Optimum Voltage Regulator Placement in a Radial

7/27/2019 Optimum Voltage Regulator Placement in a Radial

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 2, MAY 2000 879

Optimum Voltage Regulator Placement in a RadialPower Distribution NetworkAnastasia S. Safigianni, Member, IEEE, and George J. Salis

AbstractA computer algorithm for optimal voltage controlwith voltage regulators, suitable for large radial distribution net-works is given in this paper. An objective function concerning thetotal cost of the voltage regulators (investment and maintenancecost) as well as the cost of losses of the examined networks is de-veloped and constitutes the base of the algorithm. This algorithmmakes theinitial selection, installationand tapsetting of thevoltageregulators, which provide a smooth voltage profile along the net-work,utilizing former algorithmssuitably modified and optimized.Then it attempts to minimize the number of the initially selectedvoltage regulators as much as possible, by moving them in sucha way as to control the network voltage at the minimum possiblecost (maximization of the objective function). Thealgorithm is fast,efficient and reliable as its application to practical distribution net-works shows.

Index TermsRadial primary distribution networks, Voltagecontrol, Voltage regulators, Cost minimization.

I. INTRODUCTION

I F THE reinforcement of a network were required becauseof excessive voltage drop, any such reinforcement could bedeferred if the voltage drop could be sufficiently reduced by

some means, subject to economic as well as technical consid-

erations. Various devices such as capacitors and voltage regula-

tors (VRs) can be installed to reduce the voltage drop, experi-

enced at critical points of medium voltage networks. Conductor

replacements at network segments can also be used to maintain

the voltage along the entire network.

The papers [1], [2] propose reconductoring of currently

operating primary distribution networks in order to optimize

them technically as much as possible defraying the minimum

cost. Representative papers dealing with the optimization of

medium voltage networks operation by selecting (kind and

size), installing and controlling the appropriate number of ca-

pacitors, are [3][10]. Fewer papers deal with the determination

of the optimal locations and real-time control (tap positions)

of a minimum VR number, in order to minimize the peak

power and energy losses and provide a smooth voltage profile

along a distribution network with lateral branches, under timevarying conditions. Recent papers of this kind are [3], [4], [5],

[6]. Specifically an integrated method for the optimal reactive

power and voltage control of radial distribution networks by

using capacitors and VRs is given in [3], [4], [5], which are

parts of a complete study, as well as in [6]. All these papers

decouple the capacitor problem from the VR problem and

Manuscript received September 28, 1998.The authors are with the Departmentof Electrical and Computer Engineering,

Democritus University of Thrace, Xanthi (67 100), Greece.Publisher Item Identifier S 0885-8950(00)03833-5.

propose VRs for a network completely compensated with

capacitors.

The network voltage is the criterion for the selection of the

optimal VR number, locations and tap positions in [3], [4], [5].

An economic function, which estimates the power and energy

losses, is given in retrospect but this function is not utilized

during the main problem-solving process concerning the op-

timum VR placement and installation. The power flow at the

network segments is calculated by an approximate method (V-P

model, [11]).

In [6], the voltage regulation is initially attempted by

changing the tap positions at the substation and solving againthe capacitor problem. If the desirable voltage regulation is

not achieved in this way, a VR is placed at the main feeder,

next to the node where the subfeeder with the heaviest load is

connected and then the proper tap position of this VR is de-

termined. Sometimes VRs are placed at very long subfeeders

to improve their voltage profile. Consequently in this paper

the VR positions are in a way predetermined and they are not

indicated by the method.

The present paper utilizes the basic philosophy of the algo-

rithm of [3], [4], [5] only with regard to the initial VR selection,

placement and tap setting. But even in this stage it differenti-

ates the method of the above papers by calculating the currents

at the network segments by load flow analysis instead of an ap-proximate method as these papers do. After the determination of

the initial VR number and locations the optimization procedure

does not finish in opposition to [3], [4], [5], because it is true

that the resultant solution solves the problem of the excessive

voltage drop technically but it is not surely the most econom-

ical one. For this reason an objective function is developed in

the context of this paper, which includes the VR total cost and

the cost of losses of the examined network (evaluating the power

losses for thepeak load and the energy lossesaccording to an ap-

proximate annual load curve consisting of twelve distinct mean

monthly load values). Based on this function a procedure in-

vestigating the possible reduction of the number of the initially

selected VRs is evolved so as the finally proposed solution willbe the most economical one.

The application of the proposed method to a great number of

practical radial primary distribution networks has proved that

there are no restrictions according to the size of the examined

networks as the method is easy to use, very fast and efficient.

II. INITIALVOLTAGEREGULATORPLACEMENT ANDCONTROL

A power flow analysis method precedes the procedure of the

VR selection and installation in a radial distribution network, in

08858950/00$10.00 2000 IEEE

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880 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 2, MAY 2000

order to evaluate the exact node voltages and segment currents.

Thus it is possible to avoid the fallacious assumption that a ra-

dial distribution network is optimally compensated using par-

ticular capacitors, because it is impossible to have a capacitive

current absolutely equal to the inductive current at each lateral

or sublateral branch due to the tree structure of the said network.

The power flow method used in this paper, which is based on

the direct application of Kirchhoffs voltage and current laws,is analytically described in [12] and has excellent convergence

characteristics when applied to large scale weakly meshed or

radial networks. According to this method, the voltage at the

source as well as the active power and the reactive power

at all the other nodes are given. The network is swept back-

ward and forward and the segment currents as well as the

node voltages are calculated. This power flow technique pre-

supposes that the examined networks are recorded as tree data

structures, so that they can be processed without special node

numbering. This simplifies the node sweep and increases the

flexibility of the method according to the addition or subtrac-

tion of branches. The voltage at each network node i must be

limited between specific limits and affected by thesize and the character of the load, in order that the total voltage

drop along the network and for each one of the network ends is

less than a definite percentage % of the rated voltage.

If this requirement is not satisfied a voltage regulation method

must be applied.

If the maximum possible voltage level were to be achieved,

as the power losses are proportional to the current squared and

the current is inversely proportional to the voltage, it would be

theoretically desirable to put one VR at each network node. This

would lead to the minimum cost of losses . In fact VRs

are installed only at some network nodes and they maintain the

voltage every moment according to the load. This means re-

spective time variation of the network current and relative losses

saving. The costof losses after the VR installationis given

by the relation:

(1)

where :

: the annual demand cost [dr/(kW a)]

: the energy cost [dr/kWh]

: the number of the network segments

: the network losses at peak load with VRs on the

network [kW]: the network losses during the time period with

VRs on the network [kW]

: time period during which the network losses are

constant

and

h (2)

The cost lies between two limits

(3)

where is the cost of losses before the VR installation

(4)

where:

: the network losses at peak load without VRs [kW]: the network losses during the time period T without

VRs [kW]

The VR problem consists of two subproblems, that of the

optimum selection and that of the optimum control. The first

subproblem concerns the determination of the VR necessary

number and locations on the network, to achieve the desirable

voltage profile, while the second subproblem concerns the se-

lection of their tap positions. The procedure for the first VR se-

lection and installation is relative to that described in [3], [4],

[5]. The following steps are executed by sweeping the network

forward (from the source to the ends):

Localization of the nearest node to the source where the

voltage drop is out of the predetermined limits.A VR installation at this node and tap setting of this VR so

that the voltage of the node is as close as possible to the max-

imum permissible voltage, without exceeding it.

Calculation of the node voltages by load flow analysis, which

takes into account the already existing VRs. The initial node

voltages, at the beginning of the repetitive load flow proce-

dure, do not necessarily need to be identical to the source

voltage . They may be equal to the node voltages before

the VR installation at the step II.

Examination of the node voltages to see if the desirable limits

are violated. If not the VR installation procedure comes to an

end or else all the steps are repeated.

A VR tap position at the node i can be generally determined by

the relation (5).

Int (5)

where:

Int : the function which returns the integer part of its argu-

ment

: the voltage at the node i before a VR installation at

this node under peak load conditions

: the VR voltage step (0.006 25 p.u.)

During the VR installation procedure the voltage refersto peak load conditions, which means that this voltage takes its

minimum value given by the relation:

(6)

where:

: the percentage voltage drop from the source to the

node i resulting from power flow analysis.

When themethod proposes forthe VR a tappositiongreater than

its possibilities, a location closer to the source must be searched

out for this VR, which will lead to a smaller tap position, even

if the voltage drop at this location is not unacceptable.

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SAFIGIANNI AND SALIS: OPTIMUM VOLTAGE REGULATOR PLACEMENT 881

The profit because of the losses saving, after the VR installa-

tion is:

(7)

This profit increases as the voltage at the network nodes ap-

proaches its maximum permissible value. That means the tap

positions must be adjusted during the year, so that the VR output

voltage approachesits maximum value without exceeding

it. The necessary variation of the tap positions , in order to

have the maximum output voltage, is given by the relation:

int

(8)

where:

: the previous VR tap position

(9)

The above described method for the VR placement is defective

because it does not take into account the annual investment and

maintenance cost for all the installed VRs which is rela-

tively high. An objective function taking into account this cost

can be written as:

(10)

with:

(11)

where:

: the number of the network nodes

: theVR annualinvestment andmaintenancecost

[dr/a]

when a VR exists at the node i

when there is no VR at the node i

: the VR investment cost [dr]: the VR annual maintenance cost [dr/a]

: the annual capital recovery factor given by the

relation:

(12)

where :

: the annual interest rate (no inflation)

: the expected VR life.

After theVR installationaccording to theabove mentioned steps

I-IV the initial value of the objective function (10) is calculated.

Fig. 1. Block diagram of the Pull_Back_Regulators procedure.

When the method proposes more than one VR it must be deter-

mined if the voltage can be limited between the predeterminedlimits using a smaller VR number in a way that maximizes the

objective function (10).

III. ALGORITHM FOR THE RESTRICTION OF THEVOLTAGE

REGULATORS

A recursive procedure named Reg_Recursive( ,Reg) is

used to examine whether fewer VRs contribute an acceptable

voltage profile to the network whilst simultaneously increasingthe value of the objective function (10). The arguments of this

procedure, which constitute the state variables of the problem,

are the initially proposed VR number and relative information

Reg [ ] for each one of these VRs such as the cor-responding network node and tap positions. The first time the

above recursive procedure is executed, the VR number and tap

positions are those resulting from the algorithm previously de-

scribed which are referred to as Scheme 1 in the block dia-

gram of Fig. 1.

The first stage of the Reg_Recursive( ,Reg) procedure

is the Find_path( ,Reg) procedure as in Fig. 1 is shown.

During this procedure each one of the VRs is successively

moved to nodes closer to the source, which without fail belong

to the route joining directly the source and the VR location. The

total movement route for one VR depends on the current stage

of the recursive procedure and whether or not VRs are present



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at the nodes which are further away from the source and stem

from the initial position of this VR. The contribution of these

VRs to the network voltage profile depends directly on the lo-

cation and the tap position of the examined VR. Every time the

VR is moved, its tap positions are adjusted since its rated input

voltage tends to increase as the VR approaches the source and

the voltage at the new VR location must approach the maximum

permissible value without exceeding it, according to the relation(8).

The next step is the voltage computation at each node

belonging to network branches, which stem from the new

VR location and an investigation of whether some voltage

drop problem exists. If no problem exists this new location

is acceptable and the VR is moved to the next node toward

the source within a procedure trying to find the route of the

permissible VR movements. If a voltage drop problem exists

the Find_path( ,Reg) procedure for the examined VR

terminates. In this case the end of the route of the permis-

sible movements is the closest node to the source, where

the VR installation keeps between the acceptable limits the

voltage of the nodes which stem from the VR position. Theexamined VR is moved back to the node it was at before the

beginning of the above described procedure, acquiring again

the tap position which corresponds to this location and the

Find_path( ,Reg) procedure goes on examining the next

VR. When this procedure finishes, each VR is accompanied

by a path of its permissible movements. This path may be

regarded as fictitious due to the fact that both the origin and the

end of the path are situated at the initial VR location, making

actual movements redundant.

The next step of the Reg_Recursive( ,Reg) procedure

is the formulation of all the possible pairs (reg ,reg ) derived

from the set of all the installed VRs at the network.

Supposing thatset=[reg , reg , , reg ] theneach paircan

be described as (reg ,reg ), with

and

The total number of the pairs is:

(13)

For each one of these pairs the following are executed. It is

checked if there are common nodes between the routes path of

the VRs corresponding to each pair (Check_paths(reg ,reg )

procedure). If there are not, the Reg_Recursive( ,Reg)

procedure goes on dealing with the next pair (reg ,reg ). In

the opposite case, the common node furthest from the source,

named com is chosen as the node where one VR is installed

instead of the two VRs of the pair. All the VR tap positions are

adjusted according to (8) and a new power flow analysis takes

place. The network acquires a new form and the Reg_Re-

cursive procedure acquires new values of the state variables

( ,newReg), which are , and

Fig. 2. Radial feeder having four voltage regulators.

Fig. 3. The radial feeder of the Fig. 2 after the reduction of the number of the

voltage regulators.

newReg[ ], provided the VR number is decreased

by one. The value of the objective function (10) is calculated

afterwards (Calc_SF procedure) for the new situation and if

this situation is more beneficial economically than the previous

situations, it is kept as the best one resulting from the inves-

tigation procedure up to this moment. The Reg_Recursive

procedure is executed with the form Reg_Recursive( ,

newReg) despite what the result of the objective function is

(better or worse).

The Reg_Recursive( ,Reg) procedure comes to an

end when all the possible VR pairs, (reg ,reg ) have beenexamined. If this procedure has not been called inside a

previous Reg_Recursive( ,Reg) procedure, the total

Pull_Back_Regulators procedure, concerning the VR move-

ment toward the source in order to reduce their number,

finishes.

The Pull_Back_Regulators procedure can be made quite

clear with the following example. Lets suppose that four

VRs have been installed during some stage of the recursive

procedure at the nodes 7, 9, 10 and 16 of the feeder given

in Fig. 2, which is a quite hypothetical feeder (a practical

application of the optimum VR placement method to a realistic

feeder is given at the next section). The first VR set examined



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Fig. 4. Feeder examined as a practical application of the optimum VR placement method.

by the Reg_Recursive( ,Reg) procedure is set=[reg ,

reg , reg , reg ] with . Lets also suppose that the VR

paths for the first execution of the above procedure are:

path reg node 7-5-3

path reg node 9-6

path reg node 10-6

path reg node 16-14

and the six pairs to be relatively examined are:

reg reg reg reg reg reg

reg reg reg reg

reg reg

For each one of the above pairs it is checked if a common node

com exists. The node 6 is such a node for the pair (reg ,reg ).

So a VR is installed at the node 6 and the VRs of the nodes 9and 10 are subtracted. The feeder acquires a new form given in

Fig. 3, which is likely to constitute an improvement in the value

of the objective function (10). At this point the recursive proce-

dure Reg_Recursive ( ,newReg) with

is executed again for the network form given in Fig. 3. New VR

paths aredefinedand there are now three pairs to be examined.

Every time the Reg_Recursive( ,newReg) procedure

is completed the feeder acquires again its previous form.

During the detection of the most economical way to have an

acceptable voltage profile along the examined network, using

the above described recursive procedure, it is possible for a spe-

cific network form to be examined more than once at different

execution levels of this procedure. One way to avoid this repeti-

tion is to store the network forms at each level of the procedure

and to compare the current examined form with the stored forms

to decide if it is possible to reduce the proceedings. However,this procedure is at least as time consuming as the repetitive

procedure described earlier, so there is no call for its implemen-

tation.

IV. CONCLUSIONS ANDRESULTS

A computer algorithm for the voltage control of large radial

distribution networks is presented in this paper. The algorithm

takes into account the actual network data such as conductor

sizes, lateral and sublateral branches as well as load distribution

and time variation and handles fast large distribution systems as

a total and notin parts making relative approximations. It aims at

an acceptable voltage profile along the network at the minimumpossible cost. That is obtained by moving toward the source and

readjusting the initially selected VRs, which probably leads to

a reduction of their number and a positive economical result.

A feeder of the primary power distribution network of the

area of Xanthi, Greece, which belongs to the Public Power

Corporation (P.P.C.) and has 229 nodes (load locations and

branch points), has been examined as a practical application

of the optimum VR placement method described above. The

furthest feeder end is 45 km away from the source and the

feeder segments have mainly conductors of the minimum size

( mm ACSR), as Fig. 4 shows. The segment lengths are

given in Table I. The rated voltage of the feeder is 20 kV and



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TABLE IDATA ANDRESULTS OF THEAPPLICATION OF THEOPTIMUMVR PLACEMENT METHOD ON THEMEDIUM-VOLTAGEFEEDER OFFIG. 4

% of the rated voltage is taken as the acceptable voltage

variation at each distinguished node as well as at all the terminal

nodes. A capacitor of 450 kVAr has already been installed at

the node 167 of the feeder in order to minimize the losses. The



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TABLE I (Continued)DATA ANDRESULTS OF THEAPPLICATION OF THEOPTIMUMVR PLACEMENT METHOD ON THEMEDIUM-VOLTAGEFEEDER OFFIG. 4

total peak load of the feeder at the moment the optimization

procedure begins is equal to 80 A. The installed loads at the

nodes of the feeder given in Table I are coincident with the

above peak load before the optimization procedure begins. The



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standardized VRs used by P.P.C. have nominal values 5 MVA

and 10 MVA, tap range of % and tap increments 0.625 %

( tap positions). Given in Table I is also the percentage

voltage drop before the VR installation. It is obvious that the

voltage drop exceeds the permitted limits in many feeder nodes.

The application of the VR optimization method given in [3],

[4], [5] after its differentiation, in order to include load flow

analysis, indicates three VRs with nominal values 5 MVA atthe nodes 100, 112 and 139 and tap positions for the peak load

16, 16 and 15 correspondingly. This solves the voltage drop

problem as the relative column of Table I shows. At this point

the Pull_Back_Regulators procedure, proposed in this paper,

is used aiming at the restriction of the necessary VR number

and consequently of the requisite cost. Specifically through the

Reg_Recursive procedure all the VR pairs are examined in

order to replace them by one VR closer to the source. The final

result is that the usage of only one instead of three VRs is pro-

posed which is obviously a more economical solution. This VR

has nominal value 5 MVA and tap position for the peak load 13,

it is placed at the node 37 and it solves the voltage drop problem.

It is also offering to the feeder more room to increase its induc-tive load without voltage problem, compared to the case of the

three VRs, as the relative columns of Table I show.

The algorithmdescribed in this paper was coded in the Turbo-

Pascal language. The time needed for the solution of the prac-

tical problem given above is 33s using a Pentium-233 MHz.

The optimization problem examined in this paper is part of

a more general problem, which has already been examined by

the authors of the paper and aims at giving the more econom-

ical combined optimization solution for currently operating pri-

mary power distribution networks, in an annual as well as in a

long-term basis, by using all the available means (capacitors,

VRs, network reconductoring).

REFERENCES

[1] G. Salis and A. Safigianni, Economically Justified Modification of aRadial Network to an Optimal Form, Advances in Engineering Soft-ware, vol. 21, no. 1, pp. 4965, 1994.

[2] G. Salis andA. Safigianni, Economical Optimizationof a Radial PowerNetwork Based on Voltage Drop Criterion, Advances in EngineeringSoftware, vol. 22, no. 1, pp. 120, 1995.

[3] J. J. Grainger and S. Civanlar, Volt/Var Control on Distribution Systemwith Lateral Branches Using Shunt Capacitors and Voltage Regulators,Part 1: The Overall Problem, IEEE Trans. on PAS, vol. 104, no. 11, pp.32783283, November 1985.

[4] J. J. Grainger and S. Civanlar, Volt/Var Control on Distribution Systemwith Lateral Branches Using Shunt Capacitors and Voltage Regulators,Part 11: The Solution Method, IEEE Trans. on PAS, vol. 104, no. 11,pp. 32843290, November 1985.

[5] S. Civanlar and J. J. Grainger, Volt/Var Control on Distribution Systemwith Lateral Branches Using Shunt Capacitors and Voltage Regulators,Part III: The Numerical Results,IEEE Trans. on PAS, vol. 104, no. 11,pp. 32913297, November 1985.

[6] M. M. A Salama, N. Manojlovic, V. H. Quintana, and A. Y. Chikhani,

Real-Time Optimal Reactive Power Control for Distribution Net-works,International Journal of Electrical Power & Energy Systems ,vol. 18, no. 3, pp. 185193, 1996.

[7] M. E. Baran and F. F. Wu, Optimal Sizing of Capacitors Placed on aRadial Distribution System, IEEE Trans. on Power Delivery, vol. 4,no. 1, pp. 735743, January 1989.

[8] M. E. Baran and F. F. Wu, Optimal Capacitor Placement on RadialDistribution System,IEEE Trans. on Power Delivery, vol. 4, no. 1, pp.725734, January 1989.

[9] H. D. Chiang, I. C. Wang, and G. Darling, Optimal Capacitor Place-ment, Replacement and Control in Large-Scale Unbalanced Distribu-tion Systems: System Solution Algorithms A Numerical Studies,IEEETrans. on PWRS, vol. 10, no. 1, pp. 363369, February 1995.

[10] H. D. Chiang, I. C. Wang, and G. Darling, Optimal Capacitor Place-ment,Replacementand Control in Large-Scale UnbalancedDistributionSystems: System Modeling and A New Formulation, IEEE Trans. onPWRS, vol. 10, no. 1, pp. 356362, February 1995.

[11] J. J. Grainger, S. Civanlar, K. N. Clinard, and L. I. Gale, OptimalVoltage Dependent Continuous Time Control of Reactive Power onPrimary Feeders,IEEE Trans. on PAS, vol. 103, no. 9, pp. 27142722,September 1984.

[12] D. Shirmohammadi, H. W. Hong, A. Semlyen, and G. X. Luo, A Com-pensation-Based Power Flow Method For Weakly Meshed Distributionand Transmission Networks, IEEE Trans. on Power Delivery, vol. 3,no. 2, pp. 753762, May 1988.

Anastasia S. Safigianni(M97) was born in Greece in 1957. She received herDipl.-Eng. degree and Ph.D. degree fromthe Electrical Engineering Departmentof the Democritus University of Thrace, Greece, in 1981 and 1988 respectively.She is currently Assistant Professor in the Department of Electrical and Com-puterEngineering of the DemocritusUniversity of Thrace, Greece. Her teaching

interests include power systems and electrical installations. Her research inter-ests include power system planning and optimization and short-circuit lossesand forces in metal enclosed arrangements.

George J. Salis was born in Zurich, Switzerland, in 1970. He receivedhis Dipl.-Eng. degree from the Electrical Engineering Department of theDemocritus University of Thrace, Greece, in 1992 and his Ph.D. degree fromthe Electrical and Computer Engineering Department of the DemocritusUniversity of Thrace, Greece, in 1998. His research interests include computerapplication to distribution system planning and optimization.
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Optimum Voltage Regulator Placement in a Radial

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