![Bus voltage (p.u.). The normal voltage range is [0.91, 1.04]. The x-axis and y-axis represent time (hour) and per unit voltage, respectively.](https://www.researchgate.net/publication/358560812/figure/fig3/AS:11431281097638023@1668653515736/Bus-voltage-pu-The-normal-voltage-range-is-091-104-The-x-axis-and-y-axis_Q320.jpg)
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IEEE POWER & ENERGY SOCIETY SECTION
Received January 26, 2022, accepted February 6, 2022, date of publication February 11, 2022, date of current version February 22, 2022.
Digital Object Identifier 10.1109/ACCESS.2022.3151172
Residential Demand Response-Based
Load-Shifting Scheme to Increase Hosting
Capacity in Distribution System
YE-JI SON1, SE-HEON LIM 1, (Student Member, IEEE),
SUNG-GUK YOON 1, (Senior Member, IEEE),
AND PRAMOD P. KHARGONEKAR 2, (Life Fellow, IEEE)
1Department of Electrical Engineering, Soongsil University, Seoul 06978, South Korea
2Department of Electrical Engineering and Computer Science, University of California at Irvine, Irvine, CA 92697, USA
Corresponding author: Sung-Guk Yoon (sgyoon@ssu.ac.kr)
This work was supported in part by the Ministry of Science, ICT (MSIT), South Korea, through the High-Potential Individuals Global
Training Program, supervised by the Institute for Information & Communications Technology Planning & Evaluation (IITP) under
Grant 2021-0-01525; and in part by the National Research Foundation of Korea (NRF) Funded by the MSIT, Korea Government, under
Grant 2020R1F1A1075137.
ABSTRACT Increasing the use of solar photovoltaic (PV) generation in order to decarbonize the electric
energy system results in many challenges. Overvoltage is one of the most common problems in distribution
systems with high penetration of solar PV. Utilizing demand-side resources such as residential demand
response (RDR) have the potential to alleviate this problem. To increase the solar PV hosting capacity,
we propose an RDR based load-shifting scheme that utilizes the interaction between the distribution system
operator (DSO) and demand-side resources. We first model a customer utility that consists of the cost of
purchasing power, revenue from the subsidy, and discomfort due to load shifting. When an overvoltage
problem is expected, DSO issues a local subsidy, and customers in the distribution system move their load
in response. An optimization framework that minimizes the additional cost due to the subsidy while keeping
the voltages in a prescribed range is proposed. Because of the non-linearity of the power flow analysis,
we propose a sub-optimal algorithm to obtain a subsidy, prove the performance gap between the optimal
subsidy and the subsidy obtained by the algorithm. A case study shows that the proposed RDR scheme
increases the hosting capacity to almost its theoretical limit at a lower cost than the curtailment method.
INDEX TERMS Residential demand response, hosting capacity, distribution system operator, renewable
energy.
NOMENCLATURE
NSet of buses.
DSet of PV installed buses.
nIndex of bus.
iIndex of customer.
MnSet of customers in bus n.
mIndex of customer in bus Mn.
TSet of time for one day.
tIndex of period.
ptelectricity purchasing price at t.
Vt
nPhasor voltage at bus nat t.
Pt
nNet real power at bus nat t.
Qt
nNet reactive power at bus nat t.
The associate editor coordinating the review of this manuscript and
approving it for publication was Ning Kang .
Pt
Gn Real power of generator at bus nat t.
Qt
Gn Reactive power of generator at bus nat t.
Pt
Ln Real power of load at bus nat t.
Qt
Ln Reactive power of load at bus nat t.
HCnPV hosting capacity at bus n.
ρt
nEfficiency of PV generation at bus nat t.
Vt
nVoltage magnitude at bus nat t.
δt
nPhase angle at bus nat t.
Ybus Admittance matrix.
Ynk Admittance between buses nand k.
Gnk Conductance between buses nand k.
Bnk Susceptance between buses nand k.
Vmin Lower bound of the voltage regulation.
Vmax Upper bound of the voltage regulation.
pt
sSubsidy at t.
18544 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 10, 2022
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
lt
iOriginal load of customer iat t.
xt
iAdjusted load of customer iat t.
µiDiscomfort coefficient for customer i.
αRatio of shiftable load.
Gi(·) Gain from the subsidy for customer i.
Di(·) Discomfort of customer i.
Ct
i(·) Total cost of customer i.
ν∗
iLagrangian multiplier of customer i.
I. INTRODUCTION
Climate change caused by greenhouse gases is one of the
biggest challenges facing the world today. Therefore, many
countries such as the USA, EU, and Korea have made
commitments to net-zero emissions by 2050 and beyond.
As a large component of these efforts, many countries are
setting aggressive goals for renewable electric energy and
electrification in all sectors [1]. Specifically, greater use of
renewable sources such as wind and solar photovoltaic (PV)
generation is the leading strategy to help decarbonize the
electric energy power sector [2]. For example, in 2019, more
than 70 % of the newly installed generators used renew-
able energy [3], and renewable energy (including hydro)
accounted for 27 % of the total electrical energy. Solar PV has
the largest share in newly added renewable energy. In 2019,
solar PV contributed 115 GW of the total renewable capacity
of 200 GW [4]. While other renewable generators, such as
wind and hydro, are largely restricted to centralized, utility
scale deployment, solar PV is more versatile and amenable
to deployment in distribution systems [5]. However, the addi-
tion of distributed solar PV sources beyond the distribution
system hosting capacity (HC)1causes severe problems in the
distribution system as it is designed for a unidirectional power
flow. Among these, overvoltage [7] is the most common
power quality problem. Therefore, if DSO can alleviate the
overvoltage problem, the distribution system can install more
solar PV, i.e., an increase in HC.2
Conventionally, DSOs have used their resources to solve
the overvoltage problem. For example, voltage and reactive
power control methods using legacy devices such as on-load
tap changer (OLTC), capacitor banks, and static VAr com-
pensator (SVC). However, with only legacy devices, volt-
age violations in the distribution system might occur for a
short period because of their delayed response [9]. Therefore,
advanced voltage control methods are required that promptly
react for the voltage deviation. These new methods include
using smart inverters installed at solar PV and energy storage
systems (ESS). Recently, another approach to improve HC,
which uses customer resources, has been in the spotlight.
The recent rapid development in information and communi-
cation technologies (ICT) makes it possible to engage cus-
tomers in grid operations such as the residential demand
1Note that solar PV HC in a distribution system is defined as the maximum
distributed resource penetration at which the distribution system operates
satisfactorily [6].
2In this paper, solving the overvoltage problem is regarded as an increase
in HC [8].
response (RDR) [10]. As a result, DSOs can reduce or shift
customers’ load for a reliable operation of the distribution
system [11], [12].
In this work, we propose an RDR based load-shifting
scheme to increase HC in distribution systems. The proposed
RDR scheme issues a subsidy to shift load only for times
that the overvoltage is expected. In response to the sub-
sidy, customers in the distribution system move their load,
thereby resolving the overvoltage problem, thus increasing
HC. The main features of the proposed RDR scheme are
1) DSO-customer interaction, 2) customer behavior analy-
sis with respect to subsidy, and 3) a simple algorithm to
solve overvoltage while minimizing additional cost. Also,
we compare the proposed RDR scheme to the direct load con-
trol (DLC) scheme which can be regarded as the optimal HC
improvement using customer resources. The contributions of
this work are summarized as follows:
1) In the setting we propose, the DSO is responsible for
a stable operation of the distribution system, and it
can communicate with its customers. To suppress the
overvoltage, we assume that the DSO issues a subsidy
that promotes customer load shift. Unlike a general
demand response program that affects all the utility
company customers, this subsidy works only in a par-
ticular distribution system. It is because the overvoltage
from solar PV in the distribution system is a local
problem. Therefore, we utilize an interaction between
DSO and customers.
2) To design an RDR program, we model a cost function
of customers, which consists of the cost of purchasing
power, revenue from the subsidy, and discomfort due
to load shifting. Then, we derive a closed-form solu-
tion that minimizes the customer cost according to the
baseline price of power and the subsidy.
3) Because of the non-linearity of the power flow analysis,
we propose a sub-optimal algorithm to obtain a subsidy
that solves the overvoltage while minimizing the addi-
tional cost from the subsidy. Furthermore, we prove the
performance gap between the optimal subsidy and the
subsidy obtained by the algorithm depends on the step
of the proposed algorithm.
4) We compare the HC improvement of the proposed
RDR scheme with the DLC scheme. We formulate an
optimization framework for the DLC scheme, so the
HC improvement of the DLC scheme is the maximum
improvement with customer resources. A case study
shows that the HC improvement of the proposed is
almost the same as that of the DLC scheme.
The remainder of this paper is organized as follows.
We first review related works in Section II, and then describe
our system model, including the distribution system and
customer in Section III. In Section IV, the two RDR based
load-shifting schemes as an optimization framework and a
sub-optimal algorithm are presented. After demonstrating the
proposed scheme’s performance in Section V, this paper is
concluded in Section VI.
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Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
II. RELATED WORK
Solar PV HC improvement methods can be divided into two
categories: using grid resources and customer resources [13].
One of the fundamental solutions for HC improve-
ment is grid reinforcement [14]. In addition, DSOs use
voltage or reactive power control devices such as OLTC
[15], [16], capacitor bank [17], and SVR [18]. Although these
approaches can effectively improve solar PV HC, they are
very costly in terms of both money and time. Smart inverter
installed at PV generator is a powerful device that can control
reactive power. Coordinated operation of smart inverters and
SVCs can improve HC on distribution systems [18]. In [19],
the authors investigated a framework to obtain the optimal
sizing and location of ESS on medium-voltage (MV) feeders
in Germany. Electric vehicles (EVs) can impact distribution
systems negatively unless there is a coordination by DSO.
However, leveraging energy storage of EV batteries, EVs and
EV chargers can help improve HC [20].
Other HC improvement methods are based on customer-
side resources. Curtailing the solar PV output is the simplest
method in this approach. Su et al. [21] proposed an inte-
grated solar PV inverter reactive power control and real power
curtailment method to improve HC. Although curtailing the
solar PV output is a simple and powerful method, it wastes
solar energy, which is undesirable and self-defeating. EVs
can be a good solution to reduce the amount of solar PV
curtailment. To this end, a shift of EV charging demand
while managing the distribution system has been explored in
[22], [23]. They modeled the EV charging scheduling prob-
lem as an optimization framework and auction mechanism
in [23] and [22], respectively. However, these works do not
extend their scope to hosting capacity maximization. The
use of RDR to increase HC can be classified into direct and
indirect load controls. The DLC scheme allows full control of
the customers’ load who make a contract with DSO. In con-
trast, the indirect load control scheme, which generally uses
price or incentive, can indirectly shift customer loads with a
carefully designed pricing scheme [24].
In [25], the authors used demand resources to increase
HC, but they simply assumed that DSO could change cus-
tomers’ load patterns with proper incentives. Ren et al. [26]
proposed a joint scheduling and voltage regulation strategy
that uses customer loads and tap changes of a voltage regula-
tor. However, this work does not solve the voltage violation
completely, so it is not related to increasing HC. In [27],
the authors proposed a DR program that uses a water heater
to improve solar PV HC. Rahman et al. [15] showed that a
control scheme using DR and OLTC efficiently improves HC
in suburban LV networks in Australia. In [28], the authors
proposed a distributed load management scheme for HC
improvement using heating, ventilation, and air condition-
ing (HVAC) loads, electric water heater, and two-way com-
munication. All previous RDR studies for HC improvement
use the DLC scheme. That is, DSO has full control power
of customers’ load based on an assumption of the contract
between customers and DSO. However, such contracts raise
significant privacy concerns. In addition, the DLC scheme has
a scalability issue.
In this paper, we propose a load-shifting scheme based on
indirect RDR for HC improvement. We compare the proposed
scheme with the DLC scheme. Even though the DLC scheme
has full control of shiftable loads of customers, a case study
shows that the proposed RDR scheme increases HC almost
similar to the DLC scheme. Because the proposed scheme
controls customer load using subsidy, it is scalable and free
from privacy issues. We note that our proposed HC improve-
ment method can be used in addition to other methods such
as OLTC and smart inverters.
FIGURE 1. An example of a distribution system.
III. SYSTEM MODEL
A. DISTRIBUTION SYSTEM
We consider a radial distribution system with Nbuses as
shown in Fig. 1. For each bus n,Mndenotes the number of
customers connected to it. We assume that bus 1 is at a sub-
station, and some buses have installed solar PV generators,
and those solar PV generators operate by a maximum power
point tracking (MPPT) controller, so they cannot change the
reactive power independently. Each day is divided into T
periods: T=1,2,...,Tand tis used to denote the time
index. It is assumed that the electricity purchasing price to
customers at t,pt, follows the time-of-use (ToU) rate.
At each bus n, let Vt
n,Pt
n, and Qt
ndenote the phasor voltage,
net real power, and net reactive power at time t, respectively.
Net power includes generator and load terms. That is,
Pt
n=Pt
Gn −Pt
Ln (1)
Qt
n=Qt
Gn −Qt
Ln,(2)
where Pt
Gn,Pt
Ln,Qt
Gn, and Qt
Ln respectively denote generator
and load real and reactive powers at bus n. The phasor voltage
can be expressed as Vt
n=Vt
nejδt
n, where Vt
nand δt
nare the
voltage magnitude and phase angle respectively at bus n.
The admittance between buses nand kis denoted by Ynk
and consists of conductance and susceptance, that is, Ynk =
Gnk +jBnk . The admittance matrix is denoted by Ybus. Then,
we have the power flow equations at bus n:
Pn=Vn
N
X
k=1
Vk[Gkn cos(δn−δk)+Bkn sin(δn−δk)],(3)
Qn=Vn
N
X
k=1
Vk[Gkn sin(δn−δk)−Bkn cos(δn−δk)].(4)
18546 VOLUME 10, 2022
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
A DSO accounts for the stable and reliable operation of
the distribution system, such as voltage stability and outage
management [29]. More specifically, in each distribution sys-
tem, a voltage regulation range exists to supply an agreed
quality of power. Operating the voltage within the range is a
crucial responsibility for the DSO. Let Vmin and Vmax denote
the lower and upper bounds of the voltage regulation range,
respectively. Then, the voltage regulation constraint can be
written as follows:
Vmin ≤Vt
n≤Vmax .(5)
B. DSO AND CUSTOMER INTERACTION
We assume that customers have installed a smart meter and
home energy management system (HEMS).3The number of
customers who have the smart meter and HEMS is denoted
as M. Through HEMS, customers can re-schedule their con-
trollable loads such as HVAC, water heater and batteries.
Fig. 2shows this interaction. To alleviate the overvoltage
problem, the DSO announces a subsidy (pt
sin units of $/kWh)
at the overvoltage time tto customers who have HEMS. Let
lt
iand xt
idenote the original and adjusted loads of customer i
at time t, respectively.4Then, the gain from the subsidy for
customer iis given as follows:
Gi(xt
i)=pt
s(xt
i−lt
i).(6)
FIGURE 2. DSO and customer interaction through the proposed RDR
based load-shifting scheme.
While shifting load generates revenue for customers, it also
causes inconvenience. The discomfort of customer i,Diis
given by
Di(xt
i)=µi(xt
i−lt
i)2,(7)
where µiis the discomfort coefficient for customer i.
When µiis high [low] customer ifeels more [less] incon-
venience. Notably, µialways has a positive value for all
customers.
3According to the Federal Energy Regulatory Commission, more than half
of customers had a smart meter in the US in 2018, [30] and 100 % penetration
of smart meters in Italy.
4We assume that the DSO knows the original load of each customer. In the
DR program, this is called baseline estimation. The customers who partici-
pate in DR programs have an incentive to inflate their baseline, so baseline
estimation is an important research topic. Recent research [33] has designed
a DR program that requires a self-reported baseline for each customer.
IV. RDR BASED LOAD-SHIFTING SCHEME
We propose a method using customer loads to resolve the
overvoltage problem. In this section, both indirect and direct
load control schemes are presented. The proposed RDR based
load-shifting scheme is an indirect load control scheme.
To show the proposed scheme’s performance, we also present
a DLC scheme that assumes DSO has full control power for
the customer loads. Because DLC allows for complete control
of customer load, in principle, it should lead to maximum
achievable HC improvement from load shifting. Note that the
DLC scheme in this work is similar to the schemes proposed
by [15], [26].
A. INDIRECT LOAD CONTROL SCHEME
Fig. 2shows the structure of the proposed RDR based load-
shifting scheme. Before the operating day, the DSO simulates
the distribution operation for the day.5In the event of an
overvoltage, the DSO issues subsidy pt
sat that time based
on its knowledge of customer behavior. In response to the
subsidy, customers who shift their power receive gain Gi.
With sufficiently high pt
s, the overvoltage problem resolves.
However, additional cost minimization becomes an issue that
needs to be addressed in this method. We begin by analyzing
the customer’s behavior and formulate the cost minimization
problem of DSO.
1) ANALYSIS OF THE CUSTOMER SIDE
A customer with HEMS minimizes the overall cost while
supplying the load given the power purchasing price pt.
We model the cost of customer iover a day as a summa-
tion of the cost of power purchased, revenue from the sub-
sidy pt
s, and cost for discomfort due to load shifting. It can be
expressed as
Ct
i(xt
i)=X
t∈Tptxt
i−Gi(xt
i)+Di(xt
i).(8)
Now, we can define the cost minimization problem for cus-
tomer ias follows:
(C) min
{xt
i}tX
t∈T
Ct
i(9a)
subject to xt
i≥(1 −α)lt
i,∀t∈T(9b)
X
t∈T
xt
i=X
t∈T
lt
i(9c)
where αdenotes the ratio of the shiftable load to total load.
In this optimization framework, the control variable is the
customer i’s load at time t. The first constraint means that the
shifted load at each time tis bound by the maximum shiftable
load. The other constraint means that the total amount of
adjusted loads in a day is the same as that of the original loads.
As the objective function is a quadratic function and the
constraints are linear functions, the problem (C) is a con-
vex optimization problem. Also, this problem has a feasible
5It is assumed that customers’ loads and solar PV’s power output are
forecast with reasonable accuracy [32], [34].
VOLUME 10, 2022 18547
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
region that contains an interior point. For example, a solution
xt
i=lt
istrictly satisfies all the constraints. This is Slater’s
condition, which is a sufficient condition for strong duality.
We obtain a solution xt∗
ias
xt∗
i=
(1 −α)lt
i,t∈T1
lt
i+1
2µi−pt+pt
s−ν∗
i,t∈T2
(10)
where T1and T2are the time periods in which the bound-
ary condition equation (9b) meets and does not meet,
respectively. Further, we can obtain ν∗
ias follows:
ν∗
i=1
T1X
t∈T1
(−pt+pt
s)−2µiα
T1X
t∈T2
lt
i.(11)
The detailed procedures to obtain this solution are presented
in Appendix A.6
2) ANALYSIS OF THE DSO SIDE
DSOs take responsibility for the stable and reliable operation
of distribution systems. Further, they want to minimize their
operational costs. When the voltages across each bus are
within the reference voltage ranges in the proposed structure,
there is no additional cost incurred for stabilizing the distribu-
tion network. However, when an overvoltage occurs, the DSO
issues a subsidy to suppress the overvoltage. It is assumed
that DSO can estimate each customer’s reaction according to
pt
sthrough the historically collected data of each customer.7
The DSO needs to ensure all the bus voltages are in a nor-
mal range while minimizing additional costs due to subsidy.
It is mathematically formulated as
(U) min
{pt
s}tX
t∈TX
n∈NX
m∈Mn
pt
s(xt
m,n−lt
m,n) (12a)
subject to Vmin ≤Vt
n≤Vmax ,∀n∈N,∀t∈T(12b)
where t,n, and mdenote the indexes of time, bus, and
customer in a bus, respectively. Note that, in Section IV-A1,
the customer index was i, while it is {m,n}in this section,
which means the mth customer in bus n.
Unlike the customer side problem (C), the problem (U)
is not a convex problem because the voltage and power
consumption have a nonlinear relation [36]. Therefore,
we propose an algorithm to find a sub-optimal solution. The
sub-optimal algorithm adds a small price 1pto the subsidy
when the overvoltage problem occurs.
6To get a closed-form solution, the customer load modeling in this work
is simple compared to previous RDR research [12], [26]. If we model the
customer load in more detail, a closed-form solution cannot be obtained.
We perform another simulation by adding a practical constraint of the load
shifting range. The general tendency of the result is the same, but HC reduced
about 17% compared to that without the new constraint.
7Although the estimation from the DSO is not perfectly correct, the
proposed scheme can still apply to the overvoltage problem because the load-
shifting and subsidy are positively co-related [35]. However, DSO does not
know the exact response, so it can occasionally cause minor overvoltage
problems can happen sometimes.
Algorithm 1: Subsidy Exploration Algorithm
Input: topology, lt
n,et
n, and pt,∀n,t
Output: ept
s,∀t
Initialization
1: pt
s=0,∀t
Power flow calculation
2: Obtaining Vt
n, δt
n∀n,t
3: while Vt
n>Vmax ,∀n,tdo
Overvoltage
4: for t=1 to Tdo
5: if Vt
n>Vmax then
The time that overvoltage occurred
6: pt
s=pt
s+1p
7: end if
8: end for
Calculate customer load shift
9: Solve (C)
10: Update xt
n
Power flow calculation
11: Obtaining Vt
n, δt
n∀n,t
12: end while
13: return ept
s=pt
s,∀t
Although this algorithm simply increases the subsidy price
during an overvoltage occurrence, it provides a good sub-
optimal subsidy.
Proposition 1: Suppose that pt∗
sis the optimal solution of
the problem (U)in a radial distribution system. Then the
Algorithm 1converges toept
ssuch that the following inequality
holds:
ept
s−pt∗
s< 1p.(13)
Proof: The proof will show two properties at bus n:
(i) pt
s↑results in xt∗
m,n↑(xt∗
m,n↑means an increase in power
load at the bus, i.e., Pt
Ln,Qt
Ln ↑), and (ii) Pt
Ln,Qt
Ln ↑results
in Vt
n↓. Therefore, Vt
nmonotonically decreases with pt
s.
(i) We will show that the first derivative of xt∗
iwith respect
to pt
sis positive, that is, ∂xt∗
i
∂pt
s>0. From Eq. (10), it is because
∂xt∗
i
∂pt
s
=
0,t∈T1
1
2µi
.t∈T2
(14)
Therefore, when a subsidy price pt
sincreases with tfor
∀t∈T2, the power consumption at time xt∗
iincreases.8
(ii) Assuming that a typical voltage phase angle difference
in a distribution feeder is 0.1◦per mile [37],9the power flow
8For t∈T1, customers do not change their load with a change of pt
s.
Therefore, when an overvoltage problem occurs at t∈T1, there is no feasible
solution for the problem (U) using pt
s. Because this proof assumes that the
problem (U) has a solution, we do not consider this case.
9Given the large variety of systems such as urban, suburban, and rural
with heavily and lightly loaded, the assumption of 0.1◦per mile might
not be enough. Even if we relaxed this assumption as 2-3◦per mile, the
error between the original equation and approximated one is less than 0.5%.
Therefore, we can use this approximation.
18548 VOLUME 10, 2022
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
equation (3) can be approximated by
Pt
n'Vt
nX
k∈N
Vt
kGkn (15)
=(Vt
n)2Gnn +Vt
nX
k∈N,k6=n
Vt
kGkn (16)
Qt
n'Vt
nX
k∈N
Vt
k(−Bkn) (17)
= −
(Vt
n)2Bnn +Vt
nX
k∈N,k6=n
Vt
kBkn
(18)
Then, differentiating both sides with respect to Vt
n, and rear-
ranging terms results in
∂Pt
n
∂Vt
n
=X
k∈N,k6=n
(Vt
k−2Vt
n)Gkn (19)
∂Qt
n
∂Vt
n
= − X
k∈N,k6=n
(Vt
k−2Vt
n)Bkn.(20)
In power systems, Gkn <0 and Bkn >0 for ∀k6= n, and Vt
k'
1 for ∀k[36]. Therefore, ∂Pt
n
∂Vt
n>0 and ∂Qt
n
∂Vt
n>0. Assuming
that the DSO cannot control generator power, i.e., Pt
Gn and
Qt
Gn are constant, ∂Pt
Ln
∂Vt
n<0 and ∂Qt
Ln
∂Vt
n<0 from (1). Then,
∂Vt
n
∂Pt
Ln
<0 and ∂Vt
n
∂Qt
Ln
<0. This means that an increase
[decrease] of load at a bus results in a decrease [increase] of
the voltage magnitude at the bus.
Note that we assume that the voltage relationship at neigh-
boring buses is negligible in this proof. That is, ∂Vt
k
∂Vt
n=0.
With ∂Vt
k
∂Vt
n6= 0, the same result can be derived by solving
simultaneous equations.
Owing to (i) and (ii), an increase in pt
salways results
in a decrease in Vt
n. Therefore, if we keep raising pt
s, the
overvoltage problem is solved. As the Algorithm 1increases
pt
sin steps of 1p, the difference between the solution of this
algorithm ept
sand the optimal pt∗
sis at most 1p, that is
ept
s−pt∗
s< 1p.(21)
From the Proposition 1, the Algorithm 1can always find a
solution if there is one.
Corollary 1: Suppose that the Algorithm 1cannot find any
solution to the problem (U). Then the feasible set of the
problem (U)is empty.
Proof: For a proof by contradiction, suppose that the
Algorithm 1cannot find a solution of the problem (U), and
the feasible set is nonempty. Let ¯pt
s>0 be a solution of the
problem. That means Vt
n≤Vmax with ¯pt
s. The Algorithm 1
increases pt
sas 1pin each step when Vt
n>Vmax , and Vt
n
monotonically decreases with pt
s. Therefore, pt
swill be greater
than or equal to ¯pt
sby the Algorithm. In other words, the
Algorithm 1finds a solution. Since we have a contradiction,
it must be that the feasible set is nonempty.
B. DIRECT LOAD CONTROL SCHEME
In this section, we model an optimization framework for the
HC maximization problem using DLC. It is assumed that the
DSO has already made a contract with each customer who
wants to participate demand response program. Therefore,
the DSO can control the shiftable load of its customers. The
objective function of this optimization framework is a sum
of solar PV capacities in the distribution network. The HC
maximization problem is defined as:
(D) max
HCn,xt
m,nX
n∈D
HCn
subject to (9b), (9c), and (12b),(22)
where HCnand xt
m,ndenote the maximum of PV capacity
at bus nwith no voltage violation and the customer load,
respectively. They are the two two control variables for the
optimization framework. Three constraints of this problem
come from the problems (C) and (U): two customer load
constraints and one nominal voltage range constraint. The
problem (D) is not a convex optimization problem due to the
quadratic relation between Pand V. Therefore, we propose
an iterative algorithm that uses linearization of the quadratic
equation.
To see the voltage violation part clearly, we change the two
customer constraints (9b) and (9c) to the bus npoint of view,
that is
Pt
xn ≥(1 −α)Pt
Ln,∀t∈T(23)
X
t∈T
Pt
xn =X
t∈T
Pt
Ln,(24)
where Pt
xn =Pm∈Mnxt
m,nand Pt
Ln =Pm∈Mnlt
m,n. Accord-
ingly, the customer load control variable is also changed
to Pt
xn.
The proposed iterative algorithm relaxes the quadratic rela-
tion to linear using the voltage difference. The voltage at
jth iteration is defined by
Vt,j
n=Vt,j−1
n+1Vt,j
n(25)
where 1Vt,j
nis the voltage difference at jth iteration which
comes from active and reactive power change. Then, the
voltage regulation constraint (12b) can be written as
Vmin −Vt,j−1
n≤1Vt,j
n≤Vmax −Vt,j−1
n.(26)
The voltage difference at jth iteration can be obtained by
using the voltage sensitivity matrix J−1which is the inverse
form of the Jacobian matrix in the current operating condi-
tion [38]. The voltage sensitivity matrix is given as
J−1=
∂˙
θ
∂˙
P
∂˙
θ
∂˙
Q
∂˙
V
∂˙
P
∂˙
V
∂˙
Q
(27)
where ˙
θ,˙
V,˙
Pand ˙
Qdenote vectors of voltage angle, voltage
magnitude, active power and reactive power, respectively.
VOLUME 10, 2022 18549
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
The voltage difference at jth iteration 1Vt,j
nis obtained by
1Vt,j
n=X
n∈D,n6=1
∂Vt,j−1
n
∂Pt,j−1
n
1Pt,j
n+X
n∈N,n6=1
∂Vt,j−1
n
∂Qt,j−1
n
1Qt,j
n
(28)
where 1Pt,j
nand 1Qt,j
nare real and reactive power difference
at jth iteration, respectively. They are defined as
1Pt,j
n=Pt,j
n−Pt,j−1
n(29)
1Qt,j
n=Qt,j
n−Qt,j−1
n.(30)
By Eqs. (28), (29), and (30), the updated voltage regulation
constraint (26) linearized as Eqs. (31) and (32), as shown at
the bottom of the page.
Note that all the terms are constant except Pt,j
nand Qt,j
nin
Eqs. (31) and (32), so they are a linear equations. We can
easily obtain Pt,j
nand Qt,j
nusing Pt
Gn,Pt,j−1
xn , and power factor.
The linearized HC maximization problem is defined as:
(D0) max
HCn,Pt,j
xn X
n∈D
HCn
subject to (23), (24), (31) and (32) (33)
Algorithm 2: Direct Load Control Algorithm
Input: topology and Pt
Ln,∀n,t
Output: HCn,Pt
xn,∀m,n,t
Initialization
1: j=0, HCj
n=0, Pt,j
xn =Pt,j
Ln,1=+1∀m,n,t
2: while 1<do
3: j←j+1
4: for t=1 to Tdo
Power flow calculation
5: Obtain ∂Vt
n
∂Pt,j
n
,∂Vt
n
∂Qt,j
n
,∀nfrom J−1
6: end for
7: Solve (D0), i.e., obtain HCj
n,Pt,j
xn
8: Update Pt,j
n,Qt,j
n
9: 1=HCj
n−HCj−1
n
10: end while
11: return HCj
n,Pt,j
xn,∀n,t
The linearization method to obtain the voltage difference
might have a high error when 1Pt,j
nand 1Qt,j
nare high.
Therefore, we propose an iterative algorithm to obtain
an accurate solution of the problem (D0) as shown in
Algorithm 2.
V. EVALUATION
In this section, we evaluate the proposed RDR based load-
shifting scheme in terms of cost and HC.
TABLE 1. PG&E ToU pricing.
A. SIMULATION SETTINGS
For the customer loads and output power of solar PV gener-
ators, we use the Pecan Street data set of August 2019 [39],
which consists of hourly data. For the power purchasing price
from the main grid pt, the ToU price of Pacific Gas and
Electric Company (PG&E) in summer 2019 is used as shown
in Table 1.
To determine the number of shiftable loads in households,
we assume that 10 % of controllable loads are the total
amounts of shiftable loads. Examples of controllable loads
are HVAC load, water heater, and refrigerator. According to
EIA’s survey in 2015,10 we set the ratio of shiftable load α
to 5 %, that is, α=0.05. Note that as this setting is an
example, any αcan be applied to the proposed scheme.
FIGURE 3. Modified IEEE 15-bus distribution network. Bus 1 is the
substation and potential buses to install solar PV generators are buses
of 4, 5, 6, 7, 10, and 13.
The proposed load-shifting scheme is tested on the mod-
ified IEEE 11-kV, 15-bus distribution system as shown in
Fig. 3. This distribution system is a radial network, and the
substation is at bus 1. The line impedance and load data are
given in Table 2. In each bus, it is assumed that 140 customers
10Residential Energy Consumption Survey (RECS). Available:
https://www.eia.gov/consumption/residential/
X
n∈D,n6=1
∂Vt,j−1
n
∂Pt,j−1
n
Pt,j
n+X
n∈N,n6=1
∂Vt,j−1
n
∂Qt,j−1
n
Qt,j
n≥Vmin −Vt,j−1
n+X
n∈D,n6=1
∂Vt,j−1
n
∂Pt,j−1
n
Pt,j−1
n+X
n∈D,n6=1
∂Vt,j−1
n
∂Qt,j−1
n
Qt,j−1
n(31)
X
n∈D,n6=1
∂Vt,j−1
n
∂Pt,j−1
n
Pt,j
n+X
n∈N,n6=1
∂Vt,j−1
n
∂Qt,j−1
n
Qt,j
n≤Vmax −Vt,j−1
n+X
n∈D,n6=1
∂Vt,j−1
n
∂Pt,j−1
n
Pt,j−1
n+X
n∈D,n6=1
∂Vt,j−1
n
∂Qt,j−1
n
Qt,j−1
n(32)
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Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
TABLE 2. Parameters of the modified IEEE 15-bus system.
are connected to the distribution system (Mn=140). In this
case study, PV solar generators can be installed on buses 4,
5, 6, 7, 10, and 13. We analyze a case of installing solar
PV on bus 13, which is the most vulnerable position to
cause the overvoltage problem if there is no specific expla-
nation on PV solar generators. The nominal voltage range
is set to [0.91, 1.04] per unit, based on the South Korean
standard [40].
We use a Gaussian distribution to model the discomfort
coefficient for each customer µ. According to reference
works [31], [41] and the minimum price of the ToU pric-
ing, the mean and standard deviation of this distribution
are 0.2 and 0.063, respectively. The unit of the discomfort
coefficient is $/kWh2because it is the product of µand the
square of the power as shown in Eq. (7).
B. EFFECT OF µ
In Eq. (7), µirepresents the degree of discomfort for cus-
tomers. A customer with high [low] µiwill move little [much]
load shift as shown in Fig. 4. It is observed that when the
DSO issued a subsidy, the power consumption during the
subsidized time increased, and the increased load was drawn
from the other times. In this example, pt
s=0.12 at t=12
p.m., which is the solution of Algorithm 1for a 6 MW solar
PV installed on bus 13. The total shifted load in Figs. 4a
and 4b are 0.199 kWh and 1.24 kWh, respectively, and their
percentages of a total load of a day are 0.51 % and 3.66 %,
respectively.
C. OVERVOLTAGE PROBLEM
With no solar PV, no overvoltage problem occurred as shown
in Fig. 5a. The horizontal blue line with a value of 1.01 is
the voltage of the substation (bus 1). In this case study, the
bus containing the solar PV (bus 13) is the most vulnerable.
Therefore, we increase the solar PV capacity installed on
bus 13 to see the overvoltage problem. Fig. 5b shows the per-
unit voltage of bus 13 with the solar PV capacity ranging up to
7.5 MW. The first overvoltage problem occurs with 5.5 MW
solar PV at 12 p.m. because of the high output of the solar PV
at noon.
FIGURE 4. Daily power consumption curve with and without the
proposed scheme. x∗is the optimal solution of the problem (C). In this
example, pt
s=0.12 at t=12 p.m.
D. CASE WITH 6 MW SOLAR PV GENERATOR
With 6 MW solar PV, the overvoltage problem occurs at
bus 13. In the proposed RDR scheme, the DSO issued a sub-
sidy when the overvoltage occurred (12 p.m.). Algorithm 1
with 1p=0.01 finds pt∗
s=0.12 at t=12 p.m., and
pt∗
s=0 otherwise. Fig. 6shows the sum of the daily
load with and without the proposed RDR scheme. Because
of the subsidy, customers perform a load shift to the sub-
sidized period, resulting in a decrease in voltage. There-
fore, the overvoltage problem is settled as shown in Fig. 5c.
The large fluctuations from 11 to 15 hours come from the
subsidy to suppress overvoltages. In case of 6 MW solar
PV, the total energy shifted by the subsidy is 1137 kWh.
The voltages at bus 13 without and with the RDR were
1.0468 and 1.0396, respectively. The additional cost incurred
by the utility company due to the provision of subsidy
is $65.56 per day.
Another solution to the overvoltage problem is curtailment.
In the case study, the total amount of curtailed energy to make
the voltage of the bus 13 below 1.04 p.u. is 539 kWh, which
is about 1.2 % of the total energy of the solar PV in a day.
If the ToU price of PG&E is the standard charge, the value of
the curtailed energy of the solar PV is $145.6, which is about
2.2 times higher than the cost incurred by the proposed RDR
scheme.
VOLUME 10, 2022 18551
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
FIGURE 5. Bus voltage (p.u.). The normal voltage range is [0.91, 1.04]. The
x-axis and y-axis represent time (hour) and per unit voltage, respectively.
The maximum capacity of the solar PV generator installed
on bus 13 without the overvoltage problem is 5.46 MW, which
is approximately 10 % less. Via the proposed RDR scheme,
the maximum capacity of solar PV could be increased by
10 % with a daily cost of $65.56. Note that this cost does
not occur every day. It happens with the maximum output
of solar PV generators. According to Korea Meteorological
Administration,11 Korea has 28 cloudless days in a year,
so we expect that the DSO issues the RDR event up to 28 days.
We can calculate the benefit of the DSO using opportunity
cost. To install 6 MW solar PV through grid reinforcement,
11Open Meteorological Data Portal (Korean), https://data.kma.go.kr/
FIGURE 6. Total load with and without the proposed RDR based
load-shifting scheme.
the DSO needs to increase substation capacity and power
lines at the cost of about 2.7 million dollars.12 On the other
hand, the proposed RDR scheme can support 6 MW solar PV
at an average annual cost of $1,835.68, i.e., $65.56 ×28.
FIGURE 7. Subsidy result according to the capacity of solar PV generator.
E. HOSTING CAPACITY OF ONE SOLAR PV AT BUS 13
The solar PV capacity installed on bus 13 is increased.
As shown in Fig. 5b, the overvoltage problem occurs from the
solar PV capacity of 5.5 MW. However, using the proposed
RDR scheme, no overvoltage issue occurs even when the
solar PV capacity is 7.5 MW as shown in Fig. 5c. Beyond
7.5 MW, the proposed RDR scheme cannot solve the over-
voltage problem, even though all shiftable loads are moved.
Therefore, the HC of this distribution system with the pro-
posed RDR scheme is 7.5 MW.
However, this solution comes with a cost. Through the pt
s
subsidy issued, each customer could move the load to the
subsidized period. Figs. 7and 6show the subsidy issued to
solve the overvoltage problem and the moved load because
of the subsidy. The subsidy also increases with high solar
12This cost comes from a Korean case study of grid reinforcement [42].
18552 VOLUME 10, 2022
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
PV capacity, which is approximately 0.1 $/kWh at 6 MW
capacity and 2 $/kWh at 7.5 MW capacity. The horizontal
dashed line in Fig. 7represents the ToU price of PG&E,
and the price is written at the top of the figure. At 7.5 MW
capacity, the subsidy is higher than the selling price to the
customer, which means that customers earn money when they
use power during the subsidy period, i.e., so-called minus
pricing. As this adds to the financial burden of the DSO, the
effective HC with the proposed RDR scheme is set to 7 MW
without any curtailment, which is a 28.2 % increase from the
baseline HC of 5.46 MW.
FIGURE 8. Energy and cost of the proposed RDR scheme and curtailment
method.
We compared the HC of the proposed RDR scheme with
the curtailment method. Fig. 8shows the energy and cost
incurred by the two methods. In terms of energy, the amount
of curtailed energy is approximately half of the energy moved
by the proposed RDR scheme. It is because the curtailment
method directly controls the bus that the overvoltage problem
occurred, while the RDR indirectly solves the problem by
shifting all customers’ loads in the distribution system. From
the cost point of view, the value of the curtailed energy13
is higher than the cost to move energy using the proposed
method with 5.5 MW, 6 MW, 6.5 MW, and 7 MW capacity.
However, it is the opposite with a 7.5 MW capacity. It is
because the value of the curtailed energy increases linearly.
On the other hand, the cost of the RDR scheme increases
quadratically because the discomfort function D(·) in Eq. (7)
is a quadratic function. Therefore, the total cost for the shift-
ing load also increases quadratically. In addition to cost, Fig. 8
shows customer benefit from the proposed RDR scheme. The
benefit of customers consists of revenue from the subsidy and
discomfort due to load shifting. The revenue of customers
is the same as ‘‘Cost to Move the Energy’’ of the DSO,
so customers’ revenue also increases quadratically. Also,
the discomfort that negatively affects the customer benefit
increases as solar PV capacity increases.
13We use the term value for the curtailed energy because this is not the
cost of the utility company.
Note that the HC of the DLC scheme is a little higher than
that of the proposed RDR scheme. An analysis of the DLC
scheme is in the following section.
F. SCENARIOS WITH THE ESTIMATION ERRORS
So far, all the simulation results are based on an assumption
of a perfect estimation of the discomfort parameters µifor all
customers. However, this is not a practical assumption. The
DSO cannot perfectly estimate the discomfort parameters.
Therefore, we model the estimation error for µias a Gaussian
random variable iwith zero mean and variance σi. Then, the
discomfort of customer iis expressed as
µe
i=µi+i,(34)
where µe
iand µidenote the actual discomfort and the esti-
mated discomfort of customer i, respectively. When the DSO
finds a subsidy to solve overvoltage problems, it uses µi.
However, each customer iactually reacts to the subsidy
according to µe
i.
We simulate the cases with a solar PV capacity of 5.5 MW,
6 MW, 6.5 MW, 7 MW, and 7.5 MW at bus 13 and the
estimation error. We generate 100 scenarios for each case.
Although the standard deviation of iis set to 30 %, there
is no voltage violation for the case of 5.5 MW, 6 MW, and
6.5 MW solar PV. In the case of 7.0 MW and the same
standard deviation, only one scenario shows a minor voltage
rise over 1.04 p.u., i.e., 0.002 %. However, a slight error as the
standard deviation of 1 % causes voltage deviation for one-
third of the total scenarios in the case of 7.5 MW.
TABLE 3. Hosting capacity.
G. HOSTING CAPACITY FOR VARIOUS CASES
Table 3shows the HCs of legacy, the proposed indirect RDR,
and DLC schemes. The legacy scheme means distribution
system operation without RDR and DLC schemes. The num-
bers in parenthesis indicate the buses installed solar PV gen-
erators. As shown in Table 3, the difference between the HCs
of the proposed and DLC schemes is 0.69 %. Because the
HC of the DLC scheme is the theoretical HC improvement
limit, it is confirmed that the proposed RDR scheme can
almost increase HC to the maximum value. That little per-
formance gap comes from the sub-optimal subsidy obtained
by Algorithm 1. The difference betweenept
sand pt∗
sis at most
1p=0.01 as shown in Proposition1.
The proposed RDR scheme improves HC by 33.6 % com-
pared to the legacy scheme. However, as we discussed in
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Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
Section V-E, this improvement comes at a cost, and an eco-
nomic HC limit is about mid-20 %. In the case of one solar
PV installed on bus 13, we simulate with different α. As α
increases, i.e., more shiftable loads, the HC improvement also
increases.
We also simulate more cases that solar PV generators are
installed on various bus positions. Again, it is confirmed that
the HC improvement of the proposed RDR and DLC schemes
are almost the same. With the number of buses installed solar
PV, HC in the distribution system increases. It is because
power flow is distributed due to the solar PV generators in
various bus positions. Among the cases of three solar PV
generators, the case of (7, 10, 13) shows the minimum HC
because all the buses are located at the end of feeders. On the
other hand, the case of (4, 10, 13) shows the maximum HC.
Because bus 4 is close to the substation, it can install a high-
capacity solar PV generator without violating the voltage
limit.
FIGURE 9. Hosting capacity improvement of the proposed RDR scheme.
‘‘1st, 2nd, and 3rd’’ in legend stands for each bar graph in parenthesis.
Legacy scheme is written as ‘‘w/o RDR.’’
Fig. 9shows detailed information on HC for various cases.
It shows the maximum capacity of each solar PV generator.
The solar PV generator installed on bus 13 has the lowest
capacity of any bus combination because its position is the
most vulnerable. On the other hand, the solar PV generator
installed near the substation, such as bus 4, can have a larger
HC. With the proposed RDR scheme, all buses increase their
HC compared to the legacy scheme.
VI. CONCLUSION
A renewable energy-based power system is the need of the
hour. Distribution systems with high solar PV suffer from
overvoltage problems. The customer-engaged approach is
suggested as a solution to increase the HC of solar PV in the
distribution system without grid reinforcement. This paper
proposes an RDR based load-shifting scheme to increase HC.
Under this program, the DSO issues subsidies for a certain
period to solve the overvoltage problem. Because customers
move their load to the subsidized time to reduce cost, the
overvoltage problem is resolved. The proposed RDR scheme
is mathematically formulated, and a sub-optimal algorithm to
obtain a solution is proposed. It is proved that the sub-optimal
algorithm successfully finds an optimal solution with a small
error. Therefore, the proposed RDR scheme performs almost
similar to that of the DLC scheme which can be regarded as
the maximum HC. Using the modified IEEE 15-bus distri-
bution system, the case study shows an average of 33.6 %
increases in HC at diverse solar PV generator positions.
APPENDIX A
DETAILED PROCEDURES TO SOLVE (C)
The solution of the problem (C) is derived in this section.
We omit the customer index ifor simplicity, and change the
constraints into a standard convex optimization form, that is
(C) min
{xt}tX
t∈Tptxt−pt
s(xt−lt)+µ(xt−lt)2(35a)
subject to −xt+(1 −α)lt≤0,∀t∈T(35b)
X
t∈Txt−lt=0.(35c)
The Lagrangian is
L({xt}t,{λt}t, ν)
=X
tµ(xt)2+(pt−pt
s−2µlt)xt+µ(lt)2+pt
slt
+X
t
λt−xt+(1 −α)lt+νX
t
(xt−lt),(36)
where λtand νare the Lagrangian multipliers. The optimal
solution xt∗should satisfy Karush-Kuhn-Tucker (KKT) con-
ditions [43], that is
xt∗≥(1 −α)lt,∀t∈T
(37)
X
t∈T
(xt∗−lt)=0,(38)
λ∗
t≥0,∀t,(39)
λ∗
t−xt∗+(1 −α)lt=0,∀t∈T,(40)
2µxt∗+(pt−pt
s−2µlt)−λ∗
t+ν∗=0.(41)
Three possible cases can be considered to satisfy the slack-
ness condition Eq. (40):
1) λ∗
t=0, ∀t: Then, −xt∗+(1 −α)lt≤0,∀t∈T.
Using Eq. (38) and Eq. (41), the solution is obtained as
xt∗=lt+1
2µ −pt+pt
s−1
TX
t
(−pt+pt
s)!(42)
2) λ∗
t>0, ∀t: In this case, xt∗=(1 −α)lt,∀tbecause
of Eq. (40). However, this solution cannot satisfy a
constraint of Eq. (9c), so there is no solution.
3) λ∗
t=0, for t∈T1, and λ∗
t>0, for t∈T2: Then, xt∗=
lt+1
2µ−pt+pt
s−ν∗,t∈T1, and xt∗=(1 −α)lt,
for t∈T2. Using Eq. (9c) and Eq. (41), we can obtain
the Lagrangian multiplier as
ν∗=1
T1X
t∈T1
(−pt+pt
s)−2µα
T1X
t∈T2
lt.(43)
18554 VOLUME 10, 2022
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
And, the solution is
xt∗=
(1 −α)lt,t∈T1
lt+1
2µ−pt+pt
s−ν∗,t∈T2
(44)
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VOLUME 10, 2022 18555
Y.-J. Son et al.: Residential Demand Response-Based Load-Shifting Scheme to Increase Hosting Capacity
YE-JI SON received the B.S. and M.S. degrees in electrical engineering from
Soongsil University, Seoul. South Korea, in 2018 and 2020, respectively. Her
research interests include energy big data, data analysis, energy prosumer,
and demand response holding a large amount of renewable energy integration
on a distribution systems.
SE-HEON LIM (Student Member, IEEE) received the B.S. degree in elec-
trical engineering from Soongsil University, Seoul, South Korea, in 2018,
where she is currently pursuing the Ph.D. degree. Her research interests
include energy big data and distribution system operation via machine learn-
ing applications.
SUNG-GUK YOON (Senior Member, IEEE) received the B.S. and
Ph.D. degrees in electrical engineering and computer science from Seoul
National University, Seoul, South Korea, in 2006 and 2012, respectively.
From 2012 to 2014, he was a Postdoctoral Researcher with Seoul National
University. Since 2014, he has been with Soongsil University. He is cur-
rently an Associate Professor at Soongsil University. His research interests
include energy big data, game theory for power systems, and power line
communications.
PRAMOD P. KHARGONEKAR (Life Fellow, IEEE) received the B.Tech.
degree in electrical engineering from the Indian Institute of Technology
Bombay, India, in 1977, and the M.S. degree in mathematics and the
Ph.D. degree in electrical engineering from the University of Florida, in
1980 and 1981, respectively. From 1997 to 2001, he was the Chairman of
the Department of Electrical Engineering and Computer Science. He was
a Claude E. Shannon Professor of engineering science with the University
of Michigan. From 2001 to 2009, he was the Dean of the College of Engi-
neering and the Eckis Professor of electrical and computer engineering with
the University of Florida, until 2016. After working briefly as the Deputy
Director of Technology at ARPA-E, from 2012 to 2013, he was appointed
by the National Science Foundation (NSF) to work as an Assistant Director
of the Directorate of Engineering (ENG), in March 2013, a position he
held, until June 2016. He is currently the Vice Chancellor for Research and
a Distinguished Professor of electrical engineering and computer science
at the University of California at Irvine, Irvine, CA, USA. His research
interests include theory and applications of systems and control. He is a
fellow of IFAC and AAAS. He was a recipient of the IEEE Control Systems
Award, Bode Lecture Prize, the IEEE Baker Prize, the IEEE CSS Axelby
Award, the NSF Presidential Young Investigator Award, and the AACC
Eckman Award.
18556 VOLUME 10, 2022
