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Comparison among deterministic methods to design
rural mini-grids: effect of operating strategies
Davide Fioriti
Davide Poli
Paolo Cherubini
Giovanni Lutzemberger
DESTEC
University of Pisa
56122 Pisa, Italy
Email: davide.fioriti@ing.unipi.it
Andrea Micangeli
DIMA
University of Rome ”Sapienza”
Roma, Italy
Email: andrea.micangeli@uniroma1.it
Pablo Duenas-Martinez
MIT Energy Initiative
Massachusetts Institute of Technology
Cambridge, MA, United States
Email: pduenas@mit.edu
Abstract—Mini-grids are well known to be a suitable solution
to foster rural electrification in developing countries, and yet
risks and high costs are hampering their spreading. Even
though effective tools can help developers to identify the optimal
design and operation of a mini-grid, no standard approach
have emerged yet. This paper proposes a numerical comparison
among deterministic methodologies to optimize a rural mini-
grid considering the effect of different operating strategies. The
typical load-following and cycle-charging strategies are compared
to predictive approaches, as rolling-horizon and a one-shot model,
which optimizes both the design and operation together. The two
latter models allow achieving additional savings compared to tra-
ditional operating strategies, but the computational requirements
increase sharply. Results suggest that sizing methodologies using
load-following or cycle-charging strategies are more suitable for
preliminary design, while predictive approaches should be used
for the fine tuning of the size of components. This study can
provide guidance on design and operating methodologies for
rural mini-grids in developing countries.
Index Terms—isolated hybrid system; microgrids; Mixed in-
teger linear programming; off-grid energy system; optimization
I. INTRODUCTION
Increasing energy access is a key objective for developing
countries [1]. In a world where 1.1 billion people live without
electricity and 2.8 billion without adequate cooking facilities,
several challenges still have to be overcome, mainly in rural
areas [2]. Highlighted as an enabler to foster rural development
[3], [4], access to electricity is being promoted by several
governments, especially in areas close to the cities [5], but
rarely the same approach is appropriate for isolated rural areas
of developing countries. In fact, off-grid solutions are often
more appropriate in rural areas, because they exploit local
sources and prevent the installation of long power grids [6].
In particular, mini-grids that supply several customers through
a local power grid can provide a good quality electricity up
to Tier 5 (the highest level of access) [5], [7], which enables
also the development of commercial and industrial activities.
Typical mini-grids are operated by simple priority-list strate-
gies [8]–[10] that dispatch first the renewable sources, then the
energy storage devices, and finally the conventional fuel-fired
generators. In the two main approaches, namely the Load-
Following (LFS) and Cycle-Charging (CCS) Strategies, the
fuel generators are turned on only when the batteries reach
their minimum State-Of-Charge (SOC). Their basic difference
is that in the LFS the fuel-fired generators only supply the load
without recharging the battery, while in the CCS the conven-
tional generators recharge the batteries up to a fixed threshold
and are shut down afterwards. As reviewed in [10], [11] and
[12], the majority of papers and real mini-grids propose these
techniques since they do not require any forecast or expen-
sive control devices. However, recent developments in power
electronics have improved the performance and reliability of
cheap control devices, so that more advanced techniques could
be adopted without requiring expensive or complex control
schemes. Several papers highlighted the potential benefits of
using predictive approaches also for mini-grids in developing
countries [13]–[15]. Authors in [13] developed a fast rolling-
horizon tool that performs an optimal re-dispatching procedure
of the system every 6 hours, while the real-time balancing
of the mini-grid is guaranteed by simple priority-list rules.
Conversely, the methodology described in [14] proposes a
rolling-horizon approach that re-dispatches the system every
15 minutes by using variable time steps, so to reduce the
computational burden. Again, priority rules are used for the
very fast real-time balancing.
The optimal design of rural mini-grids is a trendy topic,
as proven for instance by [11], [13], [16]–[20]. This topic is
strongly related to the one of the operation, since the optimal
size of components is typically searched by simulating the
technical and economic operation of the mini-grid in different
size scenarios. Typical deterministic approaches simulate the
future behavior of the mini-grid assuming a given realistic
yearly profile of both the demand and renewable production.
In this case, classical programming techniques, such as Mixed-
Integer Linear Programming (MILP), or heuristic approaches
can be used to select the optimal size of components of the
mini-grid, with the aim of minimizing the Net Present Cost
(NPC) of the system face to such power profiles [11]. In
particular, heuristic methods iteratively investigate a number
of possible size scenarios (also based on the results of the
previous iterations) and simulate the operation of each of
them. An objective function that accounts for the investment
and operating costs is evaluated in every scenario, in order to
select the cheapest one. For example, authors in [13] developed
a method based on Particle Swarm Optimization (PSO) to
identify the optimal sizing of a typical mini-grid, including the
design of the tank and the best fuel procurement strategy. To
operate the system, a rolling-horizon predictive method was
employed, whose outcomes were compared with the results
of the classical LFS. The work in [14] describes a similar
methodology and results were compared also with CCS.
Regarding mathematical optimization techniques, MILP has
been widely used in the literature since it provides the global
optimum under given mathematical assumptions [21], [22],
thus representing the standard approach in power systems for
optimizing the system operation [23]. Authors in [24] proposed
a MILP methodology to size an isolated energy system serving
electricity and thermal loads. However, in order to reduce
the computational requirements, the authors approximated the
behavior of the system with 12 representative days, rather than
with a yearly profile. Conversely, authors in [25] proposed a
MILP-based optimization of an isolated system considering
the entire year of operation; this increased the computational
requirements up to about 3 hours, even though results were
within 5% of optimality, as specified in termination criteria.
It is important to remark that MILP approaches are limited to
piecewise-linear cost functions at best, while methodologies
with heuristic solvers can be non-linear, like in [13].
Furthermore, it is worth noticing that any sizing technique,
be it based on simulating a LFS, CCS or RHS operating
procedure, requires at least the estimation of a typical yearly
profile of demand and of renewable production, in order to
simulate what the behavior of the mini-grid would be in differ-
ent size scenarios. In particular, the operation of the mini-grid
with LFS and CCS does not require any forecasting activity,
while RHS includes a short-term prediction of the demand
and renewable production for the hours to come. Therefore,
using RHS, also the forecasting activity must be simulated,
as in [13]. In this regard, deterministic approaches capture the
behavior of the system by means of a single yearly scenario
of the demand and renewable production, thus neglecting
their uncertainties. Conversely, stochastic approaches consider
uncertainties in the design phase by analyzing a number of
scenarios whose results are weighted with their probability
[13], which increases the robustness of the approach at the
cost of higher complexity and computational requirements.
In the present paper, aimed at guiding both developers and
researchers, we highlight benefits and drawbacks of deter-
ministic design techniques combined with different operating
strategies, assuming that the typical behavior of the system
can be approximated with a yearly profile of the demand and
of the available renewable production, with a granularity of
one hour. Moreover, we propose a novel MILP approach,
called One-Shot (OS), able to optimize both the sizing and
the operation of the mini-grid assuming the perfect forecasting
of load and RES profiles. Additionally, we implemented the
methodology described in [13] with the LFS, the CCS and
the RHS strategies so to compare them with the OS. In
the RHS, the short-term forecasting errors are considered,
conversely to what happens in OS. In this preliminary activity,
we focused on deterministic approaches so to reduce both the
computational requirements and the parameters to analyze. A
case study is proposed using consumption data collected from
a real mini-grid located in Kenya.
The rest of the paper is organized as follows. Section II
describes the mathematical formulation of the OS model, while
Section III details the heuristic approaches combined with the
LFS, CCS and RHS. Section IV details the case study and
Section V reports the results.
II. ON E-SH OT (OS) MOD EL
A. Description
The OS model optimizes both the design and operation of
the system by means of MILP, which is very used in power
system [22]. In the OS procedure, the solver not only chooses
the optimal design of the system but also the best dispatching
of components for the entire simulation period, including
recharging batteries in advance with respect to real-time needs.
The optimization period is the typical year that approximates
the multi-year behavior of the system, which is an usual mini-
grid with both AC and DC bus composed by a photovoltaic
plant, a battery storage, a DC/DC converter, an inverter,
and a fuel generator. The objective is minimizing the life-
long NPC of the system, which accounts for both investment
and operating costs (fuel consumption, maintenance, and the
energy-not-served) [13].
B. Mathematical formulation
1) Objective function: The objective function is minimizing
the expected NPC detailed in (1), where CAPEX are evaluated
through piecewise linear functions of the capacity of each
component: the photovoltaic plant, the battery, the DC/DC
converter, the inverter, and the fuel generator. Details are re-
ported in equations (2) and (3). The operating costs OP E Xs,t
of each scenario and time step are averaged according to
the Sample Average Approximation method [26]. OP E Xs,t
relates to the operating costs of the generator CD,O&M,s,t ,
accounting for both maintenance and fuel expense, and of the
load curtailment CLC,s,t.
min CAP E X0+
NT
X
y=1
1
NsPNs
s=1 OP E Xs,t
(1 + d)y(1)
CAP E X0=CP V (PP V ,c) + CB(PB,c ) +
+CDCD C (PDCD C,c) + CI(PI ,c) + CD(PD,c )(2)
Cx(Px,s) = piecewise linear function (Fig. 2) (3)
OP E Xs,t =
NT=8760
X
t=1
CD,O&M,s,t +CLC ,s,t (4)
The operational costs due to the fuel and to the maintenance
of the diesel generator are reported in (5). In particular, cM
is the maintenance cost per unit of the diesel generator rated
power, fi,0and fi,1are the intercept and slope of the piece-
wise linear cost interval i with respect to the size, zD,s,t is
the binary variable that is true when the diesel is in operation
and false otherwise, and MDC is a constant large enough so
to discard the constraint when the diesel is shut down. PD,c
is the optimal design of the diesel generator.
CD,O&M,s,t ≥cMPD ,c +fi,0PD,c +fi,1PD,s,t
−(1 −zD,s,t)MD C
(5)
CD,O&M,s,t ≥0(6)
The load curtailment costs CLC,s,t are simply related to the
corresponding curtailed hourly energy PLC,s,t and to the load
curtailment cost cLC per unit of energy loss, as detailed in
(7).
CLC,s,t =cLC PLC,s,t (7)
2) Power balance: The power balances at AC and DC bus
are reported in (8) and (9), respectively. PD,s,t is the power
supplied by the generator for scenario s and time step t. The
inverter dispatching is modeled by P+
I,s,t , which is positive
when the component supplies power to the AC bus, and by
P−
I,s,t , which is positive when the component absorbs power
from the AC bus. PL,s,t is the load demand and PLC,s,t is the
load curtailment. PP V,s,t is the renewable energy exploited
and, similarly to the inverter, P+
B,s,t and P−
B,s,t model the
power supplied or absorbed by the battery, respectively. The
efficiency ηIof the inverter is considered in (9).
PD,s,t +P+
I,s,t −P−
I,s,t =PL,s,t −PLC,s,t (8)
PP V,s,t +P+
B,s,t −P−
B,s,t −P+
I,s,t
ηI
+P−
I,s,t ηI= 0 (9)
3) Diesel constraints: Constraint (10) guarantees that the
power delivered by the generator is lower than its capacity
PD,c. Constraint (11) expresses the minimum and maximum
power limit of the generator according to whether the gen-
erator operates or not, which is modelled with the binary
variable zD,s,t. The minimum working point of the generator
is expressed as a share αP d,min of its size.
0≤PD,s,t ≤PD,c (10)
αP d,minPD,c −(1 −zD ,s,t)MD≤PD,s,t ≤zD ,s,tMD(11)
4) Battery constraints: Constraints (12) and (13) guarantee
that the power exchanged by the battery is lower than the
capacity of the battery converter. Constraints (14) and (15)
force the battery not to be charged and discharged in the same
time step, which is captured by the binary variable zB,s,t. Eq.
(16) expresses the energy EB,s,t stored in the battery as a
function of the energy stored in the battery in the previous time
step, the present dispatching of the battery, and the battery
efficiency ηB. Constraint (17) specifies the maximum and
minimum limit of the energy stored in the battery, as a function
of its capacity EB,c . Its minimum level is modeled as a share
αEb,min of the capacity of the battery.
0≤P+
B,s,t ≤PB,c (12)
0≤P−
B,s,t ≤PB,c (13)
0≤P+
B,s,t ≤zB,s,t MB(14)
0≤P−
B,s,t ≤(1 −zB,s,t )MB(15)
EB,s,t =EB,s,t−1+P−
B,s,t ηB−P+
B,s,t
ηB
(16)
αEb,min EB,c ≤EB,s,t ≤EB ,c (17)
5) Inverter constraints: In analogy to the battery, con-
straints (18) and (19) guarantee that the power exchanged by
the inverter is always compliant with the size of the inverter
PI,c . Equations (20) and (21) guarantee the inverter not to
supply and absorb power from the AC bus in the same time,
which is set by binary variable zI,s,t.
0≤P+
I,s,t ≤PI ,c (18)
0≤P−
I,s,t ≤PI ,c (19)
0≤P+
I,s,t ≤zI ,s,tMI(20)
0≤P−
I,s,t ≤(1 −zI ,s,t)MI(21)
6) Photovoltaic plant: The power PP V ,s,t produced by the
PV plant is limited by its size PP V,c and by the available
hourly production PP V,Av,s,t of a 1kW-PV plant installed in
the same site, as in (22).
0≤PP V,s,t ≤PPV ,Av,pu,s,t PP V,c (22)
7) Load curtailment: The load curtailment PLC,s,t must be
lower than the load PL,s,t in (23).
0≤PLC,s,t ≤PL,s,t (23)
III. HEURISTIC-BASED SIZING METHODOLOGIES (LFS,
CCS, RHS)
A. Description
The proposed heuristic methodology is based on a PSO
approach that, as shown in Fig. 1, minimizes the NPC of the
system accounting for both investment and operating costs,
the latter related to fuel, maintenance, and energy-not-served.
The load and renewable production, which approximate the
multi-year behavior of the system, are first evaluated. Then,
the PSO procedure iteratively draws possible size scenarios
for the components of the mini-grid, as depicted in the outer
loop of Fig. 1. In the inner loop, the procedure then evaluates
the OPEX of each of them, by simulating the operation of
the system for the entire year, as described in the following
section. While authors in [13] simulated only LFS and RHS, in
this paper we also consider CCS in order to propose a complete
comparison, also including the OS method. Subsequently, the
methodology calculates the NPC of the system and when the
termination criteria are reached, the procedure stops and the
optimal size of the components is assessed.
Fig. 1. Algorithm of the proposed heuristic-based optimization.
B. Operating strategies
1) LFS: The Load-Following operating strategy is a merit-
order-list method that prioritizes the use of the renewable
energy, then the storage system, and finally the fuel generator
as a backup source. When batteries reach the minimum SOC,
the generator supplies energy only to supply the load, without
recharging the battery; otherwise, the generator is kept offline.
2) CCS: Similarly to LFS, also the Cycle-Charging strategy
prioritizes renewable energies and storage system as LFS;
however, when batteries reach the minimum SOC, the fuel
generator is turned on to supply the load and recharge the
batteries until they reach a pre-set threshold. This parameter
is also optimized in the proposed approach, similarly to the
capacity of components. The generator is assumed to supply
power at its maximum efficiency (on-off operation). This
simplification requires simulating that the generator may be
asked to produce only for a fraction of hour, while simulations
are performed with hourly resolution.
3) RHS: The rolling-horizon approach is a predictive
method that infra-daily redispatches the system to cope with
uncertainties of the forecasts, as described in [13]. Every fixed
amount of time (i.e. 6h), the power profiles of demand and
renewable production of the following 24 hours are estimated.
Then, a MILP procedure calculates the corresponding optimal
dispatch of the system. The real-time dispatching method
based on priority-list rules corrects the previous dispatch
due to intrinsic forecasting errors. This approach enables to
advance the behavior of the system, thereby the management
can achieve additional savings with respect to LFS and CCS.
The mathematical formulation is described in [13].
IV. CAS E STU DY
A. Description
The comparison of the different sizing methodologies has
been tailored to a system of 10000 consumers in the Wajir
County, Kenya. While heuristic approaches can optimize the
fuel tank including the logistics of the fuel procurement [13],
this kind of optimization is not included in the OS due to
its complexity and computational requirements. Therefore,
the optimized components of the proposed mini-grid are the
photovoltaic system, the battery storage, the battery converter,
the inverter, and the fuel generator.
B. Demand and available renewable production
The yearly load profile used for the simulations is based
on the measurements performed on a close mini-grid for the
year 2014. The data originally sampled every 30 minutes were
averaged every hour. Hourly Gaussian noise with standard
deviation of 20% of the actual demand is introduced to stress
uncertainties of the expected demand.
The available renewable production was estimated by using
the Graham method [27] tailored with data from the close
weather station of Kitale, Kenya.
As for RHS, the short-term forecasting error of demand and
RES is modeled with a Gaussian function, whose standard
deviation varies from 5% to 15% of the expected load,
depending on the distance to the real time.
C. Cost parameters and efficiencies
The investment costs of components is described in (24),
where xis the component, Pxthe corresponding nominal
capacity, C0,x is the cost of the component whose size is P0
and the parameter βxmodels the economies of scale.
C(x) = C0,x Px
P0βx
(24)
The costs of PV system and of the batteries are as-
sumed to be proportional to the installed capacity: 800$/kWp
and 350$/kWh, respectively. Their maintenance costs are
16$/kWp/y and 3$/kWh/y, respectively. On the other hand,
(a) Generator (b) Inverter (c) Battery converter
Fig. 2. Investment cost function of selected components.
TABLE I
OPTIMAL DESIGN WITH OS A ND TH E HEURI STI C AP PROA CHE S OPE RATE D WI TH LFS, CCS AN D RHS.
Strategy Exec. time NPC Load curt. PV Battery Generator DCDC Conv. Inverter SOCC C,end
(min) (k$) (%) (kWp) (kWh) (kW) (kW) (kW) (%)
LFS 1.5 1833 0.31 743 2069 127 413 247 n.a.
CCS 1.5 1819 0.47 743 2044 134 419 241 20.6
RHS 274 1780 0.07 726 2001 59 453 235 n.a.
OS1446 1774 0.06 716 1990 75 391 236 n.a.
1Relative solution tolerance: 5%
the cost functions of the inverter and of the fuel generator
are shown in Fig. 2b and Fig. 2a, respectively; the one of
the DC-DC converter is the same as of the inverter, but
discounted by 33.3% (Fig. 2c). Such pictures show both the
non-linear cost function used in heuristic approaches (LFS,
CCS and RHS) and the piece-wise linearization for OS. The
annual maintenance cost of the converters is 3$/kW/y, while
for the generator is 15c$/kW/h for each operating hour. The
efficiencies of components are 96% for the battery (roundtrip),
96% for the inverter, and 99% for the DC-DC converter. The
efficiency of the diesel increases from around 11% at the
minimum operating level (10% of the rated power) up to 33%
[13].
The economic value of load curtailment is 1$/kWh and the
fuel price is 0.8$/l.
Results were obtained using a 12-core 2.66GHz Xeon
computer with 16GB RAM.
V. RESULTS AND DISCUSSION
The optimal designs achieved with the OS and with the
three heuristic approaches based on LFS, CCS and RHS are
reported in Table I.
It is worth noticing that since OS optimizes both the
design and operation together, its global optimum represents
theoretically the lowest bound achievable with other oper-
ating strategies. In our simulations, due to computational
constraints, the solution with OS was achieved with 5% of
optimality, but it is still the cheapest one and the priority-
list methodologies are more expensive of about 3-4% with
respect to the OS method and 2-3% w.r.t. the RHS. LFS and
CCS have practically the same objective function, since their
difference is lower than 1%. Requiring less than 2 minutes,
LFS and CCS outperformed the other solutions in terms of
computational requirements. OS was the most time-consuming
procedure since it required 7.4h, by far more than RHS (4.5h).
Therefore, these results suggest that OS can be used as a
reference to compare the objective function achieved under
different operating strategies. However, it does not account
for uncertainties in the load and renewable production that
are considered in the other approaches. Moreover, integrating
the optimal sizing of the tank and the fuel logistics into
OS is quite challenging due to complexity and computational
requirements, contrary to other approaches [13]. Furthermore,
although RHS simulates the forecasting errors of both the
renewable production and demand, the objective function is
still very close to the OS, which means RHS is a promising
operating strategy for rural mini-grids.
The optimal design of the photovoltaic plant, the battery and
converters is very similar among the methodologies; instead,
the one of the generator is halved in the predictive approaches
(RHS and OS). In fact, since they analyze in advance the
possible behavior of the system, a smaller generator can
be used and operated for recharging batteries hours before.
Despite that, the total consumption of the diesel increases
because the generator supplies more energy, but predictive
approaches reduces the specific cost of diesel production
including maintenance in respect to LFS. RHS is cheaper
than CCS because the former enhances the coordination of
components thus leading to lower energy-not-served and less
components.
It is also worth noticing that the optimal threshold
SOCCC,end to stop recharging the batteries in CCS is roughly
the minimum SOC (20%); this means the CCS is collapsing
into a LFS and in fact the objective functions are very close.
VI. CONCLUSION
Aiming to provide guidance on design approaches and
operating strategies to researchers, developers and practitioners
in the field, this paper presents a detailed comparison of
the state-of-art deterministic methodologies to design mini-
grid including the effect of operating strategies. The typical
sizing methodologies, whose operation is based on priority-
list rules, LFS and CCS, were compared to a predictive RHS
approach, already discussed in the recent literature, and to a
novel One-Shot model. Since OS optimizes the design and
operation together, it can reach a global optimum that no
other strategy (LFS, CCS, or RHS) can achieve because the
future behavior of loads and RES is supposed to be known,
however, uncertainties in the short-term forecasts of resources
and demand is neglected. Results confirm this considera-
tion but also suggest that RHS is very promising since it
is practically as expensive as OS, although it accounts for
forecasting uncertainties conversely to OS. In particular, RHS
and OS enable a better coordination of components, which
allows achieving savings of 2-4% of NPC with respect to LFS
and CCS, but the computational requirements of the formers
are much higher than LFS and CCS, especially in the OS
case. The optimal size of components obtained using the four
methodologies is very similar, with the exception of the diesel
generator, whose size is roughly halved in RHS and OS due to
the predictive capabilities of these methodologies. Therefore,
LFS and CCS can be used for the preliminary design with
low computational requirements but larger costs, while RHS
and OS are more suitable for the refinement stages. Therefore,
the design guidelines highlighted in this paper can be used by
experts in the field for tailoring the operating strategy and the
design methodology of rural mini-grids.
ACKNOWLEDGMENT
The activity has been developed under the project titled
”Optimal Electrification Strategies For Rural Areas Of De-
veloping Countries Through Mini-Grids: From Social Needs
To Technical Sizing”, funded by the MIT-UNIPI project under
the MISTI framework.
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