Transmission Loss Allocation Research Articles

Influence of the Operational Constraint in the Active Transmission Losses Allocation Via Lagrange Multipliers

This paper presents an approach for the active transmission losses allocation between the agents of the system. The approach uses the primal and dual variable information of the Optimal Power Flow in the losses allocation strategy. The allocation coefficients are determined via Lagrange multipliers. The paper emphasizes the necessity to consider the operational constraints and parameters of the systems in the problem solution. An example, for a 3-bus system is presented in details, as well as a comparative test with the main allocation methods. Case studies on the IEEE 14-bus systems are carried out to verify the influence of the constraints and parameters of the system in the losses allocation.

Comparison of Several Transmission Loss Allocation Procedures

Transmission-loss is an inherent nature of power system. Determination of transmission losses for the purposes of billing in various interconnected trans-actions is an important issue to be solved exactly. Loss allocation is a procedure for subdividing the system transmission losses into fractions, the cost of which becomes the responsibility of network users. This paper focuses on transmission loss allocation procedures and provides a detailed comparison of some alternative algorithms: viz. 1) Incremental loss allocation, 2) A proportional allocation, 3) Preliminary loss allocation and 4) A direct methodology for loss allocation. A case study based on a 6-bus model power system has been provided. Finally conclusions and recommendations have been stated. Key words: Transmission loss allocation, DC optimal power flow, Deregulated power market, Loss coefficient matrix, Non-volatile procedure. DOI: 10.3329/bjsir.v44i3.4401 Bangladesh J. Sci. Ind. Res. 44(3),289-296, 2009

Transmission Loss Allocation Algorithm Using Path-Integral Based on Transaction Strategy

This paper presents a new algorithm of accurate bus-wise transmission loss allocation based on path-integrals. With rigorous theoretical analysis, a new path-integral method is developed by integrating the partial differential of the system loss along a path reflecting the transaction strategy. This path-integral enables us to remarkably enhance the accuracy in loss allocation with full consideration of nonlinearity. The accuracy has been further improved by using the ac power flow. Determining the integral path is discussed to reflect various situations of the power market. Given an integral path, the proposed algorithm provides a unique and accurate solution to the loss allocation.

A Direct and Simplified Approach to Power-flow Tracing and Loss Allocation Using Graph Theory

Power-flow tracing and transmission loss allocation have become extremely important after the privatization of the electric power industry. This article presents a simple method for power-flow tracing and transmission loss allocation based on physical flow through transmission lines. It works on the principle of proportional sharing of power between the lines at each node and can be applied easily and directly, as it requires only a solved power flow and branch-bus flow-direction matrix. The method also determines the contribution of any generator/load in the line loss. It can trace both active and reactive power flow through the network for both generator and load. The main features of this method are its simplicity and fast performance.

Usage-based transmission loss allocation under open access in deregulated power systems

This study presents a usage-based methodology of transmission loss allocation in deregulated power systems under open access. This new approach calculates the portion of real power transmission loss contributions from the generators and simultaneously the portion of real power transmission loss allocated to the loads using their contract obligations with the generators in the open access environment. A power flow procedure is used to calculate power loss in the system. It is desirable to take network loss effect of injection power at each node for calculating contribution of transmission loss by each generator and loss allocated to loads based on its contractual obligations with consumer. In this study, a methodology is proposed to calculate the total real power loss in transmission network into components to be allocated to the generators and loads. This study focuses on development and application of the equivalent loss compensation concept for open access environment. Effectiveness of the proposed algorithms has been demonstrated on sample 5-bus and IEEE-118 bus power networks.

Generation scheduling in deregulated power market taking into account transmission loss allocation

Allocating means of transmission losses and costs are presented taking into account pool and bilateral contract hybrid deregulated power market. The transmission loss is allocated according to a mathematical relationship between the node power and the line power flow for a DC power network. By the proposed method, the authors not only can allocate total loss to either generator or load node, respectively, but also can distribute it to both generator and load nodes conveniently. To ascertain the effectiveness of the proposed techniques, the authors show various simulation results based on IEEE 14-bus and Hokkaido 44-bus power systems.

Transmission Loss Allocation Based on Circuit Theories and Orthogonal Projection

This paper presents a loss allocation method based on the circuit theories and the concept of orthogonal projection for pool-based electricity markets. The method first defines the current projection component to determine the share of a generator or load on the current through a branch. Then the power flow through each branch is decomposed and the branch loss allocation is obtained. One feature of the method is that it gives intuitively clear explanation of the obtained loss allocation. The two equivalence modes of bus power injections are also discussed. The analysis shows that the equivalence that loads (generators) are converted into equivalent admittances when generators (loads) are converted into current injections reflects the practical situation and thus it is more reasonable and preferable. Comparisons with other methods and validation tests of the proposed method are provided by using several numerical examples.

USE OF COOPERATIVE GAME THEORY CONCEPTS FOR LOSS ALLOCATION IN BILATERAL ELECTRICITY MARKETS

This paper presents a cooperative game theory application (CGT) for analysing the allocation of the transactional transmission losses in bilateral electricity markets. This paper identifies a set of approaches documented in literature in the areas of application of CGT and reviews their applicability to allocations of losses in bilateral electricity markets. The allocation methods can be broadly classified into three categories, i.e., classical, new, and variants of nucleolus. In this paper, two points are focused during the study: the structure of the game and the concept of fairness behind it. The allocation concept of these methods is systematically analysed and compared, and calculations have been performed on the sample six-bus example and the standard IEEE 14-Bus System. The variants of nucleolus are shown to be among the most plausible concepts. A power flow procedure is applied to calculate the power losses for each transaction.

A circuit based method for multiarea transmission networks loss allocation

AbstractThis paper deals with the problem of transmission loss allocation in very large networks with multiple interconnected regions or countries. The main objective is to propose a method in order to identify the amount of losses that each participant in the market causes on all system areas. Transmission pricing of cross‐border trades is often difficult since individual countries may use incompatible internal transmission pricing regimes, and they are usually unwilling to disclose any sensitive information about their own systems.This paper presents a new methodology based on the loss formula concept for allocating electric losses to generators and loads, participating in multiple interconnected energy markets. The only data required are the power flows and characteristics of tie‐lines and PV Ward equivalent model of area networks from border nodes point of view. No information is required about individual loads, generations, or detailed internal networks. The methodology is illustrated on the IEEE 118 node network which is divided into three areas, each with a different internal transmission pricing methodology. The proposed methodology is shown to be simple, transparent and very fast, and it can deal effectively with multiple pricing regimes. Copyright © 2008 John Wiley & Sons, Ltd.

Analytical solution to balanced quadratic cooperative game and its application to transmission loss allocation

The coalition values of the transmission loss allocation problem exhibits a specific variation and it is possible to develop analytical solution to determine the nucleolus. So an analytical solution to determine nucleolus is achieved without use of series of linear programs. It has been applied to a six-bus system and the results are compared with other methods .It is found that his method provides fair allocation and requires less computational time. Keywords: cooperative game, transmission loss, nucleolus, power flow.

Analytical Solution to Balanced Quadratic Cooperative Game and its Application to Transmission Loss Allocation

The coalition values of the transmission loss allocation problem exhibits a specific variation and it is possible to develop analytical solution to determine the nucleolus. So an analytical solution to determine nucleolus is achieved without use of series of linear programs. It has been applied to a six-bus system and the results are compared with other methods .It is found that his method provides fair allocation and requires less computational time.

Transmission Loss Allocation Through Complex Power Flow Tracing

This paper presents a new method for transmission loss allocation. The method is based on tracing the complex power flow through the network and determining the share of each load on the flow and losses through each line. Transmission losses are taken into consideration during power flow tracing. Unbundling line losses is carried out using an equation, which has a physical basis, and considers the coupling between active and reactive power flows as well as the cross effects of active and reactive power on active and reactive losses. A tracing algorithm which can be considered direct to a good extent, as there is no need for exhaustive search to determine the flow paths as these are determined in a systematic way during the course of tracing. Results of application of the proposed method are also presented.

Transmission loss allocation based on optimal power flow and sensitivity analysis

This paper presents a new approach to the transmission loss allocation problem in a deregulated system. This approach belongs to the set of incremental methods. It treats all the constraints of the network, i.e. control, state and functional constraints. The approach is based on the perturbation of optimum theorem. From a given optimal operating point obtained by the optimal power flow the loads are perturbed and a new optimal operating point that satisfies the constraints is determined by the sensibility analysis. This solution is used to obtain the allocation coefficients of the losses for the generators and loads of the network. Numerical results show the proposed approach in comparison to other methods obtained with well-known transmission networks, IEEE 14-bus. Other test emphasizes the importance of considering the operational constraints of the network. And finally the approach is applied to an actual Brazilian equivalent network composed of 787 buses, and it is compared with the technique used nowadays by the Brazilian Control Center.

Allocation of Transmission Loss for Determination of Locational Spot pricing

The deregulation problem has recently attracted attentions in a competitive electric power market, where the cost must be earmarked fairly and precisely for the customers and the Independent Power Producers (IPPs) as well. Transmission loss is an one of several important factors that determines power transmission cost. Because the cost caused by transmission losses is about <TEX>$3{\sim}5%$</TEX>, it is important to allocate transmission losses into each bus in a power system. This paper presents the new algorithm to allocate transmission losses based on an integration method using the loss sensitivity. It provides the buswise incremental transmission losses through the calculation of load ratios considering the transaction strategy of an overall system. The performance of the proposed algorithm is evaluated by the case studies carried out on the WSCC 9-bus and IEEE 14-bus systems.

A cooperative game theory analysis for transmission loss allocation

This paper presents an analysis and discussion, based on cooperative game theory, for the allocation of the cost of losses to generators and demands in transmission systems. We construct a cooperative game theory model in which the players are represented by equivalent bilateral exchanges and we search for a unique loss allocation solution, the Core. Other solution concepts, such as the Shapley Value, the Bilateral Shapley Value and the Kernel are also explored. Our main objective is to illustrate why is not possible to find an optimal solution for allocating the cost of losses to the users of a network. Results and relevant conclusions are presented for a 4-bus system and a 14-bus system.

Transmission loss evaluation in an open electricity market using an incremental method

An improved algorithm to evaluate and allocate transmission losses in an open electricity market using an incremental method is reported. There is no exact analytical method to allocate transmission losses to market participants such as generators, loads and transactions because the total loss is a complex function of the power injection, system voltage and operational arrangement. The authors propose an incremental approach in conjunction with Newton's method in the marginal-loss calculations. This achieves loss allocations that are nonarbitrary and consistent with optimal power system operation. Transmission losses are allocated incrementally to generators, loads and transactions in proportion to their impact on nodal power changes. The method is tested on IEEE test systems as well as on the Hong Kong distribution system and the Victorian transmission system, state of Victoria, Australia. It is shown that, in contrast to current methods, the proposed integration approach accounts accurately for all transmission losses in these systems, whilst at the same time, loss allocation is done in an objective way without using any arbitrary parameters or allocation strategies.

A unified transmission loss allocation method

A new unified method which allocates transmission losses either to buses in a pool market or to individual transactions in a bilateral contract market is presented in this paper. A detailed derivation of the method is given. A bus-loss matrix and a transaction-loss matrix are developed to show the interactions between bus injections and transactions. It is further demonstrated that the “Physical-power-flow-based” method can be obtained as an approximation of this unified approach under certain simplifying assumptions. Test systems are used to illustrate how the proposed method behaves under different possible scenarios.

Generation scheduling and economic estimation of power systems including bilateral contracts

AbstractElectric power transactions are subdivided into pool transactions and bilateral contracts, as well as security transactions. A certain transaction level of, for example, bilateral contracts may affect pool transactions by causing transmission congestion and the like. In this paper, we discuss how both the market and the bilateral transaction participants share the operation cost and charge for using a network, taking account of power transmission loss allocation among generators. Following these discussions, we present an optimal scheduling method for pool participants. To ascertain the effectiveness of the proposed scheduling algorithm and to show how the bilateral contract level affects pool operation, we will demonstrate various simulation results for a model power system of an 8‐unit 44‐bus power system. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 158(2): 20–30, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20392

Optimization Approach to Real Power Tracing: An Application to Transmission Fixed Cost Allocation

Megawatt (MW) power flow tracing can assess the extent of network usage by the participants that can be effectively used for multiple objectives like transmission pricing, loss allocation, etc. MW power tracing, a post-facto analysis of power flow solution, is amenable to multiple solutions. This implies multiplicity of solution space of transmission cost and loss allocation problems. The conventional tracing methods enforce a "proportionate sharing rule" to calculate the shares. These shares are sensitive to quantity and distance as against the postage stamp method, which is immune to distance. Any of these methods will result in penalizing a set of constituents, which raises a fairness issue. This is evident from the experiences of developing countries like India. In this paper, a new paradigm is suggested that attempts to capture the best of the two methodologies by exploring multiplicity of the solution space of the tracing problem, within the given constraints. We show that the tracing problem can be formulated as a linear constrained optimization problem. We propose a tracing compliant modified postage stamp allocation method that computes a traceable solution that minimizes overall deviation from the postage stamp allocation. Results on actual data of central transmission utility of Western Regional Grid of India demonstrate the claims

Transmission Loss Allocation Based on a New Quadratic Loss Expression

This paper presents a derivation of a new quadratic expression for the transmission loss in a power system. The main advantage of this expression is the improvement in accuracy over the other existing approximations. Furthermore, this improved quadratic form allows the transmission loss to be expressed in terms of nodal power injections. This paper builds on the derived loss expression and proposes a bus-loss matrix. This matrix is useful in quantifying the interactions among different bus power injections and establishing a loss allocation scheme for individual buses. Numerical examples are used to illustrate the accuracy of the derived quadratic form and its use in loss allocation