An Analytical Approach For Dg Allocation In Primary Distribution Network

Electrical Power and Energy Systems 28 (2006) 669–678 www.elsevier.com/locate/ijepes

An analytical approach for DG allocation in primary distribution network Naresh Acharya, Pukar Mahat, N. Mithulananthan

*

Electric Power System Management, Energy Field of Study, Asian Institute of Technology, P.O. Box 4, Klong luang, Pathumthani 12120, Thailand Received 22 March 2005; received in revised form 15 December 2005; accepted 24 February 2006

Abstract This paper proposes an analytical expression to calculate the optimal size and an effective methodology to identify the corresponding optimum location for DG placement for minimizing the total power losses in primary distribution systems. The analytical expression and the methodology are based on the exact loss formula. The effect of size and location of DG with respect to loss in the network is also examined in detail. The proposed methodology was tested and validated in three distribution test systems with varying size and complexity. Results obtained from the proposed methodology are compared with that of the exhaustive load flows and loss sensitivity method. Results show that the loss sensitivity factor based approach may not lead to the best placement for loss reduction. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Distributed generation; Exact loss formula; Optimum size; Optimum location; Sensitivity factors

1. Introduction The share of distributed generators (DGs) in power systems has been slowly increasing in the last few years. According to CIGRE report [1], the contribution of DG in Denmark and the Netherlands has reached 37% and 40%, respectively, as a result of liberalization of power market in Europe. Electric Power Research Institute’s (EPRI) study forecasts that 25% of the new generation will be distributed by 2010 and a similar study by the Natural Gas Foundation believes that the share of DG in new generation will be 30% by the year 2010 [2]. The numbers may vary as different agencies define DG in different way, however, with the Kyoto protocol put in place where there will be a favorable market for DG that are coming from ‘‘Green Technologies,’’ the share of DG would increase and there is no sign that it would decrease in near future. Moreover, the policy initiatives to promote DG through*

Corresponding author. Tel.: +66 2 524 5405; fax: +66 2 524 5439. E-mail address: [email protected] (N. Mithulananthan).

0142-0615/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2006.02.013

out the world also indicate that the number will grow rapidly. As the penetration of DG in distribution system increases, it is in the best interest of all players involved to allocate DG in an optimal way such that it will reduce system losses and hence improve voltage profile. Studies have indicated that inappropriate selection of location and size of DG, may lead to greater system losses than the losses without DG [3,4]. Utilities already facing the problem of high power loss and poor voltage profile, especially, in the developing countries cannot tolerate any increase in losses. By optimum allocation, utilities take advantage of reduction in system losses; improve voltage regulation and improvement in reliability of supply [3–5]. It will also relieve capacity from transmission and distribution system and hence, defer new investments, which have a long lead-time. DG could be considered as one of the viable options to ease some of the problems (e.g. high loss, low reliability, poor power quality, congestion in transmission system) faced by the power systems, apart from meeting the energy demand of ever growing loads. In addition, the

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modular and small size of the DG will facilitate planner to install it in a shorter time frame compare to the conventional solution. It would be more beneficial to install DG in the present utility setup, which is moving towards a more decentralized environment, where there is a larger uncertainty in demand and supply. However, given the choices they need to be placed in appropriate locations with suitable sizes. Therefore, tools are needed to be developed to examine locations and sizing of such DG installation. The optimum DG allocation can be treated as optimum active power compensation, like capacitor allocation for reactive power compensation. DG allocation studies are relatively new, unlike capacitor allocation. In Ref. [6,7], power flow algorithm is presented to find the optimum DG size at each load bus assuming every load bus can have DG source. Such methods are, however, inefficient due to a large number of loadflow computations. The genetic algorithm (GA) based method to determine size and location is used in [8–10]. GA is suitable for multi-objective problems like DG allocation and can give near optimal results, but they are being computationally demanding and slow in convergence. In Ref. [11], analytical method to place DG in radial as well as meshed systems to minimize power loss of the system is presented. In this method separate expressions for radial and network system are derived and a complex procedure based on phasor current is proposed to solve the location problem. However, this method only optimizes location and considers size of DG as fixed. In this paper, an analytical expression to calculate optimum size and an effective methodology to identify the optimum location for DG placement are proposed. The methodology is computationally less demanding. The DG is considered to be located in the primary distribution system and the objective of DG placement is to reduce the losses. The cost of DG and the other associated benefits have not been considered while solving the location and sizing problem. The sizing and placement of DG is based on single instantaneous demand at peak, where the losses are maximum. The proposed methodology is suitable for allocation of single DG in a given distribution network. The rest of the paper is organized as follows: Section 2 gives a brief introduction to distributed generation, including definition, characteristic and applications. Section 3 presents the importance of selection of proper location and size of DG for minimizing distribution losses. A widely used loss sensitivity factor method is presented in Section 4. A novel and fast methodology for determining the optimum size and location of DG in distribution network is described in Section 5. Section 6 portrays the test distribution systems used in the paper. A brief summary of the software tool used to obtain the result also included in this section. Numerical results along with some observations and discussions are presented in Section 7. Finally, the major contributions and conclusions of the papers are summarized in Section 8.

2. Distributed generation Distributed generation is an electric power source connected directly to the distribution network or customer side of the meter [12]. It may be understood in simple term as small-scale electricity generation. The definition of distributed generation takes different forms in different markets and countries and is defined differently by different agencies. International Energy Agency (IEA) defines Distributed generation as generating plant serving a customer on-site or providing support to a distribution network, connected to the grid at distribution-level voltages [12]. CIGRE defines DG as the generation, which has the following characteristics [1]: It is not centrally planned; It is not centrally dispatched at present; It is usually connected to the distribution network; It is smaller than 50–100 MW. Other organization like Electric Power Research Institute defines distributed generation as generation from a few kilowatts up to 50 MW [13]. In general, DG means small scale generation. There are a number of DG technologies available in the market today and few are still in research and development stage. Some currently available technologies are reciprocating engines, micro turbines, combustion gas turbines, fuel cells, photovoltaic, and wind turbines. Each one of these technologies has its own benefits and characteristics. Among all the DG, diesel or gas reciprocating engines and gas turbines make up most of the capacity installed so far. Simultaneously, new DG technology like micro turbine is being introduced and an older technology like reciprocating engine is being improved [12]. Fuel cells are technology of the future. However, there are some prototype demonstration projects. The costs of photovoltaic systems are expected to falling continuously over the next decade. This all underlines the statement that the future of power generation is DG. Supplying peaking power to reduce the cost of electricity, reduce environmental emissions through clean and renewable technologies (Green Power), combined heat and power (CHP), high level of reliability and quality of supplied power and deferral of the transmission and distribution line investment through improved loadability are the major applications of the DG [14]. Other than these applications, the major application of DG in the deregulated environment lies in the form of ancillary services. These ancillary services include spinning and non-spinning reserves, reactive power supply and voltage control etc. [15]. DG also has several benefits like reducing energy costs through combined heat and power generation, avoiding electricity transmission costs and less exposure to price volatility. Though the DG is considered as a viable solution to most of the problems that today’s utility are facing, there are many problems (e.g. DG integration into grid, pricing, change in protection scheme, nuisance tripping etc.) that need to be addressed. Furthermore, the type of DG technology adopted will have significant bearing on the solution approach. In this study, DGs capable of supplying real power only are considered.

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3. Location and sizing issues Fig. 1 shows a 3D plot of typical power loss versus size of DG at each bus in a distribution system. From the figure, it is obvious that for a particular bus, as the size of DG is increased, the losses are reduced to a minimum value and increased beyond a size of DG (i.e. the optimal DG size) at that location. If the size of DG is further increased, the losses starts to increase and it is likely that it may overshoot the losses of the base case. Also notice that location of DG plays an important role in minimizing the losses. The important conclusion that can be drawn from Fig. 1 is that, given the characteristics of the distribution system, it is not advisable to construct sufficiently high DG in the network. The size at most should be such that it is consumable within the distribution substation boundary. Any attempt to install high capacity DG with the purpose of exporting power beyond the substation (reverse flow of power though distribution substation), will lead to very high losses. So, the size of distribution system in term of load (MW) will play important role is selecting the size of DG. The reason for higher losses and high capacity of DG can be explained by the fact that the distribution system was initially designed such that power flows from the sending end (source substation) to the load and conductor sizes are gradually decreased from the substation to consumer point. Thus without reinforcement of the system, the use of high capacity DG will lead to excessive power flow through small-sized conductors and hence results in higher losses. Based on this the DG allocation can be handled by resolving the sizing issue first followed by the location issue. However, existing technique such as loss sensitivity method finds the location issue before and sizing issue. This may not result

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in the best choice. A brief description of loss sensitivity factor method and associated problems are presented below. 4. Loss sensitivity factor method Sensitivity factor method is based on the principle of linearization of original nonlinear equation around the initial operating point, which helps to reduce the number of solution space. Loss sensitivity factor method has been widely used to solve the capacitor allocation problem [16]. Its application in DG allocation is new in the field and has been reported in [4]. 4.1. Loss sensitivity The real power loss in a system is given by (1). This is popularly referred to as ‘‘exact loss’’ formula [17]. PL ¼

N X N X ½aij ðP i P j þ Qi Qj Þ þ bij ðQi P j  P i Qj Þ i¼1

ð1Þ

j¼1 r

r

where aij ¼ V iijV j cosðdi  dj Þ, bij ¼ V iijV j sinðdi  dj Þ and rij + jxij = Zij are the ijth element of [Zbus] matrix with [Zbus] = [Ybus]1. The sensitivity factor of real power loss with respect to real power injection from DG is given by ai ¼

N X oP L ¼2 ðaij P j  bij Qj Þ oP i i¼1

ð2Þ

Sensitivity factors are evaluated at each bus, firstly using the values obtained from the base case power flow. The buses are ranked in descending order of the values of their sensitivity factors to form a priority list. The top-ranked buses in the priority list are the first to be studied alternatives location. This is generally done to take into account of the effect of nonlinearities in the system. The first order sensitivity factor are based on linearization of the original nonlinear equation around the initial operating condition and is biased towards function which has higher slope at the initial condition, that might not identify the global optimum solution. This condition is depicted in Fig. 2. Therefore, priority list of candidate location is prerequisite to get the optimum solution. Fig. 2 shows a probable case, captured from the trend of losses in Section 3. The curve with solid line has highest sensitivity factor at the initial operating condition than dotted curve, but does not give the lowest loss, as PL1 > PL2. It shows why the sensitivity factor may not give the optimum result if a number of alternative locations are not taken into account. 4.2. Priority list

Fig. 1. Effect of size and location of DG on system loss.

The sensitivity factor will reduce the solution space to few buses, which constitute the top ranked buses in the priority list. The effect of number of buses taken in priority

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losses the rate of change of losses with respect to injected power becomes zero. N X oP L ¼2 ðaij P j  bij Qj Þ ¼ 0 oP i j¼1

ð3Þ

It follows that aii P i  bii Qi þ

N X

ðaij P j  bij Qj Þ ¼ 0

j¼1;j6¼i

" # N X 1 b Q þ ðaij P j  bij Qj Þ Pi ¼ aii ii i j¼1;j6¼i

Fig. 2. Nonlinearity in loss curve.

where, Pi is the real power injection at node i, which is the difference between real power generation and the real power demand at that node: P i ¼ ðP DGi  P Di Þ

will have effect the optimum solution obtained for some system. For each bus in the priority list, the DG is placed and the size is varied from minimum (0 MW) to a higher value until the minimum system losses is found with the DG size. In this study, 30% of the total number of buses is considered in preparing the priority list for each case. The process is computationally demanding as one needs a large number of load flow solution. 4.3. Computational procedure Step 1: Run the base case load flow. Step 2: Find the sensitivity factor using Eq. (2) and rank the sensitivity in descending order to form priority list. Step 3: Select the bus with the highest priority and place DG at that bus. Step 4: Change the size of DG in ‘‘small’’ step and calculate loss for each by running load flow. Step 5: Store the size of DG that gives the minimum loss. Step 6: Compare the loss with the previous solution. If loss is less than previous solution, store this new solution and discard previous solution. Step 7: Repeat Step 4 to Step 6 for all buses in the priority list. 5. Proposed methodology In this section, a new methodology is proposed to find the optimum size and location of DG in the distribution system. This methodology requires load flow to be carried out only two times, one for the base case and another at the end with DG included to obtain the final solution. 5.1. Sizing at various locations According to Section 3, the total power loss against injected power is a parabolic function and at minimum

ð4Þ

ð5Þ

where, PDGi is the real power injection from DG placed at node i, and PDi is the load demand at node i. By combining (4) and (5) one can get (6). " # N X 1 P DGi ¼ P Di þ b Q  ðaij P j  bij Qj Þ ð6Þ aii ii i j¼1;j6¼i The above equation gives the optimum size of DG for each bus i, for the loss to be minimum. Any size of DG other than PDGi placed at bus i, will lead to higher loss. This loss, however, is a function of loss coefficient a and b. When DG is installed in the system, the values of loss coefficients will change, as it depends on the state variable voltage and angle. Updating values of a and b again requires another load flow calculation. But numerical result shows that the accuracy gained in the size of DG by updating a and b is small and is negligible. With this assumption, the optimum size of DG for each bus, given by relation (6) can be calculated from the base case load flow (i.e. without GD case). 5.2. Location to minimize losses The next step is to find the optimum DG location, which will give the lowest possible total losses. Calculation of loss with DG one at a time at each bus again requires several load flow solutions, as many as number of buses in the system. Therefore a new methodology is proposed to quickly calculate approximate loss, which would be used for the purpose of identifying the best location. Numerical result shows that approximate loss follows the same pattern as that calculated by accurate load flow. It means that, if accurate loss calculation from load flow gives minimum for a particular bus then, loss calculated by approximate loss method will also be minimum at that bus. This is verified by the simulation results shown in Figs. 9–11. What differs is the amount of losses, which is not a concern for identifying location. With this methodology one can avoid exhaustive computation and save time.

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5.3. Computational procedure Step 1: Run the base case load flow. Step 2: Find the optimum size of DG for each bus using Eq. (6). Step 3: Compute approximate loss using Eq. (1) for each bus by placing DG of optimum size obtained in step 2 for that bus. Add the injection from DG for that bus and use base case values for state variables. Step 4: Locate the bus at which the loss is minimum after DG placement. This is the optimum location for DG. Step 5: Run load flow with DG to get the final result.

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single line diagram of the test system is shown in Fig. 3. The second test system as depicted on Fig. 4 contains 33 buses and 32 branches. It is a radial system with the total load of 3.72 MW and 2.3 MVAR [18]. The third test system shown in Fig. 5 is the widely used 69 bus-68 branches radial system with the total load demand of 3.80 MW and 2.69 MVAR [19]. A computer program has been written in MATLAB 7 to calculate the optimum sizes of DG at various buses and approximate total losses with DG at different locations to identify the best location. A Newton–Raphson algorithm based load flow program is used to solve the load flow problem. 7. Simulation results

6. Test system and analytical tools

7.1. Sizes allocation

The proposed methodology is tested on three different test systems, of different sizes to show that it can be implemented in distribution systems of various configuration and size. The first system is a 30 bus-32 branches loop system with the total load of 4.43 MW and 2.72 MVAR [3]. A

Based on the proposed analytical expression, optimum sizes of DGs are calculated at various nodes for the three test systems. Figs. 6–8 show optimum sizes of DG at various nodes for 30, 33 and 69 bus distribution test systems, respectively. As far as one location is concerned, in a distribution

Fig. 3. Single line diagram of 30 bus distribution test system.

Fig. 4. Single line diagram of 33 bus distribution test system.

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Fig. 5. Single line diagram of 69 bus distribution test system.

5

Optimum DG Size (MW)

4

3

2

1

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Bus No.

Fig. 6. Optimum size of DG at various nodes for 30 bus distribution test system.

test system, corresponding figure would give the value of DG size to have a ‘‘possible minimum’’ total loss. Any regulatory body can use this as a lookup table for restricting the sizes of DG for minimizing the total power losses in the system. In 30 bus distribution test system, the optimum sizes ranging from 2.5 to 4.75 MW as shown in Fig. 6. The rang of DG sizes for the other two test systems at various locations are 0.3–4.0 MW and 0.1–4 MW, respectively. However, it is important to identify the location in which the total power loss is minimum. This can be identified with

the help of the approximate method described in subsection 5.2. 7.2. Location selection Figs. 9–11 show the approximate total power losses for 30, 33 and 69 bus distribution systems, respectively, with optimum DG sizes obtained at various nodes of respective systems. The figures also show the accurate loss. As can be from these figures the trend of the losses is captured with the help of approximate solution which is good enough

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675

5

Optimum DG Size (MW)

4

3

2

1

0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus No.

Fig. 7. Optimum size of DG at various locations for 33 bus distribution system.

Fig. 8. Optimum size of DG at various locations for 69 bus distribution system.

to identify the location that would lead to the least total power losses. Notice that approximated losses pattern of the system with optimum sizes of DG at various nodes follows the accurate losses in all the cases. In 30 bus distribution test system the best (optimum) location of DG is bus 12, where the total power losses reduced to 0.154 MW, as depicted in Fig. 9. The second best location is bus 27, where the total power losses is 0.156 MW, little higher than the first location.

In 33 bus distribution test system, the best location is bus 6 with a total power loss of 0.111 MW and the second best location is bus 7 with slightly higher total power losses as shown in Fig. 10. In 69 bus distribution test system the optimum location is obvious as shown in Fig. 10. The best location for DG installation is bus 61, in one of the lateral feeders, with a total power loss of 0.081 MW. The second best location in this test system is bus 62 with a total power loss of 0.083 MW. All these results are summarized in the next section.

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0.4

Approximate Loss Accurate Loss

Total Power Losses (MW)

0.35

0.3

0.25

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 DG Location Fig. 9. Approximate and accurate losses of 30 bus distribution test system.

0.22 Approximate Loss 0.2

Accurate Loss

Total Power Losses (MW)

0.18

0.16

0.14

0.12

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 DG Location Fig. 10. Approximate and accurate losses of 33 bus distribution test system.

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0.22

Total Power Losses (MW)

0.2

0.18

0.16

0.14

0.12

Approximate Loss

0.1

Accurate Loss

0.08

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

DG Location

Fig. 11. Approximate and accurate losses of 69 bus distribution test system.

sequent results apart from power quality and reliability improvement.

7.3. Summary Table 1 shows the summary of results, optimum location, corresponding optimum size of DG and total power loss with and without DG, of all the test systems. The reduction in real power loss for the three cases is 59.6%, 47.3% and 62.8%, respectively. As can be seen from results of various systems the location and size of DG play an important role in loss reduction of primary distribution systems. From the results obtained for the three systems one can conclude that by placing DG of optimum size at optimum location, significant reduction in loss can be achieved. Voltage profile improvement, reduction in thermal capacity of the main feeder and better voltage regulation are some con-

7.4. Comparison of results In this section, the traditional sensitivity approach for DG location selection is compared with the proposed approach and repeated load flow. Table 2 shows the best locations obtained from the loss sensitivity factor, proposed approach are repeated load flow or ‘‘exhaustive’’ approach. For the first two test systems the loss sensitivity approach is not able to identify the best locations, instead it picked up the second best location as its first choice in the 30 bus distribution test system and ninth optimum location as its first choice in the 33 bus distribution test system. This happens due to the linearization and approximation as explained Section 4. Table 2 also shows the optimum sizes of DG. The optimum sizes for locations bus 27 of 30 bus distribution system and bus 10 of 33 bus system can be verified from Figs. 6 and 7, respectively. In calculating the optimum sizes of DG at various locations, using Eq. (6), it was assumed that the values of

Table 1 Summary of the simulation results Test systems

Optimum location

Optimum DG size (MW)

Power loss (kW) Without DG

With DG

30 bus 33 bus 69 bus

Bus 12 Bus 6 Bus 61

3.3 2.49 1.81

383.61 211.20 219.28

154.87 111.24 81.44

Table 2 Comparison of the results of different approaches Test systems

30 bus 33 bus 69 bus

Loss sensitivity

Proposed approach

Repeated load flow

Optimum location

Optimum DG size (MW)

Real power loss (kW)

Optimum location

Optimum DG size (MW)

Real power loss (kW)

Optimum location

Optimum DG size (MW)

Real power loss (kW)

Bus 27 Bus 10 Bus 61

3.2 1.4 1.9

156.28 123.82 81.33

Bus 12 Bus 6 Bus 61

3.3 2.49 1.81

154.87 111.24 81.44

Bus 12 Bus 6 Bus 61

3.5 2.6 1.9

154.5 111.1 81.33

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variable remain unchanged. This is the reason why there is a small difference between the optimum size obtained from the proposed approach and repeated load flow. However, in reality, one would go for the closest size available in the market and these differences are within margin of error. 8. Conclusion Size and location of DG are crucial factors in the application of DG for loss minimization. This paper presents an algorithm to calculate the optimum size of DG at various buses and proposes a fast methodology to identify the best location corresponding to the optimum size for reducing total power losses in primary distribution network. The benefit of the proposed algorithm for size calculation is that a look up table can be created with only one power flow calculation and the table can be used to restrict the size of DG at different buses, with the view of minimizing total losses. However, if a DG is installed in the system, the look up table needs to be updated with new calculation. The proposed methodology for location selection correctly identifies the best location for single DG placement in order to minimize the total power losses. In practice, the choice of the best site may not be always possible due to many constraints. However, the analysis here suggests that the losses arising from different placement varies greatly and hence this factor must be taken into consideration while determining appropriate location. The paper also shows that the loss sensitivity factor approach for location selection may not lead to the best choice. References [1] CIGRE. Impact of increasing contribution of dispersed generation on the power system. Working Group 37.23, 1999. [2] CIGRE. CIGRE technical brochure on modeling new forms of generation and storage, November 2000. Available from: http:// microgrids.power.ece.ntua.gr/documents/CIRE-TF-380110.pdf. [3] Mithulananthan N, Oo Than, Van Phu Le. Distributed generator placement in power distribution system using genetic algorithm to reduce losses. TIJSAT 2004;9(3):55–62.

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