Optimal price-taker bidding strategy of distributed energy storage systems in the electricity spot market

Under the influence of recent power system reforms, the spot market (SM) [1][2][3] can fully restore the commodity attributes of electricity, effectively facilitate price discovery [4,5], and optimize the resource allocation [6,7]. As an emerging flexible resource in the power market, the distributed energy storage systems (DESSs) serve the dual roles of generation and consumption [8,9], thereby complicating the market dynamics for energy storage users. Currently, large-scale energy storage systems mainly operate independently in the SM, both on the generation [10,11] and grid sides [12,13]. However, there are few studies on the small-scale user-side DESSs, which participate in SM transactions [14][15][16][17], and their cooperative operational mechanisms and profit models have remained underdeveloped. Therefore, an operational price-taker bidding strategy of the DESSs, combined with users that participate in SM, has been proposed in the present study. This model combines the DESS and users, which ensures the access conditions for the DESS to participate in the SM, and at the same time the whole can be directly dispatched by the dispatching organization. This allows the DESS to fully utilize its regulating capacity and smooths out the uncertainty and volatility of the users' electricity consumption, in addition to allowing the users to adjust the time of use to reduce the cost of electricity through this route. The novel approach to enhance the profitability and reduce the payback period of the DESSs has been provided. The present paper is divided into two parts: (1) A clearing model for DESSs joint users to participate in the electricity spot market (ESM) has been constructed, while concurrently developing a profit model of price-taker DESSs in price spread; (2) A two-layer bid quantity model for DESSs joint users to participate in the SM has been proposed, where the optimal trading strategy has been devised to maximize the daily revenue of the DESSs in the upper layer, while the clearing model guides the bid quantity strategy of the upper-layer DESSs through market price signals.The clearing process in the ESM refers to the power trading center (PTC) in maximizing the social welfare or minimizing the system purchasing costs by collecting bidding data from buyers (such as users and sellers) for, e.g., conventional thermal power units (CTPUs) and renewable energy units (REUs), so as to obtain the generation plan of the generation side on the operation day, the clearing power of the user side, and the marginal clearing tariffs required for settlement before the day of settlement [18][19][20]. Allocated electricity quantities (AEQ) for both buyers and sellers will be obtained, and the marginal clearing price (MCP) can be determined (Figure 1(a)). In the ESM, the intersection between the offer curve of the user demand and the generated offer curve of the unit generation is the market clearing point. The power and price that correspond to this point are the traded electricity volume (TEV) and transaction price [21,22]. Also, the social welfare is the sum of the net surplus on the generation side and user side, namely the area of the shaded part in Figure 1(a). ( ) e , ,, , , , , , , , 1 , 1 1 1minT G M B N t g m t g m t b n t b n t b n t b t g m b n P u u P t   + = = =       + -         Minimizing RT purchase cost   = = = +    -      +                       ( ) ( ) ( ) e dis,  =     - -     - +      -      Bidding modeBidding mode without price (J K G M B N t j k t j k t g m t g m t b n t b n t b n t b T j k g m b n G t t g t g t g t g g g P P u u P t u u u u C    + = = = = = -- =   - - -       - - + -        ) ( ) ( ) u e , , , , , , , , , , , , , , 1 , 1 1 1 1 1 s , 1, 1, , 1 max 11( ) max min min min max max , ,, , , , , , ,, min min max max , , , , , 0 ,  + +    =     (2) ( ) ( ) b b dal ,nec , , , , yel das 1 1 11 N b b t b n t b n N bb d d C E EE d  + = +- (3) max , , , , , 1 N t b t b n t b n n PP  = =  (4)where ,,t j k is the charging bid of user j in segment k during the time period t; ,, Additionally, to ensure the safe and stable operation of the system, it's necessary to consider the operational constraints of CTPUs ( 5)-( 13), the operational constraint of REUs ( 14), the bidding segment constraints of NEUs ( 15)-( 17), and the system power balance constraints (18) t( )UU , 1, , 0 t g t g t g g T u u T - - - (9)( ) After that the security constrained economic dispatch (SCED) model [23,24] also needs to be centrally optimized to obtain the day-ahead AEQ and MCP for the operating day. Therefore, the model is specified below:DD , , 1, 0 t g t g t g g T u u T - - - (10)U 1 U ,, g t t g g tT Tu   - =- =  (11) ( ) D 1 D ,, 1 g t t g g tT Tu   - =- =- (12) ( ) ( ) max max load ,( ) eu , ,, , , , , , , , , , , , 1 , 1 1 1 1 1 max. . ( 5) -( 8), ( 13) -( 19)TJ K G M B N t j k t j k t g m t g m t b n t b n t b n t b t j k g m b n P P u u P t st    + = = = = =   - - -        (20)For the ESM, the users settle the power price according to the "day-ahead benchmark, real-time difference" principle [25]. The power price consists of two components: the day-ahead market that determines the power price and the deviation power price that is determined by the real-time market.The day-ahead market-clearing power tariff is the product of the day-ahead user clearing quantity in the day-ahead electricity energy market and the day-ahead marginal clearing price, and the same applies to the deviation power tariff for real-time market settlement. This dual settlement mechanism is illustrated in Figure 1(b).Currently, most researchers claim that the terminal electricity price for the user includes the market prices of electricity, transmission and distribution electricity prices (TDEPs), government funds and user surcharges [25]. In the context of the SM environment, the commodity nature of the electrical energy implies that its market price is primarily determined by the supply-and-demand dynamics [26]. Therefore, the above presented market price for the electricity is the market clearing price. It's calculated by using the PTC, which is based on the bidding information that is reported by the supply and demand participants, rather than being based on the final settlement price for end-users. Therefore, the spot spread arbitrage model for DESS considering TDEPs can be expressed as: ( ) ( ) ( ) ( ) e d e,In the process of electricity spot trading, the decision-making of each market subject's quotation needs to consider the reaction of the PTC, and the PTC is also subject to the limitations of the information declared by each market subject in the clearing of the SM. Therefore, the optimal charging and discharging problem of the DESS, which is participating in the SM, is a two-stage optimization problem. Its model framework is presented in Figure 1(c). For the upper layer, the DESS optimizes its bidding strategy with the objective to maximize the revenue in the day-ahead-real-time SM. Moreover, due to the deviation between the renewable energy output and the actual power consumption of users in the real-time market, in addition to the power reported in the day-ahead market [2,27,28], it is necessary to introduce an error penalty mechanism to penalize the parties with larger errors in the realtime market. Additionally, the customized power services (CPSs) provided by the DESS and the corresponding default costs are considered in the day-ahead power energy gain. Therefore, the objective function of the upper level can be expressed as:md d d pva pva SC W pum max F F F C C = + - -(22)( ) SOC are the upper and lower limits, respectively, of the state of charge (SOC); t SOC denotes the SOC in the time period t; E is the rated capacity; max K is the maximum times of charging and discharging.d SC u SC , 1 1 1 e T HK h t k h t k F P t  = = =  =       (23) W 1 = H h h h h x h CW  =  (24)L G L G C L G L G L   = = = = == ==   +       =      +           u , , , ,11J B s t j s t b jb G ==          =    (26)The lower layer simultaneously simulates the clearing processes of the day-ahead and real-time ESM, and its objective function is to minimize the costs of the power purchase in the market clearing. Assuming that the start-up mix of all units in the day-ahead has been determined, the calculation process of the lower layer model is as follows: firstly, determine the generation plan of each unit in the day-ahead and real-time markets and the nodal clearing prices through the SCED model, and then pass the results of the clearing results of the two markets to the upper layer, so as to guide the bid quantity strategy of the upper-layer DESS through the market price signal. Therefore, the day-ahead and realtime SCED models can be expressed as:( )e da SCED , ,, , , , , , , , 1 , 1 1 1 min. . ( 5) -(8) ( 13) -( 19)T G M B N t g m t g m t b n t b n t b n t b t g m b n F P u u P t st  + = = =   = + -        ,(36)( )e rt SCED, ,, , , , , , , , , , , , , , 1 , , 1 1 1 min. . ( 5) -( 8) ( 13) -( 19) T G M B NIn the objective function of the above SCED models, there are nonlinear terms for multiplication of binary variables with continuous variables, and the big M method [29][30][31] is adopted to linearize these nonlinear terms. Finally, the market clearing results obtained from the day-ahead and real-time spot market SCED models, which are linearized in the lower layer, are transmitted to the upper layer model to guide the DESS to make the bidding strategy. And the two layers of the linearized model are solved alternately and iteratively to determine the optimal charging and discharging strategies for the DESS to participate in the electricity spot market.To increased by 173.05%, which is due to the fact that the DESS can only obtain energy gain between 0.1 of the charge state and 0.9 of the charge state, resulting in the increase of the power trading gain in Scenario 3 is limited. Therefore, the market clearing prices in Scenarios 1 and 3 are identical.In the present study, a two-layer bid quantity model for the DESS joint users to participate in the SM has been proposed. The purpose with this model is to obtain an optimal charging/discharging strategy of the price-taker DESSs. The following conclusions have been drawn: (1) Compared to the existing single operational mode of the DESSs, the proposed multiplexing operational strategy for the participation of DESSs in the ESM can effectively improve the daily revenue by a factor larger than 1.7; (2) In scenarios where the peak-to-valley spread of time-of-use electricity pricing exceeds the maximum peak-to-valley spread of the market clearing price, the DESSs can offer customized power services to users in generating a value-added income, thereby enhancing the economic feasibility of participating in the ESM.Authors ZP, JF, ZZ and JC were employed by Shaoxing Power Supply Company State Grid Zhejiang Electric Power Co., Ltd.The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.