Circuit-theory-based method for transmission fixed cost allocation based on game-theory rationalized sharing of mutual-terms

J. Mod. Power Syst. Clean Energy https://doi.org/10.1007/s40565-018-0489-y Circuit-theory-based method for transmission fixed cost allocation based on game-theory rationalized sharing of mutual-terms Saeid POUYAFAR1, Mehrdad TARAFDAR HAGH1,2 , Kazem ZARE1 Abstract This paper proposes a new method to allocate the transmission fixed costs among the network participants in a pool-based electricity market. The allocation process relies on the circuit laws, utilizes the modified impedance matrix and is performed in two individual steps for the generators and loads. To determine the partial branch power flows due to the participants, the equal sharing principle is used and validated by the Shapley and Aumann-Shapley values as two preferred game-theoretic solutions. The proposed approach is also applied to determine the generators’ contributions into the loads, and a new concept, named circuit-theory-based equivalent bilateral exchange (EBE), is introduced. Using the proposed method, fairly stable tariffs are provided for the participants. Cross-subsidies are reduced and a fair competition is made by the proposed method due to the counter-flows being alleviated compared with the well-known Z-bus method. Numerical results are reported and discussed to validate the proposed cost allocation method. Comparative analysis reveals that the method satisfies all conditions CrossCheck date: 25 September 2018 Received: 28 February 2018 / Accepted: 26 September 2018  The Author(s) 2019 & Mehrdad TARAFDAR HAGH Saeid POUYAFAR Kazem ZARE 1 Department of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran 2 Engineering Faculty, Near East University, Mersin 10, 99138 Nicosia, North Cyprus, Turkey desired in a fair and efficient cost allocation method. Finally, the developed technique has been implemented successfully on the 2383-bus Polish power system to emphasize that the method is applicable to very large systems. Keywords Transmission fixed cost allocation, Circuit theory, Equal sharing principle, Game theory 1 Introduction Among various issues related to the modern restructured power systems well addressed most recently in the literature [1, 2], deregulation and its price-based problems [3, 4] are of utmost importance. One of these problems is transmission cost allocation (TCA). Several methodologies have been proposed in the literature concerning the problem of TCA. Traditionally, the costs were allocated to the users by the Pro-Rata method. Despite the simplicity, the method disregards the network actual extent of use. Recently, the method is enriched and used to allocate the costs of the unused capacity of the transmission facilities. The task of allocating the transmission costs to the users taking into account the network extent of use, was first introduced by the MW-mile method which is now widely applied in the literature [5]. Tracing-based methods [6–8] utilize the concept of proportional sharing principle (PSP) to trace the power flow in the network. Reference [6] proved the existence and uniqueness of a solution to the tracing problem. The technique of flow tracing has also been extended and used as an analytical tool for transmission capacity allocation in a highly renewable European electricity system [7]. Reference [8] presented a transmission congestion (TC) 123 Saeid POUYAFAR et al. tracing technique based on PSP. Nodal pricing is another approach for TCA which is based on locational marginal price (LMP) differences, and is currently developed worldwide. The proposed marginal pricing approach provides the correct economic signals to the network participants. However, it is not linked to the actual transmission infrastructure cost, thus, not able to recover the total transmission network cost (TNC) [9]. Reference [10] checked this fact in several systems around the world utilizing LMP-based TCA method, and demonstrated that the maximum network revenue obtained in these systems was only 25% of the TNC. Some authors tried to solve the issue by altering the LMPs to recover the TNC using the concept of Ramsey pricing [10], and introducing the generation and nodal injection penalties into the economic dispatch [11]. Marginal and incremental cost allocation methods, based on the concept of sensitivity indices, are other pricing schemes widely applied in the literature, until recently [12]. The main drawback of these methods is their sensitivity to the choice of the slack bus. To overcome this limitation, [5] utilized the slack bus independent distribution factors, whereas [13] suggested the concept of optimal distributed slack bus. TCA methods based on some form of equivalents have been extended in [14, 15], in which the equivalent bilateral exchange (EBE) has been built through the optimization as well as tracing-based approaches, respectively. As an alternative, the optimization approach has been used recently along with the min-max fairness criteria [16] to trace the real power in the network. The application of artificial intelligence (AI) to power system becomes popular to explore, especially in power tracing problems [17]. Effect of the possible interactions of components is often not considered in neither optimization nor AI-based methods, due to its additive complexity as well as the computation time, subsequently leading to inaccuracy in some cases. There are also a group of papers, with solid economical foundation, that incorporate the concept of cooperative game theory [18, 19] into the problem of TCA. Although the method behaves well in terms of fairness and efficiency, significantly high computation time is required, if applied to a large power system [20]. Recently, [21] proposed a benefit-based TCA scheme. The challenging issue concerning these methods is to find the exact benefit that each user takes from the transmission facilities. Reference [22] introduced a new load-following-based method to estimate the transmission costs of each participant during a specified time period before entering the market. The use of circuit theory to the TCA is another pricing scheme, widely applied in the literature [19, 23–28]. The circuit-theory-based approaches, including Z-bus model [23, 24] as well as its modified forms [26, 28], modified nodal equation (MNE) model [25], and transformer 123 analogy (TA) model [27], have an important advantage over any cost allocation method, as previously described. These methods incorporate the network characteristics directly into the allocation process. However, due to the non-linear behavior of the power systems, there is still not a unique mathematical solution for the contribution of customers into the transmission facilities under these approaches. The results rely mostly on the principle applied to split the mutual terms, as the main causes of the nonlinearity, between the participants. A group of papers use the most common sharing principles, namely, proportional [29], quadratic [30], and equal s (...truncated)