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This paper presents an optimal power flow formulation in which the generation is dispatched in order to compensate for losses allocated to different transactions. Since the loss allocation itself depends on the solution, the two problems are combined and solved together. Loss allocation scheme developed by the authors earlier [Ding Q, Abur A. Transmission loss allocation in a multiple-transaction framework, IEEE Trans Power Syst 2004;19(1):214–20] is used in this formulation. It is assumed that each transaction is entitled to select its own designated generators to compensate for its allocated losses. The case where some transactions prefer instead to let the independent system operator (ISO) to provide the loss compensation service is also considered. An optimization procedure, which yields the least-cost compensation from participating generators, is developed for this purpose by using an OPF model. Several numerical examples are included to demonstrate the proposed procedures.

Electric power industry is going through important changes as a result of restructuring. In the newly created electricity markets, sellers and buyers of electricity engage in bilateral power transactions, which take place over the transmission system and create losses. Since transmission losses are not negligible, their allocation among the participating transactions has been an issue under investigation from the very beginning. Among the schemes proposed so far for the allocation of losses [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10], there are different approaches ranging from allocating losses to generators/loads in a pool market to allocating then to individual transactions in a bi-lateral contract market. A single slack bus is often used to compensate for all the losses incurred by transactions, but it is possible to have each transaction assign its own chosen buses for the loss compensation. Such a choice will however yield a different power flow solution, necessitating further discussion of loss allocation along with loss compensation. Power flow solution algorithm should then incorporate the chosen loss allocation strategy so that the solution will yield a system state and generation dispatch consistent with this loss allocation strategy. One possible solution which uses distributed slack buses is described in [11] where losses are compensated for bilateral transactions. In [12], the same problem is formulated for the multiple-transaction case where transactions get to designate generator buses for compensation of losses allocated to them or they may opt for purchasing loss compensation service from the ISO. While very comprehensive, this approach may lead to possible inaccuracies as shown in [7] due to its use of the DC power flow approximation and the LP optimization model. This paper presents an alternative solution to the above problem. First, the multi-transaction framework definition is extended to include loss compensation entities for transactions so that each individual transaction is able to freely choose any generators instead of the system slack bus for loss compensation. Unlike some previous papers, the transactions are allowed to select a single generator or multiple generators for loss compensation and do not necessarily designate the system slack or their own generators for loss compensation. Next, the conventional power flow analysis is combined with the transaction loss allocation and transaction designated loss compensation methods which are developed by the authors in [1]. These methods allow a natural separation of losses among individual transactions in a multiple-transaction setting. This combined formulation leads to a systematic solution procedure in order to adjust generation while simultaneously allocating losses to the generators designated by individual transactions. However, if some transactions choose not to designate any specific loss compensation generators, then this will provide an opportunity for the ISO to implement a least-cost loss compensation solution. An OPF model is then utilized to optimize the loss compensation for those transactions electing to purchase the loss service from the ISO and accordingly the incurred losses are fairly allocated back to individual transactions. Consequently, all transactions will be able to either choose self-compensation or ISO-compensation for their allocated losses. The paper is organized in such a way that, the proposed formulation is presented first, followed by its implementation algorithm. Numerical examples are included at the end to illustrate the application of the proposed method to typical power systems.

This paper first extends the transaction framework definition by adding transaction loss compensating entities so that each transaction is able to choose any generators for loss compensation. It then modifies the power flow formulation to incorporate loss allocation among multiple transactions each of which compensates its own loss by its designated generators. Finally, an optimal power flow formulation with loss allocation and loss compensation is presented. In this formulation, transactions will have to choose between self-loss-compensation and purchasing ISO loss compensation service options. Since the proposed method calculates the power flow, losses and allocations iteratively, the sum of the allocated losses to each transaction will match the total system loss exactly. Numerical examples are given to illustrate that this method yields loss allocation results that are intuitively reasonable and consistent with expectations.