–53
0.56 58.58
51.72–58.58
32.37 52.62 0.33 0.65 51.72
31.92 53.28 0.51 0.56 58.58
31.27 54.22 0.52 0.56 58.58
30.02 56.05 0.53 0.56 58.27
27.36 59.96 0.46 0.65 51.72
26.80 60.78 0.45 0.65 51.72
26.22 61.63 0.48 0.65 51.72
CTA given in Table 14 along with the respective scheduled times
Tst
in Table 13 enables consumer
to select the best eco-efficient options according to his needs after consulting a diverse set of current
optimized choices for CEnet,TBD and minimal T EMiss.
= 0.8931
= 0.6214
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.00 10.00 20.00 30.00 40.00 50.00 60.00
70.00
TEMiss (Lbs.), TBD
% Reduction in CEnet
TBD TEMiss Poly. (TBD) Poly. (TEMiss)
Figure 18. Relation between % Reduction in CEnet, TBD and TEMiss for eco-efficient trade-offs.
Energies 2018,11, 3091 38 of 40
7. Conclusions and Future Work
A three-step simulation-based posteriori method for eco-efficient operations of a
DRSREODLDG-based HEMS is proposed. First, a MOGA/PO based heuristic method is
used to generate a set of 100 trade-off solutions for HEMS operation. Second, an average value
constraint filter for
TE Miss
is applied to filter out the solutions with extremely high values of
TE Miss
.
Third, an average surface fit (for
TE Miss
) is formulated in terms of
CEnet
and
TBD
using an optimal
polynomial model for regression. This method delivered an eco-efficient set of 33 trade-off solutions
between
CEnet
and
TBD
against a minimal
TE Miss
. The trade-offs were classified to enable the
consumer choice to select the best eco-efficient option. Class-I offered a maximum reduction of 36.23%
for
CEnet
against a 20% value of
TBD
, while reduction in
TE Miss
remained above 50.53%. Class-II
offered a maximum reduction of 52.18% for
CEnet
against a 36% value of
TBD
, while a reduction in
TE Miss
remained above 51.72%. Class-III offered a maximum reduction of 61.63% for
CEnet
against a
53% value of
TBD
while a reduction in
TE Miss
remained above 51.72%. The best eco-efficient solution
for a consumer was comprised of a maximum reduction of 60.78% in
CEnet
against a 45% value of
TBD and a 51.72% reduction in TEMiss.
Future work will address improved performance and extended diversification of the trade-off
parameters including
CEnet
,
TBD
and
TE Miss
for DRSREODLDG-based HEMS through the
following means:
Use of MOGA with a varied value of crossover fraction and type of crossover function from the
opted default values.
Use of other meta-heuristic and hybrid methods to generate the primary trade-offs and comparing
their performance with MOGA.
Activate normalize and robust options available for surface fitting with the polynomial model for
regression. These options are not activated in this research.
Use of other types of surface fits and the related options to achieve more efficient and
diversified solutions.
Additions of constraints regarding the life of the storage devices, starting the LDG, and the
operation of the LDG near rated power.
The development of a scheme for the integrated reduction of the carbon commodities for the
consumers and the utility through DRSREODLDG-based HEMS.
Minimization of the sum of the PV energy losses in HEMS.
Author Contributions: All authors equally contributed to this work.
Conflicts of Interest: The authors declare no conflict of interest.
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... The smart grid (SG) has emerged as a modern form of the power grid. It has two-way communication between energy consumers and producers for efficient energy management [10,11,12,13,14]. It eliminates the requirement of thermal power plants and conserves electricity. ...
... When the bidding time ends, the main smart contract calls the clearMarket function (Lines [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. This function checks the tag of each buyer and seller and trades energy according to the minimum distance between them to reduce the power losses and make trading efficient. ...
... 13 shows the results' comparison for the schemes. ...