CN111404206A - Wind-solar energy storage power generation system capacity double-layer planning method considering investment return constraint - Google Patents

Wind-solar energy storage power generation system capacity double-layer planning method considering investment return constraint Download PDF

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CN111404206A
CN111404206A CN202010315809.9A CN202010315809A CN111404206A CN 111404206 A CN111404206 A CN 111404206A CN 202010315809 A CN202010315809 A CN 202010315809A CN 111404206 A CN111404206 A CN 111404206A
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CN111404206B (en
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肖曦
杨博文
田培根
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Tsinghua University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46Controlling of the sharing of output between the generators, converters, or transformers
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/28Arrangements for balancing of the load in a network by storage of energy
    • H02J3/32Arrangements for balancing of the load in a network by storage of energy using batteries with converting means
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E70/00Other energy conversion or management systems reducing GHG emissions
    • Y02E70/30Systems combining energy storage with energy generation of non-fossil origin

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Abstract

The invention relates to a capacity double-layer planning method of a wind-solar energy storage power generation system considering investment return constraints, which comprises the steps of obtaining typical daily data of illumination radiation intensity and wind speed in the wind-solar energy storage power generation system, load demand data and parameters of various energy supply devices in the wind-solar energy storage power generation system; constructing a mathematical model of each energy supply device in the wind-solar energy storage power generation system; constructing a double-layer optimization model of the wind-solar-storage power generation system, planning the capacity of system equipment by using the maximum annual net income of the wind-solar-storage power generation system under a given return investment rate as a target by using an upper-layer optimization model, and optimizing the system operation state by using the maximum daily electricity selling income of the wind-solar-storage power generation system as a target by using a lower-layer optimization model; and solving the double-layer optimization model to obtain an optimal capacity configuration result of the wind-solar energy storage power generation system. The invention introduces the investment return constraint into the wind-solar-energy storage power generation system double-layer planning model, and can reduce the system investment cost under the condition that the total income is basically kept unchanged, thereby improving the investment return rate and shortening the investment return time limit.

Description

Wind-solar energy storage power generation system capacity double-layer planning method considering investment return constraint
Technical Field
The invention relates to the technical field of energy planning, in particular to a capacity double-layer planning method of a wind-solar energy storage power generation system considering investment return constraints.
Background
In order to solve the problems of exhaustion of traditional fossil energy and environmental pollution, renewable clean energy represented by photovoltaic and wind power is widely applied. The wind resource and the illumination resource show better complementary characteristics on a time scale. The wind-solar energy storage power generation system constructed by utilizing the complementary characteristics is also called a micro-grid system, so that the resource utilization efficiency can be effectively improved. Wind power resources and illumination resources are greatly influenced by environmental factors and have strong randomness and intermittence, so that energy storage equipment with certain capacity needs to be configured to stabilize system output, but the high energy storage price increases the cost pressure of the system. In order to improve the economy of the wind-solar energy storage power generation system, the capacities of equipment such as a photovoltaic device, a fan and an energy storage battery in the system need to be reasonably planned.
The existing integrated energy system planning first determines the structure of the system, and then selects the type of equipment and the monomer capacity required in the system. And according to the historical typical data of the renewable energy sources and the historical typical data of the loads, constructing an optimization model by taking the maximum system benefit or the minimum cost and the like as optimization targets, and solving the model by adopting a mathematical programming method or an intelligent algorithm to obtain the optimal comprehensive energy system equipment capacity.
For a specific wind-solar energy storage power generation system project, economic benefits are the most important basis for an investment builder to evaluate a wind-solar energy storage power generation system, and economic indexes adopted in existing researches only comprise relatively single targets of investment cost or net income and the like, and the economic efficiency of the whole life cycle of the system cannot be considered relatively comprehensively. Therefore, the problems of high investment cost and long investment recovery time of the whole wind-solar energy storage power generation system caused by single economic target are technical problems to be solved in the field.
Disclosure of Invention
In order to solve the problem of capacity planning of the wind-solar energy storage power generation system, the invention provides a capacity double-layer planning method of the wind-solar energy storage power generation system, which considers the investment return constraint, adds the investment return constraint in the planning, and improves the economy of the system.
In order to achieve the purpose, the invention provides a capacity double-layer planning method of a wind-solar energy storage power generation system considering return on investment constraint, which comprises the following steps:
obtaining typical daily data of illumination radiation intensity and wind speed in the wind-solar storage power generation system, load demand data and parameters of various energy supply devices in the wind-solar storage power generation system;
constructing a mathematical model of each energy supply device in the wind-solar energy storage power generation system;
constructing a double-layer optimization model of the wind-solar-storage power generation system, planning the capacity of system equipment by using the maximum annual net income of the wind-solar-storage power generation system under a given return investment rate as a target by using an upper-layer optimization model, and optimizing the system operation state by using the maximum daily electricity selling income of the wind-solar-storage power generation system as a target by using a lower-layer optimization model;
and solving the double-layer optimization model by adopting a self-adaptive inertial weight particle swarm algorithm based on the typical daily data of the illumination radiation intensity and the wind speed in the wind-solar energy storage power generation system, the load demand data and the parameters of each energy supply device in the wind-solar energy storage power generation system to obtain the optimal capacity configuration result of the wind-solar energy storage power generation system.
Further, the construction of a mathematical model of each energy supply device inside the wind-solar energy storage power generation system comprises the following steps: building mathematical models of a wind driven generator, a photovoltaic power generation system, a current conversion device and an energy storage battery; the current converting apparatus includes: the system comprises a photovoltaic converter, a fan converter, an energy storage converter and a bidirectional DC/AC converter.
Further, the mathematical model of the wind power generator is as follows:
Figure BDA0002459416670000021
PWTis the output power of the wind-driven generator, PwtrIs rated output power of wind power generator, vciIs the wind generator cut-in wind speed, vcoIs the cut-out wind speed v of the wind power generatorrIs the rated wind speed of the wind driven generator;
the mathematical model of the photovoltaic power generation system is as follows:
PPV=ηPVPstcG/Gstc(1+ηT(T-Tstc))
PPVis the output power of the photovoltaic power generation system, ηPVIs the generating efficiency of the photovoltaic power generation system, PstcIs the output power of the photovoltaic power generation system under rated conditions, G is the actual illumination radiation intensity on the photovoltaic panel, GstcIs rated illumination intensity, T is actual temperature of the photovoltaic power generation system, and TstcRated temperature of photovoltaic power generation system, ηTIs the temperature coefficient of variation of the photovoltaic power generation system;
the mathematical model of the converter equipment is as follows:
Pin=KconPout
Pinis the input power of the inverter, KconIs the converter conversion efficiency, PoutIs the converter output power;
the energy storage battery mathematical model is as follows:
Figure BDA0002459416670000031
e (t) is the residual energy of the energy storage battery at the moment t; dc(t) and dd(t) a set of mutually exclusive 0-1 state variables respectively representing charging and discharging states of the energy storage device, the mutual exclusion representing that the energy storage device only performs one action of charging or discharging at a certain time ηcIndicating charging efficiency, ηdIndicating the efficiency of discharge, Pc(t) represents the charging power, Pd(t) represents discharge power.
Further, the optimization target of the upper layer optimization model is as follows:
maxF1=Cmony-(CINV+CCON+COP)
Cmonyis the total income of electricity sold in the system year CINVIs the cost of equipment acquisition, CCONIs the construction cost COPIs the cost of operation and maintenance;
Cmony=365Cmond
Figure BDA0002459416670000032
CCON=KCONCINI
COP=KOPCINI
wherein, CmondThe daily electricity selling income of the wind and light storage power generation system is obtained; cINIIs the investment cost of system equipment; m ispvAnd mwdThe price of the photovoltaic and the fan are respectively the monomer price; n is a radical ofpvAnd NwdThe number of photovoltaic and fans; r is0Is the discount rate; y isyThe service life of the photovoltaic and the fan is prolonged;
Figure BDA0002459416670000033
representing the price of the ith converter monomer;
Figure BDA0002459416670000034
indicating the number of the i-th converters;
Figure BDA0002459416670000035
the service life of the ith converter is shown; m issIs the monomer price of the energy storage battery, NsIs the number of energy storage cells; y issThe service life of the energy storage battery; kCONThe construction cost coefficient; kOPIs a maintenance cost factor.
Further, the upper layer model constraints include:
(1) device configuration capacity constraints
Figure BDA0002459416670000041
Figure BDA0002459416670000042
Figure BDA0002459416670000043
Figure BDA0002459416670000044
Wherein,
Figure BDA0002459416670000045
and
Figure BDA0002459416670000046
the maximum configuration quantity of the photovoltaic, the fan, the current converter and the energy storage battery is respectively set;
(2) return on investment constraint
ROI≥ROIref
Wherein, the ROI is the return on investment of the wind-solar energy storage power generation systemrefIs a set value of return on investment;
the method for calculating the return on investment is as follows:
Figure BDA0002459416670000047
CMannual electricity selling income of wind-light storage power generation system CTOTALIs the total investment cost of the system.
Further, the optimization goal of the lower layer optimization model is as follows:
maxF2=Cmond
Cmondis the daily electricity selling income of the wind and light storage power generation system,
Figure BDA0002459416670000048
wherein, PoutAnd (T) respectively represents the output power of the wind-solar energy storage power generation system at the moment T, e (T) represents the real-time electricity selling price, and T represents the optimized dispatching cycle of the wind-solar energy storage power generation system.
Further, the lower layer optimization model constraint conditions include:
(1) power balance constraint
Pdcout(t)=Ppv(t)+Pwd(t)-Pbat(t)
Wherein, Pout(t) is the output power, Ppv(t) is the output power of the photovoltaic power generation system, Pwd(t) is the wind turbine output power, Pbat(t) is the absorbed power of the energy storage battery;
(2) wind driven generator output constraint
Figure BDA0002459416670000051
Wherein,
Figure BDA0002459416670000052
allowing the wind driven generator to output a minimum value at the moment t;
Figure BDA0002459416670000053
the maximum value is allowed to be output for the wind driven generator at the moment t;
(3) photovoltaic output constraint
Figure BDA0002459416670000054
Wherein,
Figure BDA0002459416670000055
allowing the photovoltaic power generation system to output a minimum value at the moment t;
Figure BDA0002459416670000056
outputting a maximum value allowed by the photovoltaic power generation system at the moment t;
(4) converter equipment output constraint
Figure BDA0002459416670000057
Wherein,
Figure BDA0002459416670000058
is the output power of the inverter at time t,
Figure BDA0002459416670000059
and
Figure BDA00024594166700000510
allowing the minimum value and the maximum value to be output for the converter at the moment t;
(5) energy storage battery charge and discharge constraints
Figure BDA00024594166700000511
Figure BDA00024594166700000512
Wherein, Pd(t) and Pc(t) power of discharging and charging the energy storage battery at time t, ηdAnd ηcFor the purpose of the discharge efficiency and the charge efficiency,
Figure BDA00024594166700000513
and
Figure BDA00024594166700000514
for the minimum and maximum power allowed for discharge,
Figure BDA00024594166700000515
and
Figure BDA00024594166700000516
minimum and maximum power allowed for charging;
(6) and (4) energy storage battery state constraint:
Figure BDA00024594166700000517
Smin≤S(t)≤Smax
S(0)=S(T)
wherein S (t) is the energy storage state of the energy storage device at the t moment, dc(t) and dd(t) are a set of mutually exclusive 0-1 state variables, η, respectivelycIndicating charging efficiency, ηdIndicating the efficiency of discharge, Pc(t) represents the charging power, Pd(t) represents discharge power, CbatFor the total capacity of the energy storage cell, SminAllowing minimum value, S, for stored energy statemaxThe maximum allowed value of the energy storage state is S (0), the initial value of the charge state of the energy storage equipment is S (T), and the charge state of the energy storage equipment after the whole scheduling period is S (T);
(7) output power fluctuation limitation:
|Pout(t)-Pout(t-1)|<KlimPR
wherein, Pout(t) the output power of the wind-solar energy storage power generation system at the moment t, KlimFor output power fluctuation limiting parameter, PRThe rated capacity of the wind-solar energy storage power generation system is obtained.
Further, the upper layer optimization model is used for solving to obtain system equipment capacity, and the system equipment capacity is input into the lower layer optimization model to be used as a lower layer model constraint condition; solving by a lower-layer optimization model to obtain daily electricity selling income C of the wind-solar storage power generation systemmondAnd inputting the data into an upper optimization model.
Further, the upper and lower layer optimization models are solved by adopting a self-adaptive inertial weight particle swarm algorithm, and the solving process comprises the following steps:
(1) inputting equipment parameters and wind and light typical day data, and determining the population number NUPDetermining the maximum number of iterations M of the upper layerUPInitializing each particle by taking the equipment capacity as each particle, and initializing an optimal value and a global optimal value of each particle of an upper layer model;
(2) calculating the inertia weight of the upper layer model;
(3) updating the speed and position of the upper layer particles;
(4) taking each particle on the upper layer as a constraint condition to be brought into the model on the lower layer, generating the initial running state of the system, and determining the population quantity NDOWNDetermining the maximum iteration number M of the lower layer modelDOWMInitializing an optimal value and a global optimal value of each particle in the lower model;
(5) calculating the inertia weight of the lower layer model;
(6) updating the speed and position of the lower layer particles;
(7) calculating the adaptive value of each particle in the lower model, namely the electricity selling income;
(8) updating the optimal value and the global optimal value of each particle in the lower model;
(9) judging whether the maximum iteration number M of the lower layer model is reachedDOWMIf not, returning to the step (5); if so, entering (10);
(10) returning an adaptive value corresponding to the global optimal value of the lower model, namely the electricity selling income to the upper model;
(11) transmitting the upward electricity selling income by using the lower layer model, and calculating the adaptive value of each particle of the upper layer model, namely net income;
(12) updating the optimal value and the global optimal value of each particle in the upper model;
(13) judging whether the maximum iteration number M of the upper layer model is reachedUP(ii) a If not, returning to the step (2); if so, entering (14);
(14) and outputting an optimal capacity configuration result.
The technical scheme of the invention has the following beneficial technical effects:
according to the method, a double-layer planning model of the wind-solar-storage power generation system is constructed, the upper layer model plans the capacity of system equipment with the maximum net income of the system, and the lower layer optimizes the running state of the system with the maximum daily electricity selling income of the system; the investment return constraint is introduced into the wind-solar-energy storage power generation system double-layer planning model, so that the system investment cost can be reduced under the condition that the total income is basically kept unchanged, the investment return rate is improved, and the investment return year is shortened.
Drawings
FIG. 1 is a flow chart of a wind-solar-storage power generation system planning;
FIG. 2 is a schematic structural diagram of a wind-solar-energy storage power generation system;
FIG. 3 is a schematic diagram of a two-layer optimization;
FIG. 4 is a schematic diagram of a solving process based on an adaptive weight particle swarm algorithm model;
FIG. 5 is a typical solar irradiance profile;
FIG. 6 is a typical solar wind speed curve;
FIG. 7 is a photovoltaic device output curve in scene 2;
fig. 8 is a wind turbine output curve in scenario 2.
Fig. 9 is a graph of the energy storage device output in scenario 2.
FIG. 10 is a curve of the output power of the wind-solar energy storage power generation system in scene 2.
Fig. 11 is an output power curve of the wind-solar energy storage power generation system before being stabilized by the energy storage device in scene 2.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
The invention provides a planning method of a wind-solar energy storage power generation system, which comprises the following steps of:
step 1, obtaining typical daily data of illumination radiation intensity and wind speed in a wind-solar storage power generation system, and specific parameters of equipment such as photovoltaic equipment, a fan, a converter and the like for calculating the output of photovoltaic power generation equipment and the output of a wind driven generator. And acquiring load demand data for calculating the electricity selling income of the system. Step 2, constructing a model of internal equipment of the wind-solar energy storage power generation system: and establishing a mathematical model of all devices in the system according to the structure of the wind-solar energy storage power generation system. The wind-solar energy storage power generation system is structurally shown in fig. 2, and comprises the following main devices: the device comprises a wind driven generator, a photovoltaic power generation system, a current conversion device and an energy storage battery. The current converting apparatus includes: photovoltaic converter, fan converter, energy storage converter, two-way DC/AC converter.
(1) The wind driven generator mathematical model is as follows:
Figure BDA0002459416670000081
PWTis the output power of the wind-driven generator, PwtrIs rated output power of wind power generator, vciIs the wind generator cut-in wind speed, vcoIs the cut-out wind speed, vrIs the rated wind speed.
(2) Photovoltaic power generation system mathematical model:
PPV=ηPVPstcG/Gstc(1+ηT(T-Tstc))
PPVis the output power of the photovoltaic power generation system, ηPVIs the generating efficiency of the photovoltaic power generation system, PstcIs the output power of the photovoltaic power generation system under rated conditions, G is the actual illumination radiation intensity on the photovoltaic panel, GstcThe rated illumination intensity is generally 1kW/m2T is the actual temperature of the photovoltaic power generation system, TstcIs rated temperature, ηTIs the temperature coefficient of variation of the photovoltaic power generation system.
(3) The mathematical model of the converter equipment is as follows
Pin=KconPout
PinIs the input power of the inverter, KconIs the converter conversion efficiency, PoutIs the inverter output power. The commutation equipment in the wind-solar energy storage power generation system comprises: photovoltaic converter, fan converter, energy storage converter, two-way DC/AC converter.
(4) The energy storage battery mathematical model is as follows:
Figure BDA0002459416670000091
e (t) is the residual energy of the energy storage battery at the moment t; dc(t) and dd(t) a set of mutually exclusive 0-1 state variables respectively representing charging and discharging states of the energy storage device, the mutual exclusion representing that the energy storage device only performs one action of charging or discharging at a certain time ηcIndicating charging efficiency, ηdIndicating the efficiency of discharge, Pc(t) represents the charging power, Pd(t) represents discharge power.
Step 3, establishing a double-layer optimization model of the wind-solar storage power generation system: and constructing a wind-solar energy storage power generation system double-layer optimization model based on return on investment limitation according to the structure of the wind-solar energy storage power generation system. The upper layer plans the capacity of the system equipment by taking the maximum annual net income of the system under the given return on investment as a target, and the lower layer optimizes the running state of the system by taking the maximum daily electricity selling income of the system as a target. The equipment capacity planning result of the upper model is transmitted to the lower model to be used as the operation constraint condition of the lower model; the lower layer model optimizes the system running state, calculates optimized electricity selling income and transmits the electricity selling income to the upper layer model; the upper layer model subtracts the system cost from the electricity selling income to obtain the net system income which is used for judging the quality of the equipment capacity planning result; and obtaining the optimal system equipment capacity combination through multiple iterations between the upper layer and the lower layer.
The structure of the double-layer optimization is shown in FIG. 3:
1. upper optimization model
And the upper layer model configures the equipment capacity of the wind-solar energy storage power generation system with the maximum annual net income of the wind-solar energy storage power generation system as a target. The specific optimization objectives are as follows:
maxF1=Cmony-(CINV+CCON+COP)
Cmonyis the annual electricity selling total income of the wind-light storage power generation system CINVThe purchase cost of wind-solar energy storage power generation system equipment, CCONThe construction cost of the wind-solar energy storage power generation system COPIs the cost of operation and maintenance. The specific formula is as follows:
(1) annual electricity selling income model
Cmony=365Cmond
Wherein, CmondThe daily electricity selling income of the wind and light storage power generation system is an optimization result of the lower-layer operation optimization model.
(2) Equipment purchase cost model
Figure BDA0002459416670000101
Wherein, CINIInvestment cost for system equipment; m ispvAnd mwdThe price of the photovoltaic and the fan are respectively the monomer price; n is a radical ofpvAnd NwdThe number of photovoltaic and fans; r is0Is the discount rate; y isyThe service life of the photovoltaic and the fan is prolonged;
Figure BDA0002459416670000102
the price of the ith converter is shown, and the total 4 converters are shown according to the structure diagram of the wind-solar energy storage power generation system shown in figure 1, and are respectively: the system comprises an energy storage converter, a photovoltaic converter, a fan converter and a DC/AC converter;
Figure BDA0002459416670000103
indicating the number of the i-th converters;
Figure BDA0002459416670000104
the service life of the ith converter is shown; m issIs the monomer price of the energy storage battery, NsIs the number of energy storage cells; y issThe service life of the energy storage battery is prolonged.
(3) Construction cost model
CCON=KCONCINI
Wherein, KCONTo build cost factors, CINIAnd investment cost of system equipment is saved.
(4) Maintenance cost model
COP=KOPCINI
Wherein, KOPIs a maintenance cost factor.
2. Upper layer model constraints
(3) Device configuration capacity constraints
Figure BDA0002459416670000105
Figure BDA0002459416670000106
Figure BDA0002459416670000107
Figure BDA0002459416670000108
Wherein,
Figure BDA0002459416670000109
and
Figure BDA00024594166700001010
the maximum configuration quantities of the photovoltaic, the fan, the current converter and the energy storage battery are respectively.
(4) Return on investment constraint
ROI≥ROIref
Wherein, the ROI is the return on investment of the wind-solar energy storage power generation systemrefIs set for the return on investment. The return on investment is the economic return that an investor receives from an investment activity. The return on investment rate is an important economic index, can reflect the comprehensive profit capacity of the investment center, and has transverse comparability because the irrelative factors of profit difference caused by different investment amounts are eliminated, thereby being beneficial to judging the profit quality of each investment project. Therefore, the invention provides that the return on investment rate constraint is added into the optimal capacity configuration of the wind-solar energy storage power generation system, and the economy of the configuration result is improved.
The method for calculating the return on investment is as follows:
Figure BDA0002459416670000111
CMannual electricity selling income of wind-light storage power generation system CTOTALIs the total investment cost of the system.
3. Lower optimization model
The lower-layer optimization model optimizes the operation state of the wind-solar energy storage power generation system by taking the maximum daily electricity selling income of the wind-solar energy storage power generation system as a target, and the specific optimization target is as follows:
maxF2=Cmond
Cmondthe system daily electricity selling income is as follows:
Figure BDA0002459416670000112
wherein, PoutAnd (t) the output power of the system at the moment t, and e (t) the real-time electricity selling price.
4. Lower layer model constraint conditions
(1) Power balance constraint
Pdcout(t)=Ppv(t)+Pwd(t)-Pbat(t)
Wherein, Pout(t) is the output power, Ppv(t) is the photovoltaic output power, Pwd(t) is the wind turbine output power, PbatAnd (t) the absorbed power of the energy storage battery.
(2) Distributed power supply output constraint
Figure BDA0002459416670000113
Figure BDA0002459416670000114
Wherein, Ppv(t) and Pwd(t) the output power of the photovoltaic generator and the wind driven generator at the moment t respectively,
Figure BDA0002459416670000115
and
Figure BDA0002459416670000116
the minimum value and the maximum value are allowed to be output for the photovoltaic time t,
Figure BDA0002459416670000117
and
Figure BDA0002459416670000118
and allowing the minimum value and the maximum value to be output for the wind driven generator at the moment t.
(3) Converter equipment output constraint
Figure BDA0002459416670000121
Wherein,
Figure BDA0002459416670000122
is the output power of the inverter at time t,
Figure BDA0002459416670000123
and
Figure BDA0002459416670000124
and allowing the minimum value and the maximum value to be output for the moment t of the inverter.
(4) Energy storage battery charge and discharge constraints
Figure BDA0002459416670000125
Figure BDA0002459416670000126
Wherein, Pd(t) and Pc(t) power of discharging and charging the energy storage battery at time t, ηdAnd ηcFor the purpose of the discharge efficiency and the charge efficiency,
Figure BDA0002459416670000127
and
Figure BDA0002459416670000128
for the minimum and maximum power allowed for discharge,
Figure BDA0002459416670000129
and
Figure BDA00024594166700001210
the minimum power and the maximum power allowed for charging.
(5) And (4) energy storage battery state constraint:
Figure BDA00024594166700001211
Smin≤S(t)≤Smax
S(0)=S(T)
wherein, S (t) is the energy storage state of the energy storage device at the t moment. dc(t) and dd(t) are a set of mutually exclusive 0-1 state variables respectively representing charging and discharging states of the energy storage device, the mutual exclusion indicating that the energy storage device performs only one action of charging or discharging at a certain time ηcIndicating charging efficiency, ηdIndicating the efficiency of discharge, Pc(t) represents the charging power, Pd(t) represents discharge power. CbatIs the total capacity of the energy storage battery. SminAllowing minimum value, S, for stored energy statemaxAnd S (0) is the initial value of the charge state of the energy storage equipment, and S (T) is the charge state of the energy storage equipment after the whole scheduling period.
(6) Output power fluctuation limitation:
|Pout(t)-Pout(t-1)|<KlimPR
wherein, Pout(t) System output Power at time t, KlimFor output power fluctuation limiting parameter, PRIs the rated capacity of the system.
Step 4, model solving: and solving the upper layer model and the lower layer model by adopting a self-adaptive inertial weight particle swarm algorithm to obtain the optimal capacity configuration result of the wind-solar energy storage power generation system. The solving process of the particle swarm optimization system based on the adaptive inertial weight is shown in fig. 4. The method comprises the following steps:
(1) inputting equipment parameters and wind and light typical day data, and determining the population number NUPDetermining the maximum number of iterations M of the upper layerUPInitializing each particle (equipment capacity), and initializing an optimal value and a global optimal value of each particle of an upper model;
(2) calculating the inertia weight of the upper layer model;
(3) updating the speed and position of the upper layer particles;
(4) taking each particle (equipment capacity combination) of the upper layer as a constraint condition to be brought into the lower layer model, generating the initial running state of the system, and determining the population number NDOWNDetermining the maximum iteration number M of the lower layer modelDOWMInitializing an optimal value and a global optimal value of each particle in the lower model;
(5) calculating the inertia weight of the lower layer model;
(6) updating the speed and position of the lower layer particles;
(7) calculating the adaptive value (electricity selling income) of each particle in the lower model;
(8) updating the optimal value and the global optimal value of each particle in the lower model;
(9) judging whether the maximum iteration number M of the lower layer model is reachedDOWM. If not, returning to the step (5). If not, entering (10);
(10) returning an adaptive value (electricity selling income) corresponding to the global optimal value of the lower model to the upper model;
(11) calculating adaptive values (net benefits) of particles (equipment capacity combination) of the upper layer model by using the running cost transmitted by the lower layer model;
(12) updating the optimal value and the global optimal value of each particle in the upper model;
(13) judging whether the maximum iteration number M of the upper layer model is reachedUP. If not, returning to the step (2). If not, entering (14);
(14) and outputting an optimal capacity configuration result.
Based on the planning method of the wind-solar energy storage power generation system, the actual engineering data of the grid-connected wind-solar energy storage power generation system with a certain rated capacity requirement of 12MW is selected for simulation. The total period of the project is 25 years. Typical solar illumination radiation intensity data is shown in fig. 5, and typical solar wind speed is shown in fig. 6.
The wind-solar-energy storage power generation system equipment parameters are shown in table 1.
TABLE 1 Equipment parameters
Figure BDA0002459416670000141
The energy storage cell parameters are shown in table 2.
TABLE 2 energy storage Battery parameters
Figure BDA0002459416670000142
In the present embodiment, theAnd the grid-connected wind-solar storage power generation system generates electric energy which is sold to a power grid. The peak time is 9-22 points per day, and the non-peak time is 0-8 points and 23-24 points per day. The unit charge duration is 15 minutes. Rated power supply (GE) signed at peak timep)3000kWh/15 min. Rated supply capacity (GE) at off-peak timesnp) It is 2000kWh/15 min. And carrying out cascade charging at the peak time and the non-peak time according to different electricity selling rules respectively. The electricity rate parameters are shown in table 3.
TABLE 3 basic parameters for electricity sales
Parameter name Numerical value
Basic electricity price Mf(US dollar/kWh) 0.1
Penalty price of electricity Mp(US dollar/kWh) 0.01
The peak-time electricity selling strategy is shown in table 4.
TABLE 4 Peak time Power selling strategy
Figure BDA0002459416670000143
Figure BDA0002459416670000151
In Table 4, E (t) is the output power in unit time period t at the peak time, GEpIs the rated power supply for the peak time period. At peak times when E (t) is less than 80% GE, in terms of minimum power limitationpOutput electric energy according to the basisSelling electricity at the price of electricity, less than 80% GEpWill generate a corresponding fine. When E (t) is greater than 80% GEpLess than 100% GEpAnd all electric energy is charged according to the basic electricity price. When E (t) is greater than 100% GEpLess than 110% GEpThen, 100% GEpPart sells electricity according to the basic electricity price, 100-110% GEpThe portion between sells electricity at 50% of the base electricity rate. When E (t) is greater than 110% GEpThen, above 110% GEpWill not calculate the electricity sales revenue. The off-peak electricity selling strategy is shown in table 5.
TABLE 5 non-spike time Electricity selling strategy
Figure BDA0002459416670000152
In Table 5, GEnpThe rated power supply amount of the non-peak time period. Slightly different from the peak time period even if the output energy in the unit time period is less than GEnpNo penalty is incurred. When E (t) is less than 100% GEnpAnd outputting electric energy to sell electricity according to the basic electricity price. When E (t) is greater than 100% GEnpLess than 110% GEnpThen, 100% GEnpPart sells electricity according to the basic electricity price, 100-110% GEnpPart of (c) sell electricity at 50% of the base electricity price. When E (t) is greater than 110% GEnpThen, above 110% GEnpWill not calculate the electricity sales revenue.
In order to study the influence of different optimization configuration targets on planning, 2 scenes are set for comparative analysis, and the specific scenes are as follows:
scene 1: and planning the capacity of the wind-solar-energy storage power generation system only by taking the annual net profit as the maximum target.
Scene 2: by adopting the method, under the constraint of the designated return on investment (the constraint value of the return on investment is 0.18), the capacity of the wind-solar-energy storage power generation system is planned with the maximum annual net income as a target.
The specific planning result is shown in table 6 according to the parameters and the planning scenario.
Table 6 device capacity configuration results
Device Scene 1 Scene 2
Photovoltaic (kW) 5763 7282
Draught fan (kW) 27500 23000
Energy storage capacity (kWh) 2805 2249
Energy storage converter (bench) 20 18
Photovoltaic converter (desk) 115 145
Fan converter (desk) 55 46
DC/AC (desk) 26 17
DC/AC (desk) 26 17
As can be seen from the data in Table 6, compared with the situation that the return on investment constraint is not considered, the photovoltaic capacity is increased from 5763kW to 7282kW after the return on investment constraint is considered to be 0.18, and is increased by 1519 kW; the fan capacity is reduced from 27500kW to 23000kW, which is 4500kW lower. The total capacity of the wind/light equipment is reduced by 2981 kW. The reduction of the total capacity of the wind and light equipment enables the energy storage capacity required by the system for stabilizing the output fluctuation to be correspondingly reduced. Thus, the energy storage capacity was reduced from 2805kWh to 2249kWh and 556 kWh. In the case of the scene 1 or the scene 2, compared with photovoltaic equipment, energy storage equipment and other equipment, the capacity of the fan is obviously higher, because the available time of the wind speed is longer all day. According to the typical day data of wind and light in fig. 5 and fig. 6, the illumination resources only exist in the daytime, increase first and decrease later along with the increase of time, and are distributed unevenly, and the wind resources are available all day and are distributed more uniformly, so that the renewable resources can be utilized more reasonably by configuring the fan with larger capacity, and the utilization efficiency of the equipment is effectively improved.
The system cost and benefit for each scenario after optimal configuration are shown in table 7.
Table 7 system economic indicators
Index of economic efficiency Scene 1 Scene 2
Annual net profit (10)6$) 6.8623 6.8028
Annual cost (10)6$) 2.2381 1.8987
ROI 0.1626 0.1833
Years of return on investment (years) 6.2 5.4
Total cost (10)7$) 5.5953 4.7469
Total profit (10)8$) 1.7155 1.7007
As can be seen from Table 7, after the return on investment limit (0.18) is added in scenario 2, the total cost of the wind-solar-energy-storage power generation system is reduced from 5.5953 × 107 to 4.7469 × 107 from 15.16%, the return on investment is increased from 0.1626 to 0.1833 with an increase of 12.73%, the annual limit of the return on investment is also shortened from 6.2 years to 5.4 years, but the total yield of the system is basically kept unchanged, and is reduced from 1.7155 × 108 to 1.7007 × 108 from 38108 to only 0.86%.
Fig. 7 is a photovoltaic device output curve in a scene 2, fig. 8 is a wind driven generator output curve, fig. 9 is an energy storage device output curve, and fig. 10 is a wind-solar-energy storage power generation system output power curve. . From the above curves, at 0-7 points, the wind resource is sufficient and the illumination radiation intensity is 0, at which time the system output is provided by the fan. And 7-19 points, the wind speed is reduced to cause insufficient output of the fan, and the illumination radiation intensity is improved to increase the photovoltaic output and stabilize the system output. After 19 o' clock the illumination radiation intensity will be 0 and the wind speed will increase, at which time the system output is provided by the fan. As can be seen from the output curves, the wind-light output has good complementary characteristics.
As can be seen from the energy storage output curve in fig. 9, the energy storage output always fluctuates around 0, and does not perform the peak clipping and valley filling functions. This is because the investment cost and replacement cost of the energy storage device are high, and it is not economical to use the energy storage device for peak clipping and valley filling of the system output, so the energy storage device mainly functions to smooth the system output. At the point 7-19, the energy storage battery is charged and discharged relatively frequently and has high power, because the output fluctuation of the system is increased due to the superposition of the fan and the photovoltaic output, and the energy storage battery needs to be charged and discharged frequently to smooth the output of the system.
Fig. 10 is a graph of the system output after energy storage settling in scenario 2. Fig. 11 is a pre-energy storage settling curve for the system output in scenario 2. Table 8 shows the difference between the maximum output power of the system before and after a unit time. As can be seen from table 8 in fig. 10 and 11, the output fluctuation of the system is large, i.e., 5590kW at maximum, before and after the fluctuation is stabilized by the stored energy, and the output fluctuation of the system is 120kW at unit time after the fluctuation is stabilized by the stored energy. The requirement that the maximum fluctuation power is 1 percent of rated capacity (12000kW) is met.
TABLE 8 maximum output fluctuation of the System
Figure BDA0002459416670000171
The invention provides a wind-solar-energy storage power generation system optimal configuration method considering investment return constraints for more comprehensively considering the economy of optimal configuration of a wind-solar-energy storage power generation system, the effectiveness of the method is verified through one embodiment, and the optimal configuration result and the operation result are analyzed. The results show that:
1) when only the net income is the maximum as the optimization target, each equipment capacity of the system is large, the investment cost is high, the investment return rate is low, and the cost recovery period is long.
2) After the investment return constraint is added on the basis of optimally configuring the capacity of the wind-solar-energy storage power generation system with the maximum net income target, the system investment cost can be reduced under the condition that the total income is basically kept unchanged, so that the investment return rate is improved, and the investment return year limit is shortened.
In summary, the invention relates to a capacity double-layer planning method for a wind-solar energy storage power generation system considering investment return constraints, which is used for acquiring typical daily data of illumination radiation intensity and wind speed in the wind-solar energy storage power generation system, load demand data and various energy supply equipment parameters in the wind-solar energy storage power generation system; constructing a mathematical model of each energy supply device in the wind-solar energy storage power generation system; constructing a double-layer optimization model of the wind-solar-storage power generation system, planning the capacity of system equipment by using the maximum annual net income of the wind-solar-storage power generation system under a given return investment rate as a target by using an upper-layer optimization model, and optimizing the system operation state by using the maximum daily electricity selling income of the wind-solar-storage power generation system as a target by using a lower-layer optimization model; and solving the double-layer optimization model to obtain an optimal capacity configuration result of the wind-solar energy storage power generation system. The invention introduces the investment return constraint into the wind-solar-energy storage power generation system double-layer planning model, and can reduce the system investment cost under the condition that the total income is basically kept unchanged, thereby improving the investment return rate and shortening the investment return time limit.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.

Claims (9)

1. A wind-solar energy storage power generation system capacity double-layer planning method considering return on investment constraint is characterized by comprising the following steps:
obtaining typical daily data of illumination radiation intensity and wind speed in the wind-solar storage power generation system, load demand data and parameters of various energy supply devices in the wind-solar storage power generation system;
constructing a mathematical model of each energy supply device in the wind-solar energy storage power generation system;
constructing a double-layer optimization model of the wind-solar-storage power generation system, planning the capacity of system equipment by using the maximum annual net income of the wind-solar-storage power generation system under a given return investment rate as a target by using an upper-layer optimization model, and optimizing the system operation state by using the maximum daily electricity selling income of the wind-solar-storage power generation system as a target by using a lower-layer optimization model;
and solving the double-layer optimization model by adopting a self-adaptive inertial weight particle swarm algorithm based on the typical daily data of the illumination radiation intensity and the wind speed in the wind-solar energy storage power generation system, the load demand data and the parameters of each energy supply device in the wind-solar energy storage power generation system to obtain the optimal capacity configuration result of the wind-solar energy storage power generation system.
2. The capacity double-layer planning method for the wind-solar-energy-storage power generation system considering the return on investment constraint is characterized in that the building of the mathematical model of each energy supply device inside the wind-solar-energy-storage power generation system comprises the following steps: building mathematical models of a wind driven generator, a photovoltaic power generation system, a current conversion device and an energy storage battery; the current converting apparatus includes: the system comprises a photovoltaic converter, a fan converter, an energy storage converter and a bidirectional DC/AC converter.
3. The wind-solar-energy-storage power generation system capacity double-layer planning method considering return on investment constraint according to claim 2, characterized in that the wind power generator mathematical model is as follows:
Figure FDA0002459416660000011
PWTis the output power of the wind-driven generator, PwtrRated output power of wind power generatorRate, vciIs the wind generator cut-in wind speed, vcoIs the cut-out wind speed v of the wind power generatorrIs the rated wind speed of the wind driven generator;
the mathematical model of the photovoltaic power generation system is as follows:
PPV=ηPVPstcG/Gstc(1+ηT(T-Tstc))
PPVis the output power of the photovoltaic power generation system, ηPVIs the generating efficiency of the photovoltaic power generation system, PstcIs the output power of the photovoltaic power generation system under rated conditions, G is the actual illumination radiation intensity on the photovoltaic panel, GstcIs rated illumination intensity, T is actual temperature of the photovoltaic power generation system, and TstcRated temperature of photovoltaic power generation system, ηTIs the temperature coefficient of variation of the photovoltaic power generation system;
the mathematical model of the converter equipment is as follows:
Pin=KconPout
Pinis the input power of the inverter, KconIs the converter conversion efficiency, PoutIs the converter output power;
the energy storage battery mathematical model is as follows:
Figure FDA0002459416660000021
e (t) is the residual energy of the energy storage battery at the moment t; dc(t) and dd(t) a set of mutually exclusive 0-1 state variables respectively representing charging and discharging states of the energy storage device, the mutual exclusion representing that the energy storage device only performs one action of charging or discharging at a certain time ηcIndicating charging efficiency, ηdIndicating the efficiency of discharge, Pc(t) represents the charging power, Pd(t) represents discharge power.
4. The capacity double-layer planning method for the wind-solar-energy-storage power generation system considering the return on investment constraint according to claim 1 or 2, characterized in that the optimization objectives of the upper-layer optimization model are as follows:
max F1=Cmony-(CINV+CCON+COP)
Cmonyis the total income of electricity sold in the system year CINVIs the cost of equipment acquisition, CCONIs the construction cost COPIs the cost of operation and maintenance;
Cmony=365Cmond
Figure FDA0002459416660000022
CCON=KCONCINI
COP=KOPCINI
wherein, CmondThe daily electricity selling income of the wind and light storage power generation system is obtained; cINIIs the investment cost of system equipment; m ispvAnd mwdThe price of the photovoltaic and the fan are respectively the monomer price; n is a radical ofpvAnd NwdThe number of photovoltaic and fans; r is0Is the discount rate; y isyThe service life of the photovoltaic and the fan is prolonged;
Figure FDA00024594166600000310
representing the price of the ith converter monomer;
Figure FDA00024594166600000311
indicating the number of the i-th converters;
Figure FDA0002459416660000039
the service life of the ith converter is shown; m issIs the monomer price of the energy storage battery, NsIs the number of energy storage cells; y issThe service life of the energy storage battery; kCONThe construction cost coefficient; kOPIs a maintenance cost factor.
5. The wind-solar-energy-storage power generation system capacity double-layer planning method considering return-on-investment constraint according to claim 4, wherein the upper-layer model constraint condition comprises:
(1) device configuration capacity constraints
Figure FDA0002459416660000031
Figure FDA0002459416660000032
Figure FDA0002459416660000033
Figure FDA0002459416660000034
Wherein,
Figure FDA0002459416660000035
and
Figure FDA0002459416660000036
the maximum configuration quantity of the photovoltaic, the fan, the current converter and the energy storage battery is respectively set;
(2) return on investment constraint
ROI≥ROIref
Wherein, the ROI is the return on investment of the wind-solar energy storage power generation systemrefIs a set value of return on investment;
the method for calculating the return on investment is as follows:
Figure FDA0002459416660000037
CMannual electricity selling income of wind-light storage power generation system CTOTALIs the total investment cost of the system.
6. The wind-solar-energy-storage power generation system capacity double-layer planning method considering return on investment constraint according to claim 5, characterized in that the optimization model of the lower layer has the optimization objectives of:
max F2=Cmond
Cmondis the daily electricity selling income of the wind and light storage power generation system,
Figure FDA0002459416660000038
wherein, PoutAnd (T) respectively represents the output power of the wind-solar energy storage power generation system at the moment T, e (T) represents the real-time electricity selling price, and T represents the optimized dispatching cycle of the wind-solar energy storage power generation system.
7. The wind-solar-energy-storage power generation system capacity double-layer planning method considering return-on-investment constraint according to claim 6, wherein the lower-layer optimization model constraint condition comprises:
(1) power balance constraint
Pdcout(t)=Ppv(t)+Pwd(t)-Pbat(t)
Wherein, Pout(t) is the output power, Ppv(t) is the output power of the photovoltaic power generation system, Pwd(t) is the wind turbine output power, Pbat(t) is the absorbed power of the energy storage battery;
(2) wind driven generator output constraint
Figure FDA0002459416660000041
Wherein,
Figure FDA0002459416660000042
allowing the wind driven generator to output a minimum value at the moment t;
Figure FDA0002459416660000043
the maximum value is allowed to be output for the wind driven generator at the moment t;
(3) photovoltaic output constraint
Figure FDA0002459416660000044
Wherein,
Figure FDA0002459416660000045
allowing the photovoltaic power generation system to output a minimum value at the moment t;
Figure FDA0002459416660000046
outputting a maximum value allowed by the photovoltaic power generation system at the moment t;
(4) converter equipment output constraint
Figure FDA0002459416660000047
Wherein,
Figure FDA0002459416660000048
is the output power of the inverter at time t,
Figure FDA0002459416660000049
and
Figure FDA00024594166600000410
allowing the minimum value and the maximum value to be output for the converter at the moment t;
(5) energy storage battery charge and discharge constraints
Figure FDA00024594166600000411
Figure FDA00024594166600000412
Wherein, Pd(t) and Pc(t) power of discharging and charging the energy storage battery at time t, ηdAnd ηcFor the purpose of the discharge efficiency and the charge efficiency,
Figure FDA00024594166600000413
and
Figure FDA00024594166600000414
for the minimum and maximum power allowed for discharge,
Figure FDA00024594166600000415
and
Figure FDA00024594166600000416
minimum and maximum power allowed for charging;
(6) and (4) energy storage battery state constraint:
Figure FDA0002459416660000051
Smin≤S(t)≤Smax
S(0)=S(T)
wherein S (t) is the energy storage state of the energy storage device at the t moment, dc(t) and dd(t) are a set of mutually exclusive 0-1 state variables, η, respectivelycIndicating charging efficiency, ηdIndicating the efficiency of discharge, Pc(t) represents the charging power, Pd(t) represents discharge power, CbatFor the total capacity of the energy storage cell, SminAllowing minimum value, S, for stored energy statemaxThe maximum allowed value of the energy storage state is S (0), the initial value of the charge state of the energy storage equipment is S (T), and the charge state of the energy storage equipment after the whole scheduling period is S (T);
(7) output power fluctuation limitation:
|Pout(t)-Pout(t-1)|<KlimPR
wherein, Pout(t) the output power of the wind-solar energy storage power generation system at the moment t, KlimFor output power fluctuation limiting parameter, PRThe rated capacity of the wind-solar energy storage power generation system is obtained.
8. The wind-solar energy-storage power generation system capacity double-layer planning method considering return on investment constraint according to claim 7, characterized in that the upper-layer optimization model is used for solving and obtaining the system equipment capacity, and the system equipment capacity is input into the lower-layer optimization model to be used as the constraint condition of the lower-layer model(ii) a Solving by a lower-layer optimization model to obtain daily electricity selling income C of the wind-solar storage power generation systemmondAnd inputting the data into an upper optimization model.
9. The wind-solar energy-storage power generation system capacity double-layer planning method considering the return on investment constraint according to claim 7, wherein the upper and lower layer optimization models are solved by adopting a self-adaptive inertial weight particle swarm algorithm, and the solving process comprises the following steps:
(1) inputting equipment parameters and wind and light typical day data, and determining the population number NUPDetermining the maximum number of iterations M of the upper layerUPInitializing each particle by taking the equipment capacity as each particle, and initializing an optimal value and a global optimal value of each particle of an upper layer model;
(2) calculating the inertia weight of the upper layer model;
(3) updating the speed and position of the upper layer particles;
(4) taking each particle on the upper layer as a constraint condition to be brought into the model on the lower layer, generating the initial running state of the system, and determining the population quantity NDOWNDetermining the maximum iteration number M of the lower layer modelDOWMInitializing an optimal value and a global optimal value of each particle in the lower model;
(5) calculating the inertia weight of the lower layer model;
(6) updating the speed and position of the lower layer particles;
(7) calculating the adaptive value of each particle in the lower model, namely the electricity selling income;
(8) updating the optimal value and the global optimal value of each particle in the lower model;
(9) judging whether the maximum iteration number M of the lower layer model is reachedDOWMIf not, returning to the step (5); if so, entering (10);
(10) returning an adaptive value corresponding to the global optimal value of the lower model, namely the electricity selling income to the upper model;
(11) transmitting the upward electricity selling income by using the lower layer model, and calculating the adaptive value of each particle of the upper layer model, namely net income;
(12) updating the optimal value and the global optimal value of each particle in the upper model;
(13) judging whether the upper layer mold is reachedMaximum number of iterations M of typeUP(ii) a If not, returning to the step (2); if so, entering (14);
(14) and outputting an optimal capacity configuration result.
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