CN116914860B - Power supply capacity configuration optimization method and system for multi-energy complementary power generation system - Google Patents
Power supply capacity configuration optimization method and system for multi-energy complementary power generation system Download PDFInfo
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Abstract
The invention discloses a power supply capacity configuration optimization method and system of a multi-energy complementary power generation system, wherein the method comprises the steps of obtaining a capacity configuration scheme of each power supply in the multi-energy complementary power generation system, and obtaining the running cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme; constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme, and constructing an inner layer optimization model according to the operation cost; and determining a capacity allocation scheme which minimizes the sum of the allocation operation cost and the operation cost of all power supplies according to the outer layer optimization model and the inner layer optimization model. The inner layer optimization model can accurately simulate the annual hourly scheduling operation process of the system. The invention provides a two-layer optimization model for the power capacity configuration problem of a grid-connected type multi-energy complementary system consisting of power supplies such as wind power, photovoltaic, hydroelectric power, thermal power, pumped storage, mixed pumped storage, electrochemical energy storage and the like, and can accurately evaluate the long-term operation economic benefit and the power supply reliability of the system.
Description
Technical Field
The invention discloses a power supply capacity configuration optimization method and system of a multi-energy complementary power generation system, and belongs to the technical field of multi-energy complementary power generation.
Background
The development of clean low-carbon renewable energy sources such as wind power, photovoltaic and the like has become a great strategic measure for global energy crisis alleviation, climate change countermeasures and ecological environment improvement. However, wind power and photovoltaic are affected by wind speed, solar radiation, temperature and other natural factors, the output power has obvious randomness, fluctuation and intermittence characteristics, peak regulation and frequency modulation pressure of a power grid are increased, safe, economical and stable operation of a power system is not facilitated, and the consumption of the power grid to wind power and photovoltaic is limited. Therefore, constructing a power generation system with complementary multiple functions and coordinated supply and demand is an important way to improve the utilization rate of renewable energy sources.
At present, the related researches of power supply capacity optimization configuration mostly adopt system typical daily scheduling optimization to replace time-series operation simulation every year every hour, and the economy and the power failure risk of the long-time operation process of the system cannot be accurately reflected. The multi-power complementary system with the water, fire and wind energy storage is simulated in an annual operation mode every hour, and due to the fact that the power supply is multiple in variety and long in optimization time period, the scheduling optimization model constructed according to the hour scale is large in scale and difficult to directly solve, and an efficient solving algorithm needs to be designed.
Disclosure of Invention
The invention aims to provide a power supply capacity configuration optimization method and system for a multi-energy complementary power generation system, which are used for solving the technical problem that an optimization model in the prior art cannot accurately evaluate the long-term running economy and power supply reliability of the system.
The first aspect of the invention provides a power capacity configuration optimization method of a multi-energy complementary power generation system, which comprises the following steps:
acquiring a capacity configuration scheme of each power supply in the multi-energy complementary power generation system, and acquiring the running cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme;
constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme, and constructing an inner layer optimization model according to the operation cost;
and determining a capacity allocation scheme which minimizes the sum of the allocation operation cost and the operation cost of all power supplies according to the outer layer optimization model and the inner layer optimization model.
Preferably, the power source comprises a new energy power station and a hydropower station;
the operation cost comprises the inter-network exchange cost of the system electric quantity, the waste electricity loss cost of the new energy power station and the waste water loss cost of the hydropower station;
the new energy power station comprises one of a wind power station and a photovoltaic power station.
Preferably, the power supply further comprises a thermal power station;
the operating costs also include fuel costs of the thermal power plant and carbon emission reduction costs of the thermal power plant.
Preferably, the sum of the output of all the power stations in the inner layer optimization model is equal to the load demand of the multi-energy complementary power generation system.
Preferably, the power output of the hydropower station is determined according to the power generation efficiency, the power generation flow rate and the power generation head.
Preferably, the power generation flow rate of the hydropower station is determined by using a 0-1 integer programming.
Preferably, the obtaining manner of the water discarding loss cost of the hydropower station in the inner layer optimization model is as follows:
acquiring a daily water level control value of each hydropower station under a daily scale;
under the constraint of the daily water level control value of each hydropower station, acquiring the water level control value of each hydropower station in an hour scale, and optimizing the water discarding loss cost of each hydropower station in the water level control value of each hydropower station in the hour scale.
Preferably, the power supply further includes a pumped storage power station, and the water level control value of the pumped storage power station is obtained by:
acquiring a daily water level control value of each pumped storage power station under a daily scale;
and under the constraint of the daily water level control value of each pumped storage power station, acquiring the water level control value of each pumped storage power station in an hour scale.
The second aspect of the invention provides a power capacity configuration optimization system of a multi-energy complementary power generation system, which comprises an information acquisition module, a model construction module and a configuration scheme determination module;
the information acquisition module is used for acquiring a capacity configuration scheme of each power supply in the multi-energy complementary power generation system and acquiring the running cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme;
the model construction module is used for constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme and constructing an inner layer optimization model according to the operation cost;
the configuration scheme determining module is used for determining a capacity configuration scheme which enables the sum of configuration operation cost and operation cost of all power supplies to be minimum according to the outer layer optimization model and the inner layer optimization model.
Compared with the prior art, the power supply capacity configuration optimization method and system for the multi-energy complementary power generation system have the following beneficial effects:
the power supply capacity allocation optimization method and system for the multi-energy complementary power generation system provided by the invention provide a two-layer planning model for the power supply capacity allocation problem of the grid-connected multi-energy complementary system consisting of wind power, photovoltaic, hydroelectric power, thermal power, pumped storage, mixed pumped storage, electrochemical energy storage and other power supplies, and can accurately evaluate the economic benefit and power supply reliability of the system in long-term operation.
The inner layer model of the invention provides an efficient solving algorithm for time scale layer-by-layer decomposition and progressive optimization, and the operation process of the system is scheduled every year and every hour by the accurate simulation system. The method is a long-and-short-time nested system annual hourly operation scheduling optimization method, effectively shortens the solving time of the inner-layer optimization model, can accurately simulate the annual operation economic benefit of the system, and provides evaluation indexes for the power supply capacity configuration scheme generated by the outer-layer model. The method can provide technical support for planning and constructing the multi-energy complementary base, and is suitable for popularization and application in the capacity refinement configuration of the large-scale multi-energy complementary system.
The invention provides a linearization conversion method for nonlinear relation between hydropower station output and flow and water head, which approximates and describes nonlinear equation constraint in an inner layer optimization model by a group of linear equations, so that the inner layer optimization model can be converted into a linear mixed integer programming model, and therefore, efficient solution is obtained.
Drawings
FIG. 1 is a schematic flow chart of a power capacity configuration optimization method of a multi-energy complementary power generation system according to an embodiment of the invention;
FIG. 2 is a detailed flowchart of a power capacity configuration optimization method of a multi-energy complementary power generation system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a power capacity configuration optimizing system of a multi-energy complementary power generation system according to an embodiment of the present invention.
In the figure, 101 is an information acquisition module; 102 is a model building module; 103 is a configuration scheme determination module.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth such as the particular system architecture, techniques, etc., in order to provide a thorough understanding of the embodiments of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
The first aspect of the present invention provides a method for optimizing power capacity configuration of a multi-energy complementary power generation system, as shown in fig. 1 and fig. 2, including:
step 1, acquiring a capacity configuration scheme of each power supply in the multi-energy complementary power generation system, and acquiring the running cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme.
In the embodiment of the present invention, the preset time period may be a long period, for example, half a year, full year, etc.
And 2, constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme, and constructing an inner layer optimization model according to the operation cost.
And 2.1, constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme.
The outer layer optimization model of the invention optimizes the scale of each power station in the power generation system, and is determined according to the sum of the configuration operation cost and the operation cost of all the power stations.
Illustratively, taking a multi-energy complementary power generation system comprising a wind power station, a photovoltaic power station and a pumped-storage power station as an example, an external layer optimization model is as shown in formula (1):
(1)
in the formula (1), the components are as follows,、/>and->The configuration operation and maintenance cost (the current cost value of the construction and operation and maintenance cost) of the wind power station, the photovoltaic power station and the pumped storage power station respectively; />The running cost of the multi-energy complementary power generation system in a preset time period is optimized through an inner layer optimization model; />Is a discount coefficient.
When other types of power stations exist, the configuration operation and maintenance cost of the other power stations is added in the formula (1), and the operation cost of the other power stations is taken into consideration.
The outer layer optimization model of the embodiment of the invention can be optimized by adopting an improved particle swarm algorithm, and can also adopt other heuristic optimization algorithms, such as a genetic algorithm, an ant colony algorithm and the like.
And 2.2, constructing an inner layer optimization model according to the operation cost.
(1) In the embodiment of the invention, when the power supply in the multi-energy complementary power generation system comprises a new energy power station and a hydropower station, the operation cost comprises the inter-network exchange cost of the system electric quantity, the waste electricity loss cost of the new energy power station and the waste water loss cost of the hydropower station, and the inner layer optimization model is the sum of the inter-network exchange cost of the system electric quantity, the waste electricity loss cost of the new energy power station and the waste water loss cost of the hydropower station. Wherein the new energy power station comprises a wind power station and a photovoltaic power station.
(2) When the power supply in the multi-energy complementary power generation system comprises a new energy power station, a hydropower station and a thermal power station, the operation cost comprises the fuel cost of the thermal power station, the carbon emission reduction cost of the thermal power station, the network exchange cost of the system electric quantity, the waste electricity loss cost of the new energy power station and the waste water loss cost of the hydropower station. The inner layer optimization model is the sum of the fuel cost of the thermal power station, the carbon emission reduction cost of the thermal power station, the network exchange cost of the system electric quantity, the waste electricity loss cost of the new energy power station and the waste water loss cost of the hydropower station.
Taking a power supply including a wind power station, a photovoltaic power station, a hydropower station and a thermal power station as an example, the inner layer optimization model in the embodiment of the invention is as shown in formula (2):
(2)
in the formula (2),the method is characterized in that the method is a thermal power unit fuel cost function and is obtained according to piecewise linear coal consumption coefficients; />Carbon emission reduction for thermal power unitCost; />For thermal power station->At->The output of the time period; />Is->The exchange cost between unit networks in a period; />For the system in->The amount of inter-network exchange of time periods; />Is->The unit new energy electricity discarding loss cost in the time period; />For wind power station->At->Predicting the force of the time period; />For wind power station->At->Grid-connected output of period>For photovoltaic power station->At->Predicting the force of the time period;for photovoltaic power station->At->Grid-connected output in a period; />For hydropower station->At->Water reject amount of the period.
In the optimization process of the inner-layer optimization model, a plurality of condition constraints are required to be met, and the constraints which are required to be met by the power supply in the multi-energy complementary power generation system are described by taking a wind power station, a photovoltaic power station, a hydropower station, a thermal power station, a pumped storage power station and an electrochemical storage power station as examples, specifically comprising:
(1) Power balance constraint: in a preset time period, the sum of the output of all the power stations is equal to the load requirement of the multi-energy complementary power generation system, as shown in a formula (3):
(3)
in the formula (3), the amino acid sequence of the compound,for hydropower station->At->The output of the time period; />、/>Respectively is pumped storage power station->At->Generating power and pumping power in a period of time; />For electrochemical energy-storage power stations->At->Pumping out force in a period of time; />Is a multi-energy complementary power generation system>Load demand for the time period.
(2) Hydropower station constraint
Hydropower station power description and water balance, such as formula (4) and formula (5):
(4)
(5)
hydropower station flow and reservoir capacity upper and lower boundary conditions are as shown in formulas (6) to (8):
(6)
(7)
(8)
wherein,for hydropower station->Is a coefficient of force; />,/>,/>And->Hydropower stations respectively->At->The flow rate, the power generation water head and the storage capacity of the period; />,/>,/>,/>,/>And->Hydropower stations respectively->Upper and lower bounds of the maximum reservoir capacity, excess flow and force.
(3) Pumped storage power station restraint
The following constraint conditions are applicable to construction forms such as pure pumped storage, mixed pumped storage, energy storage pump stations and the like.
Flow balance of the upper and lower libraries:
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
pumped storage power station and energy storage mill can not carry out pumping and power generation operation simultaneously:
(17)
(18)
(19)
wherein,and->0, 1 variable, ">Time pumped storage power station->At->Pumping force in time period->Time pumped storage power station->At->Generating power in a period of time; />And->Pumping and generating efficiency are respectively carried out; />,/>,/>Andrespectively is pumped storage power station->At->Pumping flow, generating flow, pumping output and generating output in the period; />And->The maximum output force of pumping water and generating electricity is respectively; />And->Respectively is pumped storage power station->At->Natural flow of reservoirs up and down in time period; />And->Generating electricity flow for hydropower stations of the upper reservoir and the lower reservoir; />And->The water disposal amounts of the upper reservoir and the lower reservoir are respectively; />And->Respectively is pumped storage power station->At->The reservoir capacity of the upper reservoir and the lower reservoir in the time period; />And->Respectively is pumped storage power station->At->Pumping lift and generating head in time period; />,/>,/>,/>The upper and lower boundaries of the reservoir capacity of the upper and lower reservoirs are respectively; />Is a unit time interval; />Is a very large number, +.>Gravitational acceleration.
For mixed pumped storage, when the upper reservoir or the lower reservoir is the hydropower station of the built reservoir,and->Respectively correspond to->And->;/>And->Respectively correspond to->And->;/>And->Respectively correspond to->And->;/>And->Respectively correspond to->And->The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->Index numbers of hydropower stations for the upper reservoir and the lower reservoir.
(4) Electrochemical energy storage power station restraint
(20)
(21)
(22)
(23)
(24)
(25)
Wherein,and->0, 1 variable, ">Time electrochemical energy storage station->At->Time period charging->Time electrochemical energy storage station->At->Discharging in a time period; />And->Electrochemical energy storage respectively->Charge and discharge efficiency; />For electrochemical energy-storage power stations->At->The amount of electricity in the time period; />And->Respectively chemical energy storage power station->At->Charging and discharging power of the period; />For electrochemical energy-storage power stations->Is set to the maximum power of (a).
(5) Thermal power output limiting constraint
And (5) limit of climbing speed of the thermal power generating unit:
(26)
thermal power output boundary condition:
(27)
(28)
(29)
wherein,and->Respectively is thermal power station->The output climbing and load shedding rate of the hydraulic pump; />And->Respectively is thermal power station->At the position ofMinimum and maximum output for a period of time; />For thermal power station->At->The starting number of the time period>For thermal power station->Is a single-machine capacity of (a),and indexing the start-stop period of the thermal power generating unit, wherein the thermal power is used for controlling the number of the start-up units according to the start-stop period.
(6) Boundary condition of wind power and photovoltaic power supply power
(30)
(31)
(7) System rotation reserve constraint
Considering that the pumped storage unit can realize the rapid conversion between power generation and pumping, the standby capacity which can be provided in the pumping state is the sum of pumping power and maximum power generation, namely when the pumped storage station is in the pumping state, the positive rotation standby is to stop pumpingConversion to maximum power generation condition +.>Negative rotation is used as the same.
Positive rotation reserve constraint:
(32)
negative rotation reserve constraint:
(33)
wherein,for the system in->The spare capacity is rotated at the moment.
In the embodiment of the invention, the output of the hydropower station in the inner-layer optimization model is determined according to the power generation efficiency, the power generation flow and the power generation water head of the hydropower station.
The power generation water head of the hydropower station is determined by the water level at the upstream and the downstream, and the power generation water head can be described as a linear function of the reservoir capacity, namely:
(34)
in the method, in the process of the invention,、/>are all constant.
When the power generation output of the hydropower station is calculated in the model, a water head and reservoir capacity functional formula (34) is substituted into the hydropower transfer function, and the relationship between the power generation output of the hydropower station, the power generation flow and the reservoir capacity is obtained as follows:
(35)
the power generation output in the formula (32) is a quadratic function of the power generation flow multiplied by the reservoir capacity, so that the model is a nonlinear problem, and difficulty is brought to model solving. The model is converted to a linear mixed integer programming problem for solution by the following linearization process.
First, the reservoir is filled withIs discretized to obtain->Discrete variables. A set of 0-1 variables is introduced->,/>Then->The expression can be as follows:
(36)
in the method, in the process of the invention,is->The hydropower station is->Generating flow during time period, +.>To be->Flow rate of electricity generated by hydropower stationThe first discretized value, < >>Is a variable of 0-1, and +.>,/>Is the number of total discrete values.
Then there are:
(37)
(38)
further linearizing the formula (38) to obtain the formulas (39) - (42):
(39)
(40)
(41)
(42)
the invention provides a linearization conversion method for nonlinear relation between hydropower station output and flow and water head, which approximates and describes nonlinear equation constraint in an inner layer optimization model by a group of linear equations, so that the inner layer optimization model can be converted into a linear mixed integer programming model, and therefore, efficient solution is obtained.
The system operation mode is usually required to be simulated in an hour-by-hour mode; the model constructed according to the hour scale is large in scale and difficult to directly solve, so that the model is decomposed and nested according to the time scale to solve, and the method comprises the following steps of: firstly, taking the day as a scale, taking the electric quantity balance of the system into consideration for operation scheduling optimization, and solving to obtain the daily water level control values of each hydropower station and pumped storage power station of the system. Next, under the constraint of the daily water level control value, economic dispatch optimization within the daily day of the system is performed on an hour scale. By nesting in a long time scale and a short time scale, the model scale is effectively reduced, and the commercial solving software can carry out efficient solving, so that the system operation optimization result can be obtained every hour throughout the year.
The specific acquisition mode of the water discarding loss cost of the hydropower station in the inner layer optimization model is as follows:
acquiring a daily water level control value of each hydropower station under a daily scale;
under the constraint of the daily water level control value of each hydropower station, the water level control value of each hydropower station in the scale of hours is obtained, and the water discarding loss cost of the hydropower station under the water level control value of each hydropower station in the scale of hours is optimized.
In the embodiment of the invention, the power supply further comprises a pumped storage power station, and the specific acquisition mode of the water level control value of the pumped storage power station is as follows:
acquiring a daily water level control value of each pumped storage power station under a daily scale;
under the constraint of the electricity discarding loss cost and the daily water level control value of each pumped storage power station, the water level control value of each pumped storage power station in the scale of hours is obtained, and the operation cost of each pumped storage power station is determined under the constraint of the water level control value of each pumped storage power station in the scale of hours.
The invention develops a scheduling optimization method for the annual hourly operation of a long-time nested system, effectively shortens the solving time of an inner layer optimization model, accurately simulates the annual economic benefit of the annual operation of the system, and provides an evaluation index for a power supply capacity configuration scheme generated by an outer layer model. The method can provide technical support for planning and constructing the multi-energy complementary base, and is suitable for popularization and application in the capacity refinement configuration of the large-scale multi-energy complementary system.
And 3, determining a capacity allocation scheme which enables the sum of the allocation operation cost and the operation cost of all power supplies to be minimum according to the outer layer optimization model and the inner layer optimization model.
A second aspect of the present invention provides a power capacity configuration optimization system of a multi-energy complementary power generation system, as shown in fig. 3, including an information acquisition module 101, a model construction module 102, and a configuration scheme determination module 103;
the information acquisition module 101 is configured to acquire a capacity configuration scheme of each power supply in the multi-energy complementary power generation system, and acquire an operation cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme;
the model construction module 102 is used for constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme, and constructing an inner layer optimization model according to the operation cost;
the configuration scheme determining module 103 is configured to determine a capacity configuration scheme that minimizes a sum of configuration operation costs and operation costs of all power sources according to the outer layer optimization model and the inner layer optimization model.
The power supply capacity allocation optimization method and system for the multi-energy complementary power generation system provided by the invention provide a two-layer planning model for the power supply capacity allocation problem of the grid-connected multi-energy complementary system consisting of wind power, photovoltaic, hydroelectric power, thermal power, pumped storage, mixed pumped storage, electrochemical energy storage and other power supplies, and can accurately evaluate the economic benefit and power supply reliability of the system in long-term operation.
The foregoing description is only a few examples of the present application and is not intended to limit the present application in any way, and although the present application is disclosed in the preferred examples, it is not intended to limit the present application, and any person skilled in the art may make some changes or modifications to the disclosed technology without departing from the scope of the technical solution of the present application, and the technical solution is equivalent to the equivalent embodiments.
Claims (6)
1. The power supply capacity configuration optimization method of the multi-energy complementary power generation system is characterized by comprising the following steps of:
acquiring a capacity configuration scheme of each power supply in the multi-energy complementary power generation system, and acquiring the running cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme;
constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme, and constructing an inner layer optimization model according to the operation cost;
determining a capacity allocation scheme which minimizes the sum of the allocation operation cost and the operation cost of all power supplies according to the outer layer optimization model and the inner layer optimization model;
the power supply comprises a hydropower station, and the nonlinear hydropower transfer function is linearized by discretizing the flow of a reservoir of the hydropower station and introducing auxiliary variables;
the acquisition mode of the abandoned water loss cost of the hydropower station in the inner layer optimization model is as follows:
acquiring a daily water level control value of each hydropower station under a daily scale;
under the constraint of the daily water level control value of each hydropower station, acquiring the water level control value of each hydropower station with the hour as a scale, and optimizing the water discarding loss cost of each hydropower station with the water level control value of each hydropower station with the hour as the scale;
the power supply also comprises a pumped storage power station, and the water level control value of the pumped storage power station is obtained by the following steps:
acquiring a daily water level control value of each pumped storage power station under a daily scale;
and under the constraint of the daily water level control value of each pumped storage power station, acquiring the water level control value of each pumped storage power station in an hour scale.
2. The method for optimizing power capacity configuration of a multi-energy complementary power generation system according to claim 1, wherein the power source comprises a new energy power station;
the operation cost comprises the inter-network exchange cost of the system electric quantity, the waste electricity loss cost of the new energy power station and the waste water loss cost of the hydropower station;
the new energy power station comprises a wind power station and a photovoltaic power station.
3. The method for optimizing power capacity configuration of a multi-energy complementary power generation system according to claim 2, wherein the power source further comprises a thermal power station;
the operating costs also include fuel costs of the thermal power plant and carbon emission reduction costs of the thermal power plant.
4. The method for optimizing power capacity configuration of a multi-energy complementary power generation system according to claim 2, wherein the sum of the output of all the power stations in the internal layer optimization model is equal to the load demand of the multi-energy complementary power generation system.
5. The method for optimizing power capacity configuration of a multi-energy complementary power generation system according to claim 4, wherein the power output of the hydropower station is determined according to the power generation efficiency, the power generation flow rate and the power generation head.
6. A power supply capacity configuration optimizing system of a multi-energy complementary power generation system based on the power supply capacity configuration optimizing method of a multi-energy complementary power generation system according to any one of claims 1 to 5, characterized by comprising an information acquisition module, a model construction module and a configuration scheme determination module;
the information acquisition module is used for acquiring a capacity configuration scheme of each power supply in the multi-energy complementary power generation system and acquiring the running cost of the multi-energy complementary power generation system in a preset time period under the capacity configuration scheme;
the model construction module is used for constructing an outer layer optimization model according to the configuration operation cost and the operation cost of the capacity configuration scheme and constructing an inner layer optimization model according to the operation cost;
the configuration scheme determining module is used for determining a capacity configuration scheme which enables the sum of configuration operation cost and operation cost of all power supplies to be minimum according to the outer layer optimization model and the inner layer optimization model.
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