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University of Abertay Dundee UK. ABSTRACT. Recently, allocation transmission losses have become a major issue in both regulated and deregulated system.
Allocation of Transmission Losses using Three Different Proportional Sharing Methods

F. Ansyari, C. S. Özveren, D. King University of Abertay Dundee UK

ABSTRACT Recently, allocation transmission losses have become a major issue in both regulated and deregulated system. Two main reasons for this are performance and costs issues. Consequently, there have been a large number of investigations undertaken in the area of transmission loss allocation. These methods encompass a wide variety of techniques ranging from proportional sharing, pro-rata to incremental methods (marginal allocation, and unsubsidised marginal allocation). The issue of loss allocation is going to be at forefront of the discussions due to recent deregulation and privatisation attempts in Indonesia. In this paper after a brief statement of loss allocation problem we will provide a detailed comparison of three alternative algorithms from the proportional sharing (PS) approaches: Power Flow Tracing, Proportional Sharing Allocation, and Tracing Active - Reactive Power Flow method. A 4-bus simple meshed network will be used to test these methods. The results of the calculations will be compared with each other and then conclusions about the applicability of PS approach in Indonesia will be stated. Keywords: Transmission loss allocation, deregulated system, proportional sharing.

1. INTRODUCTION In a deregulated system, where transmission lines are operated by an independent system operator, transmission losses are charged proportionally to generators and loads (demands). Therefore, the accuracy of transmission losses allocation is a major issue for all market participants, as a fraction of differences in the calculation could mean a loss or gain of significant sums of income. On the other hand, in a regulated system similar to PT PLN, the Indonesian state electricity company’s, loss charging calculation is typically based on loss measurement at each sub-station. Therefore the transmission system operator is responsible for most of the losses, although the biggest loss contributors are actually the distribution system operators. The demands are proportionally charged to the losses depends on their consumption for different prices. The end users are not charged for these losses, and this situation does not really reflect the operational realities and constraints. In deregulated systems fairness of loss costing and charging mechanisms, where the biggest source of losses should be charged proportionally according to their loss levels, is one of the stated universal objectives. One of several ways to improve electricity business performances is by both calculating and

allocating transmission losses to each participant accurately and transparently. Allocation of the losses will directly influence cost incurred by each participant, which in turn will affect the participant’s business performance significantly. To date research conducted on calculating transmission losses can be grouped into 3 different groups: Pro-rata, Incremental marginal allocation and Proportional sharing allocation. The pro-rata allocation approach [4] allocates losses based on the amount of energy consumed by loads and produced by generators. The approach does not depend on the network and is unable to trace power flow. Consequently, the allocation would not be ‘fair’ for certain loads or generators. Generators do not obtain incentive although they are closed to loads and vice versa. The incremental marginal allocation [4] is based on the economic concept where a transmission network is described as a black box with injection points connected to it. The allocation uses loss coefficients calculated on the change in loss as a result of a change in bus injection. This method is highly dependent on the choice of slack bus and can produce negative and positive losses allocation to certain buses. The proportional sharing introduced by Bialek [2, 3] describes that each node as a perfect mixer

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2 where power flowing out of a node is reckoned to be the proportional sum of the power flowing into the node. This assumption is based on Kirchhoff’s current law and the current division principle.

PD1

This paper will investigate recently reported approaches of transmission losses allocation that can be classified under the proportional sharing principles: Acha et al’s method [1], Bialek’s method [2, 3], and Kirschen et al’s method [5, 6].

PD2

After determining the source dominions, including all the branches that belong to more than one dominion, the power contribution of the relevant dominions and/or local source to total branch flow and related nodes needs to be found. In each node, power contributions of the relevant dominions and/or local source to the node’s load need to be found as well. Finally, power losses in each dominion can then be calculated. Based on figure 1, the dominion’s contributions are obtained by the following equations.

Pmk' = PD' 1 + PD' 2 + ...PD' n + PG' ,

(1)

PD' i = PDi × C P' mk ,

(2)

' G

P = PG × C C P' mk =

' Pmk

,

(3) ' mk

P , PD1 + PD2 + ... + PDn + PG

(4)

P

mk

k

~

PG

PL

m

Figure 1. Contributions of active power dominions to branch mk

2. TRANSMISSION LOSS ALLOCATION METHODS OF PROPORTIONAL SHARING

In branches which are common to two or more dominions, proportionality is used to determine the power flow contribution of each dominion to the common branch.

''

mk

PDn

For a critical comparative evaluation, the chosen methods have been applied to a 4-bus network reported in [2, 3]. The results and comparative analysis of the simulations, presented with our conclusions for the Indonesian Electricity Supply Industry will be discussed in relevant sections of this paper.

2.1 Acha et al’s Method of Proportional Sharing The first method we are going to investigate was introduced by Acha et al where losses are allocated by using the concept of dominions [1] and described by the authors as power auditing algorithm. The concept of dominion is at the centre of the power tracing algorithm. A dominion is obtained from a load flow solution of the power network.

'

P

. . .

The equations above apply at the sending end of the branch. The contribution of the n inflows at receiving end of branch mk is determine by the following expressions:

Pmk'' = PD''1 + PD'' 2 + ... PD''n + PG'' ,

(5)

PD''i = PD i × C P''mk ,

(6)

PG' ' = PG × C

C P''mk = Where: PG :

'' P mk

,

Pmk'' , PD1 + PD2 + ... + PDn + PG

(7) (8)

Power produced by generator

C Pm : Contribution coefficients

PDi

:

Power contributions of domain

PL

: :

bus m Active power load 1,2, ……, n.

i

Di to

For the case of active load, that is PL , the variables

C PL and PPL replace C P''mk and Pmk'' respectively in equations (5) – (8). 2.2 Bialek’s Method of Proportional Sharing The second approach we have investigated, that uses Proportional Sharing principle to allocate transmission losses was reported by Bialek [2,3]. The following equations below explain the tracing of power upstream from the loads to the generating sources. Starting from a solved load flow solution, the power balance equation at node

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3

∑F

i considering the power inflows from “upstream” is defined by (9)

Pi g =

ijk

j

C ik =

∑P

g ij

+ PGi for I = 1,2,...,n

(13)

Ik

(9)

j∈α iu n

[ ]

Pi g = ∑ Au−1 ik PGk for i = 1,2,...,n

(10)

k =1

[A ]

−1 u ij

1  Pji = −  0 Pj 

Where the following notations have been used: Cij : Contribution of generator i to the load and the outflow of common j

for i = j for j = α iu otherwise

Cik : Contribution of generator i to the load and the outflow of common k : Flow on the link between commons j and k

F jk

Fijk : Flow on the link between commons j and k

g

Pi is the unknown gross nodal power flow through node i, in line i-j,

g ij

P is the unknown gross line flow

α iu is the set of nodes supplying node i,

and PGi is the power generation in node i. The line flows

due to generator i : Inflow of common k

Ik

The equations above are used to calculate the contribution of each generator to each common.

Pijg also can be expressed as a

proportion of the flows into the upstream node j. By continuing this process, the contribution of system’s generators to the i-th gross nodal power can be expressed according to (10). Au is the upstream distribution matrix and PGk

is the

generation at node k. 2.3 Kirschen et al’s Method of Proportional Sharing This method was introduced by Kirschen et al where a network was divided into the ‘domain’ of each generator. The domain of a generator is defined as set of busses that are reached by the power produced by this generator. Power from a generator reaches a particular bus if it is possible to find a path through the network, from the generator to the bus, for which the direction of travel is always consistent with the direction of the flow as computed by power flow programme.

3. CASE STUDY In this section, the three different methods will be used for investigating the impact of different loss allocation approaches. A 4-bus simple meshed network which is adapted from Bialek’s network [2, 3] will be used to test them and the results will be compared with each other (figure 2). 300

The computation of the contributions is governed by the following equations:

Fijk = Cij * F jk Ik =

∑F

jk

(11) (12)

200 82

218

L2

83

4 171

112

115 60

59 173

225 1 400 G1

This method also uses the assumption of proportionality which provides a basis of the recursive method for determining contribution of each generator to the load in each common.

L1

3

2 114 G2

Fig. 2: A 4-bus simple meshed network used to illustrate the comparisons 4. TEST RESULTS AND DISCUSSION 4.1 Result Table I shows that the results are actually same between the different algorithms where the losses are allocated to each line from each source (generator).

j

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4 TABLE I Losses Allocated To Each Line Using the Three Compared Loss Allocation Approaches

Branch

1-2 1-3 1-4 2-4 4-3 Total

Acha D1 D2 1.00

7.00 3.00 0.68 0.60 12.28

0 0 0 1.32 0.40 1.72

Methods Bialek G1 G2

Kirschen G1 G2

1.00 7.00 3.00 0.68 0.60 12.28

1.00 7.00 3.00 0.68 0.60 12.28

0 0 0 1.32 0.40 1.72

0 0 0 1.32 0.40 1.72

TABLE II Losses Allocated To Every Load Using the Three Compared Loss Allocation Approaches Load bus 1 2 Total

Methods Acha 9.76 4.24 14.00

Bialek 9.76 4.24 14.00

Kirschen 9.76 4.24 14.00

TABLE III Losses Allocated To Every Generating Bus Using the Three Compared Loss Allocation Approaches Generating bus 1 2 Total

Methods Acha 12.28 1.72 14.00

Bialek 12.28 1.72 14.00

Kirschen 12.28 1.72 14.00

The three different methods also allocate the losses to each load and generator which are shown in Table II and III.

Kirschen claims his algorithm facilitate systematic and intuitive understanding of the principles and also claims extremely first algorithm that does not require the inversion of the matrix and is therefore not limited by the inverted ability of the matrix. However the algorithm is effect an implicit matrix inversion. Both Acha’s power auditing algorithm based on the concept of dominions and Kirshen’s method based on the concept of domains are based on spanning trace like algorithms from the graph theory can be proven to be special cases of the Bialek’s approach which is based on the concept of connection matrix again from the general graph theory. All three methods require matrix inversion; however, Acha’s and Kirschen’s methods achieve this without having to explicitly form the matrix. 5. CONCLUSIONS From discussion above, the following conclusions can be drawn: 1. The proportional sharing principles are used by the three methods and always produce positive loss allocation. 2. All of the three methods will produce results with a same degree of accuracy if a software tool is used. 3. Although all methods produce the same results, it can not be proven that these methods are more accurate than other methods. 4. Matrix based Bialek’s method enable us to solve the allocation quicker due to its simplicity and suitability for matrix based numerical analysis methods. 5. Because of producing the same results, all of these approaches are appropriate for application in a regulated system such as the Indonesian Electricity Supply Industry.

4.2 Discussion These methods are based on proportionality principle and will not produce negative loss allocation. Possibility of the results of those methods to be different is merely due to roundingup process during calculation steps. However, it will be easier, faster, and more accurate if a special software tool is employed to solve allocation.

6. ACKNOWLEDGEMENT The authors express their gratitude to PT PLN, Indonesia state electricity company, for providing the financial resources that enabled these studies to be conducted

7. REFERENCES The differences of each method depend on how the calculations are arranged; that are dividing the network into several parts referring their sources, using matrix and step by step calculations from one node to another node in the network. All of these calculations will produce the same results.

1. Acha, E. et al. 2004. Facts: modelling and simulation in power networks: London. John Wiley & Sons Ltd.

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5 2. Bialek, J. 1996. Tracing the flow of electricity. IEE Proc. Generation, transmission and distribution. vol. 143. No 4. 3. Bialek, J. 1997. Topological generation and load distribution factors for supplement charge allocation in transmission open access. IEEE Transaction on Power Systems. 12. No 3. 4. Conejo, A. J. et al. 2002. Transmission loss allocation: a comparison of different practical algorithms. IEEE Transaction on Power Systems. vol. 17. No 3. 5. Kirschen, D. Allan, R., and Strbac, G. 1997. Contributions of individual generators to loads and flows. IEEE Transaction on Power Systems. 12. No 1. 6. Kirschen, D. and Strbac, G. 1999. Tracing active and reactive power between generators and loads using real and imaginary current. IEEE Transaction on Power Systems. 14. 4. AUTHORS' ADDRESS The authors can be contacted at School of Computing and Creative Technologies, University of Abertay Dundee, Scotland, UK Firman Ansyari Email: [email protected] C. S. Özveren, Email: [email protected] D. King Email: [email protected]

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