As the foundation of the electricity market, the pricing scheme can affect the bidding behavior of market participants and thus determine the market clearing results. In this paper, we compare and analyze the characteristics of the strategic bidding behavior of generators and corresponding market clearing results with truthfully modeled generator output range under the pay-as-bid pricing scheme and locational marginal pricing scheme. First, we formulate the bi-level strategic bidding problems under two pricing schemes. Second, through the theoretical derivation, we show that the minimum output of the generator has a significant impact on the comparative conclusion between two pricing schemes, which is commonly neglected by existing studies. Then, considering the minimum output of the generator, the quantitative analysis of consumer payment and system operational cost under two pricing schemes is summarized. Finally, the numerical analysis shows some new insights about the comparative conclusion for two pricing schemes.

In electricity markets, when considering discrete characteristics, the electricity prices are normally derived by the Lagrangian dual problem of a mixed integer linear programming problem. However, this pricing problem faces distinct computational challenges. In this letter, we develop a neighborhood extreme point based constraint generation method to efficiently solve the non-convexity pricing problem. Decomposing the pricing model into a master problem and slave problems, the proposed algorithm utilizes the efficient strategies to iteratively generate constraint sets from the slave problems and properly introduce an inducing function into the objective of the master problem to accelerate the convergence. Adopting proposed strategies can decrease the required iterations by 84.6% on average in cases of the Polish 2383-bus system with different congested scenes.

In electricity markets, dispatch instructions and price signals are typically derived from the primal and dual solutions of the market clearing models. The prevailing market clearing methods can be summarized as: determining dispatch instructions to maximize social welfare, and subsequently calculating prices to support a competitive equilibrium. However, this sequential approach may violate critical market operation requirements, such as consumer payment reduction and price caps. Inherent conflicts often exist between these economic properties and market operation requirements. Since some of these properties are jointly determined by dispatch and pricing decisions, the sequential optimization approach inherently limits the ability to realize the full coordination benefits. To address this gap, this paper proposes a novel market clearing method that co-optimizes dispatch instructions and price signals to balance conflicting market objectives. Firstly, this paper analyzes the conflict mechanism between the aforementioned properties and requirements under the prevailing market clearing paradigms. Secondly, a co-optimization market clearing method to trade off conflicting properties and requirements is proposed. The basic idea and general mathematical formulation of the proposed method are introduced. The distinctions and connections between the proposed method and existing methods are clarified. Thirdly, the application of the proposed method is explored in typical scenarios involving consumer payment reduction and price caps. Finally, numerical analysis demonstrates that the proposed method achieves a flexible balance between conflicting properties and requirements. For instance, it can significantly reduce consumer payments by 80.33 % while limiting increases in system operation costs to within 1.98 %; alternatively, it can reduce lost opportunity costs to zero under price caps at the expense of a 0.52 % increase in system operation costs.

For distribution utilities, it is important to match the power reliability service with the demand of users. However, since there are partial overlaps in the power supply paths of different nodes, the reliability of different nodes has the inherent coupling relation based on the network topology. The improvement of reliability level on individual nodes can hardly be separately controlled without causing any influence on other nodes. To solve this problem, this paper aims to study the co-optimization method of reliability service provision and pricing for the distribution utility. First, a joint placement method of common devices for reliability enhancement is presented. The coupling relationship between the load recovery states of different load nodes under the same fault is conveniently expressed. Second, a service menu design approach is introduced to determine the level and price of candidate reliability services. It considers that users have differentiated evaluations of service and select the service in the menu according to their profit maximization. Third, to overcome the free-riding issue that users receive unnecessarily high-reliability service, the load-shedding compensation method is proposed to exactly match the reliability level received by users to the service level selected by users. After the model transformation, the optimization model is formulated as a mixed integer linear programming problem. An acceleration algorithm with convergence guarantee is developed to mitigate the computational burden.

Among the pricing schemes, locational marginal pricing is the most widely adopted scheme in current electricity markets. Despite the nice properties, theoretical study and practical experience have shown that considering the strategic bidding behaviors of market participants, locational marginal pricing may result in excessive consumer payment and prejudices market efficiency. In this paper, we propose an optimization-based partial marginal pricing method to reduce consumer payment under strategic bidding. The advantages of the locational marginal pricing method are reserved to the best extent while the remaining problems are delicately handled. To achieve this, we first analyze the characteristics and problems of the locational marginal pricing scheme and present a partial marginal pricing structure. Second, we establish an optimization-based partial marginal pricing model, in which discriminatory price components are introduced in price formulation and the pricing properties including competitive equilibrium and revenue adequacy are formulated as constraints. Third, to verify the performance of the proposed pricing scheme considering the strategic bidding, a bi-level strategic bidding problem of the generator under the proposed pricing method is established and transformed into a mixed integer linear programming problem. The numerical results indicate that under the conventional pricing methods, the consumer payments under strategic bidding can be up to 16.67 times higher than those under truthful bidding, while the proposed method can effectively reduce excessive consumer payments by 92.1% while maintaining the desired pricing properties.

The operational characteristics of generators cause non-convexity in the electricity market. The presence of non -convexity implies that market participants will bear lost opportunity costs under linear prices, which motivates them to violate the dispatch decisions or obtain excess profits through strategic bidding. To resolve this issue, finding a reasonable pricing scheme under non-convexity is a research field of great concern. Currently, most studies regard uplift payments as an indicator to quantify the effectiveness of a pricing scheme. It is usually recognized that convex hull pricing is a promising pricing method with nice incentive properties because it minimizes the uplift payment and thus improves market transparency. However, whether the pricing mechanism can guide truthful bidding has not been thoroughly investigated. In this paper, considering the complex market clearing process, we propose a framework with certain qualifications to analyze the incentive properties under different pricing schemes. Then, conclusions regarding the incentive property of different pricing schemes are provided. The effectiveness and correctness of the proposed method are validated using the numerical results of case studies.

For the pricing in the non-convex electricity markets, the various pricing properties including supporting a competitive equilibrium, non-discrimination, cost recovery of participants, and revenue adequacy of the market operator can hardly be simultaneously fulfilled. Current pricing methods cannot balance these properties because there lacks a computationally tractable pricing model that explicitly formulates these properties as objective functions or constraints. In this paper, we propose a pricing optimization model taking prices as decision variables and taking important pricing properties as objective functions or constraints. Based on duality theory, the Karush-Kuhn-Tucker conditions of the self-dispatch problem processed by convex relaxation are extended to construct the constraints related to supporting a competitive equilibrium. Taking advantage of the modeling flexibility, the constraints for non-discrimination, cost recovery, and revenue adequacy are established. The delicately designed pricing optimization model is a linear programming problem with an acceptable computational burden. It applies to the market clearing problem with non-convexity, time-coupling and network transmission characteristics. To be specific, the application of the proposed pricing method for the unit commitment problem is provided. The reasonability, scalability, and tractability of the proposed approach are illustrated in systems with over 2000 buses. Numerical experiments show that the proposed method shows better performance compared with other representative pricing methods.

电价的科学性和合理性对电力市场的调节配置至关重要.作为常用的边际定价形式,节点电价表达为对偶乘子的线性函数.基于基本的定价原理,文中梳理了节点电价的物理内涵,说明了基于边际定价原理推导的节点电价与系统稀缺资源价格之间的内在联系,并论证了其合理性.基于此,提出了具有可扩展性的统一电价表达式,将电价扩展为对偶乘子和转移分布因子的一般函数形式.以线路越限造成价格尖峰为典型应用场景,建立了以电价为优化变量的定价模型,在IEEE 30节点系统及波兰2383节点系统中验证了所提电价机制的实际应用价值.

In major electricity markets, the market clearing model is currently solved in a sequential manner. However, this practice produces uplift payments because the self-dispatch of market participants is calculated over the whole dispatch horizon. In this letter, the uplift payments incurred by the sequential dispatch manner are analyzed. A pricing model that reduces the uplift payments is presented.

Reasonable electricity pricing is the foundation of electricity markets. Locational marginal price is a commonly used electricity pricing mechanism. However, the formulations of locational marginal price are not consistent in existing studies. Also, the properties of this pricing method, such as incentive compatibility and market surplus, are not formally proved in a general dispatch formulation. In this study, we generalize the price formulation and revisit the definition and property of electricity prices. We find that electricity price should be a service-level concept rather than a node-level concept, which means that the electricity price may deviate for different market participants at the same node due to their different contributions to the system-wide constraints. Under this service-level concept, the properties of the incentive compatibility and non-negative market surplus are proved. The specific price formulation is analyzed based on a co-optimization model of energy and reserve. Case studies show that using the proposed pricing method, the prices for wind power and load include an additional component as a charge for the requirement of spinning reserve. The nice pricing properties maintain for the proposed method, which has distinct advantages compared with the node-based LMP formulation.