VAR Control in Distribution Networks

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 in-jection from distributed generators can be used to mitigate thevoltage/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 reactivepower 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 thesearch for an optimal solution extremely complex. So, a subop-timal approach is proposed based on methods of sequential convexprogramming (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 andillustrate the efficacy of using distributed generators as distributedreactive power resource.

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

I. INTRODUCTION

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 theirpower 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, awell controlled integrated operation of DGs with the main gridcan not only meet the challenges but can contribute ancillaryservices like voltage/VAR support [6], [7]. Motivated by thisidea, recent research has focused primarily on two aspects ofDG’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.The authors are with the Department of Electrical and Computer Engineering,

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 online

at 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], powerelectronics interface at PCC is used to implement a PI feedbackcontrol for regulating the local voltage. [10] and [11] extend theidea 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 bypower electronics interface at PCC. Even though, we can notneglect the importance of efficient interface at PCC, these priorefforts consider voltage regulation only at PCC and not acrossthe 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 anddistributed approaches for regulating the distribution networkvoltage by controlling DG capacity. In [15], it is shown that at aparticular instant, either voltage or power factor of network canbe regulated. Hence a method of selective switching betweenpower factor and voltage control is proposed with maximumutilization for distributed generation resources. To incorporatestochastic nature in distributed generation and time variation inload, [16] employs probabilistic network configuration modelin finding out the effect of DG penetration on voltage regula-tion. A similar approach is taken in [17] where Monte Carlosimulations are performed on various case studies to determinethe effect of DGs on voltage regulation in low voltage grids.Considering DGs as ad hoc infrastructure for quick voltagesupport, especially in emergency situations, [18] proposes amultiagent based dispatching scheme for communication be-tween DGs. Considering DGs presence in distribution network,[19] formulates an optimization problem with the objective ofminimizing power losses. A genetic algorithm is presented in[19] for controlling the taps of load tap changer (LTC), size ofsubstation 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 forvoltage/VAR support has motivated us to consider DGs asdistributive reactive power resource. In [20], a multiobjec-tive voltage/VAR control problem is formulated assumingDGs presence, and a Nondominated Sorting Genetic Algo-rithm (NSGA) is proposed to solve the optimization problem.Similarly, authors in [21] propose a hybrid algorithm basedon the Ant Colony genetic algorithm for solving nonlinearvoltage/VAR control problem. A comprehensive comparisonof stochastic search methods is discussed in [22] for optimizingdaily 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 ofobtained solution can never be guaranteed [23], [24]. Further-more, an exact stopping criterion is hard to obtain in suchmethods, making actual run time calculations nondeterministic.Unlike stochastic search methods, interior point based methods[25], such as SCP [26] have been shown to scale effectivelyand in a deterministic manner with problem size. Deterministicruntime and guarantees in optimality are important for real timevoltage/VAR control. The authors in [27] and [28] present areal time control framework for controlling of end-user reactivepower devices to mitigate low voltage problems at transmissionlevel. Steepest distance method is used in [27], and Newtonsmethod is used in [28] to calculate the optimal reactive powerinjection. However, both these solutions are local in nature[25].Considering unpredictability and local optimality in search

methods, our paper aims to demonstrate a deterministic runtimeand close to optimal, optimization technique for voltage/VARsupport. For this, we specifically consider distribution networksthat consist of multiple low capacity DGs. For example, thismodel accommodates the scenario with residential generatorssuch as small wind turbines, solar panels, etc. We first formu-late the power flow equation that capture the impact of reactivepower injection by the DGs across the entire distribution net-work. Then, we treat reactive power as a vital resource not onlyfor voltage regulation, but also for phase imbalance correction.As reactive power injection has a natural trade-off relative toreal power injection by DGs, it becomes critical to optimally usethe reactive power of DGs. We accomplish this by formulatingan 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 onminimum and maximum reactive power a DG can inject basedon economic viability and limitations of power electronics inter-face. Thermal limits on distribution lines are not considered inour formulation. In most distribution networks with exceptionof those in dense urban areas, the lines are loaded much belowtheir thermal capacity [29]. Hence, thermal limits can be ex-cluded from the constraints. However, if needed it can be alwaysincluded in the problem formulation. The resulting optimiza-tion is nonconvex, making the quest for global optimal solutionvery complex. Fig. 1 shows different approaches which can beadopted to solve this problem. One of the direct approaches isbranch 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 interiorpoint 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 problemand use sequential convex programming (SCP) to determine thesolution. This is a suboptimal approach with polynomial run-time. We demonstrate the quality of our suboptimal solutionby comparing it with the global optimum obtained via branchand bound method. Finally, using the IEEE 123 node test feeder[32], we validate our approach. Also, it can be observed thatusage of DGs decreases the dependency on voltage regulatorand 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 useDGs 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 variousnodes. In Section III an optimization problem is formulated tocalculate net reactive power injection required to meet the distri-bution network constraints. Section IV presents the results andanalysis of simulation done for radial network and IEEE 123node standard test feeder case. Finally, conclusions and possiblefuture 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 bestar-connected with capability to generate power in each phase.Although we have considered loads and generators to be threephase star connected, this configuration allows us to accommo-date single and two phase loads and generators by assuming theloads 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. Wehave 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 beeasily incorporated by introducing additional linear terms in theformulation.

Notation

We use normal-faces to define scalars and bold-faces to de-fine matrices and vectors; denotes element wise complexconjugate operation of vector/matrix ; denotes elementwise absolute value of vector/matrix ; denotes ele-ment wise product of two vectors/matrices , . Superscriptat element indicates that element corresponds to phasewhere . Similarly indicates a composite


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

vector of elements corresponding to phase , , . Subscriptand 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 lumpedload of the lateral connected at node . Similarly, representsthe 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 groundvoltage, 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 atnode can be represented as

(1)where is the three phase currentflowing from node to node , and the impedance matrix isthree 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 areat the same potential, i.e., . Equating andin 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 expressedas

(6)

In matrix form, the overall voltage current relation for the entirenetwork 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)


Simplifying (9) and representing in real and reactive powerform,

(10)

In steady state, net power at any node is difference betweenpower 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 arethe 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 distributionnetworks can be expressed as

(12)

Equation (12) can be also obtained by following alternatemodeling 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 canbe used to provide reactive power as ancillary service. How-ever, low power generators are mostly owned by residentialcustomers, and are paid only for the real power they inject inthe network. Additionally, these small DGs may have somemaximum and minimum value of reactive power injection con-straints based on the power electronics interface and economicviability. 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 constraintsare 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 stochasticmodels for distributed generation capability. So, presently wehave constraints on vector sum of real and reactive powergenerated by each DG. When we do not have sufficient dis-tributed generation, we assume that the main grid can providethe needed capacity without any limit. We also assume that realand reactive component of load, i.e., , at each nodeis 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 theincrease in reactive power contribution; equality constraints,and represent the power flow (12); is limit on net

power generation capacity of individual generators; inequalityconstraint, represents 5% voltage regulation; representstolerance on phase imbalance, and captures the limits on


maximum and minimum reactive power injected by individualDGs.It can be observed that, because of constraints , , , and, (13) is a nonconvex optimization problem. This problem

can be solved using branch and bound method that guaranteesoptimal solution. However, the prohibitive complexity associ-ated with branch and bound method makes it impractical forreal time voltage/VAR control application. Alternatively, onemay choose to use suboptimal stochastic search methods basedon evolutionary/genetic algorithms. These methods also sufferfrom high complexity, poor repeatability, with no certificate ofsolution quality. Therefore we attempt to transform our non-convex optimization problem into convex form, and comparethe quality of suboptimal solution with global optimal solution.This approach is of low complexity, fast, and is best suited forproblems 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 ofassures that the objective function is convex. Additionallyis symmetric so that large positive and negative reactive powerinjectors are equally undesirable. Also assuming fair policyfor all the generators, we set all regressors to 1. In standardconvex optimization problem, the inequality constraints areconvex function and the equality constraints are affine. How-ever, equality constraints in our formulation, especially thepower flow constraints and are highly nonlinear. Also,the phase imbalance correction constraint in inequalityconstraint is nonconvex. Therefore, we apply the method offirst order approximation on and to get affine equalityconstraints.The first step in our reformulation is to find 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 affine approximation of nonlinearequality constraints, via Taylor series expansion. The first orderTaylors series approximation of power flow equation can be ex-pressed as

(15)

where ; is the trust region with radius around thefeasible point , defined as

and are the Jacobian of power flow equation constraintsand , defined as

(16)

where

and

(17)

where

Similarly, the affine approximation of equality constrainton net generation capacity of individual generators can beexpressed as

(18)

where

The three phase imbalance correction constraint is theonly 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 sameduring 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


(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 solvedagain. Thus, (20) is solved iteratively till the solution convergesto an optimal point. In every iteration a new feasible solutionis obtained which is better than previous solution.Solving thereformulated problem (20) by SCP is fast but finding a globaloptimal solution to original problem is not guaranteed. In nextsection, we show the complexity and convergence analysis ofour approach and compare it with global solver based on branchand bound method.

IV. RESULT ANALYSIS

In this section, we show the effectiveness of our approach byanalyzing 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. 2with the following setup.1) Simulation Setup:• System base values: 4.16 kV and 100 kVA.• Number of nodes: 11 nodes (including the grid connectingnode 0).

• Load profile: Constant power star connected spot load., ,

.• Generation profile: Three phase DGs with equal generationcapacity in all phases. ,

. We assume that there is no constraint on gen-eration capability at the grid, both in terms of active andreactive power. Thus our optimization problem takes gridpower as a variable and we get the optimal power drawnfrom 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 inSection IV-A4.)

• Line impedance: Constant line impedance between allnodes: , as defined in (2). Further we assume that allnodes are 1000 feet apart. The value of (2) per mile is

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

TABLE IIREACTIVE POWER INJECTION PROFILE (IN KVAR)

• Phase imbalance tolerance: , i.e., phase differencebetween 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 ofreactive power by distributed generators can support networkconstraints. To validate our claim, we first simulate the abovesetup, without any distributed generation. We observe that theproblem is infeasible, i.e., voltage/VAR needs to be supportedby voltage regulator/capacitor banks. So, in the next step wesimulate 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 withinthe 5% regulatory safety limit. Phase profile indicates phaseimbalance correction within tolerance of . It can be observedfrom reactive power injection profile (unconstrained ),that the grid acts as the major source of reactive power, withsmall generators injecting minimum reactive power. The reac-tive power injected by distributed generators increases as wemove away from the grid. This again confirms that grid itselfcan not support voltage/VAR control for distant nodes. Theobjective function on the optimization problem (20) aims tofairly distribute reactive power injection among all distributedgenerators. This can be inferred from the reactive power in-jection by nodes closer to the grid. While constraints at thesenodes can be satisfied by the grid itself, some reactive powercontinues to be injected by these nodes. This results in lowreactive power injection from generators at distant nodes. Tofurther illustrate the effectiveness of our approach, we constrainthe reactive power injection at node 10 to 8 kVAR or 0.8 pu.


Table II also shows reactive power injection profile, obtainedafter constraining reactive power injection on generator at node10, . Tocompensate for the insufficient reactive power at node 10, itcan be observed that our approach increases the reactive powerinjection on nodes 0 to 9. In next subsection, we analyze thecomputational complexity of our approach and compare it withglobal 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, andit certifies the quality of its solution to be -optimal [30]. Thecomputational complexity of branch and bound algorithm de-pends on: 1) complexity of computing the lower and the upperbound 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 thereare such variables then complexity is . For a problem with4 nodes, (3 voltage, 3 phase, 3 real power, and 3 reactivepower 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 relativelyvery 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 sequenceof equality constrained problems. The worst case complexityis , where is the number of variables and is thenumber of constraints [25]. For our approach we use interiorpoint method first to get feasible point. Further it takesto compute the affine approximation of nonconvex constraints.Thus in our approach SCP iterations are effective to the orderof . For problem with 4 nodes, , and(6 constraints per phase per node), the worst case complexityis . Thus our approach has far less computationalcomplexity compared to exponential time complexity of branchand 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 increasedthe 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 interfacein 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 thethree phase reactive power injection profile obtained from bothSCP based approach and BB method. The SCP based solutionrequires, 0.006% (1892.32 kVAR) more reactive power com-pared to global minimum (1892.21 kVAR) obtained from BB

TABLE IIIREACTIVE POWER INJECTION (IN KVAR) PROFILE (SCP VRS. BB)

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

methods. Thus, with very small compromise in optimality, weachieve significantly lower computational complexity and runtime. It can be observed that both the approaches, extract max-imum reactive power (60% of total generation capacity) fromDGs. In the next subsection, we consider the IEEE 123 nodetest feeder, as a test case to evaluate our approach on large scaledistribution network.

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

Fig. 3 shows a IEEE 123 node modified test node feeder witharbitrarily 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 isarbitrarily single, two or three phase, each of 10 kVA asshown 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 distributionnetworks including mathematical models of these compo-nents.

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


TABLE IVREACTIVE POWER INJECTION PROFILE (IN KVAR)

• All three phase loads are assumed to be constant power starconnected 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 tosatisfy the network constraints (20). Once again our solutionconsiders grid as major source of reactive power. The gener-ation profile is mixed with one, two and three phase generatorsarbitrarily located in the network. As before, the solution resultsin fair distribution of reactive power injection among all DGs.

V. CONCLUSION

In this paper, we present the efficacy of using distributed gen-erators as a reactive power resource. Reactive power injectionby distributed generators is constrained by economic viabilityand 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 workare treated at network level to address the voltage/VAR con-trol. The optimization problem being nonconvex, we propose asuboptimal approach based on sequential convex programming(SCP). The proposed approach provides a near optimal solutionwith much lower computation complexity (runtime) relative toa global solver based on branch and bound method. Further wehave shown the practicality of our approach by simulating a123 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 anadditional objective. In our future work, we aim to address thevoltage/VAR control using stochastically varying loads and dis-tributed generation. We will also include the impact of commu-nication infrastructure on our control framework.

REFERENCES

[1] P. P. Barker and R. W. De-Mello, “Determining the impact of dis-tributed generation on power systems: Part 1—Radial distribution sys-tems,” in Proc. Power Eng. Soc. Summer Meet., Jul. 2000, vol. 3, pp.1645–1656.

[2] G. Pepermansa, J. Driesenb, D. Haeseldonckxc, R. Belmansc, and W.D’haeseleer, “Distributed generation: Definition, benefits and issues,”Energy Policy, vol. 33, pp. 787–798, 2005.

[3] F. Bastiao, P. Cruz, and R. Fiteiro, “Impact of distributed generationon distribution networks,” in Proc. 5th Int. Conf. Eur. Electr. Market(EEM), May 2008, pp. 1–6.

[4] T. Khoan and M. Vaziri, “Effects of dispersed generation (DG) on dis-tribution systems,” in Proc. IEEE Power Eng. Soc. Gen. Meet., Jun.2005, vol. 3, pp. 2173–2178.

[5] J. Driesen and R. Belmans, “Distributed generation: Challenges andpossible solutions,” in Proc. IEEE Power Eng. Soc. Gen. Meet., Oct.2006.

[6] G. Joos, B. T. Ooi, D. McGillis, F. D. Galiana, and R. Marceau,“The potential of distributed generation to provide ancillary services,”in Proc. IEEE Power Eng. Soc. Summer Meet., 2000, vol. 3, pp.1762–1767.

[7] F. Li, J. D. Kueck, D. T. Rizy, and T. King, A “Preliminary analysisof the economics of using distributed energy as a source of reactivepower supply,” Oak Ridge National Laboratory (ORNL), Oak Ridge,TN, Tech. Rep. (ORNL/TM-2006/014), 2006.

[8] H. Li, F. Li, Y. Xu, D. Rizy, and J. Kueck, “Dynamic voltage regulationusing distributed energy resources,” in Proc. 19th Int. Conf. Electr.Distrib. (CIRED), Vienna, Austria, May 2007.

[9] M. Triggianese, J. Morren, S. de Haan, and P. Marino, “Improved andextended DG capability in voltage regulation by reactive and activepower,” in Proc. Int. Conf. Power Eng., Energy, Electr. Drives (POW-ERENG), Apr. 2007, pp. 583–588.

[10] H. Li, F. Li, Y. Xu, D. Rizy, and J. Kueck, “Interaction of multiple dis-tributed energy resources in voltage regulation,” in Proc. Power En-ergy Soc. Gen. Meet.—Convers. Del. Electr. Energy 21st Century, Jul.2008, pp. 1–6.

[11] L. Huijuan, L. Fangxing, X. Yan, D. Rizy, and J. Kueck, “Adaptivevoltage control with distributed energy resources: Algorithm, theo-retical analysis, simulation, and field test verification,” IEEE Trans.Power Syst., vol. 25, pp. 1638–1647, Aug. 2010.

[12] J. Morren, S. de Haan, and J. Ferreira, “Distributed generation unitscontributing to voltage control in distribution networks,” in Proc. 39thInt. Univ. Power Eng. Conf. (UPEC), 2004, vol. 2, pp. 789–793.

[13] D. Geibel, T. Degner, C. Hardt, M. Antchev, and A. Krusteva, “Im-provement of power quality and reliability with multifunctional PV-in-verters in distributed energy systems,” in Proc. 10th Int. Conf. Electr.Power Quality Utilisation (EPQU), Sep. 2009, vol. 25, pp. 1–6.

[14] P. Vovos, A. Kiprakis, A. Wallace, and G. Harrison, “Centralized anddistributed voltage control: Impact on distributed generation penetra-tion,” IEEE Trans. Power Syst., vol. 22, pp. 476–483, Feb. 2007.

[15] D. N. Gaonkar, P. Rao, and R. Patel, “Hybrid method for voltage reg-ulation of distribution system with maximum utilization of connecteddistributed generation source,” in Proc. IEEE Power India Conf., Jun.2006, pp. 5–10.

[16] S. Chun-Lien, “Stochastic evaluation of voltages in distribution net-works with distributed generation using detailed distribution operationmodels,” IEEE Trans. Power Syst., vol. 25, pp. 786–795, May 2010.

[17] F. Demailly, O. Ninet, and A. Even, “Numerical tools and modelsfor Monte Carlo studies of the influence on embedded generation onvoltage limits in LV grids,” IEEE Trans. Power Del., vol. 20, pp.2343–2350, Jul. 2005.

[18] M. Baran and I. El-Markabi, “A multiagent-based dispatching schemefor distributed generators for voltage support on distribution feeders,”IEEE Trans. Power Syst., vol. 22, pp. 52–59, Feb. 2007.

[19] T. Niknam, A. Ranjbar, and A. Shirani, “Impact of distributed gener-ation on volt/VAR control in distribution networks,” in IEEE BolognaPower Tech Conf. Proc., Jul. 2003, pp. 7–14.


[20] P. Hrisheekesha and J. Sharma, “Evolutionary algorithm based op-timal control distribution system dispersed generation,” Int. J. Comput.Appl., vol. 14, pp. 31–37, Feb. 2010.

[21] T. Niknam, “A new approach based on ant colony optimization fordaily volt/var control in distribution networks considering distributedgenerators,” Int. J. Comput. Appl., vol. 49, pp. 3417–3424, 2008.

[22] J. Olamaie and T. Niknam, “Daily volt/var control in distribution net-works with regard to DGs: A comparison of evolutionary methods,” inProc. IEEE Power India Conf., 2006, p. 6.

[23] S. K. Johannes, Stochastic Optimization. New York: Springer, 2007.[24] J. C. Spall, Introduction to Stochastic Search and Optimiza-

tion. Hoboken, NJ: Wiley, 2003.[25] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge,

U.K.: Cambridge Univ. Press, 2004.[26] S. Boyd, “Sequential convex programming,” Stanford Univ., Stanford,

CA, 2010 [Online]. Available: http://www.stanford.edu/class/ee364b/lectures/seq_slides.pdf

[27] K. Rogers, R. Klump, H. Khurana, A. Aquino-Lugo, and T. Overbye,“An authenticated control framework for distributed voltage supporton the smart grid,” IEEE Trans. Smart Grid, vol. 1, pp. 40–47, Jun.2010.

[28] A. Aquino-Lugo, R. Klump, and T. Overbye, “A control frameworkfor the smart grid for voltage support using agent-based technologies,”IEEE Trans. Smart Grid, vol. 2, pp. 173–180, Mar. 2011.

[29] H. L. Willis, Power Distribution Planing Reference Book. BocaRaton, CA: CRC, 2004.

[30] R. Horst and T. Hoang, Global Optimization: Deterministic Ap-proaches. New York: Springer, 1996.

[31] S. Boyd and J. Mattingley, “Branch and bound methods,” StanfordUniversity, Stanford, CA, 2007 [Online]. Available: http://www.stan-ford.edu/class/ee364b/notes/bb_notes.pdf

[32] W. H. Kersting, “Radial distribution test Feeders—Distribution systemanalysis subcommittee report,” inProc. IEEE Power Eng. Soc. SummerMeet., 2001.

[33] W. H. Kersting, Distributed System Modeling and Analysis. BocaRaton, CA: CRC, 2002.

[34] F. D. Torre, A. Dolara, S. Leva, and A. Morando, “Faults analysistheory and schemes of four-phase power systems,” Proc. IEEE Pow-erTech Bucharest, pp. 1–7, Jul. 2009.

[35] F. D. Torre, S. Leva, and A. Morando, “Symmetrical components andspace-vector transformations for four-phase networks,” IEEE Trans.Power Del., vol. 23, no. 4, pp. 1–7, Jul. 2008.

Siddharth Deshmukh (M’07–S’10) received the B.E. degree in electronics andtelecommunication discipline 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, statistical

signal 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 1997 and 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&MUniversity, 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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VAR Control in Distribution Networks