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1226 IEEE TRANSACTIONS ON SMART GRID, VOL. 3, NO. 3, SEPTEMBER 2012

Voltage/VAR Control in Distribution Networksvia Reactive Power Injection Through

Distributed GeneratorsSiddharth Deshmukh , Student Member, IEEE , Balasubramaniam Natarajan , Senior Member, IEEE , and

Anil Pahwa , Fellow, IEEE

Abstract— This paper demonstrates how reactive power injection from distributed generators can be used to mitigate the

voltage/VAR control problem of a distribution network. Firstly,power flow equations are formulated with arbitrarily located dis-

tributed generators in the network. Since reactive power injectionis limited by economic viability and power electronics interface,we formulate voltage/VAR control as a constrained optimizationproblem. The formulation aims to minimize the combined reactive

power injection by distributed generators, with constraints on: 1)

power flow equations; 2) voltage regulation; 3) phase imbalancecorrection; and 4) maximum and minimum reactive power injec-tion. The formulation is a nonconvex problem thereby making the

search for an optimal solution extremely complex. So, a subop-timal approach is proposed based on methods of sequential convex

programming (SCP). Comparing our suboptimal approach withthe optimal solution obtained from branch and bound method,we show the trade-off in quality of our solution with runtime. Wealso validate our approach on the IEEE 123 node test feeder and

illustrate the ef ficacy of using distributed generators as distributed

reactive power resource.

Index Terms— Convex optimization, distributed generation, dis-tribution network, sequential convex programming, voltage/VAR control.

I. I NTRODUCTION

R ECENTLY, there is growing interest in distributed gener-ation at or near the point of power consumption [1]. Dis-tributed generators (DGs) feeding power at the distribution net-

work level improve network reliability and reduce overall en-

ergy loss. Additionally, DGs enable operators to increase their

power supply capacity within the existing infrastructure [1], [2].

Integration of DGs in a distribution system poses many chal-

lenges in terms of: 1) power quality; 2) voltage regulation; 3)

protection; 4) reliability; and safety issues [1]–[5]. However, a

well controlled integrated operation of DGs with the main grid

can not only meet the challenges but can contribute ancillaryservices like voltage/VAR support [6], [7]. Motivated by this

idea, recent research has focused primarily on two aspects of

DG’s contribution to voltage control: 1) effective interfacing

Manuscript received July 19, 2011; revised December 12, 2011; acceptedMarch 21, 2012. Date of publication June 08, 2012; date of current versionAugust 20, 2012. This work was funded by Department of Energy grant #:DE-EEC0000555. Paper no. TSG-00254-2011.

Theauthors arewith theDepartment of Electrical andComputerEngineering,Kansas State University, Kansas, KS 66506 USA (e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSG.2012.2196528

of DG at point of coupling (PCC), and 2) managing and opti-

mizing multiple DGs power contribution. In [8] and [9], power

electronics interface at PCC is used to implement a PI feedback

control for regulating the local voltage. [10] and [11] extend the

idea of local voltage control in presence of multiple DGs. An-

other approach to regulate local voltage is shown in [12] and

[13], where active and reactive power of DG is controlled by

power electronics interface at PCC. Even though, we can not

neglect the importance of ef ficient interface at PCC, these prior efforts consider voltage regulation only at PCC and not across

the entire distribution network.

Another thrust area of research relates to the centralized

and distributed control of DGs to regulate distribution net-

work voltage. The author in [14] compares centralized and

distributed approaches for regulating the distribution network

voltage by controlling DG capacity. In [15], it is shown that at a

particular instant, either voltage or power factor of network can

be regulated. Hence a method of selective switching between

power factor and voltage control is proposed with maximum

utilization for distributed generation resources. To incorporate

stochastic nature in distributed generation and time variation inload, [16] employs probabilistic network configuration model

in finding out the effect of DG penetration on voltage regula-

tion. A similar approach is taken in [17] where Monte Carlo

simulations are performed on various case studies to determine

the effect of DGs on voltage regulation in low voltage grids.

Considering DGs as ad hoc infrastructure for quick voltage

support, especially in emergency situations, [18] proposes a

multiagent based dispatching scheme for communication be-

tween DGs. Considering DGs presence in distribution network,

[19] formulates an optimization problem with the objective of

minimizing power losses. A genetic algorithm is presented in

[19] for controlling the taps of load tap changer (LTC), size of

substation capacitor, and voltage amplitudes of DG.

While many of the DGs are currently assumed to inject

only real power, advances in power electronics and need for

voltage/VAR support has motivated us to consider DGs as

distributive reactive power resource. In [20], a multiobjec-

tive voltage/VAR control problem is formulated assuming

DGs presence, and a Nondominated Sorting Genetic Algo-

rithm (NSGA) is proposed to solve the optimization problem.

Similarly, authors in [21] propose a hybrid algorithm based

on the Ant Colony genetic algorithm for solving nonlinear

voltage/VAR control problem. A comprehensive comparison

of stochastic search methods is discussed in [22] for optimizing

daily voltage/VAR control problem. Even though variants of

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DESHMUKH et al.: VOLTAGE/VAR CONTROL IN DISTRIBUTION NETWORKS VIA REACTIVE POWER INJECTION THROUGH DISTRIBUTED GENERATORS 1227

stochastic search methods have been proposed, optimality of

obtained solution can never be guaranteed [23], [24]. Further-

more, an exact stopping criterion is hard to obtain in such

methods, making actual run time calculations nondeterministic.

Unlike stochastic search methods, interior point based methods

[25], such as SCP [26] have been shown to scale effectively

and in a deterministic manner with problem size. Deterministic

runtime and guarantees in optimality are important for real time

voltage/VAR control. The authors in [27] and [28] present a

real time control framework for controlling of end-user reactive

power devices to mitigate low voltage problems at transmission

level. Steepest distance method is used in [27], and Newtons

method is used in [28] to calculate the optimal reactive power

injection. However, both these solutions are local in nature

[25].

Considering unpredictability and local optimality in search

methods, our paper aims to demonstrate a deterministic runtime

and close to optimal, optimization technique for voltage/VAR

support. For this, we specifically consider distribution networks

that consist of multiple low capacity DGs. For example, thismodel accommodates the scenario with residential generators

such as small wind turbines, solar panels, etc. We first formu-

late the power flow equation that capture the impact of reactive

power injection by the DGs across the entire distribution net-

work. Then, we treat reactive power as a vital resource not only

for voltage regulation, but also for phase imbalance correction.

As reactive power injection has a natural trade-off relative to

real power injection by DGs, it becomescritical to optimally use

the reactive power of DGs. We accomplish this by formulating

an optimization problem where the objective is to minimize ag-

gregate reactive power injected at various PCCs, with basic con-

straints on: 1) voltage regulation across the nodes of network,

and 2) phase imbalance correction. We also place constraints on

minimum and maximum reactive power a DG can inject based

on economic viability and limitations of power electronics inter-

face. Thermal limits on distribution lines are not considered in

our formulation. In most distribution networks with exception

of those in dense urban areas, the lines are loaded much below

their thermal capacity [29]. Hence, thermal limits can be ex-

cluded from the constraints. However, if needed it can be always

included in the problem formulation. The resulting optimiza-

tion is nonconvex, making the quest for global optimal solution

very complex. Fig. 1 shows different approaches which can be

adopted to solve this problem. One of the direct approaches is

branch and bound (BB) method. The BB method gives a globaloptimal solution but with disadvantage of exponential runtime

[30], [31]. Another direct approach is to directly apply interior

point method on nonconvex problem. This approach has poly-

nomial run time but it only gives a feasible solution. In our ap-

proach, we transform the original problem to a convex problem

and use sequential convex programming (SCP) to determine the

solution. This is a suboptimal approach with polynomial run-

time. We demonstrate the quality of our suboptimal solution

by comparing it with the global optimum obtained via branch

and bound method. Finally, using the IEEE 123 node test feeder

[32], we validate our approach. Also, it can be observed that

usage of DGs decreases the dependency on voltage regulator and capacitor banks for voltage/VAR control. Our results and

Fig. 1. Different optimal solution methods.

analysis illustrate that it is not only feasible but prudent to use

DGs to provide voltage/VAR support in distribution networks.

This paper is organized as follows: Section II formulates the

power flow equation with DGs located arbitrarily at various

nodes. In Section III an optimization problem is formulated to

calculate net reactive power injection required to meet the distri-

bution network constraints. Section IV presents the results and

analysis of simulation done for radial network and IEEE 123

node standard test feeder case. Finally, conclusions and possible

future work are presented in Section V.

II. THREE PHASE DISTRIBUTION SYSTEM MODEL

A three phase distribution network can be modeled as ra-dial interconnection of mathematical equivalents of the corre-

sponding network components as given in [33]. For mathemat-

ical consistency, we assume all loads are three phase star con-

nected loads. Similarly, all the generators are considered to be

star-connected with capability to generate power in each phase.

Although we have considered loads and generators to be three

phase star connected, this configuration allows us to accommo-

date single and two phase loads and generators by assuming the

loads and generators on unconnected phases to be zero.

In practical distribution networks, there is mixture of con-

stant impedance, constant current and constant power loads. We

have considered all loads to be constant power loads in our anal-ysis. This assumption of constant power loads results in a non-

linear mathematical model. Other forms of load models can be

easily incorporated by introducing additional linear terms in the

formulation.

Notation

We use normal-faces to define scalars and bold-faces to de-

fine matrices and vectors; denotes element wise complex

conjugate operation of vector/matrix ; denotes element

wise absolute value of vector/matrix ; denotes ele-

ment wise product of two vectors/matrices , . Superscript

at element indicates that element corresponds to phasewhere . Similarly indicates a composite

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Fig. 2. Three phase radial distribution network with DG.

vector of elements corresponding to phase , , . Subscript

and indicate generator and load at node .

A. Power Flow Analysis

We consider a radial distribution model as shown in Fig. 2,

where at every node there is a generation source and load. We as-

sume that the load represent the apparent power of lumped

loadof the lateral connected at node . Similarly, represents

the apparent power generated at the lateral. At any node ,

the absence of a generator or load is captured by setting the cor-

responding term or to . represents the ground

voltage, and is considered as reference for the system. rep-

resents the neutral voltage at node . Considering voltage vector

at node with ground as reference, voltage at

node can be represented as

(1)

where is the three phase current

flowing from node to node , and the impedance matrix is

three phase impedance matrix between node and node .

In block matrix form, (1) can be represented as

(2)

Typically, neutral and ground are connected, and hence they are

at the same potential, i.e., . Equating and

in second row of (2), we get

(3)

Substituting from (3) into first row of (2), we get corre-

sponding Kron’s reduction form

(4)

where

(5)

Here, is equivalent three phase impedance matrix be-

tween node and . Defining equivalent admittance matrix

, and applying Kirchoff’s current law,

current entering from a node into the network can be expressed

as

(6)

In matrix form, the overall voltage current relation for the entire

network modeled in Fig. 2 can be represented as

(7)

where element of is defined as

Next, the power injected at node can be expressed as. Substituting the value of from (7), we can

rewrite as

(8)

where is row of matrix. Representing the equiv-

alent admittance matrix in real and imaginary part,

and three phase voltage in polar form

and substituting in (8) gives

(9)

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Simplifying (9) and representing in real and reactive power

form,

(10)

In steady state, net power at any node is difference between

power generated and consumed at that node. Therefore,

(11)

Here, is the three phase apparent power generated at node

; is three phase apparent load at node ; and are

the real and reactive power generated at node ; and and

are the real and reactive components of load at node .

Equating (10) and (11), the power flow equations that capture

the impact of reactive power injection from DGs in distribution

networks can be expressed as

(12)

Equation (12) can be also obtained by following alternate

modeling approaches as discussed in [34], [35]. In the next sec-

tion, an optimization problem, minimizing reactive power in-

jection is formulated for voltage/VAR control in distributionnetwork.

The power flow equations in (12) constitute an essential con-

straint in quantifying the effect of individual DGs on entire dis-

tribution system.

III. VOLTAGE/VAR CONTROL OPTIMIZATION FORMULATION

Distributed generators connected to distribution network can

be used to provide reactive power as ancillary service. How-

ever, low power generators are mostly owned by residential

customers, and are paid only for the real power they inject in

the network. Additionally, these small DGs may have some

maximum and minimum value of reactive power injection con-

straints based on the power electronics interface and economic

viability. In this section, we formulate an optimization problem

to determine the optimal reactive power injection by DGs de-

sired to satisfy the following requirements: 1) voltage is main-

tained within safety limits; 2) power flow (12) are satisfied; 3)

individual DGs minimum/maximum reactive power constraints

are met; and 4) phase imbalance is mitigated. For phase imbal-

ance correction, we assume that the phase angle varies from 0 to

, and we limit the phase difference between any two phases

at a node to be greater than , where is the tol-

erance of phase imbalance.

We formulate the optimization problem by assuming that the

net generation capacity, i.e., of individual DGs is fixed,

known or predictable. Future work will include stochastic

models for distributed generation capability. So, presently we

have constraints on vector sum of real and reactive power

generated by each DG. When we do not have suf ficient dis-

tributed generation, we assume that the main grid can provide

the needed capacity without any limit. We also assume that real

and reactive component of load, i.e., , at each node

is known.

The optimization problem can be expressed as

subject to

(13)

where, in objective function , are the regressors indi-

cating preference of generators in reactive power contribution;

choice of function indicate the dislike or penalty for the

increase in reactive power contribution; equality constraints,

and represent the power flow (12); is limit on net

power generation capacity of individual generators; inequality

constraint, represents 5% voltage regulation; represents

tolerance on phase imbalance, and captures the limits on

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maximum and minimum reactive power injected by individual

DGs.

Itcan beobservedthat, because ofconstraints , , , and

, (13) is a nonconvex optimization problem. This problem

can be solved using branch and bound method that guarantees

optimal solution. However, the prohibitive complexity associ-

ated with branch and bound method makes it impractical for

real time voltage/VAR control application. Alternatively, one

may choose to use suboptimal stochastic search methods based

on evolutionary/genetic algorithms. These methods also suffer

from high complexity, poor repeatability, with no certificate of

solution quality. Therefore we attempt to transform our non-

convex optimization problem into convex form, and compare

the quality of suboptimal solution with global optimal solution.

This approach is of low complexity, fast, and is best suited for

problems where suboptimal solution close to true optimal solu-

tion is acceptable.

A. Convex Form Analysis

The objective function in above optimization problem(13) is formulated as a regression problem formulation.

In this work, we assume a quadratic penalty function, i.e.,

. This choice of

assures that the objective function is convex. Additionally

is symmetric so that large positive and negative reactive power

injectors are equally undesirable. Also assuming fair policy

for all the generators, we set all regressors to 1. In standard

convex optimization problem, the inequality constraints are

convex function and the equality constraints are af fine. How-

ever, equality constraints in our formulation, especially the

power flow constraints and are highly nonlinear. Also,

the phase imbalance correction constraint in inequalityconstraint is nonconvex. Therefore, we apply the method of

first order approximation on and to get af fine equality

constraints.

The first step in our reformulation is tofind a feasible solution

(14)

where and .To obtain a feasible solution we apply the interior point algo-

rithm on the original problem. This gives a local optimal point.

The next step is to obtain af fine approximation of nonlinear

equality constraints, via Taylor series expansion. The first order

Taylors series approximation of power flow equation can be ex-

pressed as

(15)

where ; is the trust region with radius around the

feasible point , defi

ned as

and are the Jacobianof power flow equation constraints

and , defined as

(16)

where

and

(17)

where

Similarly, the af fine approximation of equality constraint

on net generation capacity of individual generators can be

expressed as

(18)

where

The three phase imbalance correction constraint is the

only nonconvex inequality constraint in our optimization for-

mulation. If we maintain a small trust region , the differ-

ence between the three phases will not change sign. Therefore,

the maximum and minimum phase angle will remain the same

during an iteration. Thus, if in our feasible solu-

tion, can be restated as

(19)

Finally, the convex transformed form of the original opti-

mization problem corresponds to

subject to Constraint , and of (13), and

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(20)

The next step in SCP is to solve (20) based on the basic fea-

sible solution (14). The new solution is plugged in , , ,

and constraints to get a new instance of (20), and is solved

again. Thus, (20) is solved iteratively till the solution converges

to an optimal point. In every iteration a new feasible solution

is obtained which is better than previous solution.Solving the

reformulated problem (20) by SCP is fast but finding a global

optimal solution to original problem is not guaranteed. In next

section, we show the complexity and convergence analysis of

our approach and compare it with global solver based on branch

and bound method.

IV. R ESULT A NALYSIS

In this section, we show the effectiveness of our approach by

analyzing a small-scale radial distribution network and a modi-

fied IEEE 123-node test feeder system.

A. Radial Distribution Network

First, we consider a radial distribution case shown in Fig. 2

with the following setup.

1) Simulation Setup:

• System base values: 4.16 kV and 100 kVA.

• Number of nodes: 11 nodes (including the grid connecting

node 0).

• Load profile: Constant power star connected spot load.

, ,

.

• Generation profile: Three phase DGs with equal generation

capacity in all phases. ,

. We assume that there is no constraint on gen-

eration capability at the grid, both in terms of active and

reactive power. Thus our optimization problem takes grid power as a variable and we get the optimal power drawn

from grid as a part of our solution.

• Limit on reactive power injected by individual DGs:

(we have assumed 100% reactive power con-

vertibility; however, it can be less as simulated in

Section IV-A4.)

• Line impedance: Constant line impedance between all

nodes: , as defined in (2). Further we assume that all

nodes are 1000 feet apart. The value of (2) per mile is

TABLE IVOLTAGE (IN PU) AND PHASE (IN DEGREES) PROFILE

TABLE IIR EACTIVE POWER I NJECTION PROFILE (IN KVAR)

• Phase imbalance tolerance: , i.e., phase difference

between any two phases is between 115 to 125 .

2) Simulation Result: Normally, in a distribution network,

voltage/VAR is controlled by use of voltage regulators and ca-

pacitor banks. In this paper, we claim that optimal injection of

reactive power by distributed generators can support network constraints. To validate our claim, we first simulate the above

setup, without any distributed generation. We observe that the

problem is infeasible, i.e., voltage/VAR needs to be supported

by voltage regulator/capacitor banks. So, in the next step we

simulate the system with all the distributed generators set ac-

cording to a set generation profile.

Tables I and II shows the voltage, phase and reactive power

injection profile obtained from our suboptimal approach.

Voltage profile indicates operation of radial network within

the 5% regulatory safety limit. Phase profile indicates phase

imbalance correction within tolerance of . It can be observed

from reactive power injection profi

le (unconstrained ),that the grid acts as the major source of reactive power, with

small generators injecting minimum reactive power. The reac-

tive power injected by distributed generators increases as we

move away from the grid. This again confirms that grid itself

can not support voltage/VAR control for distant nodes. The

objective function on the optimization problem (20) aims to

fairly distribute reactive power injection among all distributed

generators. This can be inferred from the reactive power in-

jection by nodes closer to the grid. While constraints at these

nodes can be satisfied by the grid itself, some reactive power

continues to be injected by these nodes. This results in low

reactive power injection from generators at distant nodes. To

further illustrate the effectiveness of our approach, we constrain

the reactive power injection at node 10 to 8 kVAR or 0.8 pu.

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Table II also shows reactive power injection profile, obtained

after constraining reactive power injection on generator at node

10, . To

compensate for the insuf ficient reactive power at node 10, it

can be observed that our approach increases the reactive power

injection on nodes 0 to 9. In next subsection, we analyze the

computational complexity of our approach and compare it with

global solver based on branch and bound algorithm.

3) Complexity Analysis: In this subsection, we analyze and

compare the computational complexity and runtime of our ap-

proach with global solver based on branch and bound method.

The branch and bound method is a nonheuristic approach, and

it certifies the quality of its solution to be -optimal [30]. The

computational complexity of branch and bound algorithm de-

pends on: 1) complexity of computing the lower and the upper

bound functions; 2) number of rectangles to partition; and 3)

edge (variables) to partition. In the worst case if we assume,

that each side of rectangle has to be split in parts, and there

are such variables then complexity is . For a problem with

4 nodes, (3 voltage,3 phase,3 real power, and 3 reactive power variables for each node) variables, the worst case com-

plexity is . Since variables in our case are continuous,

can have large value, and thus worst case runtime is relatively

very large for practical distribution networks.

The complexity for our approach depends on: 1) complexity

of interior point method; 2) complexity of SCP iteration; and 3)

number of SCP iterations. Interior point method solves the opti-

mization problem by applying Newton’s algorithm on sequence

of equality constrained problems. The worst case complexity

is , where is the number of variables and is the

number of constraints [25]. For our approach we use interior

point method first to get feasible point. Further it takesto compute the af fine approximation of nonconvex constraints.

Thus in our approach SCP iterations are effective to the order

of . For problem with 4 nodes, , and

(6 constraints per phase per node), the worst case complexity

is . Thus our approach has far less computational

complexity compared to exponential time complexity of branch

and bound method.

4) Optimal Solution Comparison: In this subsection we com-

pare the SCP based suboptimal solution with branch and bound

(BB) based global optimal solution. The simulation setup is sim-

ilar to Section IV.A with three modifications. Firstly, to em-

phasize on reactive power drawn from DGs, we have increased

the distance between adjacent nodes. Following are the intern-

odal distances in 1000 ft unit: ; ;

; ; ; ; ;

; ; . Secondly, we reduce the

number of nodes with DGs with their increased generation ca-

pability, i.e., , .

Finally, we include a constraint on power electronic interface

in converting total power to reactive power. That is, we as-

sume that maximum of 60% of total generated power can be in-

jected as reactive power by individual DGs. Table III shows the

three phase reactive power injection profile obtained from both

SCP based approach and BB method. The SCP based solution

requires, 0.006% (1892.32 kVAR) more reactive power compared to global minimum (1892.21 kVAR) obtained from BB

TABLE IIIR EACTIVE POWER I NJECTION (IN KVAR) PROFILE (SCP VRS. BB)

Fig. 3. IEEE 123 node test feeder with distributed generators.

methods. Thus, with very small compromise in optimality, we

achieve significantly lower computational complexity and run

time. It can be observed that both the approaches, extract max-

imum reactive power (60% of total generation capacity) from

DGs. In the next subsection, we consider the IEEE 123 node

test feeder, as a test case to evaluate our approach on large scale

distribution network.

B. Simulation With Standard Test Case—IEEE 123 Node Test

Feeder

Fig. 3 shows a IEEE 123 node modified test node feeder with

arbitrarily located low power distributed generators. The fol-

lowing are the modification to the standard test case:

• Node 149 is connected to grid, and nodes represented by

are with generation capability. Generation capacity is

arbitrarily single, two or three phase, each of 10 kVA as

shown in Fig. 3.

• For simplicity in simulation, we do not consider shunt ca-

pacitors, voltage regulators, and transformers in the net-

work; however, our approach is applicable to distribution

networks including mathematical models of these compo-

nents.

• Three phase switches are set according to [32].

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TABLE IVR EACTIVE POWER I NJECTION PROFILE (IN KVAR)

• All three phase loads are assumed to be constant power star

connected spot loads.

Our simulation setup is as same as subsection A, with addi-

tional constraint on reactive power injected by grid,

, and . Table IVshows distributed reactive power injection profile required to

satisfy the network constraints (20). Once again our solution

considers grid as major source of reactive power. The gener-

ation profile is mixed with one, two and three phase generators

arbitrarily located in the network. As before, the solution results

in fair distribution of reactive power injection among all DGs.

V. CONCLUSION

In this paper, we present the ef ficacy of using distributed gen-

erators as a reactive power resource. Reactive power injection

by distributed generators is constrained by economic viability

and power electronic interface. So, it is important to optimallyutilize reactive power injected by distributed generators. An op-

timization problem is formulated with the objective to mini-

mize injected reactive power, while satisfying constraints re-

lated to: 1) voltage regulation; 2) phase imbalance correction;

and 3) power flow. Thus distributed generators in our work

are treated at network level to address the voltage/VAR con-

trol. The optimization problem being nonconvex, we propose a

suboptimal approach based on sequential convex programming

(SCP). The proposed approach provides a near optimal solution

with much lower computation complexity (runtime) relative to

a global solver based on branch and bound method. Further we

have shown the practicality of our approach by simulating a

123 node IEEE test feeder. Since this paper focuses on reac-

tive power minimization, the effect of voltage/VAR on system

losses is not considered while optimizing the control problem.

However, problem can be reformulated to include losses as an

additional objective. In our future work, we aim to address the

voltage/VAR control using stochastically varying loads and dis-

tributed generation. We will also include the impact of commu-

nication infrastructure on our control framework.

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Siddharth Deshmukh (M’07–S’10) received theB.E. degree in electronics andtelecommunicationdiscipline from the National Institute of Technology, Raipur,India, in 2004 and the M.Tech. degree from the Indian Institute of Technology,Delhi, in 2006. Since Fall 2010, he has been working toward the Ph.D. degreeat Kansas State University, Manhattan.

His research interest includes network control and optimization, statisticalsignal processing, and communication theory.

Balasubramaniam Natrajan (S’98–M’02–SM’08) received the B.E degree inelectrical engineering from Birla Institute of Technology and Science, Pilani,India, in 1997and the Ph.D. in electrical degree from Colorado State University,Fort Collins, in 2002.

Since Fall 2002, he has been a Faculty Member in the Department of Elec-trical and Computer Engineering, Kansas State University, Manhattan, wherehe is currently an Associate Professor and the Director of the Wireless Commu-nication (WiCom) and Information Processing Research Group. He was alsoinvolved in telecommunications research at Daimler Benz Research Center,Bangalore, India, in 1997. He has published a book titled Multi-carrier Tech-nologies for Wireless Communications (Kluwer, 2002) and holds a patent oncustomized spreading sequence design algorithm for CDMA systems. His re-search interests include spread spectrum communications, multicarrier CDMAand OFDM, multiuser detection, cognitive radio networks, sensor signal pro-cessing, distributed detection, and estimation and antenna array processing.

Anil Pahwa (F’03) received the B.E. (honors) degree in electrical engineeringfrom Birla Institute of Technology and Science, Pilani, India, in 1975, the M.S.degree in electrical engineering from University of Maine, Orono, in 1979, andthe Ph.D. degree in electrical engineering from Texas A&M University, CollegeStation, in 1983.

Since 1983, he has been with Kansas State University, Manhattan, where presently he is a Professor in the Electrical and Computer Engineering Depart-ment. He worked at ABB-ETI, Raleigh, NC, during sabbatical from August1999 to August 2000. His research interests include distribution automation,distribution system planning and analysis, distribution system reliability, andintelligent computational methods for distribution system applications.

Dr. Pahwa is a member of Eta Kappa Nu, Tau Beta Pi, and ASEE.

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