Positive-Sum Game-Based Capacity Configuration Planning Method of Solar-Wind-Battery System Designed for Black-Start

For achieving the carbon peaking and carbon neutrality goals, the renewable energy and the battery energy storage will be developed more rapidly. Te participation of the solar-wind-battery renewable energy system (SWBS) in black-start can improve the resilience of the power grid. Aiming at the balance between the capacity demand of SWBS participating in black-start and the beneft of SWBS, this paper proposes a positive-sum game-based SWBS capacity confguration planning method. First, a levelized cost of energy-(LCOE-) based full life cycle index is presented and constructs an economic beneft model of SWBS considering the participation of wind and solar power plants in carbon trading. Second, a black-start capacity demand model is constructed considering the continuous power demand on the auxiliary devices of the operated thermal power generator. Taking the economic beneft of SWBS and the black-start capacity requirement into account, this paper establishes a positive-sum game-based SWBS capacity optimal confguration model, in which maximizing the economic benefts of SWBS as an objective. Tird, the simulation analysis is carried out by using a real power system, and results verify that the proposed method can achieve the optimal balance between the feasibility of black-start and the economic beneft of the SWBS.


Introduction
With greater dependence of customers on electricity, the economic and social loss caused by blackouts is becoming more and more serious [1,2]. As the primary process of power system restoration, the key to black-start is to choose a black-start power source [3]. In China, the conventional black-start scheme adopts hydropower units with an excellent self-starting ability as the black-start power source. Te development of wind, solar power, and energy storage technology provides more choices for black-start power source of regional power system [4,5].
As a black-start power source, how to reasonably allocate the capacity of solar-wind-battery system (SWBS) will need to be discussed, and it is also an optimization and competition problem. First, the capacity confguration should not be too small, which should meet the power needs of units to be started in the black-start process; otherwise, the whole process of black-start cannot be ensured successfully; second, the excessive capacity confguration will lead to the inability to consume more renewable energy and the idle waste of energy storage device, resulting in the economic beneft reduction of SWBS. With the implementation of the carbon peaking and carbon neutrality policy and the adjustment of connected-grid price policy of renewable energy, the economic beneft modelling of SWBS should not only consider the power plant's investment costs but also comprehensively consider the levelized cost of energy (LCOE) of the power plant and the income of wind farm and solar power plant participating in carbon trading. On this basis, the research on a capacity confguration planning strategy of SWBS for black-start is carried out in this paper.
At present, there are relevant studies on the participation of renewable energy in black-start process. Te authors in [6] propose an electricity pricing method for incentivizing renewable energy to participle in a black-start process. In [7], the power coordination strategy for the black-start based on model predictive control is proposed. Te authors in [8] propose a power coordination control strategy, and it uses the energy storage system to balance the power of power system during the black-start process. In the abovementioned research studies, however, the analysis on the capacity confguration of SWBS is not enough which leads to the unclear power demand of SWBS participating in blackstart and cannot guarantee the economy of SWBS. Te authors in [9] propose a robust optimization model for capacity confguration of PV storage systems considering multiple uncertainties; the authors in [10] design a feasibility evaluation method for verifying SWBS is suitable as a blackstart power source and evaluate the output power of SWBS through the power evaluation index, which provides an idea for the capacity demand confguration of SWBS; the authors in [11] discuss the carbon emission cost on the basis of investment cost and operation and maintenance cost to optimize the capacity confguration of SWBS. Aiming at the contradiction between pursuing the overall optimal operation of microgrid and the individual interest for diferent investors, the authors in [12] construct a game model from the perspective of the optimal annual average revenue to solve the optimal capacity confguration of SWBS. Te authors in [13] propose a hierarchical capacity confguration strategy for SWBS virtual power plant from the perspective of optimal comprehensive operation costs. Te abovementioned research studies mostly use IRR (internal rate of return) for the consideration of the economic benefts of power generation; however, with the further development of many types of renewable energy generation, LCOE is more suitable for the power generation industry to evaluate the cost of diferent types of power generation projects than IRR.
LCOE difers from a power station's construction or investment cost but includes the total cost of all the occurred and predictable factors in the whole design life cycle [14]. Te authors in [15] optimized the design of solar power station's array spacing and inclination angle based on LCOE. Based on the original LCOE evaluation model, the authors in [16] added the tax cost after considering depreciation of tax and the additional cost caused by loss and proposed a solar power generation beneft model adapted to the current situation of China to analyze the development trend of solar grid-connection. Te abovementioned research provides the idea of modelling the economic benefts of renewable energy power plants based on LCOE in China.
Based on the shortcomings of the abovementioned research studies, this paper studies the capacity confguration of SWBS as a black-start power source and proposes a capacity confguration model based on the positive-sum game. First, the paper analyzes the continuous power demand of black-start to ensure that the confgured capacity for SWBS can support full stage of black-start for thermal power plants. Second, considering the LCOE and the electricity sales revenue of wind power, solar, and energy storage power station as well as benefts of carbon trading to wind power plant and solar power plant, this paper establishes the whole life cycle beneft model of SWBS. Based on the positive-sum game model, the capacity confguration of SWBS is carried out. According to the case studies, the goal of optimal beneft is achieved on the basis of ensuring the success rate of blackstart.
Te main contributions of this paper are as follows: (1) An economic efciency model for SBWS is constructed based on the whole life cycle LCOE and the electricity sales revenue of each power station as well as the income of wind power station participating in carbon trading is considered which is more comprehensive and accurate for the construction of economic beneft model of the power station; (2) A capacity demand model of black-start considering the continuous power demand of auxiliary equipment of the started thermal power generators is proposed, and this model can ensure that SBWS can continuously and efectively provide adequacy power for black-start load in the black-start process; (3) Te economic benefts of SWBS is considered with LCOE and carbon trading as an objective function. Te optimal confguration strategy of SWBS capacity based on the positive-sum game is proposed, and in the proposed strategy, the black-start power source confguration not only meets the power demand of black-start but also maximizes the economic benefts of SWBS in the whole life cycle.

Economic Benefit Model of SWBS Based on LCOE
2.1. Structure of Black-Start Power Sources. In this paper, solar power, wind power, and energy storage are selected as the power source for auxiliary equipment of thermal power plant in the black-start stage. Te energy storage power station must be equipped with an uninterrupted DC power source with sufcient capacity. Te confgured DC power source capacity should be able to support the normal operation of each system of the energy storage station in the process of black-start until successful black-start. Te energy storage power station should be equipped with a capability to started by itself and be able to take power from the battery to realize the self-starting operation of the energy storage station, solar power station, and wind farm under the condition of losing the uninterrupted DC power source. Due to the uncertainty of black-start time, the renewable energy output at diferent black-start moments is also different, and the energy storage station's state-of-charge (SOC) is also random. But the process of black-start is continuous [17]. As a black-start power, SWBS must provide continuous and sufcient power support for thermal power plant. Terefore, in addition to solar power station, wind power station, and operational energy storage power station, another special energy storage in reserve should be confgured to cooperate with the operational energy storage and renewable energy power stations to complete the black-start process. Te composition of SWBS black-start power is shown in Figure 1.  [14]. In this paper, considering the impact of value-added tax deduction of fxed assets and residual value of recovered assets on the life cycle cost of a solar project [18,19], the model of whole life cycle kilowatt hour cost of the solar power station (C LCOE-PV ) is shown by the following equation: where C PV 0 is the initial investment of solar power station; n is the service life; n' is the fxed assets value-added tax deduction period; i is the running year (1, 2, 3, . . .); μ is the expected rate of return (discount rate) of the solar power station; A i PV is the operating cost of solar power station in year i; V i PV is the deduction of fxed assets value-added tax of the solar power station in year i; R PV is the residual value of solar power station; and Q i PV is the generation capacity of solar power station in year i.
(2) Revenue from Solar Power Sales. Te income level of the solar power station is determined by the illumination conditions in the area where the solar power station is located. Te revenue from electricity sales is evaluated by the annual equivalent hours of utilization in the area and the service life of the solar power station.
where R in PV is the solar power sales revenue; p price PV is the price in unit of solar power sales; R b is the subsidy for gridconnected solar policy; P PV is the PV installed capacity; η PV t is the efciency of solar power generation; and h is the annual equivalent utilization hours of the solar.

(3) Carbon Emission Reduction Benefts of Solar Power Plant.
Te basic principle of carbon trading is that one contractor party obtains the greenhouse gas emission reduction amount by paying to the other party. Te buyer can use the purchased emission reduction amount to mitigate the greenhouse efect to achieve its emission reduction goal [20]. With the gradual maturity of the carbon trading market, the contribution of carbon trading income to reducing the cost of electricity consumption will also increase [21]. Considering the carbon trading income of solar, the carbon trading income of solar power plants (R co2-PV ) is given by the following equation: where E co 2 PV represents the annual carbon dioxide emission reduction of solar power plants; p co 2 is the price of carbon dioxide emission reduction; λ co 2 represents the weight of carbon dioxide per kilowatt hour; and k co 2 represents the market carbon trading coefcient. International Transactions on Electrical Energy Systems wind power project and the recovery of residual value of assets on the cost of wind power project in the whole life cycle [19], the model of the whole life cycle power cost of wind power stations C LCOE_W is given by the following equation:

LCOE and Revenue of Wind Power Station
where C W 0 is the initial investment of wind power station; μ ′ is the expected rate of return of the wind power plant; A i W is the operating cost of the wind power plant in the year i; V i W is the VAT deduction of fxed assets in the i year of the wind power station; R W is the residual value of wind power station; and Q i W is the power generation of the wind power station in the year i.
(2) Wind Power Sales Revenue. Te wind speed and other conditions in the area where the wind power station is located to determine the proft level of the wind power station. Te annual equivalent utilization hours of the region and the service life of the wind power station are used to evaluate the electricity sales income, as shown in equation (5). According to relevant policies, unlike solar, there is no subsidized electricity price for the wind power grid.
where R in W is the wind power sales revenue; p price W is the price in unit of wind power sales; P W is the installed capacity of wind power; η W t is the power generation efciency of wind power; and h ′ is the annual equivalent utilization hours of wind power.

(3) Carbon Emission Reduction Benefts of Wind Power
Stations. Wind power, as the clean energy, can participate in carbon emissions trading. Tis paper considers the carbon trading income of wind power installation capacity, as shown in the following equation: where R co 2 W is the carbon trading income of wind power stations; E co 2 W is the annual carbon dioxide emission reduction of wind power stations; and Q W is the annual wind power generation.

LCOE and Revenue of Energy Storage Power Station.
Te energy storage power station planned in this paper includes an operational storage power station and a reserved energy storage power station. Te reserved energy storage power station supplies its power at the black-start moment to improve black-start reliability.

Life Cycle Cost of Energy Storage Power Station
(1) Initial Investment Cost. Te initial investment cost refers to the equipment and construction cost invested in constructing an energy storage system [22]. According to the energy and power characteristics of the energy storage system, the initial investment cost (C s ) can be divided into capacity cost and power cost.
where C e is the energy cost of the energy storage system and C p represents the power cost of the energy storage system.
(2) Operation and Maintenance Cost. Te operation and maintenance cost of an energy storage power station (C y ) accounts for 1% ∼ 10% of the system cost, which is related to the type of battery, as shown in the following equation: where C ye and C yp represent the operation and maintenance costs corresponding to the energy part and the power part of the energy storage system, respectively and λ y is the ratio of operation and maintenance cost to system cost.
(3) Residual Value of Power Station. Te residual value of the power station (R r ) is the residual value of the energy storage power station after the end of service, excluding the disposal cost. As shown in (9), the residual value of the more commonly used lithium iron phosphate battery energy storage power station in the market is about 5% of the system cost: where R re and R rp represent the residual value of the power station corresponding to energy part of the energy storage system and power part of the energy storage system, respectively, and λ r represents the ratio of the residual value of the power station to the system cost.
(4) Additional Costs. Te additional costs of energy storage power station (C o ) mainly include bank loan interest, project management fee, and other additional costs, and its ratio to the cost of energy storage system reaches 10%-20%.
where C oe and C op are the additional costs corresponding to the energy part of the energy storage system and the power part of the energy storage system and λ o represents the ratio of additional cost and system cost.
where C BES is the life cycle cost of an energy storage power station and μ ″ is the discount rate of the power storage station.

LCOE of Energy Storage
Station. Te energy storage system's LCOE is calculated after the whole life cycle cost of energy storage station is levelled with its total power generation. Te details are shown in the following equation: where C LCOE BES is the per kilowatt hour cost of energy storage power station; θ DOD is the discharge depth; C BES represents the life cycle cost of an energy storage power station; E sum is the total power generation in the whole life cycle of the energy storage power station; and m represents the cycle life of the energy storage station at the designed discharge depth.

Te Whole Life Cycle Revenue of Energy Storage Power
Station. Te grid-connected electricity quantity of an energy storage station refers to the sum of annual electricity quantity delivered to power grid in the life cycle of energy storage system, which is related to energy storage capacity, self-discharge rate, cycle decay rate, annual cycle times, and discharge depth. Te circulating electricity quantity in the life cycle of energy storage power station is shown in the following equation: where E BES is the circulating electricity quantity in the life cycle of energy storage power station; Q BES is the capacity of energy storage power station; η BES is the energy efciency of energy storage system; and ξ i is the decay rate of energy storage capacity. Te life cycle beneft calculation of energy storage power station is shown by the following equation: where R in BES is the life cycle benefts of the energy storage power station; p price BES is the price of electricity sold when energy storage is used for operational output; and C BES b is the cost of reserved energy storage.

Black-Start Power Demand.
Most of the auxiliary machines are asynchronous motors. Te asynchronous motors will always be in the locked rotor state before reaching the rated torque. Te large starting current will cause a great impact on the fragile recovery process of the auxiliary power system, resulting in voltage drop on the auxiliary power side and then cause the failure of black-start [23]. Terefore, the black-start power source needs sufcient capacity to meet active and reactive power demand of auxiliary machine when it starts. Te power demand of SWBS hybrid generation system should be satisfed frst when it is used as black-start power source. Te capacity of black-start power source should not be less than the accumulated value of actual operation load in consideration of the auxiliary equipment required for operation during the start-up of the thermal power units. At the same time, when the black-start power source starts a maximum capacity auxiliary machine through the gridconnected transformer of thermal power plant, the shorttime overload capacity of the transformer should be considered. Te power demand of black-start power source is shown in the following formula: where n i�1 P a,i represents the sum of required power by the auxiliary machine; P m represents the rated power of the maximum capacity auxiliary machine; K q represents the starting current multiple of the maximum capacity auxiliary machine; and k b indicates the overload multiple that the transformer can withstand.

Continuous Output Demand of SWBS.
From the perspective of continuous output, the SWBS needs to continuously and efectively provide power for the blackstart load during the black-start process. So, the output International Transactions on Electrical Energy Systems power of the SWBS should have a certain time persistence, that is, the electricity generated by SWBS during the blackstart period should be greater than or equal to the one consumed by the black-start load. Te start-up credibility defned as black-start stage i is shown in the following equation: where T i represents the time of black-start stage i; P D,i represents the output power of SWBS in black-start stage i; and P lim,i represents the required lower limit power in blackstart stage i. It should be ensured that φ i ≥ 1 when it is any stage i of black-start.

Capacity Confguration of SWBS Black-Start.
Positive-sum games are mostly used in economic felds such as business negotiations. Positive-sum games are games in which a number of participants engage in alliance and cooperation, and in the end, the benefts of both sides of the game increase. For the coalition, the overall beneft is greater than the sum of the benefts that would have been realized if each participant had operated individually; for the coalition, each member receives no less than what it would have received if it had not joined the coalition. Tis paper takes the whole life cycle beneft of SWBS as the objective function and constructs a capacity confguration model based on the positive-sum game and solving the model to obtain the optimal SWBS capacity confguration. It is assumed that each power station has independent dispatching output right during the black-start process. Te positive-sum game model of capacity confguration of SWBS is as follows: (1) Alliance participants: power capacity P 1 and energy capacity S 1 of operational energy storage power stations, the reserved energy storage power capacity P 2 and energy capacity S 2 , the capacity of solar power station P 3 , and capacity of wind power station P 4 . Tese SWBS parameters constitute a cooperative alliance {P 1 , S 1 ,P 2 , S 2 ,P 3 , P 4 }. (2) Strategy set and constraint conditions: the output of various power sources selected in each period i during the black-start process is taken as the strategy set in the positive-sum game model, as shown in the following equation: where x j,i represents the power source output coefcient of type j power source participating in blackstart in period i. With the strategy set X j,i , the output constraints that the SWBS shall meet during the black-start process are shown in the following equation: where η PV,i and η W,i represent the actual power generation efciency of solar and wind power during black-start period i, respectively; x 3,i and x 4,i represent the output coefcients of the solar power stations and wind power stations participating the black-start in period i.
Considering the time duration of the power required for black-start, the output power duration of the SWBS in each period should meet the constraint, as shown in the following equation: where P lim,i represents the required capacity of the auxiliary machine in period i. During the black-start process, the energy storage station needs to ensure that there is no excessive discharge after the power source and its state-ofcharge is within the safety threshold, the constraints are shown in the following equation: where SOC j,i−1 represents the state-of-charge of the j-type energy storage station in period i − 1; SOC max , SOC min represent the maximum and minimum allowable state-of-charge of the energy storage station, respectively; and t j,i refers to the time that the j-type black-start power source participated in the black-start in period i. Equation (21) indicates the initial capacity of an operational energy storage power station.
where S 1,i−1 represents the initial capacity of the period i−1 of the operational energy storage power station; (3) SWBS economic proft function: according to the SWBS economic beneft model constructed above, the beneft function of SWBS is shown in the following equation: where R all is the total benefts of SWBS; R in BES is the beneft of energy storage power station; R in PV is the solar power sales revenue; R in W is the wind power sales revenue; R co 2 PV is the carbon trading income of solar power plants; and R co 2 W is the carbon trading income of wind power stations.

International Transactions on Electrical Energy Systems
According to the revenue function, the strategy set is continuously adjusted until the comprehensive economic beneft of the whole system reaches the maximum. Once the overall economic beneft of black-start power is optimal, it means that the SWBS black-start power not only meets the power demand of black-start but also maximizes the economic beneft in the daily non-black-start period. Te change of capacity of any black-start power unit will break the balance and reduce the overall beneft. In this balance, all black-start power consumption plans are Nash equilibrium solutions under the positive-sum game. Te SWBS blackstart power capacity confguration process is shown in Figure 2.
Te optimal output strategy (X * j,i ) can be obtained to satisfy the following equation: where R all (X * j,i ) is the total beneft of SWBS under the optimal output strategy X * j,i and R all (X j,i ) is the total beneft of SWBS under the output strategy X j,i .
When the game satisfes the following conditions, there is a unique Nash equilibrium solution: (1) the fnite number of participants; (2) the strategy space is closed and bounded; and (3) the revenue function is continuous and convex in the strategy space.
In this paper, the revenue function of the SWBS blackstart system is a continuous convex function; so, the positive-sum game strategy set composed of the SWBS combined power source system has a Nash equilibrium point, and the Nash equilibrium solution is unique.

Typical Situation of Solar and Wind Power Output.
In this paper, the capacity of the scene is confgured by taking the sunny weather in spring in Huainan area of Anhui Province as an example. Using the positive-sum game-based SWBS capacity confguration method proposed in this paper, the SWBS capacity is allocated by considering the power demand of the SWBS participating in black-start with the SWBS full life cycle benefts. Te period from 9:00 to 15:00 and 23:00 to 01:00 are taken as the research period, 9:00, 11: 30 and 15:00, 23:00 and 01:00 at night are selected as blackstart moments, respectively. Te typical daily output curve of solar and wind power is shown in Figures 3 and 4.
Taking starting a 300 MW thermal power unit as an example, the active power of its auxiliary machine is 13 MW. Black-start can be divided into four stages when the thermal power plant put into auxiliary equipment loads in steps. Te main auxiliary machine parameters are shown in Table 1.
Te capacity demand of inner black-start evaluates the total capacity of black-start power around the power demand of auxiliary equipment of the thermal power plant. For 13 MW auxiliary equipment, considering SWBS selfconsumption (5%), transmission line loss (2%), and retaining a certain margin (2%), case 1 can get at least 29.6 MW active power by (15) according to the minimum power demand and the short-time overload capacity of the grid-connected side transformer; in case 2, considering the continuous output demand of black-start power source, ensuring that the auxiliary power participating in the startup at each stage can be met, and the black-start process can run smoothly; so, the active power demand can reach 32.8 MW.

Power Capacity Confguration for SWBS Black-Start.
Based on the 6-hour black-start time in the current blackstart scheme, wind power fuctuates less and PV output fuctuates more during the daytime, as PV is at a high  climbing output stage around 9:00 and can maintain a high output level for a period of time around 11:30, while it is at a low downhill stage around 15:00, so 9:00, 11:30, and 15:00 are chosen as the black-start moments during the daytime; at night, the peak moment 23:00 and the trough moment 01:00 of the wind power output are selected as the night black-start moments. Te resulting SWBS capacity confguration ensures the feasibility of black-start at any time of the day.
(1) In the typical daytime of a day, three moments of 9: 00, 11:30, and 15:00 are selected for black-start, and the method proposed in this paper is used to calculate the capacity ratio of the SWBS positive-sum game model. Te specifc results are as follows.
As can be seen from Figure 5, in the daytime blackstart, due to the sufcient output of PV and wind power, more PV with lower cost is confgured. Correspondingly, considering the coordinated scheduling of individual participant and the optimal interests of the whole alliance, the operational energy storage that can absorb more renewable energy and obtain profts is also confgured with more capacity.
Considering the volatility of renewable energy sources, a small amount of reserve energy storage is confgured to improve the reliability of the blackstart. (2) In the night of a typical day, two moments of 23 : 00 and 01 : 00 are selected for black-start, and the results are as shown in Figure 6.
Considering the demand for black-start at night, the solar output of solar is 0 and the wind storage is used as the power source for black-start. At night, wind power needs to provide more output, and at the same time, to ensure the reliability of black-start, more energy storage output needs to be confgured.     International Transactions on Electrical Energy Systems According to the energy storage output coefcient in the black-start stage in Figure 7, considering the SOC constraint of operational energy storage, the reserved energy storage with high SOC needs more output. At night, the solar power station cannot provide power support, and the operational energy storage is constrained by the state of SOC. Te reserved energy storage needs to provide fast and efective power support at the time of black-start. Terefore, compared with the daytime, the night-time black-start requires more high-power reserved energy storage to ensure the smooth progress of the black-start process.
Conventional multiobjective methods often only consider their own interests, while positive-sum game has the advantage of considering both the coordinated scheduling of individual participants and the optimal interests of the whole alliance.
It can be seen from Figure 8 that the capacity confguration under the positive-sum game model takes into account the output strategies of the participants in the blackstart process. Compared with the confguration results of multiobjective optimization, more PV and wind power with lower cost are confgured, and black-start standby energy storage also provides more active power support. However, in the multiobjective optimal confguration, when the active power demand of black-start is met, the subsequent confguration process aims to pursue the economy of SWBS; so, the operational energy storage provides more active power support, while less black-start reserved energy storage is confgured.
According to the capacity confguration results, the whole life cycle beneft of SWBS is calculated, and the economic benefts of the proposed method and the traditional multiobjective method are compared, as shown in Figure 9. Te economics of SWBS under the diferent methods at the confgured capacity at each moment are shown in Table 2.
It can be seen from Figure and Table 2 that compared with the traditional multiobjective method, the capacity confguration results of the proposed method in this paper increase the economic beneft by 2.32%∼7.51%.
In this paper, the positive-sum game capacity confguration model is solved by programming, and the convergence is shown in Figure 10. Te results of SWBS capacity confguration are shown in Table 3      not only meet the power demand of black-start but also reduce the input cost of the SWBS and maximize its full life cycle economic benefts.

Conclusion
In view of the problem of balance between black-start power demand and economic beneft of wind and solar energy storage station in the capacity confguration of the SWBS as a black-start power source, this paper established an economic beneft model of SWBS considering comprehensive cost and beneft, analyzed the output demand of SWBS participating in black-start, proposed the capacity confguration strategy of SWBS as a black-start power source, and carried out the capacity confguration of SWBS. Te main conclusions are as follows: (1) Tis paper constructs the economic revenue model of wind and solar energy storage station by considering the life cycle electricity cost and carbon trading income of wind and solar energy storage station, which can calculate the economic beneft of confgured power station more comprehensively and precisely.
(2) According to the analysis on output demand of SWBS participating in black-start, the model of the power demand of black-start and the continuous output demand of SWBS is proposed, which ensures that SWBS can continuously and efectively provide enough power for black-start load in the process of black-start and provides the premise and basics for the confguration of SWBS blackstart power source. (3) Taking the economic benefts of SWBS considering LCOE and carbon trading income as the objective function, the optimal capacity confguration strategy of SWBS based on positive-sum game is proposed. Te SWBS black-start power proposed in this paper not only meets the power demand of black-start but also maximizes the economic benefts of SWBS in the whole life cycle, so as to achieve the optimal balance between the power demand of black-start and the economic beneft of SWBS.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest regarding the publication of this paper.  International Transactions on Electrical Energy Systems 11