CN115730747A - Multi-subject benefit distribution method of comprehensive energy system and application thereof - Google Patents
Multi-subject benefit distribution method of comprehensive energy system and application thereof Download PDFInfo
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Abstract
A multi-subject benefit distribution method of an integrated energy system is based on an improved share value, and comprises the following steps: comprehensively considering the multi-energy coordination planning characteristics of the energy supply and demand system, taking the lowest daily operation cost and the lowest environmental cost as target functions, and taking load balance and user comfort as constraint conditions to establish a multi-comprehensive energy system operation optimization model; considering the economic efficiency and the renewable energy consumption responsibility, constructing a multi-main-body independent operation cost and benefit model and a cooperative operation cost and benefit model of the comprehensive energy system, wherein each main body can obtain additional benefit through resource optimization configuration and reasonable formulation of a linkage mechanism; solving the multi-target optimization problem based on the improved hybrid multi-target particle swarm optimization algorithm, wherein the algorithm has high convergence speed and high solving precision, and can solve the multi-main-body operation optimal scheme of the comprehensive energy system; and establishing a multi-subject benefit distribution model of the comprehensive energy system.
Description
Technical Field
The invention relates to a benefit distribution method, in particular to a comprehensive energy system multi-agent benefit distribution method based on an improved share value.
Background
An Integrated Energy System (IES) is an energy supply system for mutually coupling various heterogeneous energy sources such as cold, heat, electricity, gas and the like, and the characteristics of transverse multi-energy complementation and longitudinal source-network-load-storage coordination can obviously improve the energy utilization efficiency, reduce the system operation cost and reduce the carbon dioxide emission. The comprehensive energy system consists of different power generation main bodies and load users, and the reasonability and fairness of benefit distribution of each participant after energy conservation and profit gain play a vital role in popularization and application of the comprehensive energy system. Currently, the Shapley value method only considers single contribution of each subject to the system, and neglects other contributions made by the subjects in the coordinated operation. In terms of the comprehensive energy system, in the multi-agent optimization process, the respective systems inevitably cause resource waste or shortage due to the reason that the devices cannot be tightly coupled and the like during operation, so that the energy supply cost of the systems is greatly increased. Therefore, in addition to economy, optimization of the operation of each subject in the integrated energy system is also a factor to be considered.
Prior art, as in chinese patent application, publication number: CN111192164A discloses a micro-grid combined game optimization sharing and benefit distribution method considering uncertain wind power,
prior art, as in chinese patent application, publication number: CN111192164A discloses a microgrid combined game optimization sharing and benefit allocation method considering uncertain wind power, and the allocation method based on the shape value is adopted to allocate the received electricity price difference profit, so that the economy can be improved, but the operation optimization of each main body in the microgrid needs to be further improved. Therefore, the invention establishes the comprehensive energy system operation optimization model and meets the optimal operation requirements of all main bodies.
As in the chinese patent application, publication No.: CN114374219A provides a capacity optimization configuration method, a configuration terminal and a storage medium method of a comprehensive energy system, wherein a Shapely value method is adopted to distribute cooperation profits to obtain a profit distribution scheme, but the operation risk and uncertainty factors of a park system are not considered. Therefore, the kernel method is introduced to improve the traditional Shapley value method, and the shortage of Shapley values in consideration of risk factors is made up by carrying out weighted average on the distribution scheme of the Shapley values and the kernel method;
as in the chinese patent application, publication No.: CN115115266A discloses a cooperative game-based garden integrated energy system distributed optimization method and system, which adopts a Shapley value method to distribute benefits of marginal contribution rates of the whole multi-garden integrated energy system, takes the benefit of the contribution average value of each alliance as a distribution idea, and does not consider that the assumed risks of each alliance are inconsistent, distribution errors may occur, and fairness is influenced. Therefore, the invention designs an improved Shapley value method, relieves the phenomenon of mean 'fairness', and effectively reduces distribution errors.
Disclosure of Invention
In order to solve the defects in the prior art, the invention discloses a benefit distribution method, which comprises the following technical scheme:
a multi-subject benefit distribution method of an integrated energy system is based on an improved share value, and is characterized in that: the method comprises the following steps:
step 1: comprehensively considering the multi-energy coordination planning characteristics of the energy supply and demand system, taking the lowest daily operation cost and the lowest environmental cost as target functions, and taking load balance and user comfort as constraint conditions to establish a multi-comprehensive energy system operation optimization model;
and 2, step: considering the economic efficiency and the renewable energy consumption responsibility, constructing a multi-main-body independent operation cost and benefit model and a cooperative operation cost and benefit model of the comprehensive energy system, wherein each main body can obtain additional benefit through resource optimization configuration and reasonable formulation of a linkage mechanism;
and step 3: the multi-objective optimization problem is solved based on the improved hybrid multi-objective particle swarm optimization algorithm, the algorithm is high in convergence speed and solving precision, and the multi-main-body operation optimal scheme of the comprehensive energy system can be obtained.
And 4, step 4: and establishing a multi-subject benefit distribution model of the comprehensive energy system, and performing benefit distribution by using an improved Shapley value method to ensure that the benefits adaptive to the incremental investment are obtained on the basis of ensuring the respective basic benefits of the multi-subject of the comprehensive energy system, thereby realizing benefit balance and ensuring the improvement of the overall operation stability and management efficiency of the comprehensive energy system.
The invention also discloses a nonvolatile storage medium, which is characterized by comprising a stored program, wherein the program controls the equipment where the nonvolatile storage medium is located to execute the method when running.
The invention also discloses an electronic device which is characterized by comprising a processor and a memory; the memory is stored with computer readable instructions, and the processor is used for executing the computer readable instructions, wherein the computer readable instructions execute the method.
Advantageous effects
The method is based on the improved Shapley value method to distribute the benefits among all main bodies in the comprehensive energy system, minimizes the environmental cost as an optimization target, considers the influence of uncertainty factors to solve the target optimization problem, and enables the benefit distribution result to be more convincing and fair;
the thought and the built model provided by the invention can provide theoretical support and practical reference for problems in the aspects of construction, operation and the like of a comprehensive energy system, so that different related participating subjects can know input and output more clearly and intuitively;
the invention establishes a phase change heat storage capacity profit model of a cooperative game and realizes the secondary allocation of the profits of the energy storage system.
Drawings
FIG. 1 is a flow chart of a benefit distribution method according to the present invention.
FIG. 2 is a diagram of an improved hybrid multi-objective particle swarm optimization algorithm of the present invention.
Detailed Description
A benefit distribution method is a comprehensive energy system multi-agent benefit distribution method based on improved share values, and is characterized in that: the method comprises the following steps:
step 1: comprehensively considering the multi-energy coordination planning characteristics of the energy supply and demand system, and establishing a multi-comprehensive-energy system operation optimization model by taking the lowest environmental cost, the balanced load and the comfort level of a user as constraint conditions;
1. operation optimization model of comprehensive energy system
(1) Objective function
A Combined Cooling Heating and Power (CCHP) system taking natural gas as fuel and a gas boiler are important power and heat supply units of a comprehensive energy system and are also important sources of system pollutant emission. The environmental cost of operating an integrated energy system mainly includes the following two aspects: environmental losses and non-environmental losses due to energy production pollutants; the pollution discharge fee charged by the relevant departments. The environmental cost minimization model is as follows:
in the formula C E -environmental cost (dollar); p k (t) — power (kW) of emission source k at time t;
-the emission coefficient (kg/Kw) of the pollutant j from the emission source k; delta. For the preparation of a coating E，j -unit cost (dollar/kg) of contaminant j; zeta EC-p -pollutant emission penalty cost (dollar).
(2) Constraint conditions
1) Load balancing power
The comprehensive energy system is an energy supply and demand system with multi-energy coordination planning. The main objects of the system load balance are electricity, heat, cold and natural gas. Electrical load balancing refers to the fact that power supply inside and outside the system must meet power load requirements inside the system; the heat load balance mainly means that the heat generated by the system can meet the requirement of the system, and if the heat can not meet the requirement, the system needs to purchase a certain amount of heat from a heating power company; the cold power balance mainly means that the demand of the system for cold cannot exceed the cold air quantity generated by systems such as CCHP and the like. The energy balance within the system is constrained as follows:
1) Electrical load balancing constraints
P grid-buy (t)+P WT (t)+P PV (t)+P CCHP (t)+P EES-dis (t)＝P grid-sell (t)+P EEs-char (t) (2)
In the formula P grid-buy (t) -the integrated energy system purchases power (kW) for the electricity grid; p grid-sell (t) -power (kW) when the integrated energy system sells electricity to the grid; p is WT (t) -wind power output power (kW); p pv (t) -distributed photovoltaic power generation output power (kW); p is CCHP (t) -CCHP electrical output power (kW); p EES-dis (t) -work of discharge of the BatteryRate (kW); p EES-ch (t) -charging power (kW) of the battery.
2) Thermal load balancing constraints
H h_grid (t)+H HP (t)+H AC (t)+H CCHP (t)+H h_re (t)＝H load (t)+H h_st (t) (3)
In the formula H h_grid (t) -heat exchange power (kW) between heating companies and integrated energy systems; h HP (t) -heat pump output power (kW); h AC (t) -air conditioner output power (kW); h CCHP (t) -CCHP thermal output power (kW); h h_re (t) -power of heat released by the thermal storage system (kW); h load (t) — heat load (kW) within the system; h h_st (t) -power of heat stored in the thermal storage system (kW).
3) Cold load balancing constraints
L HP (t)+L AC (t)+L CCHP (t)+L l_re (t)＝L lodd (t)+L l_st (t) (4)
In the formula L CCHP (t) -the heat pump outputs the power of the cooling load (kW); l is AC (t) -power of the air conditioner output cooling load (kW); l is h_re (t) -the cold storage system releases the power of the cold load (kW); l is load (t) — the cooling load (kW) within the system; l is h_st (t) -the power (kW) at which the cold storage system stores the cold load.
4) Natural gas load balance constraint
In the formula P ng_grid (t) -power (kW) of natural gas supplied to the system by the natural gas grid; p ng_st (t) -the power (kW) released by the gas storage system in the system;
-the power generation efficiency (%) of gas power generation; p ng_life (t) -residential gas load (kW) in the regional energy system.
(3) Plant operating constraints
The main energy supply equipment in the regional comprehensive energy system introduced by the patent comprises distributed power generation equipment (photovoltaic and wind power), a combined cooling heating and power system and an energy storage device. Wherein, the output power of each device should satisfy the power limit and the output climbing constraint, so the following constraint conditions should be satisfied:
1) Energy plant capacity and slope operation limits
P i，t，min ≤P i，t ≤P i，t，max (6)
P f，t，min ≤P f，t ≤P f，t，max (7)
In the formula P i，t，max -an upper limit of active power output of the dispatchable power generation unit; p i，t，min -a dispatchable power generation unit active power output lower limit; p f，t，max -an upper limit of active power output of the non-dispatchable power generating unit; p f，t，min The lower limit of the active output of the non-dispatchable power generation unit.
When the load of the power generation unit capable of being dispatched is increased or decreased, the following steps are provided:
when the load of the non-scheduling power generation unit is increased or decreased, the following steps are performed:
in the formula P i，t -canPower output (kW) of the dispatch-type power generation unit at time t; p f，t Power output (kW) at time t of the non-dispatchable power generation unit.
2) Energy storage system operation constraints
(1) Electrical energy storage
SOC min ≤SOC(t)≤SOC max (12)
SOC start (t)＝SOC end (t) (15)
SOC in the formula min -minimum value of electrical energy storage state of charge; SOC max -maximum value of electrical energy storage state of charge;
-efficiency of battery charging;
-the efficiency of the battery discharge;
-the maximum charging current (a) allowed by the battery;
-the maximum discharge current (a) allowed by the battery; SOC (system on chip) start (t) -the remaining capacity of the battery at the beginning time of the energy storage system scheduling cycle; SOC end (t) -the remaining capacity of the battery at the end of the energy storage system scheduling cycle.
(2) Thermal energy storage
H h_st_min ≤H hst (t)≤H h_st_max (16)
H h_st_start (t)＝H h_st_end (t) (18)
In the formula H h_st_min -minimum value of thermal energy storage charge state; h h _ st_max -maximum value of thermal energy storage charge state;
-efficiency of thermal energy storage;
-efficiency of thermal energy release; h h_st_start (t) -battery remaining capacity at the start time of the thermal storage system scheduling cycle; h h_st_end (t) -remaining capacity of the battery at the end of the thermal storage system scheduling period.
(3) Cold energy storage
H c_st_min ≤H cst (t)≤H c_st_max (19)
H c_st_start (t)＝H c_st_end (t) (21)
In the formula H c_st_min -minimum value of cold stored energy state of charge; h c_st_max -maximum value of cold stored energy state of charge;
-efficiency of cold energy storage;
-efficiency of cold energy release; h c_st_start (t) -the remaining capacity of the battery at the start time of the scheduling period of the cold storage system; h c_st_end (t) -remaining capacity of the battery at the end time of the scheduling period of the cold storage system.
(4) Environmental constraints
The CCHP system and the gas boiler in the regional integrated energy system are important power supply and heat supply equipment, and both use non-clean energy natural gas as fuel, so the CCHP system and the gas boiler are also important sources of pollutant emission in the integrated energy system. The main pollutants discharged are SO2, NOx, CO2, CO and the like, when the pollutants discharged by the system are less than the maximum allowable discharge amount specified by an environmental policy, the environmental cost of the REIS system is equal to the environmental loss caused by the pollutants produced by energy sources and non-environmental loss caused by the environmental loss, and conversely, the environmental cost of the REIS system also comprises the pollutant discharge penalty cost besides the environmental cost caused by the pollutants.
In the formula C E -environmental cost (dollar); p k (t) — power (kW) of emission source k at time t;
-the emission coefficient (kg/Kw) of the pollutant j from the emission source k; delta. For the preparation of a coating E,j -unit cost (yuan/kg) of contaminant j; zeta EC-p -pollutant emission penalty cost (dollar);
-maximum allowed emissions (kg/Kw) as specified by environmental policy.
(5) User comfort constraints
The user is a main participant of the regional energy system, and the corresponding way for the user to participate in the regional energy system is to adjust the operating state of the energy supply device. When the user adjusts the operating state of the energy supply device, it is ensured that the comfort of its own energy utilization is not affected while responding to the scheduling of the electric/thermal/air grid. In the operation optimization model of the regional integrated energy system established by the invention, the temperature and the energy consumption are used for evaluating the comfort degree of a user to the regional integrated energy system.
1) Temperature restraint
T min (t)＜T(t)＜T max (t) (23)
In the formula T min (t) -a lower temperature limit (deg.C) that the temperature control apparatus can provide to the user's needs; t (T) -the temperature of the user's room (C.); t is a unit of max (t) -the upper temperature limit (deg.C) that the temperature control device can provide to the user's demand.
2) Runtime constraints
The demand response load in the integrated energy continuously operates within a certain time, and the operating time limit is as follows:
in the formula x i (t) -the operational state of the transferable load; t is t on (x i ) -the time at which the plant starts to run; Δ t (x) i ) -a device scheduling period.
And 2, step: considering the economic efficiency and the renewable energy consumption responsibility, constructing a multi-main-body independent operation cost and benefit model and a cooperative operation cost and benefit model of the comprehensive energy system, wherein each main body can obtain additional benefit through resource optimization configuration and reasonable formulation of a linkage mechanism;
(1) Cost and benefit model for multi-main-body independent operation of comprehensive energy system
1) Combined Cooling Heating and Power (CCHP) system
The subsystem is complementary with grid-connected electric power energy, can supply power, heat and cold for users at the same time, improves the energy utilization efficiency of the system, realizes the energy ladder utilization, and is a basic unit of a comprehensive energy system. The economic model for CCHP can be expressed by the following formula:
in the formula C CCHP Cost item for CCHP;
initial investment cost for CCHP;
-system operation maintenance costs;
consumption cost of-natural gas; r is CCHP -revenue item for CCHP; e CCHP The output power of CCHP;
output power price; w CCHP Heat supply of-CCHP;
heat supply price; f CCHP Refrigeration capacity of CCHP;
-refrigeration price;
2) Photovoltaic system
Solar energy is used as renewable resources, can better promote new source consumption and reduce pollution, is a key ring of a long-term energy strategy, and is widely applied to a comprehensive source system. Photovoltaic power generation is a novel source realization form of distributed energy development to a certain stage. The photovoltaic power generation cost and benefit model is as follows:
in the formula C PV Cost item for photovoltaics;
-initial investment cost;
-photovoltaic system installation cost;
- (maintenance cost); b is PV -revenue item for photovoltaics;
-photovoltaic grid-access power;
power price and power quantity on line
Riding device
Namely photovoltaic internet access income;
photovoltaic spontaneous self-power consumption; p t Power-purchase price of electricity, self-power consumption
At the price of electricity purchase P t Namely the electricity purchasing cost saved by photovoltaic;
3) Energy storage battery
The energy storage technology is closely related to the popularization and application of new energy and the development of a power grid, can reduce the negative influence of randomness and intermittence of new source power generation on an energy system to a certain extent, is beneficial to smooth output of electric energy, and plays a role in peak clipping and valley filling. The cost-benefit model for energy storage batteries is as follows:
in the formula C STE Cost item for energy storage batteries;
initial investment cost of energy storage batteries;
mounting cost;
the operation and maintenance cost;
charge-discharge cost, equal to the rated charge-discharge capacity of the energy storage battery multiplied by the price of electricity during charge-discharge; r STE -income item of energy storage battery;
-the amount of battery discharge;
-price of electricity at the time of discharge;
4) Heat storage tank
The heat storage tank can be seamlessly integrated with a thermal power plant, solar energy, wind energy and other conventional electric energy, and can be flexibly combined, and various electric heating comprehensive source systems based on phase change energy storage can be flexibly constructed. Plays a vital role in energy production and consumption links, and can achieve the purposes of new energy consumption, demand side response promotion, peak regulation and clean heating. The cost benefit model for a thermal storage tank is as follows:
in the formula C HS Cost of the heat storage tank;
initial investment cost of the heat storage tank;
mounting cost;
- (maintenance cost);
-thermal cost of consumption during thermal storage; r HS The income of the energy storage tank is mainly the indirect income brought by the power consumption of the heat storage tank for reducing the heat storage and release;
heat released from the heat storage tank;
-the amount of electricity consumed by the electrical heating device per unit of supplied heat; p is E -price of power consumed;
5) Fan blower
The fan power generation can better utilize renewable energy, promote the consumption of new energy and reduce pollution, is an important part of a long-term energy strategy, and is widely applied to a comprehensive energy system. The fan power generation cost benefit model is as follows:
in the formula C WT Cost item of fan;
-initial investment costs;
fan system installation costs;
-operation and maintenance costs; b is WT -a fan return term;
-the amount of power on the wind turbine;
-price of electricity on line, amount of electricity on line
Riding device
Namely the fan net surfing income;
-the self-power consumption of the fan; p t Power purchase price and self-power consumption
At the price of electricity purchase P t Namely, the electricity purchasing cost saved by the fan;
6) Electric refrigeration
The electric refrigeration core equipment is a double-working-condition cold water main machine, can refrigerate and store cold in a low electricity price period, and releases the stored cold in a high electricity price period. The system can support the optimization regulation and control of the power system, and realize intelligent and automatic demand response. The cost benefit model for electric refrigeration is as follows:
in the formula C HS Cost item for electrical refrigeration;
initial investment cost for electrical refrigeration;
-electrical refrigeration installation cost;
-cost of power consumed in refrigeration; r STE -income item of electric refrigeration;
refrigerating capacity of electric refrigeration;
-refrigeration price for electric refrigeration;
7) Electric heating
Electric heating, i.e. converting electric energy into heat energy, comprises an electric boiler, an electric heater and the like. Its COP is not more than 1, and its efficiency is lower than that of heat pump. Usually, the heat storage module is required to be additionally arranged, so that the night off-peak electricity can be fully utilized for heating, the expenditure is saved, the capacity expansion construction cost of the power grid can be reduced by peak clipping and valley filling, and the economic efficiency is favorably improved. The cost-effective model of electric heating is as follows:
in the formula C HS Cost item for electric heating;
initial investment cost for electrical heating;
-installation cost of electrical heating;
-cost of electricity consumed in heat storage; r STE -income item of electric heating;
heating capacity of electric heating;
heating price of electric heating;
8) Air source heat pump
The performance of the heat pump is mainly divided into refrigeration performance and heating performance, and taking an air source heat pump as an example, the heat pump can utilize high-level energy to enable heat to flow from low-level heat source air to a high-level heat source. The low-level heat energy (such as heat contained in air, soil and water) which can not be directly utilized is converted into the high-level heat energy which can be utilized, so that the aim of saving part of high-level energy (such as coal, gas, oil, electric energy and the like) is fulfilled. In addition, the heat pump can realize heating and cooling, really realizes multiple purposes, and can be matched with an electric refrigerating system and an electric boiler system for use. The heat pump system in the comprehensive energy system can effectively improve the energy utilization efficiency of the comprehensive energy system and realize the coupling complementary comprehensive utilization of multiple devices. The fan power generation cost benefit model is as follows:
in the formula C ASHP Cost item of air source heat pump;
initial investment cost of air source heat pump;
installation cost of air source heat pump;
-thermal cost of consumption during thermal storage; r ASHP -revenue item for air source heat pump;
air source heat pump refrigerating capacity;
air source heat pump refrigeration price;
air source heat pump heating;
air source heat pump heating price;
9) Ice storage tank
The initial investment cost of the ice storage air conditioning system mainly comprises equipment investment cost, equipment installation cost and the like, and can be expressed as follows:
C 4a ＝C gz +C az (41)
in the formula C 4a Primary investment cost of ice cold storage air conditioning system; c gz -cost of equipment purchase; c az -cost of installation of the apparatus.
The ice storage device consists of an electric refrigerator and an ice storage tank, and a cost model of the ice storage tank can be calculated by the following formula:
in the formula C IST -cost of ice storage tank (dollars); v IST -volume of ice storage tank (m 3); q c -cold storage (kJ); gamma ray I -latent heat of phase change of ice (kJ/kg); ρ -the density of ice (kg/m 3).
The economic optimization scheduling of the micro-grid containing the ice storage air conditioning system takes the fuel cost and the electricity purchasing and selling cost (income) of the micro-grid system into consideration, establishes a single-target optimization model with the minimum economic operation cost, and achieves the purposes of peak clipping and valley filling of the power load and reduction of the operation cost of the system. The dispatching cycle is 24 hours, the economic cost comprises the fuel power generation cost and the electricity purchasing and selling cost, and the following steps are carried out:
in the formula C F (t) — fuel cost for the t period; c b (t) — -the cost of electricity purchase for the t period; c s (t) — the revenue of electricity sold during the t period.
(2) Multi-main-body cooperative operation cost and income model of comprehensive energy system
The incremental cost in the integrated energy system cooperation mode is mainly investment increased for obtaining incremental income, and comprises the secondary construction cost of a system park, the line (pipe network) transformation cost and the increased transportation loss cost, and the formula is as follows:
C ADD ＝C INV +C LOSS (45)
in the formula C ADD -incremental cost in collaboration mode; c INV -increased investment costs for building an integrated energy system; c LOSS -increase of the cost of transportation losses of the line (pipe network); c sys -secondary construction costs of the system; m is the number of lines (pipe network) to be modified; l is i -the length of the modified ith line (pipe network); p i -the cost per unit length of the ith line; n-the number of rebuilt lines (pipe network); Δ L j -reconstructing the length of the line (pipe network); p j The unit length of the jth line (pipe network) is rebuilt.
From the perspective of increment yield of the comprehensive energy system, firstly, the phenomena of wind abandonment and light abandonment are indirectly relieved by new energy power generation represented by photovoltaic, the self-consumption rate of the photovoltaic is improved, the loss of buying and buying of the photovoltaic power generation is reduced, the electricity price difference is mainly the difference between the electricity price on the photovoltaic and the peak-valley electricity price mean value, and the indirectly increased electric energy sales yield can be calculated by the following formula:
in the formula R 1 -increased yield by increasing the photovoltaic self-absorption rate; I.C. A PV -distributed photovoltaic installed capacity; h PV -the annual number of hours of use of distributed photovoltaic power generation; p a -local peak to valley electricity price means;
-photovoltaic on-grid electricity prices; delta alpha-increased photovoltaic power generationThe rate of consumption.
The electricity purchasing loss is reduced by effectively cutting off the peak in the park, the electricity price difference is mainly the difference between the electricity purchasing peak value electricity price and the average electricity purchasing price, namely the peak-valley electricity price average value, can be represented by the following formula:
R 2 ＝ΔQ hl (P h -P a ) (48)
in the formula R 2 -peak clipping gains for campus improvement; delta Q hl -increased peak clipping power; p h -local peak electricity prices.
Because the comprehensive energy system is a park system combining distributed energy and energy storage equipment, the CCHP increases the electricity selling income in the system through translational power generation, and the optimized operation income of the CCHP is related to the translational power generation and the local peak-valley electricity price difference value:
R 3 ＝ΔQ MOVE (P h -P l ) (49)
in the formula R 3 -optimizing the operating yield of the CCHP tri-generation unit; delta Q MOVE -the amount of electricity that the CCHP generates moves from the valley segment to the peak segment; p l -the valley time electricity price.
The newly-added heat storage tank device can flexibly adjust the generated energy of the power generation system and reduce the unreasonable consumption of the power resources of the park, so the income of the heat storage tank can be roughly calculated by the following formula:
in the formula R 4 -a revenue item for the heat storage tank arrangement;
-heat release of the heat storage tank;
-the amount of electricity consumed by the electric heating apparatus per unit of supplied heat.
To sum up, the incremental total profit R in the cooperative operation mode ADD Can be moved from belowCalculating by the formula:
R ADD ＝R 1 +R 2 +R 3 +R 4 (51)
and step 3: the multi-target optimization problem is solved based on the improved hybrid multi-target particle swarm optimization algorithm, the algorithm is high in convergence speed and solving precision, and the optimal scheme of multi-main-body operation of the comprehensive energy system can be obtained
When the traditional method is adopted to process the multi-target optimization problem, multiple targets are often required to be converted into a single target for solving, and the problems of complex calculation, poor robustness and the like exist in target weight selection which depends on empirical judgment. Therefore, an improved Hybrid Multi-Objective Particle Swarm Optimization (HMOPSO) is proposed herein based on the conventional Multi-Objective Particle Swarm Optimization in order to converge the population as soon as possible and to distribute the non-inferior solutions more widely and uniformly over the Pareto frontier. The algorithm flow is shown in fig. 1.
With reference to fig. 1, the improved hybrid multi-objective particle swarm optimization algorithm comprises the following specific steps:
(1) And initializing the population.
(2) And calculating an objective function value, and sorting by using a Pareto priority sorting method.
(3) Adding the non-inferior solutions in the population into the elite set, and removing the inferior solutions in the elite set.
(4) And (4) carrying out adaptability distribution on the elite concentrated solution according to a congestion distance sorting method, and selecting a global optimal solution according to adaptability probability. And updating the position and the speed of the individual according to the individual optimal solution and the selected global optimal solution.
(5) And performing cross mutation on the solutions in the elite sets, and replacing the solution in the elite sets with the new solution if the obtained new solution dominates the solution in the elite sets.
(6) And if the maximum iteration times are reached, turning to the step 7, otherwise, turning to the step 3, and performing the next iteration.
(7) And outputting the Pareto solution set. Meanwhile, in order to avoid the influence of human factors on the planning result, a final solution is screened out from the Pareto solution set in a balanced mode by using a fuzzy membership function. The larger the comprehensive satisfaction obtained by calculating the fuzzy membership function, the better the solution, and the calculation formula is:
in the formula, mu m,i Satisfaction of the ith objective for the mth non-inferior solution mx; f. of i (x m ) Is a non-inferior solution x m The ith target value of (a);
is the maximum value of the ith target;
is the minimum value of the ith target; mu.s m Is a non-inferior solution x m Comprehensive satisfaction of all targets; m is the number of non-inferior solutions; l is the target number.
And 4, step 4: establishing a multi-subject benefit distribution model of the comprehensive energy system, and utilizing an improved Shapley value method to distribute benefits so as to obtain benefits adaptive to incremental investment on the basis of ensuring respective basic benefits of the multi-subject of the comprehensive energy system, thereby realizing benefit balance, and ensuring the improvement of the integral operation stability and management efficiency of the comprehensive energy system
The 2 common benefit distribution methods in cooperative game are Shapley value method and kernel method. The sharley value can avoid the average distribution, but the risk sharing factor for the members is not considered, so that the traditional sharley value distribution method cannot solve the problem comprehensively. The nucleolus method aims at forming a scheme which is not objected to by all people and generates a final distribution scheme on the premise of considering risk sharing, but easily causes average 'fairness'. The kernel method was thus introduced to improve the traditional sharley value by weighted averaging the sharley value with the kernel method's distribution scheme. On one hand, the defect of the Shapley value in consideration of risk factors is made up; on the other hand, the phenomenon of mean 'fairness' caused by a kernel method is relieved, and distribution errors are effectively reduced.
(1) Traditional sharey value method.
The traditional Shapley value method comprises 3 characteristics of effectiveness, symmetry and additivity. The benefit allocation strategy of the sharley value method can be obtained based on 3 characteristics. Let N be the member set of the federation, N = {1,2, …, i, …, N }, S be any subset of set N.
In the formula
Profit assigned to member i based on traditional sharey-value method; y (| S |) is a weighted value; z (S) is the profit value for federation S containing member i; z (S-i) is the profit margin for federation S that does not contain member i.
(2) Nucleolus method. The nucleolus method includes proportional nucleolus method and minimum nucleolus method 2. The proportional kernel method is a value for increasing a certain proportion of development income on the basis of alliance income, and income distribution is a solution of linear programming of an equation (23). The objective function is min ζ.
In the formula:
profits based on the proportional kernel method for member i; z (i) is the revenue for member i not federating with other members.
The minimum kernel method refers to the same additional amount of development added on the basis of the alliance revenue, which is allocated as the solution of the linear programming in equation (48) with the objective function of min ζ.
(3) The Shapley value method was modified.
The improved Shapley value method is a method for correcting the traditional Shapley value method by combining a proportional kernel method and a minimum kernel method, and the specific correction method is shown as a formula (49).
π 1 +π 2 +π 3 ＝1 (50)
In the formula pi j The j-th profit sharing method is weighted.
The method comprehensively considers the multi-energy coordination planning characteristics of the energy supply and demand system, takes the lowest daily operation cost and the lowest environmental cost as target functions, and establishes a multi-comprehensive energy system operation optimization model by taking load balance and user comfort as constraint conditions; considering the economic efficiency and the renewable energy consumption responsibility, constructing a multi-main-body independent operation cost benefit model and a cooperative operation cost benefit model of the comprehensive energy system, and obtaining additional benefits by each main body through resource optimization configuration and formulation of a reasonable linkage mechanism; solving the multi-target optimization problem based on the improved hybrid multi-target particle swarm optimization algorithm, wherein the algorithm has high convergence speed and high solving precision, and can solve the multi-main-body operation optimal scheme of the comprehensive energy system; according to the optimal operation scheme, a multi-agent benefit distribution model of the comprehensive energy system is established, and benefit distribution is performed by using an improved Shapley value method, so that benefits adaptive to incremental investment can be obtained on the basis that respective basic benefits of the multi-agent of the comprehensive energy system are guaranteed, and accordingly, benefit balance is achieved, the enthusiasm of multi-agent cooperation of the comprehensive energy system is improved, and the overall operation stability and the management efficiency of the comprehensive energy system are improved.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A multi-subject benefit distribution method of an integrated energy system is based on an improved share value, and is characterized in that: the method comprises the following steps:
step 1: comprehensively considering the multi-energy coordination planning characteristics of the energy supply and demand system, taking the lowest daily operation cost and the lowest environmental cost as target functions, and taking load balance and user comfort as constraint conditions to establish a multi-comprehensive energy system operation optimization model;
step 2: considering the economic efficiency and the renewable energy consumption responsibility, constructing a multi-main-body independent operation cost and benefit model and a cooperative operation cost and benefit model of the comprehensive energy system, wherein each main body can obtain additional benefit through resource optimization configuration and reasonable formulation of a linkage mechanism;
and step 3: solving a multi-target optimization problem based on an improved hybrid multi-target particle swarm optimization algorithm, and solving a multi-main-body operation optimal scheme of the comprehensive energy system;
and 4, step 4: and establishing a multi-subject benefit distribution model of the comprehensive energy system, and performing benefit distribution by using an improved Shapley value method to ensure that the benefits adaptive to the incremental investment are obtained on the basis of ensuring the respective basic benefits of the multi-subject of the comprehensive energy system, thereby realizing benefit balance and ensuring the improvement of the overall operation stability and management efficiency of the comprehensive energy system.
2. The integrated energy system multi-agent benefit allocation method according to claim 1, characterized by: the step 1 further comprises the following steps:
(1) Daily operating cost minimum objective
Carrying out optimization analysis based on simulated IES typical daily operating conditions, and when laying a foundation for determining an IES planning optimized energy structure, carrying out correlation analysis of IES typical load attribute characteristics and output equipment by taking 24 hours as a time scale and taking the optimal daily operating cost as an objective function:
in the formula
-the amount of total fuel consumption of plant m, m3;
C w_m maintenance costs of the plant m, dollars/kWh;
P i EN -purchase amount of energy i, kWh;
P i CE -carbon emission from energy i, kgC;
(2) Environmental cost minimization objective
The environmental cost minimization model is as follows:
in the formula C E -environmental cost (dollar); p k (t) — power (kW) of emission source k at time t;
-the emission coefficient (kg/Kw) of the pollutant j from the emission source k; delta E,j -unit cost (dollar/kg) of contaminant j; zeta Ee-p -pollutant emission penalty cost (dollar).
3. The integrated energy system multi-agent benefit allocation method according to claim 1, characterized by: the constraint conditions comprise the following contents:
the energy balance constraints within the system are as follows:
1) Electrical load balancing constraints
P grid-buy (t)+P WT (t)+P PV (t)+P CCHP (t)+P EEs-dis (t)＝P grid-sell (t)+P EES-char (t) (2)
In the formula P grid-buy (t) -the integrated energy system purchases power (kW) for the electricity grid; p grid-sell (t) -power (kW) when the integrated energy system sells electricity to the grid; p WT (t) -wind power output power (kW); p pv (t) -distributed photovoltaic power generation output power (kW); p CCHP (t) -CCHP electrical output power (kW); p EES-dis (t) -discharge power (kW) of the battery; p is EES-ch (t) -charging power (kW) of the battery;
2) Thermal load balancing constraints
H h_grid (t)+H HP (t)+H AC (t)+H CCHP (t)+H h_re (t)＝H load (t)+H h_st (t) (3)
In the formula H h_grid (t) -between heating companies and integrated energy systemsHeat exchange power (kW); h HP (t) -heat pump output power (kW); h AC (t) -air conditioner output power (kW); h CCHP (t) -CCHP thermal output power (kW); h h_re (t) -power of heat release (kW) of the thermal storage system; h load (t) — heat load (kW) within the system; h h_st (t) -power of the thermal storage system storing heat (kW);
3) Cold load balancing constraints
L HP (t)+L AC (t)+L CCHP (t)+L l_re (t)＝L load (t)+L l_st (t) (4)
In the formula L CCHP (t) -the heat pump outputs the power of the cooling load (kW); l is AC (t) -power of the air conditioner output cooling load (kW); l is h_re (t) -the cold storage system releases the power of the cold load (kW); l is a radical of an alcohol load (t) — the cooling load (kW) within the system; l is h_st (t) -the cold storage system stores the power of the cold load (kW);
4) Natural gas load balance constraint
In the formula P ng_grid (t) -power (kW) of the natural gas grid supplying natural gas to the system; p ng_st (t) -power released by the gas storage system in the system (kW); omega CCHP_e -the power generation efficiency (%) of gas power generation; p ng_life (t) -residential gas load (kW) in regional integrated energy systems;
(3) Plant operating constraints
The main energy supply equipment in the regional comprehensive energy system comprises distributed power generation equipment, a combined cooling heating and power supply system and an energy storage device, wherein the output power of each equipment meets the power limit and the output climbing constraint, so the following constraint conditions are provided:
1) Energy plant capacity and slope operation limits
P i，t，min ≤P i，t ≤P i，t，max (6)
P f，t，min ≤P f，t ≤P f，t，max (7)
In the formula P i，t，max -an upper limit of active power output of the dispatchable power generation unit; p i，t，min -a dispatchable power generation unit active power output lower limit; p f，t，max -an upper limit of active power output of the non-dispatchable power generating unit; p f，t，min -an active power output lower limit of the non-dispatchable power generation unit;
when the load of the power generation unit capable of being dispatched is increased or decreased, the following steps are provided:
when the load of the non-scheduling power generation unit is increased or decreased, the following steps are performed:
in the formula P i，t -power output (kW) at time t of the dispatchable power generation unit; p f，t -power output (kW) at time t of the non-dispatchable power generating unit;
2) Energy storage system operation constraints
(1) Electrical energy storage
SOC min ≤SOC(t)≤SOC max (12)
SOC start (t)＝SOC end (t) (15)
In the formula SOC min -minimum value of electrical energy storage state of charge; SOC max -maximum value of electrical energy storage state of charge;
-efficiency of battery charging;
-the efficiency of the battery discharge;
-the maximum charging current (a) allowed by the battery;
-the maximum discharge current (a) allowed by the battery; SOC start (t) -the remaining capacity of the battery at the beginning time of the energy storage system scheduling cycle; SOC end (t) -battery remaining capacity at the end of the energy storage system scheduling cycle;
(2) thermal energy storage
H h_st_min ≤H hst (t)≤H h_st_max (16)
H h_st_start (t)＝H h_st_end (t) (18)
In the formula H h_st_min -minimum value of thermal energy storage charge state; h h_st_max -maximum value of thermal energy storage charge state;
-efficiency of thermal energy storage;
-efficiency of thermal energy release; h h_st_start (t) -battery remaining capacity at the start time of the thermal storage system scheduling cycle; h h_st_end (t) -battery remaining capacity at the end time of the thermal storage system scheduling period;
(3) cold stored energy
H c_st_min ≤H cst (t)≤H c_st_max (19)
H c_st_start (t)＝H c_st_end (t) (21)
In the formula H c_st_min -minimum value of cold stored energy state of charge; h c_st_max -maximum value of cold stored energy state of charge;
-efficiency of cold energy storage;
-efficiency of cold energy release; h c_st_start (t) -the remaining capacity of the battery at the start time of the scheduling period of the cold storage system; h c_st_end (t) -the remaining capacity of the battery at the end time of the scheduling period of the cold storage system;
(4) Environmental constraints
When the pollutant discharged by the system is less than the maximum allowable discharge amount specified by the environmental policy, the environmental cost of the REIS system is equal to the environmental loss caused by the energy production pollutant and the non-environmental loss caused by the energy production pollutant, and conversely, the environmental cost of the REIS system also comprises the pollutant discharge penalty cost in addition to the environmental cost caused by the pollutant per se:
in the formula C E -environmental cost (dollar); p is k (t) — power (kW) of emission source k at time t;
-the emission coefficient (kg/Kw) of the pollutant j from the emission source k; delta. For the preparation of a coating E,j -unit cost (dollar/kg) of contaminant j; zeta EC-p -pollutant emission penalty fees (dollar);
-maximum allowed emissions (kg/Kw) specified by environmental policies;
(5) User comfort constraints
1) Temperature restraint
T min (t)＜T(t)＜T max (t) (23)
In the formula T min (t) -a lower temperature limit (deg.C) that the temperature control apparatus can provide to the user's needs; t (T) -the temperature of the user's room (C.); t is max (t) -the upper temperature limit (° c) that the temperature control device can provide to a user's demand;
2) Runtime constraints
The demand response load in the integrated energy source continuously operates within a certain time, and the operation time is limited as follows:
in the formula x i (t) -the operational state of the transferable load; t is t on (x i ) -the time at which the plant starts to operate; Δ t (x) i ) -a device scheduling period.
4. The integrated energy system multi-entity benefit allocation method of claim 1, wherein: the step 2 further comprises the following steps:
(1) Cost and benefit model for multi-main-body independent operation of comprehensive energy system
1) Combined Cooling Heating and Power (CCHP) system
The economic model for CCHP can be expressed by the following formula:
in the formula C CCHP Cost item for CCHP;
initial investment cost for CCHP;
-system operation maintenance costs;
consumption cost of- (natural gas) —; r CCHP Revenue terms for CCHP; e CCHP The output power of CCHP;
output power price; w CCHP Heat supply of-CCHP;
heat supply price; f CCHP Refrigeration capacity of CCHP;
-refrigeration price;
2) Photovoltaic system
The photovoltaic power generation cost and benefit model is as follows:
in the formula C PV Cost item for photovoltaics;
initial investment cost;
-photovoltaic system installation cost;
- (maintenance cost); b is PV -revenue item for photovoltaics;
-photovoltaic grid-access power;
power price and power quantity on line
Riding device
Namely photovoltaic internet access income;
photovoltaic self-power consumption；P t Power purchase price and self-power consumption
At the price of electricity purchase P t Namely the electricity purchasing cost saved by photovoltaic;
3) Energy storage battery
The cost-benefit model for energy storage batteries is as follows:
in the formula C STE Cost item for energy storage batteries;
initial investment cost of energy storage batteries;
mounting cost;
- (maintenance cost);
charge-discharge cost, equal to the rated charge-discharge capacity of the energy storage battery multiplied by the price of electricity during charge-discharge; r STE -income item of energy storage battery;
-the amount of battery discharge; p t dis -price of electricity at the time of discharge;
4) Heat storage tank
The cost benefit model for a thermal storage tank is as follows:
in the formula C HS Cost of the heat storage tank;
initial investment cost of the heat storage tank;
installation cost;
the operation and maintenance cost;
-thermal cost of consumption during thermal storage; r is HS The income of the energy storage tank is mainly the indirect income brought by the power consumption of the heat storage tank for reducing the heat storage and release;
heat released from the heat storage tank;
-the amount of electricity consumed by the electrical heating device per unit of supplied heat; p E -price of power consumed;
5) Fan blower
The fan power generation cost benefit model is as follows:
in the formula C WT Cost item of fan;
initial investment cost;
-fan system installation cost;
the operation and maintenance cost; b is WT Income item of the fan;
the fan is powered on;
power price and power quantity on line
Riding device
Namely the fan surfing benefits;
fan self-power consumption; p t Power purchase price and self-power consumption
At the price of electricity purchase P t Namely, the electricity purchasing cost saved by the fan;
6) Electric refrigeration
The cost benefit model for electric refrigeration is as follows:
in the formula C HS Cost item for electric refrigeration;
initial investment cost for electrical refrigeration;
-electrical refrigeration installation cost;
-cost of power consumed in refrigeration; r STE -income item of electric refrigeration;
refrigerating capacity of electric refrigeration; p t dis -refrigeration price for electric refrigeration;
7) Electric heating
The cost-effective model of electric heating is as follows:
in the formula C HS Cost item for electric heating;
initial investment cost for electrical heating;
-installation cost of electrical heating;
-cost of electricity consumed in heat storage; r STE -income item of electric heating;
heating capacity of electric heating; p t dis Heating price of electric heating;
8) Air source heat pump
The fan power generation cost benefit model is as follows:
in the formula C ASHP Cost item of air source heat pump;
initial investment cost of air source heat pump;
installation cost of air source heat pump;
-thermal cost of consumption during thermal storage; r ASHP -revenue item for air source heat pump;
air source heat pump refrigerating capacity;
air source heat pump refrigeration price;
air source heat pump heating capacity;
air source heat pump heating price;
9) Ice storage tank
The initial investment cost of the ice storage air conditioning system mainly comprises equipment investment cost, equipment installation cost and the like, and can be expressed as follows:
C 4a ＝C gz +C az (41)
wherein C = 4a Initial investment cost of ice cold storage air conditioning system; c gz -cost of equipment purchase; c az -equipment installation cost;
the ice cold storage device consists of an electric refrigerator and an ice storage tank, and a cost model of the ice storage tank can be calculated by the following formula:
in the formula C IST -cost of ice storage tank (dollars); v IST -volume of ice storage tank (m 3); q c -cold storage (kJ); gamma ray I -latent heat of phase change of ice (kJ/kg); ρ -density of ice (kg/m 3);
the method comprises the steps of economically and optimally scheduling the micro-grid containing the ice storage air-conditioning system, considering fuel cost and electricity purchasing cost of the micro-grid system, and establishing a single-target optimization model with the minimum economic operation cost to achieve the purposes of peak clipping and valley filling of power load and reduction of the operation cost of the system; the dispatching cycle is 24 hours, the economic cost comprises the fuel power generation cost and the electricity purchasing and selling cost, and the following steps are carried out:
in the formula C F (t) — -fuel cost for the t period; c b (t) — -the cost of electricity purchase for the t period; c s (t) — the revenue of electricity sold during the t period.
(2) Multi-main-body cooperative operation cost and income model of comprehensive energy system
The incremental cost in the integrated energy system cooperation mode is mainly the investment increased for obtaining incremental income, and comprises the secondary construction cost, the line transformation cost and the increased transportation loss cost of a system park, and the formula is as follows:
C ADD ＝C INV +C LOSS (45)
in the formula C ADD -incremental cost in collaboration mode; c INV Increased investment costs for building integrated energy systems; c LOSS -increase of the cost of transportation losses of the line (pipe network); c sys -secondary construction costs of the system; m is the number of lines (pipe network) to be modified; l is i -the length of the modified ith line (pipe network);P i -the cost per unit length of the ith line; n-the number of rebuilt lines (pipe network); Δ L j -reconstructing the length of the line (pipe network); p is j The unit length cost of the jth line (pipe network) is rebuilt;
the new energy power generation represented by photovoltaic indirectly relieves the phenomena of wind abandonment and light abandonment, improves the self-consumption rate of photovoltaic, reduces the loss of buying and buying of photovoltaic power generation, and the electricity price difference is mainly the difference between the photovoltaic on-grid electricity price and the peak-valley electricity price mean value, and the indirectly increased electric energy sales income can be calculated by the following formula:
in the formula R 1 -increased yield by increasing the photovoltaic self-absorption rate; i is PV -distributed photovoltaic installed capacity; h PV -the annual number of hours of use of distributed photovoltaic power generation; p is a -local peak to valley electricity price means;
-photovoltaic on-grid electricity prices; delta alpha-increased self-absorption rate of photovoltaic power generation;
the electricity purchasing loss is reduced by effectively cutting off the peak in the park, the electricity price difference is mainly the difference between the electricity purchasing peak value electricity price and the average electricity purchasing price, namely the peak-valley electricity price average value, can be represented by the following formula:
R 2 ＝ΔQ hl (P h -P a ) (48)
in the formula R 2 -peak clipping gains for campus improvement; delta Q hl -increased peak clipping power; p h -local peak electricity prices.
Because the comprehensive energy system is a park system combining distributed energy and energy storage equipment, the CCHP increases the electricity selling income in the system through translational power generation, and the optimized operation income of the CCHP is related to the translational power generation and the local peak-valley electricity price difference value:
R 3 ＝ΔQ MOVE (P h -P l ) (49)
in the formula R 3 -optimizing the operating yield of the CCHP tri-generation unit; delta Q MOVE -the amount of electricity that the CCHP generates moves from the valley segment to the peak segment; p l -electricity price at valley time;
the newly-added heat storage tank device can flexibly adjust the generated energy of the power generation system and reduce the unreasonable consumption of the power resources of the park, so the income of the heat storage tank can be roughly calculated by the following formula:
in the formula R 4 -a revenue item for the heat storage tank arrangement;
-heat release of the heat storage tank;
-the amount of electricity consumed by the electrical heating apparatus per unit of supplied heat;
to sum up, the incremental total profit R in the cooperative operation mode ADD Can be calculated from the following formula:
R ADD ＝R 1 +R 2 +R 3 +R 4 (51)。
5. the integrated energy system multi-entity benefit allocation method of claim 1, wherein: the step 3 further comprises the following steps:
the improved hybrid multi-objective particle swarm optimization algorithm comprises the following specific steps:
(1) Initializing a population;
(2) Calculating a target function value, and sorting by using a Pareto priority sorting method;
(3) Adding the non-inferior solutions in the population into the elite set, and removing the inferior solutions in the elite set;
(4) Carrying out adaptability distribution on the elite concentrated solution according to a congestion distance sorting method, and selecting a global optimal solution according to adaptability probability; updating the position and the speed of the individual according to the individual optimal solution and the selected global optimal solution;
(5) Performing cross variation on the solutions in the elite sets, and if the obtained new solution dominates the solutions in the elite sets, replacing the dominated solution with the new solution;
(6) If the maximum iteration times are reached, turning to the step (7), otherwise, turning to the step (3) for next iteration;
(7) Outputting a Pareto solution set; meanwhile, a final solution is screened out by weighing the solution set of Pareto by using a fuzzy membership function, the better the solution with the larger comprehensive satisfaction degree obtained by calculating the fuzzy membership function is, and the calculation formula is as follows:
in the formula, mu m，i Satisfaction of the ith objective for the mth non-inferior solution mx; f. of i (x m ) Is a non-inferior solution x m The ith target value of (a); f. of i max Is the maximum value of the ith target; f. of i min Is the minimum value of the ith target; mu.s m Is a non-inferior solution x m Comprehensive satisfaction of all targets; m is the number of non-inferior solutions; l is the target number.
6. A non-volatile storage medium, comprising a stored program, wherein the program, when executed, controls an apparatus in which the non-volatile storage medium is located to perform the method of any of claims 1 to 5.
7. An electronic device comprising a processor and a memory; the memory has stored therein computer readable instructions for execution by the processor, wherein the computer readable instructions when executed perform the method of any one of claims 1 to 5.
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