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| Analyzing Pricing Problem in Electricity Market from an Optimization Perspective |
| Wang Yi1, Yang Zhifang1, Yu Juan1, Wen Xu2 |
1. State Key Laboratory of Power Transmission Equipment & System Security and New Technology Chongqing University Chongqing 400044 China;
2. Southwest Branch of State Grid Corporation of China Chengdu 610041 China |
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Abstract In the electricity market, electricity prices usually consist of dual solutions to the primal problem such as market clearing or dispatch problem, which has nice economic significance. However, when the primal problem is faced with problems such as degeneracy and constraint violation, the pricing method based on the dual solutions cannot guarantee the ideal pricing properties. Recently, some methods were presented to solve these pricing problems, but they can hardly balance the diverse market requirements for pricing properties. Therefore, this paper proposes a general optimization pricing framework considering the pricing property requirements, and several different forms of optimization pricing models, to satisfy the regulatory requirements on the pricing properties of the market operator.
First, from an optimization perspective, a general optimization pricing framework is developed, and the universal-form basic optimization pricing model which can analytically characterize cost recovery, incentive compatibility, revenue adequacy, fairness, and other pricing requirements is analyzed in detail. Secondly, typical objective function and constraint settings of the basic optimization pricing model are analyzed, based on the optimization theory and duality theory, linear programming models equivalent to the bi-level programming models are constructed, and the differences and connections between the proposed pricing methods and the existing pricing methods are interpreted. Third, taking a multi-period economic dispatch model and price spiking problem in the electricity market as an example, the practicality of the proposed method is illustrated. A suitable basic pricing optimization model and a model transformation method are selected, and a linear programming pricing optimization model considering multiple pricing property constraints is established. Finally, the proposed optimal pricing method can achieve flexible trade-offs between different properties. By reasonably regulating the prices' optimization space, the proposed method is comparable to the locational marginal pricing (LMP) method in terms of calculation time.
The numerical simulation is developed in IEEE 30 bus system and Polish 2 383 bus system. We compared pricing methods M1~M8, where M1 and M2 are respectively corresponding to the LMP based on the original dispatch model and modified dispatch model, and M3~M8 are based on the proposed pricing model with different objectives and constraint settings. The results show that M1, M3, and M4 can ensure zero lost opportunity cost (LOC) for all market participants; M2 leads to an unambiguous LOCs for market participants because the real dispatch space is not considered; M5~M8 lead to LOCs for market participants as it attempts to balance the properties of the price cap, product revenue shortfall, market surplus, and total consumer payments.
The following conclusions can be drawn from the simulation analysis: the optimal pricing method proposed in this paper can be adapted to market requirements by reasonably setting the model objective function and constraints. In terms of method selection, M3 or M4 can be used to ensure incentive compatibility and not to introduce non-scarce resources into the pricing, where price spikes and multiple solutions of price are mitigated according to the corresponding objective settings; M5 can be used to minimize LOC under the price limit and not to introduce non-scarce resources into the pricing; M6 can be used to minimize LOC and revenue shortfall under the price limit; M7 or M8 is used to further integrate the market surplus and total consumer payment.
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Received: 10 June 2022
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2023, Vol. 38 
