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A Novel Transmission Loss Allocation Method based on Transmission Usage

Baseem Khan, Ganga Agnihotri Department of Electrical Engineering

Maulana Azad National Institute of Technology Bhopal, India

baseem_khan04@yahoo.com, ganga1949@gmail.com

Abstract— In the present work authors presents a novel method for transmission loss allocation to users (generators and loads). In the proposed methodology transmission losses are allocated to users based on their usage of the transmission line. After usage allocation particular loss allocation indices (PLAI) are evaluated for loads and generators. The proposed method is simple and easy to implement on the large scale power system. Further a comparison is presented between proposed methodology and losses allocated by nucleolus approach.

Keywords-Transmission loss allocation; particular loss allocation indices; Nucleolus value

I. INTRODUCTION

Restructuring of electricity supply industry has taken place around the world. The main aim behind this restructuring is to introduce competition and increase efficiency and quality of services in this industry. Initially Indian power sector operated as a vertically integrated structure in which all the functions are governed and controlled by government. After the restructuring deregulation is introduced in the ESI (Electricity Supply Industry) industry. In India this process is started after the enactment of the electricity act 2003. After deregulation the regulated structure of the ESI is converted into a deregulated structure in which all the three major functions are performed by three separate companies namely GENCOS (Generation Company Ltd.), TRANSCO (Transmission Company Ltd) and DISCOMS (Distribution Company Ltd). Competition is introduced in the entire three sectors. Various IPP (independent power producer) come in the field of generation. They generate power and sell to the CTU (Central Transmission Utility) or TRANSCO. Similarly it is easy to introduce competition in distribution. But it is difficult to introduce competition in the transmission sector due to its monopolistic nature. It is not possible to build a separate transmission line for every generation facility. Hence transmission cost allocation is very complicated task in the deregulated environment. Several methodologies and their variants are presented to solve the problem of transmission pricing cost allocation till date.

There are various factors such as transmission embedded cost allocation, transmission loss cost pricing, congestion management etc. These should be considered before the introduction of competition in the electricity sector.

In this paper a novel transmission loss allocation method is presented. Many different loss allocation schemes proposed in this area but no single method gained universal

acceptance. The brief overview of loss allocation methods and comparative study can be found in [1]. The existing transmission loss allocation methods can classify into prorata method, marginal methods, power flow tracing based methods, and circuit theory based methods. Prorata method is one of the classical methods which are easy to implement and understand. It is characterized by the allocation of electric losses proportional to the power delivered by each generator and each load. It is also assumed an equal allocation 50% to generator and 50% of the loads. Regardless of the positive aspects, the main disadvantage of the method is that it does not take into account the transmission grid thus two identical loads located at different distances from the generators are treated in the same way [2]. In marginal procedure incremental transmission coefficients are used for allocation of transmission losses to demands and generators. Normalization is performed after the assignment because this allocation procedure typically results in over-recovery [3]. The use of power flow tracing methods for allocation of transmission losses is proposed in [4] and [5]. In this method proportional sharing principle is combined with load flow results. Certain assumptions also made in these methods. The methods based on circuit theory are simple and easy to implement. In this category method based on Z- bus matrix is proposed by A. J. Conejo et al. This method presents a new procedure for allocating transmission losses to generators and loads in the context of pools operated under a single marginal price derived from a merit-order approach. The procedure is based on the network Z-bus matrix [6]. The main difficulty in allocating losses to loads or generators to bilateral contracts by circuit theory is that, despite approximations the final allocations always contain a certain degree of arbitrariness. Recently several new algorithms and methods are also proposed such as in [14] a method based on complex power flow tracing is proposed. This method topologically determines the contribution of generators and loads to losses in transmission lines. In [8] author decomposed transmission losses into three components. Analytical proofs of the proposed loss decomposition are presented along with methods of allocating each component to the parties contributing to it. A method based on a combination of cooperative game theory and circuit theory is presented in [7]. A two step procedure is used for allocation of transmission losses. The Aumann Shapley method and circuit theory are used to calculate the participation of each real and imaginary components. In [9] a new algorithm is proposed for transmission loss allocation which is used path integral and based on transaction strategy. A new path integral method is developed by integrating the partial differential of the system loss along a path reflecting the transaction strategy. A usage based transmission loss allocation method

is proposed in [10]. This new method calculates the portion of real power transmission loss contribution from the generators and simultaneously the portion of the real power transmission loss allocated to the loads using their contract obligations with the generators in the open access environment. In [11] method based on circuit theory and the concept of orthogonal projection for pool based electricity market is proposed.

In this paper authors presents a method for transmission loss allocation. Transmission losses are allocated to users based on their usage of the transmission line. A comparison also presents between proposed method and nucleolus approach. The rest of the paper is organized as follows: section two presents the proposed method of loss allocation. Section three provides an overview of nucleolus approach. Fourth section presents results of the proposed methodology and nucleolus approach on an IEEE 6 bus system followed by a conclusion.

II. PROPOSED METHODOLOGY

Let represents the total number of line in the system. is total number of generators and

is total number of loads in the system. In the first step losses done by each generator (load) in each line is given by:

For loads particular loss allocation indices are:

Where

Hence total losses allocated to Load in all the transmission lines is given by:

Where

is the total loss allocated to load LT. In this proposed method authors allocated 77% losses to loads and 23% losses to generators [12].

III. NUCLEOLUS SOLUTION CONCEPT

The nucleolus is a solution concept introduced by Schmeidler in 1969. Two important characters of nucleolus are, respectively, 1) every game has one and only one nucleolus, and 2) unless the core is empty, the nucleolus is at the core.

The goal of using the nucleolus concept is to find a way to fairly allocate the power losses that are jointly created by all transactions. Suppose is the set of each transaction’s allocation losses, is the set of the loss allocation imputation, and is the loss

of the transaction coalition . The nucleolus is based on the minimum core and is represented by

Where represents an arbitrary small real number, is the coalition excess value of imputation ,

namely, is the maximum of excess value; and is the loss, which is created by the alternation of the member of transactions’ coalition S, namely

Use linear programming (LP) to solve (1), namely

Where is the coalition of all transactions, and is all nonempty sub coalitions of transactions [13].

The total loss allocation for each transaction should be the summation of the loss created by all transactions and one created by the individual transaction, namely

IV. RESULTS AND DISCUSSION

The proposed method is implemented on an IEEE 6 bus system. In this section results are discussed. The work follows the ratio for transmission loss allocation between generators and loads as 23%:77% in pool market. According to this trend the allocation of transmission loss has been splited in two parts: one for generators to allocate 23% of transmission loss and another for loads to allocate 77%.

TABLE I. LOSS ALLOCATION FOR IEEE 6 BUS SYSTEM

Loads Lines L4 (MW) L5 (MW) L6 (MW)

1-2 0.004392 0.0036402 0.000968 1-4 .00536659 0.004447 0.00119 1-5 0.005364 0.004444 0.00118 2-3 0 0 0 2-4 0.0064240 0.00365646 0.0059195 2-5 0.00240774 0.00137 0.0022219 2-6 0.0024091 0.00137045 0.002221 3-5 0 0.00359378 0.00841 3-6 0 0.0032975 0.0077 4-5 0 0 0 5-6 0 0.0009765 0.000024

Total 0.026363 0.026796 0.029834

Now the nucleolus solution concept is applied to an IEEE 6 bus system.

TABLE II. TRANSACTION DATA OF IEEE 6 BUS SYSTEM

Trans. No. user supplier Transactio

n Quantity 1 D4 G1 0.731

2 D5 G2 0.725

3 D6 G3 0.714

1&2 D4,D5 G1,G2 1.461

1&3 D4,D6 G1,G3 1.448

2&3 D5, D6 G2,G3 1.444

1,2&3 D4,D5,D6

G1,G2,G3 2.184

TABLE III. TRANSACTION LOSSES FOR IEEE 6 BUS SYSTEM

Transaction combination

Active power losses

1 0.031 2 0.025 3 0.014

1&2 0.061 1&3 0.048 2&3 0.044

1,2&3 0.084

A. Nucleolus solution for transmission losses allocation Equation (4) is used to calculate interaction losses ,

namely

Substitute values into (5); then

The solutions of (8) are

From (7), the active power loss allocation of each transaction, respectively, is

TABLE IV. COMPARISON BETWEEN PROPOSED METHODOLOGY AND NUCLEOLUS APPROACH

LOAD Proposed PLAI Approach Nucleolus Approach

L4 0.026363

L5 0.026796

L6 0.029834

V. CONCLUSION

In this paper authors proposed a new method for transmission loss allocation based on usage allocation. This method is simple and easy to implement in large power system. Further this method considers network topology hence avoid the problem of cross subsidy. Results allocated by this method are less volatile in nature as a comparison of marginal participation. This method provides information about load participation in every line. The method gives similar results as prorate method but eliminate its drawbacks. The result of the IEEE 6-bus system is given to demonstrate effectiveness of the proposed method through comparisons with nucleolus approach.

VI. REFERENCES

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[4] J. W. Bialek, “Topological generation and load distribution factors for supplement charge allocation in transmission open access,” IEEE Trans. Power Syst., vol. 12, pp. 1185–1193, Aug. 1997.

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[6] A. J. Conejo, F. D. Galiana, and I. Kockar, “Z-bus loss allocation,” IEEE Trans. Power Syst., vol. 16, pp. 105–110, Feb. 2001.

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