distribution system voltage regulation and var compensation for differen static load models.pdf

Distribution system voltage regulationand var compensation for different staticload modelsN. Mithulananthan, M. M. A. Salama, C. A. Canizares and J. ReeveDepartment of Electrical and Computer Engineering, University of Waterloo, Waterloo, CanadaE-mail: [email protected]

Abstract Voltage regulation computations for distribution systems are strongly dependent on power flow solutions.The classical constant power load model is typically used in power flow studies of transmission or distributionsystems; however, the actual load of a distribution system cannot just be modeled using constant power models,requiring the use of constant current, constant impedance, exponential or a mixture of all these load models toaccurately represent the load. This paper presents a study of voltage regulation of a distribution system using differentstatic load models. The effect of shunt capacitor compensation is also studied and illustrated in this paper forsystems with different static load models.

Keywords distribution systems; power flow; static load models; voltage regulation

Introduction

Voltage regulation is an important subject in electrical distribution engineering.It is the utilities’ responsibility to keep the customer voltage within specifiedtolerances. The performance of a distribution system and quality of the serviceprovided are not only measured in terms of frequency of interruption but inthe maintenance of satisfactory voltage levels at the customers’ premises.According to Gonen,1 a high steady-state voltage can reduce light bulb life andreduce the life of electronic devices. On the other hand, a low steady-statevoltage leads to low illumination levels, shirking of television pictures, slowheating of heating devices, motor starting problems, and overheating in motors.However, most equipment and appliances operate satisfactorily over some‘reasonable’ range of voltages; hence, certain tolerances are allowable at thecustomer’s end. Thus, it is common practice among utilities to stay withinpreferred voltage levels and ranges of variations for satisfactory operation ofapparatus as set by various standards such as ANSI (American NationalStandard Institution). For example, power acceptability curves given by IEEE(IEEE orange book, IEEE standard 446) and FIPS (United States FederalInformation Processing Standard) indicate that steady-state voltage regulationsshould be within+6% to−13% for satisfactory operation of various electricaldevices.2Voltage regulation calculations depend on the power flow solutions of a

system. Most of the electrical loads of a power system are connected to low-voltage/medium-voltage distribution systems rather than to a high-voltagetransmission system. The loads connected to the distribution system are cer-tainly voltage dependent; thus, these types of load characteristics should be

International Journal of Electrical Engineering Education 37/4

385Voltage regulation for different static load models

considered in load flow studies to get accurate results and to avoid costlyerrors in the analysis of the system. For example, in voltage regulation improve-ment studies, possible under- or over-compensation can be avoided if moreaccurate results of load flow solutions are available, as demonstrated in thispaper. However, most conventional load flows use a constant power loadmodel, which assumes that active and reactive powers are independent ofvoltage changes. In reality, constant power load models are highly questionablein distribution systems, as most nodes are not voltage controlled; therefore, itis very important to consider better load models in these types of load flowproblems.In this paper, distribution system voltage regulation and the effect of shunt

capacitor compensation on this regulation for different static load models arestudied. The paper is organized as follows: the next section briefly reviewsdifferent types of static load models. Power flow equations and a MATLAB-based solution technique, as well as the definition of voltage regulation andmethods to improve it are then discussed. Details of the distribution test systemused in this paper follow, together with a discussion of some interesting simu-lation results. Finally, major contributions of this paper are highlighted.

Static load models

In power flow studies, the common practice is to represent the composite loadcharacteristic as seen from power delivery points. In transmission system loadflows, loads can be represented by using constant power load models, asvoltages are typically regulated by various control devices at the delivery points.In distribution systems, voltages vary widely along system feeders as there arefewer voltage control devices; therefore, the V –I characteristics of load aremore important in distribution system load flow studies.3–5Load models are traditionally classified into two broad categories: static

models and dynamic models. Dynamic load models are not important in loadflow studies. Static load models, on the other hand, are relevant to load flowstudies as these express active and reactive steady state powers as functions ofthe bus voltages (at a given fixed frequency). These are typically categorized asfollows:6

Constant impedance load model (constant Z). A static load model where thepower varies with the square of the voltage magnitude. It is also referred to asconstant admittance load model.

Constant current load model (constant I). A static load model where the powervaries directly with voltage magnitude.

Constant power load model (constant P). A static load model where the powerdoes not vary with changes in voltage magnitude. It is also known as constantMVA load model.


386 Mithulananthan et al.

Exponential load model. A static load model that represents the powerrelationship to voltage as an exponential equation in the following way:

P=P0 AVV0Ba, Q=Q0 AVV0Bbwhere P0 and Q0 stand for the real and reactive powers consumed at a referencevoltage V0 . The exponents a and b depend on the type of load that is beingrepresented, e.g., for constant power load models a=b=0, for constant currentload models a=b=1 and for constant impedance load models a=b=2.Table 1 shows typical values of a and b for several types of loads encounteredin power systems;6 it is interesting to note that none of these loads has a zeroexponent.

Polynomial load model. A static load model that represents the power-voltagerelationship as a polynomial equation of voltage magnitude. It is usuallyreferred to as the ZIP model, as it is made up of three different load models:constant impedance (Z ), constant current (I ) and constant power (P). The realand reactive power characteristics of the ZIP load model are given by

P=P0 CaP AVV0B2+bP AVV0B+cPDQ=Q0 CaQ AVV0B2+bQ AVV0B+cQDwhere a

P+bP+cP=aQ+bQ+cQ=1, and P0 and Q0 are the real and reactive

power consumed at a reference voltage V0 . In this paper, three types of staticload models, i.e., constant power, constant current and constant impedance,are considered to demonstrate their effect on voltage regulation calculations indistribution systems. The studies presented in this paper can be readily extendedto other load models as well.

Power flow equations and voltage regulation

Power flow studies are of great importance in planning and designing futureexpansions of power systems. The main information obtained from power flow

TABLE 1. A sample of fractional load exponents

Load component a b

Incandescent lamps 1.54 —

Room air conditioner 0.50 2.50Furnace fan 0.08 1.60Battery charge 2.59 4.06

Compact fluorescent lamps 0.95–1.03 0.31–0.46Fluorescent lamps 2.07 3.21



studies is the magnitude and angle of the phasor voltage at each node, and thereal and reactive power flowing in each line. With this information, the voltageregulation of any feeder in the system can be easily computed.

Power flowIn general, if a node in a power system is considered (Fig. 1), the followingequations can be readily written by considering the real and reactive powerbalance:

Pk=Pgk

−PLk

, Qk=Qgk

−QLk

where Pgk

and Qgk

are the real and reactive power generated at node k; PLkand Q

Lk

are the real and reactive power loads at node k, which could beconstant or a function of the bus voltage magnitude; and P

kand Q

kare the

real and reactive power injected into the system,7 i.e.,

Pk=Vk∑N

l=1YklVlcos (d

k−dl−hkl)

Qk=Vk∑N

l=1YklVlsin (d

k−dl−hkl)

where Vkand V

lare bus voltage magnitudes at nodes k and l, together with

their respective phase angles dkand d

l; Ykland h

klare the magnitude and angle

of the kl entry in the Y-bus matrix; and N is the total number of nodes inthe system.A set of non-linear equations can be established for the system by considering

the power balance and injected power in terms of system parameters. Thus,these equations can then be solved by using any non-linear equation solvingtechnique (e.g. Newton–Raphson). In this paper, these equations are solved,for different static load models, using a MATLAB routine (fsolve ) based onleast square optimization techniques; the main steps of this program are asfollows:

1. Read the data and form the Y-bus matrix of the distribution system.

G To other Nodes

Load PLk, QLk

Pgk, QgkPk,Qk

Fig. 1 Power balance at node k.



2. Generate the symbolic set of nonlinear power flow equations by assumingthat the substation node is a PV bus while all other nodes are load buses.

3. Assume an initial guess (all voltages equal to the substation voltage andall angles equal to zero).

4. Solve the set of nonlinear equations with the fsolve command inMATLAB.

Voltage regulationOnce a load flow solution is obtained, the voltage regulation of any feeder canbe calculated as follows:1

V Reg.=|Vs |−|Vr ||Vr |

1100

where Vs is sending-end voltage and Vr is receiving-end voltage. In distributionsystems, this regulation may be typically improved by using one or more ofthe following techniques:

(a) Increasing primary voltage.(b) Activating voltage regulating equipment at the substations bus such as

capacitors or LTCs.(c) Balancing of loads on primary feeders.(d) Increased size of feeder conductor.(e) Transferring loads to new feeders.(f ) Installing new substations and primary feeders.(g) Installing shunt capacitors or SVCs on primary feeders.

The most economical way of improving voltage profiles along a feeder, andthus voltage regulation and overall system performance, is by using shuntcapacitors. Hence, the effect of shunt capacitors on voltage regulation withdifferent static load models is studied in this paper.

Simulation results

The topology of many distribution systems is like a tree with several lateraland sub-lateral branches; the root of the tree is the feeding node or feedingsubstation. This kind of general structure of distribution systems (a radial type)has been fully exploited to develop some efficient load flow methods in thepast.8,9 In the present work, a similar type of system is used to analyze theeffect of various voltage dependent load models in distribution system voltageregulation.The distribution system used in this paper is depicted in Fig. 2. It is a

balanced three-phase radial system that consists of 30 nodes and 29 segments;there are three sub-feeders and one main feeder. It is assumed that all the loadsare fed from the substation located at node 1. The loads belonging to onesegment are assumed to be placed at the end of each segment. The system datawas extracted from Ref. 10.



1 2 3 4 5 6 7 8 9 10 11 12

13

14

15

16

17 18 19 20 21 22 2324

252627

28

29

30

SUB-1 SUB-3

SUB-2

SUB STATION MAIN FEEDER

Fig. 2 Single-line diagram of the test distribution system.

The studies presented in this paper consist of two parts. The first part consistsof the load flow solutions and voltage regulation computations for the testsystem with different static load models. The second part focuses on varcompensation by shunt capacitors with different static load models and itseffect on the system voltage regulation.

Voltage regulationInitially, load flow solutions for the test distribution system with (Fig. 2)constant power load models were obtained by using the developed MATLABprogram, and these results were validated by comparing them to those obtainedwith a standard power flow program (PFLOW11 ).Tables 2 and 3 compare the load flow solutions obtained for different static

TABLE 2 Voltage magnitude along the main feeder: classical load (cons P) vs. constantcurrent (cons. I)

Voltage (p.u.)Difference

Node Classical (cons. P) Cons. I (p.u.)

1 1.0000 1.0000 0.0000

2 0.9824 0.9845 0.00213 0.9670 0.9711 0.00414 0.9460 0.9528 0.0068

5 0.9279 0.9372 0.00936 0.9109 0.9226 0.01177 0.9008 0.9136 0.0128

8 0.8958 0.9091 0.01339 0.8903 0.9043 0.014010 0.8880 0.9023 0.0143

11 0.8866 0.9010 0.014412 0.8862 0.9007 0.0145



TABLE 3 Voltage magnitude along the main feeder: classical load (cons P) vs. constantimpedance (cons. Z)

Voltage (p.u.)Difference

Node Classical (cons. P) Cons. Z (p.u.)

1 1.0000 1.0000 0.00002 0.9824 0.9859 0.0035

3 0.9670 0.9737 0.00674 0.9460 0.9573 0.01135 0.9279 0.9434 0.0155

6 0.9109 0.9303 0.01947 0.9008 0.9220 0.02128 0.8958 0.9179 0.0221

9 0.8903 0.9135 0.023210 0.8880 0.9117 0.023711 0.8866 0.9105 0.0239

12 0.8862 0.9102 0.0240

load models against solutions obtained using the classical (constant power)load model. The voltage profiles along the main feeder for these cases areshown on Fig. 3. As can be seen in Tables 2 and 3, different load models resultin different load flow solutions, as expected; the difference between the solutionsincreases as one moves away from the substation or feeding point. Thesedifferences in voltage may lead to significantly different design approaches in

1 2 3 4 5 6 7 8 9 10 11 120.88

0.9

0.92

0.94

0.96

0.98

1

Vol

tage

(pu

.)

Nodes

Constant PQConstant CurrentConstant Impedance

Fig. 3 Voltage profiles along the main feeder: classical load (cons. P), constant current,and constant impedance load models.



a distribution system. Hence, proper load models should be considered in orderto obtain more accurate results.Table 4 shows the distribution system voltage regulation calculated with

different static load models. The voltage regulation computed for constantpower load models is the highest of all loads models, as one would expect,since power demand does not change with voltage variations, whereas for theother models the power demand decreases as the voltage goes down.

CompensationIn order to see the effect of var compensation (shunt capacitors) on voltageregulation, various simulations were performed for different sizes of shuntcapacitors. Shunt capacitors are installed on the main feeder at two-thirds ofits length from the substation (Golden Rule). Voltages and thus voltage regu-lation of the main feeder are calculated for the different load models and fordifferent shunt capacitor sizes. The results obtained from these calculations areshown in Tables 5, 6, and 7, and the corresponding voltage profiles of the mainfeeder are depicted in Figs. 4, 5 and 6. Figure 7 summarizes these resultsby showing the voltage regulation of the main feeder for different shuntcapacitor sizes.

TABLE 4 Voltage regulation of the main feeder with diVerent load models

Load model Voltage regulation (%)

Constant power 12.84Constant current 11.02Constant impedance 9.87

TABLE 5 Voltage magnitudes for diVerent compensation levels (cons. P)

Voltage (p.u.)

Node 5 Mvar 4 Mvar 3 Mvar 2 Mvar 1 Mvar

1 1.0000 1.0000 1.0000 1.0000 1.0000

2 0.9877 0.9867 0.9857 0.9847 0.98363 0.9772 0.9754 0.9734 0.9714 0.96924 0.9615 0.9588 0.9558 0.9527 0.9494

5 0.9484 0.9447 0.9408 0.9367 0.93246 0.9364 0.9318 0.9267 0.9217 0.91647 0.9267 0.9220 0.9170 0.9118 0.9064

8 0.9218 0.9170 0.9120 0.9068 0.90149 0.9164 0.9117 0.9066 0.9014 0.895910 0.9142 0.9095 0.9044 0.8992 0.8937

11 0.9129 0.9081 0.9030 0.8978 0.892312 0.9125 0.9077 0.9027 0.8974 0.8919



TABLE 6 Voltage magnitudes for diVerent compensation levels (cons. I)

Voltage (p.u.)


1 1.0000 1.0000 1.0000 1.0000 1.00002 0.9893 0.9885 0.9876 0.9866 0.98563 0.9804 0.9787 0.9770 0.9751 0.9731

4 0.9668 0.9644 0.9617 0.9589 0.95605 0.9557 0.9524 0.9489 0.9451 0.94136 0.9456 0.9414 0.9370 0.9324 0.9276

7 0.9366 0.9324 0.9280 0.9234 0.91868 0.9321 0.9279 0.9235 0.9189 0.91419 0.9273 0.9231 0.9187 0.9141 0.9093

10 0.9253 0.9211 0.9167 0.9121 0.907311 0.9240 0.9198 0.9154 0.9108 0.906012 0.9237 0.9195 0.9151 0.9104 0.9056

TABLE 7 Voltage magnitudes for diVerent compensation levels (cons. Z)

Voltage (p.u.)


1 1.0000 1.0000 1.0000 1.0000 1.0000

2 0.9905 0.9897 0.9888 0.9879 0.98703 0.9825 0.9810 0.9793 0.9776 0.97574 0.9705 0.9682 0.9657 0.9631 0.9603

5 0.9606 0.9575 0.9543 0.9508 0.94726 0.9518 0.9489 0.9438 0.9395 0.93507 0.9434 0.9395 0.9354 0.9312 0.9267

8 0.9392 0.9353 0.9313 0.9270 0.92269 0.9347 0.9308 0.9268 0.9226 0.918110 0.9328 0.9290 0.9250 0.9207 0.9163

11 0.9317 0.9278 0.9238 0.9196 0.915212 0.9313 0.9275 0.9235 0.9192 0.9149

Observe that the system with constant power load model presents the highestvoltage regulation values followed by the constant current load model andthen the constant impedance load model, as expected. The voltage regulationfor all static load models appears to vary approximately linearly with the sizeof the shunt capacitor; however, the slopes change with the load model, withthe effectiveness of the capacitor compensation being highest for the systemwith constant power load models.To illustrate the importance of selecting the proper load models in the

reactive power compensation problem, consider the following sample case: to



1 2 3 4 5 6 7 8 9 10 11 12

0.9

0.92

0.94

0.96

0.98

1

Nodes

Vol

tage

(pu

.)

5 MVar4 MVar3 MVar2 MVar1 MVar

Fig. 4 Voltage profiles along the main feeder with constant power load models fordiVerent compensation levels.

1 2 3 4 5 6 7 8 9 10 11 120.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Node

Vol

tage

(pu

.)


Fig. 5 Voltage profiles along the main feeder with constant current load models fordiVerent compensation levels.

achieve a voltage regulation of 10%, a 5 Mvar capacitor would be needed inthe case of constant power loads models, whereas only a 2 Mvar capacitorwould be required if the loads are modeled as constant current and no compen-sation would be required if constant impedance load models are used. Hence,by properly modeling the load on a distribution system, over-design and theassociated extra costs can be avoided.



1 2 3 4 5 6 7 8 9 10 11 120.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Node

Vol

tage

(pu

.)


Fig. 6 Voltage profiles along the main feeder with constant impedance load models fordiVerent compensation levels.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 57

8

9

10

11

12

13

Capacitor Size (MVar)

% V

olta

ge R

egul

atio

n

Const. PQConst. Curr.Const. Imp.

Fig. 7 Voltage regulation for diVerent capacitor compensation levels.

Conclusions

This paper demonstrates how voltage regulation calculations in distributionsystems vary with different static load models. Systems with constant powerload models present high voltage drops along a feeder, and thus high voltageregulation, followed by systems with constant current load models and thenby systems with constant impedance load models. Hence, it is important to



choose the load models more suitable for a given system in order to obtainaccurate results.Shunt capacitor compensation improves system voltage regulation for all

types of loads. However, different sizes of shunt capacitors are required fordifferent types of static load models to achieve proper voltage regulations. Byproperly selecting the load models, efficient designs can be obtained for varcompensation in distribution systems.

References

1 T. Gonen, Electric Power Distribution System Engineering (McGraw Hill, New York, 1986).

2 G. T. Heydt, Electric Power Quality, 2nd edn (Stars in a Circle Publications, West LaFayette,

IN, 1991).

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models effects’, IEE Proc. C, 134(1) (1987), 27–30.

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(1977) 162–165.

5 M. H. Haque, ‘Load flow solution of distribution systems with voltage dependent load

models’, Int. J. Electric Power System Res., 36 (1996), 151–156.

6 T. Van Cutsem and C. Vournas, Voltage Stability of Electric Power Systems, Power Electronics

and Power System Series, Kluwer, 1998.

7 J. D. Glover and M. Sarma, Power System Analysis and Design, 2nd edn (PWS Publishing

Company, Boston, 1993).

8 C. G. Renato, ‘New method for the analysis of distribution networks’, IEEE T rans. Power

Delivery, 5 (1) (1990), 391–396.

9 D. Das, H. S. Nagi, and D. P. Kothari, ‘Novel methods for solving radial distribution

networks’, IEE Proc. Generation T ransmission and Distribution, 141(4) (1994).

10 M. M. A. Salama and A. Y. Chikhani, ‘A simplified network approach to the var control

problem for radial distribution systems’, IEEE T rans. Power Delivery, 8(3) (1993), 1529–1535.

11 C. A. Canizares et al., ‘PFLOW: continuation and direct methods to locate fold bifurcations

in AC/DC/FACTS power systems’, University of Waterloo, August 1998. Available at

http://www.power.uwaterloo.ca.


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distribution system voltage regulation and var compensation for differen static load models.pdf