A multi-market scheduling model for a technical virtual power plant coalition☆

0 Introduction

The surge in the installed capacity of distributed energy resources (DERs) has brought unprecedented challenges to the energy consumption and scheduling of power systems [1].To effectively utilize DERs and maintain the operational security of power systems, technical virtual power plants (TVPPs) have emerged as a crucial element for future power systems.This concept has attracted considerable interest in recent years primarily because of its facilitative role in integrating DERs[2].The TVPP represents an entitative distribution system incorporating DERs, which is equivalent to a microgrid in terms of definition.Unlike commercial virtual power plants (CVPPs),TVPPs consider the operational characteristics of both DERs and the network[3].The maturity of electricity market regulations allows TVPPs to engage in market transactions.Furthermore, TVPPs can also benefit by providing ancillary services to the main grid,such as voltage support and peak regulation services, which cannot be offered by general end users [4,5].

Considerable effort has been devoted to the optimal scheduling of DERs within a TVPP,including deterministic scheduling [6], stochastic optimization [7], and robust optimization methods [8].Moreover, the optimization of TVPPs under market regulations plays a vital role in reducing costs.In the current electricity markets, TVPPs are allowed to submit bids based on predicted and realtime prices.Volatile market prices present significant challenges for the scheduling of TVPPs.Numerous studies have explored bidding strategies for TVPPs.In[9],an optimal bidding strategy in the day-ahead market for a TVPP was proposed in which the uncertainties of renewable energy, load variation, and market prices were modeled using a hybrid stochastic/robust optimization method.Reference [10] proposed a robust optimization-based bidding strategy for a combined wind storage system.

Despite extensive research on bidding strategies, their applicability has been limited in some instances in China.For example, in most provincial markets, a single TVPP often fails to satisfy the minimum megawatt requirement for participation in ancillary service markets.One possible solution is to form a coalition or cooperative entity involving multiple TVPPs.Several concepts have been studied to address this issue.For instance,the concept of an aggregator was introduced to involve several small-scale microgrids in the real-time balancing of market bidding via a two-layer market framework [11].In [12], the concept of a networked microgrid(NMG)was proposed,which refers to a collaborative framework in which multiple electrically neighboring TVPPs or microgrids are interconnected and scheduled as units.In [13], a price-maker bidding and offering model for an NMG in a pool-based day-ahead energy market was proposed.The aforementioned multiagent joint scheduling studies are based on relatively mature electricity markets and lack simulation research under the specific regulations of China’s electricity market.

In the context of the electricity market in China, apart from the energy market, two important types of markets,the ancillary service market and the real-time balancing market, play crucial roles in ensuring market stability.The ancillary service market primarily focuses on peak regulation services, and the bidding strategy for the joint energy and ancillary service markets considering the specific conditions of the electricity market in China are addressed in [14-16].Another significant market, the real-time market, is typically addressed through rolling optimization.In [17], a two-layer scheduling model was proposed in which day-ahead scheduling uses one day as a time scale for economic scheduling, whereas real-time scheduling is adjusted based on day-ahead scheduling.Reference [18] proposed a two-layer real-time scheduling model for microgrids based on an approximate future cost function.Reference [19] proposed a real-time rolling scheduling strategy that considered the operation interval division of distributed generators and batteries in a microgrid.Additionally,to prevent excessive deviations between real-time power consumption and the day-ahead power purchase plan,most studies,including[17-19],incorporate a price penalty mechanism in real-time scheduling;that is,the deviation between the actual power consumption and the day-ahead planned consumption will result in a penalty price, typically several times the penalty electricity price.

Most provinces in China have established preliminary operational electricity markets, with Shandong, Guangdong,Shanxi,Zhejiang,and Gansu being particularly representative.The rules regarding virtual power plants(VPPs) in the spot electricity market are summarized and categorized in Table 1.

A review of the aforementioned studies reveals the following research gap.Most studies focus on only one aspect, such as day-ahead scheduling, real-time dispatching, or bidding strategy in the energy and ancillary service market, and no research has considered the operational processes of market participants in the current multimarket environment in China.This indicates a deficit in the operational and bidding strategies encompassing the entire process of market participation.In this study,scheduling for the TVPP coalition was studied in a specific market framework,considering the day-ahead joint energyand ancillary service markets as well as the real-time balancing market.The main contributions of this study are summarized as follows:

Table 1 Regulation for VPPs in China’s typical provincial electricity markets.

ProvinceEnergy marketServices provided by VPPs in ancillary service marketEntry conditions for ancillary service market Gansuno rulesPeak regulation (Price bidding without quantity bidding)100 MW capacity Demand response services (Quantity and price bidding)1 MW capacity Frequency regulation (Price bidding without quantity bidding)Equip AGC device Guangdongno rulesFrequency regulation (Price bidding without quantity bidding)Equip AGC device ShandongParticipate with quantity bidding (Voluntary price bidding)Ramping ancillary service (Submit ramp rate)5-MW capacity Frequency regulation (Price bidding without quantity bidding)Equip AGC device ShanxiParticipate with quantity and price bidding Frequency regulation (Price bidding without quantity bidding)Equip AGC device Zhejiangno rulesFrequency regulation (Price bidding without quantity bidding)Equip AGC device

· Nonlinear models for the entire process of TVPP participation in the market are simulated, encompassing the energy and ancillary service markets, which contain the frequency regulation and ramping ancillary services ranging from day-ahead scheduling to real-time dispatching.Appropriate linearization methods are proposed to efficiently solve these models.

· An improved Shapley value method is used for profit distribution that considers the capacity contributions of TVPPs.

· A profitability analysis was conducted using a transitional electricity market in China as a case study, and the operational simulation of TVPPs under actual deviation settlement mechanisms,such as the revenue recovery mechanism, is examined.

The remainder of this paper is organized as follows:Section ‘Motivation and framework’ describes the electricity market framework, Section ‘Scheduling model for TVPP coalition’ describes the market rules and modeling of the TVPPs, Section ‘Model Linearization’ describes the linearization of the model, Section ‘Case study’ presents a case study in a specific market setting,and Section‘Conclusion’ provides the conclusions.

1 Motivation and framework

With the evolution of China’s electricity market, most provinces have established their own electricity markets.The electricity spot market consists of energy and ancillary service markets,where the ancillary services include ramping and frequency regulation services.Because the power capacity of a single TVPP may be insufficient to participate in the ancillary service market, this study examines a scheduling strategy for a TVPP coalition.

1.1 Market operation framework

In the day-ahead stage, the scheduling plan is formulated by the TVPP coalition based on the predicted market-clearing prices, and then the bids are submitted in the energy and ramping ancillary service market.In the real-time stage, TVPPs can provide frequency regulation services, and the unbalanced power should be purchased from the real-time market.If a significant deviation exists between the actual power consumption and the day-ahead power purchase plan, corresponding penalties will be incurred.In this study,the penalty,or revenue recovery mechanism, refers to reclaiming the profits obtained by exploiting the difference between the dayahead and real-time electricity prices.

When a TVPP coalition participates in the ramping ancillary service market, it provides an upward ramping capacity by reducing electricity consumption and a downward ramping capacity by increasing electricity consumption.The valid ramping capacity is determined using the baseline load.According to the market rules, the baseline load of the TVPP coalition is defined as the average daily power consumption over the most recent five days, which does not participate in the ramping ancillary services market.Fig.1 depicts the market operational framework and timeline.The real-time market is cleared by rolling scheduling every 2 h,and the initial condition of each rolling schedule is determined by the day-ahead scheduling result and the previous rolling scheduling result.

1.2 Market residual supply curve

Market clearing occurs at the intersection of the supply and demand bidding curves.As shown in Fig.2,the residual supply curve is a stepwise, monotonically increasing curve.Residual supply curves consist of several powerprice pairs.The intersection point is the clearing point where λbuy is the cleared price.

1.3 Coordinated scheduling framework

Fig.3 shows the proposed coordinated scheduling framework for the TVPP coalition.The TVPP coalition,comprising multiple TVPPs, is characterized by clearly defined geographical and electrical boundaries and is interconnected through information exchange.The coordinator of the TVPP coalition collects information from each constituent TVPP, submits collective bids to the market operator, receives the outcomes of the market clearings, and schedules internal power transactions within the TVPP coalition.

2 Scheduling model for TVPP coalition

2.1 Physical model for TVPPs

The operation cost of TVPP,which consists of the cost of controllable generators (CGs) and battery energy storage systems (BESSs), is expressed in (1).

where m is the index of TVPP, i is the index of the CG; k denotes the index of the BESS, Ci,m represents the total operation cost of CG i in TVPP m, Ck,m is the total operation cost of BESS k in TVPP m; Cfuel,i,m, CS,i,m, COM,i,m,Ce,i,m, and CDP,i,m are the fuel, start-up, operation/maintenance, environmental, and depreciation costs of CG i in TVPP m,respectively;and COM,k,m and CDP,k,m are the operation/maintenance and depreciation costs of BESS k in TVPP m, respectively.Erated,k,m is the energy capacity of BESS k in TVPP m, CE,k,m is its cost per unit capacity,Prated,k,m is the power capacity,and CP,k,m is its cost per unit capacity.Detailed calculation formulas for each cost coefficient can be found in[20] and are not listed in this paper owing to space limitations.Lloss,k,m is the loss factor of battery lifetime calculated using Eq.(18).

The CG constraints of an individual TVPP are

Fig.1 Market operation framework and timeline.

where Pi,s,m,t denotes the output power of CG i at time t in TVPP m in scenario s; and represent the minimum and maximum power output of CG i in TVPP m,respectively; Ui,s,m,t represents the binary on/offvariable of CG i in TVPP m in scenario s; T is the number of time slots of the scheduling horizon; Ustart,i,s,m,t is the binary start-up variable of CG i (1 for start-up and 0 otherwise)in TVPP m in scenario s; Ushut,i,s,m,t denotes the binary shut-down variable of CG i(1 for shut-down and 0 otherwise) in TVPP m in scenario s; MOTi,m and MDTi,m denote the minimum up and down time of CG i in TVPP m,respectively; Δup,i,m and Δdown,i,m represent the ramp-down and ramp-up limits of CG i in TVPP m,respectively.Constraint(5)is the power limit of CG i in TVPP m in scenario s,and Constraints(6)and(7)describe the service time limits.Service time constraints prevent the CGs from starting up and shutting down frequently, including the minimum startup time as represented in Eq.(6) and the minimum shutdown time as represented in Eq.(7).Constraint (8)represents the ramping limit of CG i in TVPP m in scenario s.

Constraints (9)-(13) limit the operation of the BESS.

where SOC k,s,m,t denotes the state of charge(SOC)of BESS k in TVPP m in scenario s; Pch,k,s,m,t and Pdh,k,s,m,t represent the charging and discharging power of BESS k in TVPP m in scenario s, respectively; ηch,k,m and ηdh,k,m represent the charging and discharging efficiency of BESS k in TVPP m, respectively; k,m is the self-discharge ratio of BESS k in TVPP m; and denote the minimum and maximum SOC bounds of BESS k in TVPP m, respectively; Δt is the time step; and represent the maximum charging and discharging power bounds of BESS k in TVPP m, respectively; and Pk,s,m,t is the output power of BESS k at time t in TVPP m in scenario s.

The SOC formula is represented in Eq.(9), Eqs.(10)and (11) limit the SOC and power of the BESSs, respectively, and Eq.(13) guarantees that the SOC remains unchanged after the scheduling period.

Fig.2 Market residual supply and TVPP bidding curve.

Fig.3 Coordinated scheduling framework for TVPP coalition.

Other constraints include the following power exchange limits and power balance constraints:

where Pbuy,m,t is the power purchased from the main grid to TVPP m,and Ubuy,m,t is the binary variable(1 for purchasing and 0 otherwise).Psell,m,t denotes the power sold from TVPP m to the main grid,and Usell,m,t is the binary variable(1 for selling and 0 otherwise).P-sell,m and P-buy,m represent the maximum power that can be sold to and purchased from the main grid, respectively, in TVPP.Pd,s,m,t, Pwt,s,m,t,Ppv,s,m,t are the load, wind power, and photovoltaic power,respectively; and Pm,t represents the power injected into TVPP m from other TVPPs.The power exchange limits are enforced by Constraints (14)-(16), and Eq.(17) represents the power balance constraint.

Additionally, the lifetime of the battery is considered.The SOC is an important factor for the lifetime of a battery, and different SOC values lead to different lifecycle degradation rates.The relationship between the SOC levels and the effective degradation rate for the commonly used lithium-ion and lead-acid batteries is shown in

Fig.4 [21].The calculation for Lloss is expressed as

where Ethroughput is a fixed constant in this model representing the overall energy throughput in the battery lifetime,and Eloss is the cumulative energy throughput in the scheduling period T, which is formulated as

where the weighting degradation rate f （SOC k,t ） is associated with SOC.

2.2 Network constraints among TVPPs

Based on the DistFlow model, the network constraints among the TVPPs are as follows [22]:

where Pm,t and Qm,t represent the active and reactive power injected into TVPP m,respectively; anddenote the active and reactive power transaction flows from TVPP m to TVPP m′,respectively;vm,t is the square of the voltage at TVPP m; Imm′,t denotes the square of the current in branch and represents its upper limit; and vm and denote the squares of the upper and lower limits of the voltage at TVPP m, respectively.Eqs.(20) and(21) represent the power balance constraints at TVPP m.Eq (22) represents Ohm’s law constraint, and its physical significance is the voltage balance constraint.Eqs.(23)and (24) are the current and voltage constraints, respectively; and Eq.(25) represents the second-order cone constraint.The voltage of the TVPPs was supported by the main grid; therefore, sufficient reactive power existed in the network.

2.3 Scheduling model in the energy and ramping ancillary service market

(1) Day-ahead Stage

In the day-ahead stage,the TVPP coalition participates in the energy market and simultaneously increases the ancillary service market.The objectives and cost functions are as follows:

where Eq.(26)is the objective function that minimizes the net cost of the TVPP coalition; T denotes the set of time slots of scheduling horizon; Cbuy,t represents the electricity purchase cost influenced by the TVPP coalition’s bidding and cleared by the market; Csell,t is the profit from selling electricity; BR,t is the revenue of ramping ancillary service calculated in Eq.(37); ps denotes the probability of scenario s; M and S are the set of TVPPs and scenarios,respectively; λbuy,t denotes the clearing price of the energy market in the day-ahead stage; λsell,t denotes the selling price from the TVPP to the main grid;Pbuy,t and Psell,t represent the total TVPP coalition power purchased and sold,respectively; and the calculation of Cbuy,t and Csell,t is performed using Eqs.(27) and (28), respectively.

The constraints of ramping ancillary market are

Fig.4 Relation between SOC and weighting degradation rate.

(2) Real-time stage

In the real-time stage,the TVPPs consider the real-time prices and results of the day-ahead scheduling to adjust the outputs of the CGs and the power purchase in real-time dispatching.Moreover, a revenue recovery mechanism is incorporated into the real-time stage.The objective function for real-time dispatching is expressed as

where χ0 is the maximum deviation coefficient.Constraint(41) prevents arbitrage through the price differentials between the day-ahead and real-time markets.

Ancillary services for frequency regulation must be considered in the real-time phase.The revenue from the frequency regulation is calculated as

where λf,t represents the frequency regulation price, Pf,t denotes the power of frequency regulation at time t, and YAGC,t is the regulation performance index at time t.The frequency regulation of TVPPs is achieved by adjusting the real-time purchased electricity.The relationship between Pf,t and PRTbuy,t is expressed as

where Uf,t denotes the binary variable for the frequency regulation service (1 for participating in frequency regulation and 0 for non-participation),and Af,t is the frequency regulation control signal with a value range of {-1, 0, 1}.A value of-1 indicates a positive frequency regulation signal requiring the TVPP coalition to reduce real-time power consumption, and a value of 1 indicates a negative frequency regulation signal requiring the TVPP coalition to increase real-time power procurement.A value of 0 indicates no need for frequency regulation.

Real-time prices are cleared every 15 min, and the TVPP coalition self-reschedules based on the initial conditions, such as the SOC values of the BESSs, power purchase plan, and power of the CGs.The ramping service capacity is determined in the day-ahead stage, and the TVPP coalition provides the ramping capacity during real-time operation.The real-time scheduling constraints follow the same formulations as (1)-(19), (27)-(30), and(41)-(44) in the day-ahead scheduling model, except for Constraint (13).

(3) Cost allocation based on improved Shapley value

The objective of a TVPP coalition is to generate profits from the energy and ramping-service markets.Therefore,an effective allocation method is crucial to increase members’ willingness to participate.The Shapley value was selected for revenue allocation in this study because it can effectively quantify the marginal contributions of all members, facilitating fair cost allocation [23-26].Owing to the capacity entry requirements of the ramping ancillary service market, the capacity of each TVPP contributes to the revenue in the ramping market.Therefore, an improved Shapley value accounting for the weight of the TVPP capacities was employed for the cost allocation in this study.

Based on the Shapley value definition, a cooperative game can be defined by a couple (N, v), where N is the set of players and N = {1,..., m,..., n}.The benefits for each coalition member can be calculated as

where φm denotes the benefit to Player m through cooperation,D denotes the subset of N,d is the number of players in set D, and v（D ） represents the value of coalition D.

In Eq.(45),the Shapley value assumes that all coalition participants have the same weight of 1/n,which is unlikely because of the different TVPP capacities.Therefore,weights were introduced to the Shapley values.Using unanimity games,the Shapley value （）is defined as[27]

where is the weight vector representing the bargaining power of players, u is the size of subset U, and is the weight of TVPP m.αD represents the contribution value of the combination that includes TVPP m, which is formulated as

The weight vector was determined by the installed generation capacity of each TVPP,which indicates its contribution to the profits and minimum capacity access requirements for the ramping ancillary service market.

3 Model Linearization

As listed in Section ‘Case study’, the majority of constraints are linear, except for Constraints (19), (27), (38)and(39).In Constraint(19),the weighted degradation rate curve f （SOCt ） is non-linear.Similarly, Constraint (27)takes a quadratic form.Constraints (38) and (39) for ramping ancillary services are piecewise functions and nonlinear.For an efficient solution, several linearization methods were employed to manage the aforementioned nonlinearities.In addition, the fuel cost for the CGs expressed in Eq.(2) was linearized using the piecewise approach referenced in [20].

3.1 Linearization of battery lifetime

As illustrated in Fig.4, f （SOCt ） is a non-linear function; thus, Eq.(19) is a non-linear constraint.Consequently, a piecewise linearization method was implemented to address this issue [20].First, the cumulative function of f （SOCt ） was calculated as

where fint （SOC t ） is the integral function of f （SOC t）.Assuming that fint （SOC t ） is divided into n segments, the analytical representation is expressed as

where Constraints (53) and (54) show the linear relationship between SOC t and,zr is a non-negative auxiliary variable, and yr is a binary auxiliary variable.

The effective cumulative throughput Eloss is recalculated as a function of fint （SOC t ） based on Eqs.(19) and (53) as

where SOC 0 denotes the initial SOC.By substituting Eq.(58) into (18), Lloss can be calculated using a linear formulation.

3.2 Linearization of bidding model

For load-based TVPPs, the price of the surplus energy sold by the TVPP coalition to the main grid is regarded as fixed.Conversely, the price of electricity purchased by the TVPP coalition from the main grid can be influenced by the power demand of the TVPP coalition.As Pbuy,t and λbuy,t are variables, Constraint (27) is nonlinear.

Two auxiliary binary variables, πl,t and μl,t, were introduced to locate the intersection point.πl,t =1 denotes that the intersection point is on the lth segment of the residual supply curve at time t, μl,t = 1 means that the segment where the intersection point is located is horizontal, and μl,t = 0 means the segment is vertical.Subsequently, Constraint (27) can be linearized as Eqs.(59)-(61):

where al,t and bl,t represent the horizontal and vertical distances, respectively, between the intersection and starting points of segment l of the residual supply curve.

Because only one intersection point exists between the bidding and residual supply curves, πl,t is limited to

The horizontal al （t ） and the vertical bl （t ） distances shown in Fig.2 are bounded by

3.3 Linearization of ramping service

Constraints(33)and(34)contain the product of continuous and binary variables, which are linearized as Eqs.(67) and (68), respectively, by the Big-M method and the two ancillary variables rDN,t and rUP,t.

Constraints(38)and(39),which are segmentation functions, are linearized as (69) and (70), respectively, as

In summary, Eqs.(1)-(18), (20)-(26), (28)-(37), and(40)-(70) constitute the proposed mixed-integer secondorder cone programming (MISOCP) model for the participation of the TVPP coalition in the joint energy and ramping ancillary service market, which can be efficiently solved by most shell solvers.

4 Case study

The proposed model was implemented on a PC with an Intel i7-12700 CPU and 8-GB RAM.All the simulations were performed using MATLAB and solved using CPLEX 12.10.

4.1 Test system

In this study,the rules primarily refer to electricity market regulations in Shandong Province, as it is one of the few continuously operating markets in China.Several case studies were conducted using a test system containing three TVPPs.Without a loss of generality, the test system can include any arbitrary number of TVPPs.The TVPP coalition here consisted of two or three types of CGs,and the configuration of each TVPP is shown in Table 2 where LB and UB represent the lower and upper limits,respectively; MT, FC, DE, WT, and PV denote microturbine, fuel cell, diesel engine, wind turbine, and photovoltaics, respectively.

Lithium-ion and lead-acid batteries each having a capacity of 2.4 MWh and an output power limit of 0.8 MW were considered in this study.TVPP1 included one lead-acid and one lithium-ion battery, TVPP2 included two lead-acid batteries, and TVPP3 included two lithium-ion batteries.The maximum, minimum, and initial SOC of both battery types were 100, 20, and 50 %, respectively.The power limit at the point of common coupling was 5 MW for each TVPP.

The day-ahead market residual supply curves were constructed based on the data in [28] and partially modified based on the Shandong Province electricity market, and the real-time electricity market prices were derived from the Shandong Province electricity market data.

The market rules in Shandong Province state that the minimum power threshold to participate in the ancillary service market as a VPP is 5 MW with an output duration not less than 1 h.The downward ramping opening hours are assumed to be from 8:00 to 11:00, and the upward ramping market is open from 13:00 to 16:00 in the ramping ancillary market.The load and output power of the WT and PV in each TVPP are shown in Fig.5.The shaded areas are scenarios generated by the Monte Carlo method[29] using the joint probability distribution function.The value of parameters c1,c2 and c3 in Eqs.(38)and(39)were 1.2, 0.7, and 0.5, respectively [30].

4.2 Simulation results

(1) Scheduling Results of TVPP Coalition

The scheduling period was 24 h with 15-min steps,resulting in 96 time slots, and the computation time was62 s.Fig.6 shows the clearing prices of the day-ahead energy market and the corresponding bidding curves of the TVPP coalition, as well as the market residual supply curves for t = 36 and t = 56 of the day-ahead scheduling.Electricity prices were derived from the actual operation data of the Shandong Province electricity market on April 12, 2023, which was a working day.These figures indicate that the electricity demand from the TVPP coalition led to an increase in the day-ahead market-clearing price in the 10th hour.However,the clearing price at t=56 remained unchanged because the electricity price is generally high at this time.Therefore, the CGs within the TVPP coalition increased generation to reduce the electricity purchased from the main grid, thereby avoiding higher electricity prices.

Table 2 Main parameters of CGs (Unit: MW).

TypeMTFCDEWTPVBESS TVPP1LB0.050.040.0400-1.6 UB3.221.20.811.6 TVPP2LB0.05-0.0400-1.6 UB3.2-1.21.51.51.6 TVPP3LB0.050.04-00-1.6 UB2.41.2-211.6

Fig.5 Forecast data of each TVPP.

Fig.6 Bidding and residual supply curves for selected hours.

Fig.7 Day-ahead scheduling results of TVPP coalition.

Fig.8 Real-time scheduling results of TVPP coalition.

The scheduling results for the day-ahead and real-time stages of the TVPP coalition are shown in Fig.7 and Fig.8,respectively,and all the values depicted in these figures represent the TVPP coalition’s total power.Negative and positive values of the BESSs symbolize the charging and discharging states, respectively.CGs increase their output during periods of high electricity prices and minimize their output during periods of low electricity prices.The scheduling costs for day-ahead optimization and real-time operations were 25,532 yuan and 25,090 yuan,respectively.In the day-ahead stage, hours 10-12 are the lowest-price periods,resulting in a significant charge accumulation for the BESSs during these hours.In the realtime stage, owing to the revenue recovery mechanism,the unbalanced power purchased in the real-time market shows extremely small changes in comparison to the dayahead power purchase plan, making it difficult to discern in Fig.8.

Owing to the limited revenue from the frequency regulation service and relatively small total capacity of the TVPP alliance, the TVPPs provided frequency regulation capacities of 875, 50, and 21.9 kWh during the periods t = 31, 44, and 63, respectively.The total revenue from the frequency-regulation service was only 36 yuan.

Fig.9 Ramping capacity of TVPP coalition.

Fig.9 shows the baseline load, power purchase plan,and ramping capacity of the TVPP coalition.TVPPs offer downward ramping capacity by increasing power purchases and offer upward ramping capacity by reducing power purchases.The TVPP coalition provided 5.67-MWh downward ramping capacity, which lasted for 1 h and 15 min in hour 11:00 (t = 41-44) by charging the BESSs.The baseline load during the upward ramping opening hours was too low to provide an upward ramping capacity;therefore,no upward ramping capacity existed as shown in Fig.9.The downward ramping powers are listed in Table 3.The bidding power in each period satisfied the 5-MW lower limit of the ramping service market.

Fig.10 shows the power flow between the TVPPs.Owing to the lower capacities of TVPP3, TVPP1 and TVPP2 primarily delivered power to TVPP3.

(2) Scheduling Results of BESSs

Fig.11 shows the output power and SOC of the batteries for each TVPP.During the day-ahead stage in TVPP1,the SOC of the lead-acid battery remained consistently above 0.4, whereas that of the lithium-ion battery was maintained between 0.2 and 0.6.This is because the leadacid battery has a lower degradation rate at higher SOC levels, while the lithium-ion battery has a low lifetime loss within the SOC range 0.2-0.6 as illustrated in Fig.4.

TVPP2 included two lead-acid batteries,and the batteries maintained an SOC value above 0.4,with the ability to be fully charged (SOC =1).TVPP3 included two lithium-ion batteries which were prevented from fully charging to reduce the degradation of the life cycle.

Table 3 Downward ramping power.

Timet = 41t = 42t = 43t = 44 Bidding power/MW5.055.515.836.30 Valid power/MW5.055.515.836.30

Fig.10 Power flow between TVPPs.

In the real-time stage, the scheduling results of the BESSs exhibited relatively small charging and discharging power during hours 1:00-5:00 and 13:00-15:00, compared to the day-ahead stage depicted in Fig.11(a).This is because the real-time net load experiences fluctuations,and the TVPP coalition prioritizes the use of batteries to mitigate these fluctuations,which is more economical than purchasing electricity or using generators for stabilization.

(3) Cost allocation

The costs of each TVPP were determined based on their capacities and the Shapley values mentioned in Section ‘Simulation Results’.We used two distinct types of Shapley values, and the corresponding results are listed in Table 4.

The results in Table 4 show that the largest profit share,approximately half of the earnings of the ramping ancillary service,was allocated to TVPP3 based on the conventional Shapley value, followed by TVPP1 and TVPP2.However,this method does not consider the differences in the TVPP capacities, resulting in a relatively similar profit allocation.The weighted Shapley value method allocates profits based on installed generation capacities.TVPP1, which had the largest capacity, received the highest profit, whereas TVPP3, which had the smallest capacity, gained the least profit.Simultaneously,the profit differences were not excessively large, ensuring profitability for each TVPP and fair allocation based on their capacity size.

4.3 Comparative analysis of penalty mechanism

In addition to the revenue recovery mechanism, most studies have incorporated penalty prices to reduce deviations in power consumption in the real-time market.This section compares the revenue recovery and price-penalty mechanisms.In the latter, the unbalanced power incurs an additional penalty price of 0.5 times the real-time price.

Fig.12 shows the real-time scheduling results for the TVPP coalition with the penalty price.Unbalanced power refers to a deficit between the real-time electricity demand and the day-ahead plan.The most unbalanced power is purchased between 12:00 and 14:00 because of the low real-time price.Fig.13 shows the detailed unbalanced power under the price penalty mechanism.Compared to the scheduling results under the revenue recovery mechanism shown in Fig.8,Fig.13 demonstrates that the TVPP coalition significantly adjusted its actual power consumption based on the real-time prices driven by the price penalty mechanism.Moreover, under the price penalty mechanism, the real-time operational cost for the TVPP coalition was 23,583 yuan, saving 1237 yuan compared to that of the revenue recovery mechanism,where the revenue from frequency regulation services was only 7.8 yuan.However, in the price penalty mechanism, when a significant difference exists between the day-ahead and realtime electricity prices, the TVPP coalition may adjust its power consumption significantly to reduce operational costs, which is detrimental to the stable operation of the market.

Fig.11 BESS scheduling results.

Table 4 Cost Allocation based on Shapley Value (Unit: yuan).

Operation modeTVPP1 TVPP2 TVPP3 Operation cost without allocating ancillary service revenue 11,354 10,483 5089 Conventional Shapley value Operation cost10,730 98884521 Ancillary service revenue 624595568 Weight Shapley valueOperation cost10,542 99364643.8 Ancillary service revenue 812547445.2

Fig.12 Real-time scheduling results with penalty price.

4.4 Comparative analysis in different scenarios

Fig.13 Unbalanced power with penalty price.

Fig.14 Day-ahead scheduling results on July 8.

To verify the generality of the above results,the electricity prices in the Shandong electricity market for two days,July 8 (weekend) and April 14 (weekday), were used to simulate the operation of the day-ahead stage.The baseline load was recalculated based on the selected days.The scheduling results for these two days reveal the behavior of the BESSs on days with stable electricity prices.Additionally,visible changes occurred in the baseline load on July 8 compared to that on April 12, indicating the impact of the baseline load on ramping ancillary services.

Figs.14 and 15 depict the scheduling results and ramping capacity,respectively,using the market data from July 8.Owing to variations in the baseline load compared to that of April 12 and July 8,the TVPP coalition was unable to provide any ramping capacity.The BESSs charged only in hour 2:00, which is the lowest point of the electricity prices.The energy throughput of BESSs was relatively limited owing to the smoothness of prices within the scheduling period.

Fig.16 illustrates the operational results using the market electricity prices on April 22.The day-ahead clearing price on April 22 exhibited low fluctuations.Consequently,the economic benefits of the BESSs’ operations were low.Therefore, the BESSs primarily provided a downward ramping capacity to generate profits.Fig.17 shows the baseline load, power purchase plan, and ramp capacity.

Fig.15 Ramping capacity on July 8.

Fig.16 Day-ahead scheduling results on April 14.

Fig.17 Ramping capacity on April 14.

In conclusion, significant price variations lead to considerably different electricity consumptions by a TVPP coalition across different operating days in the electricity spot market.This contribution to substantial fluctuations in the baseline load across different operating days makes an accurate assessment of ramping capacity unreasonable.

5 Conclusion

This paper proposes a scheduling model for TVPPs jointly participating in multiple markets, including the day-ahead energy and ramping service markets, as well as the real-time balancing market and frequency regulation service market.The case study shows that, in the day-ahead stage, the TVPP coalition provides ramping capacity by the charging of BESSs and the ramping capacity is greatly influenced by the baseline load.In the realtime stage,two deviation penalty mechanisms are incorporated.Under the revenue recovery mechanism, profits gained from arbitrage are all reclaimed, contributing to a lower deviation compared with the price penalty mechanism between the TVPP coalition’s actual power consumption and the day-ahead planned power consumption.The revenue of the ramping service is allocated by the weighted Shapley value which reflects capacity contribution of each TVPP compared to the traditional Shapley value.

CRediT authorship contribution statement

Yiqiao Shen: Writing - original draft, Data curation.Jing Meng: Funding acquisition.FuLong Song: Validation,Supervision.Chunyang Liu:Methodology,Conceptualization.Xiaozhong Chen: Software.Hanrun Wang:Visualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by Science and Technology Foundation of Global Energy Interconnection Group Co.LTD.(SGGE0000JYJS2310046).