Optimal Placement Of Dg

1

Optimal Placement and Sizing of Distributed Generation on Radial Feeder with Different Static Load Models Tuba GÖZEL

M. Hakan HOCAOGLU

Abstract--Due to the increasing interest on renewable sources in recent times, the studies on integration of distributed generation to the power grid have rapidly increased. In order to minimize line losses of power systems, it is crucially important to define the size and location of local generation to be placed. There have been studies, to define the optimum location of distributed generation. Additional to the current studies in the literature, in this study, the optimum size and location of distributed generation that will be placed in the radial system will be defined by an analytical method so as to minimize total power loss for the uniformly, centrally and increasingly distributed system profile. Additionally the analytical approach will also be evaluated against classical grid search algorithm for different load models.1 Index Terms-- distributed generation, radial systems, power loss, optimal placement, static load models

I. INTRODUCTION In recent times, due to the increasing interest on renewable sources such as; hydro, wind, solar, geothermal, biomass and ocean energy, all over the world, the number of studies on integration of distributed resources to the grid have rapidly increased. Distributed generation (DG), which consists of distributed resources, can be defined as electric power generation within distribution networks or on the customer side of the network [1]. DG affects the flow of power and voltage conditions at customers and utility equipment. These impacts may manifest themselves either positively or negatively depending on the distribution system operating characteristics and the DG characteristics. Positive impacts are generally called “system support benefits”, and include: voltage support and improved power quality; loss reduction; transmission and distribution capacity release; improved utility system reliability. On account of achieving the above benefits, the DG must be reliable, dispatchable, of the proper size and at the proper locations [2], [3]. Energy cost of distributed resources as compared to fossil resources is generally high whereat the factors of social and environmental benefits could not be included in cost account. Accordingly, most of the studies to determine the optimum

Ulas EMINOGLU

Abdulkadir BALIKCI

location and size of DG for minimum power loss could not take generation cost into account. In order to minimize line losses of power systems, it is crucially important to determine the size and location of local generation to be placed. There have been number of studies to define the optimum location of DG. The mathematical approaches on the optimum DG placement for minimum power losses are as follows: optimal load flow with second order algorithm method [4], genetic algorithm and Hereford Ranch algorithm which can find optimum [5], Fuzzy-GA method [6], tabu search approach [7], the algorithm to determine the near optimal [8], 2/3 rule, which is often used in capacitor placement studies [9], and analytical approach in radial as well as networked systems [10]. Particularly, reference [10] demonstrates an analytical approach to determine exclusively the optimal location to place a DG in radial systems to minimize the total loss of the system. This study takes the size of DG as total load size and in respect of the size of DG obtains the optimal location of DG in radial systems without optimizing size of DG. In all of the studies, cited above [4]-[10], the loads are generally modeled as constant power or constant current types of loads. Since most of the distribution system loads are uncontrolled, effects of this type of load models on optimum sizing and location should be questioned. Accordingly, in this paper, an analytical approach, which is used to optimally size and locate the DG to the radial systems, will be parametrically analyzed by giving particular emphasis to the effects of load models. The study, presented in this paper, undertakes an analysis on the effects of the load modeling to the optimal placement and size of DG in a radial feeder which is determined using the analytical approach [10] to minimize the power losses for uniformly, centrally and increasingly distributed load profile. In order to do so, a radial feeder is simulated with different load types to examine the system loss and voltage profile. The values of DG size and placement for minimizing power loss which is determined by the analytical approach is validated against the results obtained by the classical grid search algorithm for each types of loads. II. THEORETICAL ANALYSIS

This work is supported by State Planning Organization of Turkey (Project No: 2003K120530).

To simplify the analysis, transmission lines with uniformly distributed parameters are considered, R and L per unit length

2 are the same along the feeder while shunt capacitor (C and G) per unit length are neglected. Loads are distributed along the line with the phasor current density Id(x). The phasor feeder current at point x is x (1) I ( x) = Id ( x)dx

∫

For uniformly distributed load profile, the phasor current density Id(x) can be used (8). Besides, for centrally and increasingly distributed load profile, the phasor current densities Id(x) can be taken (9) and (10) to calculated total power loss with.

0

Assuming the per unit length impedance of the line is Z=R+jX (Ω/km), the length of line is u, the end of line is chosen as reference. Thus, the total power loss is

Id ( x) = I

(8)

2

u x  Ploss = ∫  ∫ Id ( x) dx  .Rdx   0 0 

(2)

The voltage drop between point x and receiving end can be calculated by using (3). x x

Vdrop( x) =

∫ ∫ Id ( x)dx.Zdx

  I .x Id ( x) =    I .(u − x)

0≤ x≤u/2

(9)

u/2≤ x≤u

(3)

0 0

Consider a DG is added into the feeder at the location x0, as injected current source Idg. When the change in the load current density, resulted from the addition of DG, is neglected, the feeder current after adding DG can be written as follows:  x  ∫ Id ( x ) dx  I ( x ) =  x0  Id ( x ) dx − Idg  ∫0

0 ≤ x ≤ x0

(4)

x0 ≤ x ≤ u

Power loss and voltage drop after adding DG is obtained from (4). The total power loss and voltage drop in the feeder are given in (5) and (6) respectively. 2

2

x0 x u  x   Ploss = ∫  ∫ Id ( x) dx  .Rdx + ∫  ∫ Id ( x)dx − Idg  .Rdx     x 0 0 0 0  

xx 0 ≤ x ≤ x0  ∫ ∫ Id ( x)dx.Zdx  Vdrop( x) =  x00 x0 x x  Id ( x)dx.Zdx + ( Id ( x)dx − Idg )Zdx x0 ≤ x ≤ u ∫∫ ∫∫ x0 0  0 0

(5)

(6)

The goal is to minimize total power loss in the system by adding a DG on a particular point with optimum size. The objective is to minimize power losses, Ploss, in the system by injected current, Idg, from a particular place, x0. The main constraints are to restrain the voltages along the feeder within 1±0.05pu and maximum DG size must be selected as total load size ( ∑ I load ). d Ploss dIdg

0

(10)

The derivations of total power loss per size of DG, Idg, and location of DG, x0, are obtained for all distributed load profile. The values of the derivations, being equal to zero, are found out as the optimal size and placement of DG. B. The Results of Theoretical Analysis Optimal Size and Placement for adding DG The solution of (7) for the uniformly distributed system 2

A. Determination of Optimal Size and Placement for added DG

d Ploss dx0

Id ( x) = I .(u − x)

(7)

Optimal placement and sizing of DG is determined by using (7) then the voltages along the feeder are checked to be within the acceptable range. If the voltages along the feeder are not satisfied, optimal sizing and placement of DG are changed to the nearest values to take the feeder voltages to the voltage limits.

gives that the optimal size of DG is determined as 3 I.u by analytically and its size equals to 67% of the total load. Accordingly, it is obtained that for centrally distributed and increasingly distributed systems, the optimum size of DG equals to 80% of the total load size. The optimal placement of DG is provided such as 0.33, 0.446 and 0.225 of radial feeder length from the end of the feeder for uniformly, centrally and increasingly distributed system, respectively. Fig. 1 shows that for each system (uniformly, increasingly and centrally distributed load profile) the optimal placement of DG, x0 curve, which changes with the size of DG from zero to total load size, total power loss, Plossx0 curve, which corresponds the optimal placement of DG, x0 curve, in the same way the optimal size of DG, Idg curve, which changes with the placement of DG from the receiving end (zero) to the sending end (u, the length of line), total power loss, PlossId, curve, which corresponds the optimal size of DG, Idg curve. The intersection point of the x0 curve and the Idg curve is the optimal size and placement for placing DG. In Fig 1, this intersection point is shown as the minimum of the Plossx0 curve and PlossIdg curve.

3 In Table 1, theoretical results of optimal placement and size of DG to minimize power loss are given for each distributed system. The total power loss of the each distributed system decreases when DG is located by optimally as demonstrated in [10]. Moreover, when the size of DG is optimized, the decrease on the power losses becomes more significant. For the optimal placing of DG with and without optimal size, it is seen that optimal placement of DG affected by the load profile when DG is located by optimally with its optimal value. On the other hand, optimal placement of DG is the same for the uniformly and centrally distributed load profile when only optimal location of DG is used. (a) Uniformly distributed load profile

III. STATIC LOAD MODELS Load models, used in power system studies, are classified into two categories: static models and dynamic models. Static load models for active and reactive power are expressed in a polynomial or an exponential form. The characteristic of the exponential load models can be given as: V P = Po   Vo

np

  , 

V Q = Qo   Vo

  

nq

(11)

Where np and nq stand for load exponents, Po and Qo stand for real and reactive powers at the nominal voltage. V and Vo stand for load bus voltage and load nominal voltage, respectively. Special values of the load exponents can cause specific load types such as 0: constant power 1: constant current 2: constant impedance. The values of these coefficients are determined for different load types in transmission and distribution systems. Usually data, determined from experience, could be used for the estimation. Common values for the exponents of static load model for different load components are given in Table 2.

(b) Centrally distributed load profile

(c) Increasingly distributed load profile Fig. 1 The optimal placement and size for adding DG and total power loss TABLE 1 THEORETICAL ANALYSIS RESULTS OF A RADIAL FEEDER WITH DIFFERENT LOAD TYPES Without DG

Load Types

With DG calculated upon optimal placement Optimal placement of DG (x0)

Percent of power loss reduction (%)

Total power loss

Total power loss

Uniformly Distributed Load

I 2 Ru3 / 3

I 2 Ru 3 / 12

υ/2

%75.00

Centrally Distributed Load

23 I 2 Ru 960

I 2 Ru 5 / 320

υ/2

%86.96

Increasingly Distributed Load

0.133I 2 Ru 5

0.0155I 2 Ru5

0.29.υ

%88.39

5

With DG calculated upon optimal placement and size Total power loss 1 2 3 I Ru 27

2.10−3 I 2 Ru 5

9.4.10−3 I 2Ru5

Optimal placement of DG (x0)

Optimal size placement of DG (x0)

Percent of power loss reduction (%)

1 u 3

2 I.u 3

%88.89

0.446.υ

1 2 I .u 5

%91.52

0.225.u

2 2 I .u 5

%92.95

4 TABLE 2 COMMON VALUE OF EXPONENTS FOR DIFFERENT STATIC LOAD MODELS [11], [12]

Load Component Battery Charge Fluorescent Lamps Constant Impedance Air Conditioner Constant Current Pumps, Funs other Motors Compact Fluorescent Lamps Small Industrial Motors Constant Power

np 2.59 2.07 2 0.5 1 0.08 0.95-1.03 0.1 0

nq 4.06 3.21 2 2.5 1 1.6 0.31-0.46 0.6 0

Exponential load modelsmay be valid for only a limited voltage range, which are ± 10% of 1 pu voltage level. For the high and low voltage magnitude levels, the models are inadequate for some load type i.e. motors and lighting [11][13]. The load types have important effects of the power system studies such as; power flow analysis and voltage stability. Traditionally, most of the conventional load flow methods, for transmission and distribution systems, use the constant-power load model. The constant power load model is highly questionable, especially for a distribution system where most of the buses are uncontrolled. For this reason, static load models, given in (11), are more important and it must be taken into distribution systems analysis such as determination of the optimal size and placement for adding DG in radial systems. IV. SIMULATIONS AND ANALYSIS A radial feeder with 13-bus, as shown in Appendix Fig A1, is used as a test network to analyze the effects of load modeling on the optimum size and location of DG by varying load exponents from 0 to 10 having load profile with uniformly, centrally and increasingly distributions. A power flow algorithm, developed for radial distribution systems with voltage sensitive loads [13], is employed for the solution. System parameters, load sizes for all load types and total load sizes are given in Appendix Table A1. Two different cases are examined. In the first case, optimal placement is obtained by adding DG, whose size is equal to the size of total load to minimize power loss (OPDG). In the second case, optimal placement and size for adding DG is obtained (OPSDG). OPDG and OPSDG are calculated by a grid search algorithm for each load model. General flowchart for grid search algorithm to minimize power losses is shown in Fig. 2. The grid search algorithm is applied by adding DG to each bus, changing the size of DG from 0% of total load power to 100% of total load power DG in the ratio of 10% and varying load exponents from 0 to 10 having load profile with uniformly, centrally and increasingly distributions. The optimal size and placement of placing DG to minimize power loss is determined. Thereafter, the voltages along the feeder are checked to be in acceptable range. If the voltages are not

satisfied the optimum values are omitted and again the optimum values are searched at the voltage limits. The same flowchart is applied for OPDG without changing DG size. In Table 3, optimal values for different static load models are shown. For OPSDG, optimal DG’s size is decreased in all distribution types when load voltage dependence is increased. Optimal location remains unchanged in centrally distributed profile. In uniformly and increasingly distributed types, optimal location is shifted one bus from the source. For OPDG, optimal location can not be determined with high voltage dependent loads. On account of at high voltage dependent loads the voltages along the feeder go beyond to the limit and the system power loss with OPDG is more than the case without DG. BEGIN

SET system param eters

FO R np=nq=0:10 (np, nq load exponents)

FO R x0=1:N (x0=bus no for adding DG) (N=total bus number)

FOR idg=0:ΣPload (idg=D G size ΣPload=total load ) Calculate power flow and pow er loss

Find m inimum power loss O m it unsuitable values 0.95pu≤V ≤1.05pu are all bus voltages in acceptable range?

Y es Determ ine x0, idg for m inimum power loss

Print all optim al values for np=nq=0:10

END

Fig. 2 General flowchart of grid search algorithm

No

5 TABLE 3 OPTIMAL SIZE AND PLACEMENT FOR PLACING DG WITH DIFFERENT STATIC LOAD MODELS

Power losses, given in Fig. 3, are calculated according to different placement along the feeder and different sizing of DG with constant power, current and impedance for each distributed load profile. From Fig. 3, it is seen that optimal size and placement of DG reach an agreement with the theoretical analysis for constant power, current and impedance load models. V. CONCLUSION (a)

Uniformly distributed load profile

(b)

Centrally distributed load profile

This study presents and evaluates an analytical method which is used to determine the optimal placement and sizing of DG in a radial feeder, so as to minimize total power loss for the uniformly, centrally and increasingly distributed system profile. The optimal size and location of the DG, which is determined by the analytical approach detailed here, is also evaluated against classical grid search algorithm for different load models. It is indicated that; optimal size and placement of DG are different for each distributed load profile; optimal size and placement of the theoretical analysis are valid for constant power, current and impedance load models. It is found that while optimum size of the DG is heavily under influence of the load models, the optimum location does not change with the chosen model. In this study, the optimal size and placement of DG with various load types are determined for different static load models. In practice, the load profile is not as given in this study even so general information concerning sizing and placement of DG is assured. The determination of the optimal size and placement for multiple DGs, and with a networked system will be undertaken by considering the other constraints as a future work.

(c) Increasingly distributed load profile Fig. 3 Total power losses in respect of placing DG each size and location with constant power, current and impedance

6 VI. APPENDIX

Fig. A1 .A Radial Feeder TABLE AI PARAMETERS OF THE SYSTEM IN FIGURE 2

Line Parameters Load Profile Uniformly distributed Centrally distributed Increasingly distributed

R = 0.538 Ω/km X = 0.4626 Ω/km R=0.8608 pu X=0.74016 pu Line length between two buses : 2.5km Bus Voltage = 12.5 kV Load at each bus [MW] 1 2 3 4 5 6 7 8 9 10 11 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.06 0.12 0.18 0.24 0.3 0.36 0.42 0.36 0.3 0.24 0.18 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.3 0.33 0.36 0.39

VII. REFERENCES [1] [2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12] [13]

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12 0.3 0.12 0.42

13 0.3 0.06 0.45

Total Load [MW] 3.9 2.94 3.51

VIII. BIOGRAPHIES Tuba Gözel was born in Konya in Turkey. She received the B.Sc degree in Electrical-Electronics Engineering from Selcuk University in 1994 and M. Sc degree in ElectricalElectronics Engineering from Gebze Institute of Technology in 2002. She has worked as research assistant and has continued to Ph.D. program at the same institute. M. Hakan Hocaoglu was born in Hatay in Turkey. He received the B.Sc. and M.Sc. degrees from Marmara University, Turkey. He obtained the Ph.D. degree in 1999 from Cardiff School of Engineering, UK. From 1988 to 1993, he worked at Gazinatep University, Turkey as a Lecturer. Since 1999, he has been with the Electronics Engineering Department of Gebze Institute of Technology, Turkey as an Assistant Professor. He is a member of IEE. Ulas Eminoglu was born in Kars in Turkey, on November 25, 1978. He received the B. Sc degree in Electrical-Electronics Engineering from Inonu University in 2000 and M. Sc degree in Electrical-Electronics Engineering from Nigde University in 2003. He joined Gebze Institute of Technology in 2003 as research assistant and has studied distribution systems load flow analyses and power electronics. He has continued to Ph.D. program at the same institute from 2003. Abdulkadir Balikci was born in Kahramanmaras, Turkey. He received his B.Sc. degree from Gazi University, Ankara, Turkey in 1992. From 1994 to 2003, he pursued his M.Sc. and Ph.D. degrees in the Department of Electric and Computer Engineering, Polytechnic University, Brooklyn, New York. He received his M.Sc. Degree in January 1997 and his Ph.D. Degree in June 2003. He is currently working at Gebze Institute of Technology, Gebze, Turkey as an Assistant Professor.