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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.

VOLUME 10, 2022 18545

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

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

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

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)

18550 VOLUME 10, 2022

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

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

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

VOLUME 10, 2022 18553

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

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

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