A multi-energy system capacity configuration method based on fractional programming theory

Abstract

The application discloses a kind of based on fractional programming theory's multi-element energy system capacity configuration method, first establish the energy system operation model including system power balance, new energy output, energy storage and electric boiler;Then build the day operation model under multiple scenarios, and then establish the capacity benefit evaluation function of multi-element energy system;Further, build the multi-element energy configuration model of fractional programming;Finally, the fractional programming model is linearized by variable substitution and decomposition algorithm, and finally the capacity configuration strategy of multi-element energy system is obtained by solver.

Description

Technical Field

[0001] This invention belongs to the field of new energy capacity configuration technology, and more specifically, relates to a capacity configuration method for multi-energy systems based on fractional programming theory. Background Technology

[0002] Faced with increasingly severe global environmental and energy problems, countries are actively developing new energy systems, primarily based on clean energy, to achieve energy transition. Diversified energy systems are gradually becoming a key method for optimizing energy structures. Due to the fluctuating, intermittent, and uncertain nature of new energy output, a single energy supply model cannot leverage the complementarity and synergy among various energy sources, leading to resource waste and supply-demand imbalances. Diversified energy systems consider the different characteristics of various energy sources, integrating diverse resources to improve overall energy utilization efficiency and promote the development of green and efficient energy systems.

[0003] For investors, the economic benefits of a project are a crucial consideration. Maximizing the cost-effectiveness of diversified energy resource allocation while ensuring power system stability is a key research focus. Current energy allocation models typically employ three methods to address economic aspects: minimizing total cost, constrained investment cost, and game theory. Minimizing total cost, using total cost as the objective function, can reduce total project expenses but may lead to high initial investment costs and poor long-term economic benefits. Constrained investment cost methods use investment cost as a constraint, helping to control early-stage investment costs, but the investment plan may not be optimal, potentially resulting in excessive later operating costs and reduced long-term economic benefits. Game theory models are complex, require strict data, and are computationally difficult, making them challenging to apply. Therefore, a new allocation method is needed that can improve project economic benefits while being easy to apply. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a capacity configuration method for a multi-energy system based on fractional programming theory. By analyzing the impact of each energy source on the system operating cost, a fractional programming model is established to obtain the configuration strategy with the highest return on investment.

[0005] To achieve the above-mentioned objectives, this invention provides a capacity configuration method for a multi-energy system based on fractional programming theory, characterized by comprising the following steps:

[0006] (1) Construct an operational model for a multi-energy system;

[0007] (2) Construct a capacity benefit evaluation function for a multi-energy system;

[0008] (3) Construct a capacity configuration model for a multi-energy system;

[0009] (4) Linearize the capacity configuration model of the multi-energy system, and then solve the capacity configuration strategy of the multi-energy system through the solver.

[0010] The objective of this invention is achieved as follows:

[0011] This invention presents a capacity allocation method for a multi-energy system based on fractional programming theory. First, an energy system operation model is established, including system power balance, new energy output, energy storage, and electric boilers. Then, daily operation models under multiple scenarios are constructed, leading to the establishment of a capacity benefit evaluation function for the multi-energy system. Further, a fractional programming multi-energy allocation model is constructed. Finally, the fractional programming model is linearized using variable substitution and decomposition algorithms, and the capacity allocation strategy for the multi-energy system is obtained by solving the problem using a solver.

[0012] Furthermore, the capacity configuration method for multi-energy systems based on fractional programming theory in this invention also has the following advantages:

[0013] Beneficial effects:

[0014] (1) Establish a capacity benefit evaluation function to intuitively evaluate the impact of multiple energy sources on the economic benefits of the system and provide a reference for the optimization of multiple resource allocation schemes;

[0015] (2) A capacity allocation model based on fractional programming theory is proposed, with the goal of maximizing the rate of return on investment, in order to obtain an allocation strategy with the best economic benefits. By using the form of fractional objective function, the economic benefits of investment are expressed more accurately, which makes up for the shortcomings of common allocation methods in terms of long-term economic benefits.

[0016] (3) By linearizing the fractional programming model through variable substitution and approximating it with the cutting plane, the solution speed of the fractional model is greatly accelerated and it is easy to solve. Attached Figure Description

[0017] Figure 1 This is a flowchart of the capacity configuration method for a multi-energy system based on fractional programming theory, as described in this invention.

[0018] Figure 2 This is a diagram showing the power flow structure of a multi-energy system;

[0019] Figure 3 This is a diagram illustrating the capacity benefit evaluation function obtained using this invention;

[0020] Figure 4 This is a diagram showing the configuration capacity under different wind power investment parameters obtained using this invention; Detailed Implementation

[0021] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0022] Example

[0023] In this embodiment, we establish a relevant model of capacity configuration for a multi-energy system in MATLAB simulation software, and then solve it using a solver to obtain the optimal capacity configuration strategy for the multi-energy system. Below, we combine... Figure 1 As shown, the present invention provides a detailed description of a capacity configuration method for a multi-energy system based on fractional programming theory, which specifically includes the following steps:

[0024] S1. Construct an operational model for a multi-energy system;

[0025] In this embodiment, Figure 2 This describes the power flow in a multi-energy system. Photovoltaic power plants and wind farms supply power to electrical loads and electric boilers. Electric boilers provide heat energy through electro-thermal conversion to meet heat load demands. When there is surplus output power from photovoltaic power plants and wind farms, the excess electrical energy is stored in energy storage devices. If the photovoltaic and wind power output is lower than the load, the energy storage devices discharge to balance the load. If the load is still lower than the load, the power is output to the grid.

[0026] Based on the above principles, the operation models of a multi-energy system are constructed, including: the power balance model of the multi-energy system, the output models of wind power and photovoltaic power, the operation model of energy storage devices, and the operation model of electric boilers.

[0027] The power balance model for a multi-energy system is as follows:

[0028]

[0029] Where t∈{1,2,…,T}, and T represents the total number of sampling times. and These represent the output power of the photovoltaic power plant and the wind farm in the s-th scenario at time t, respectively. Let be the output power of the power grid in the s-th scenario at time t. and Let P be the discharge and charge power of the energy storage device in the s-th scenario at time t. l,t Let be the electrical load power in the s-th scenario at time t. Let be the output power of the electric boiler in the s-th scenario at time t;

[0030] The power output models for wind farms and photovoltaic power plants are as follows:

[0031]

[0032]

[0033] in, and B represents the output power of the wind farm and the photovoltaic power station in the s-th scenario at time t, respectively. wt and B pv C represents the capacity of the wind farm and the photovoltaic power station being sampled, respectively. w and C p These represent the required wind power capacity and photovoltaic capacity, respectively.

[0034] The operating model of the energy storage device is as follows:

[0035]

[0036] Among them, P e,max η represents the maximum power of the energy storage device. ch and η dis These represent the charging and discharging efficiencies of the energy storage device, respectively. In this embodiment, η ch =η dis =0.95; Let E be the amount of electricity stored by the energy storage device in the s-th scenario at time t. emax This represents the maximum capacity of the energy storage device, where Δt is the sampling interval;

[0037] In this embodiment, the first two formulas of the energy storage device operation model define the upper and lower limits of the charging and discharging power; Formula 3 describes the variation law of the stored energy in adjacent time periods; Formula 4 defines the upper and lower limits of the stored energy.

[0038] The operating model of the electric boiler is as follows:

[0039]

[0040] Among them, P eb,max This indicates the maximum power of the electric boiler. η represents the thermal power output of the electric boiler in the s-th scenario at time t. eb Indicates the electro-thermal conversion efficiency. Let P represent the heat load required in the s-th scenario at time t; Formula 1 specifies the electric power of the electric boiler, Formula 2 describes the electrothermal power conversion of the electric boiler, and Formula 3 represents the heat power balance. In this embodiment, P is taken as... eb,max =200kW, η eb =0.8;

[0041] In this embodiment, we take T = 24, and collect the known parameters in the operation model of the multi-energy system according to the sampling times t ∈ {1, 2, ..., T}, such as... wait.

[0042] S2. Construct a capacity benefit evaluation function for a multi-energy system;

[0043] S2.1 Construct the objective function for the daily operating cost of a multi-energy system;

[0044]

[0045] In this embodiment, the low-peak period T is taken. L The electricity price is λ, calculated from 23:00 to 8:00 the next day. l = 0.43 yuan / kWh; peak period T H Electricity price λ is from 8:00 to 23:00. h = 1.18 yuan / kWh.

[0046] The objective function for the daily operating cost of a multi-energy system is expressed in matrix form as follows:

[0047]

[0048] The capacity to be configured is defined as θ = [C w C p E emax ;P e,max [Including wind power, solar power capacity, energy storage capacity and maximum energy storage power, A, b, B and c represent constant coefficients of the operation model, and x represents system operation variables;]

[0049] In this embodiment, assuming the multi-energy system operates in S = 56 scenarios, the objective function for the daily operating cost of the multi-energy system in the s-th scenario with a configured capacity of θ is expressed in matrix form as follows:

[0050]

[0051] Among them, superscript Indicates transpose; x s Let S be the operating variable of the multi-energy system in the s-th scenario, specifically represented as: c s Let c represent the coefficient matrix for the s-th scenario. s x s The number of elements in the middle is equal, among which The coefficient corresponding to each time point is λ l or λ h When time t is a low-price period, the corresponding electricity price λ l When time t is during peak hours, the corresponding electricity price λh The coefficients for all other positions are 0; A s b s B s Let A and B represent the constant coefficient matrices corresponding to the operating model of the multi-energy system in the s-th scenario, respectively, and satisfy: A s x s ≤b s +B s θ;

[0052] S2.2. Combining different scenarios, the sum of the daily operating costs of the multi-energy system under different scenarios with a configured capacity of θ is obtained, expressed as:

[0053]

[0054] Where, ρ s Let ρ represent the probability that the multi-energy system is in the s-th scenario. s =1 / 56;

[0055] S2.3, The capacity benefit evaluation function for a multi-energy system is as follows:

[0056] V(θ)=v av (0)-v av (θ)

[0057] Where V(θ) represents the capacity benefit evaluation function of the multi-energy system when the configured capacity is θ, θ is the capacity to be configured, and θ = [C w C p E emax ;P e,max ], C w For wind power installed capacity, C p For photovoltaic installed capacity, E emax For energy storage capacity, P e,max Maximum energy storage power; v av (0) represents the sum of daily operating costs under different scenarios when the configured capacity is 0, v av (θ) represents the sum of daily operating costs under different scenarios when the configured capacity is θ.

[0058] In this embodiment, Figure 3 This represents the numerical variation of the capacity benefit evaluation function under different θ values, with E fixed. emax :P e,max =3:1, C w and C p Four points were evenly selected between 0kW and 20kW, E emax Four points were evenly selected between 0kW and 30kW. Figure 3 It can be seen that wind power capacity has the greatest impact on the economic benefits of the system, followed by photovoltaic power, while energy storage devices have the least impact.

[0059] S3. Construct a capacity configuration model for a multi-energy system;

[0060] Investment cost function for constructing a multi-energy system;

[0061]

[0062] Among them, C in κ represents the total investment cost of a multi-energy system, and κ represents the unit cost parameter. κ = [κ w ;κ p ;κ e ;κ ep ], κ w ;κ p ;κ e ;κ ep κ0 represents the unit capacity cost of wind farms, photovoltaic power plants, and energy storage devices, and the unit cost of power devices, respectively; κ0 represents the fixed cost of deploying wind power, photovoltaic, and energy storage devices.

[0063] In this embodiment, κ is taken. w = 5500 yuan / kW, κ p =4200 yuan / kW, κ e =1200 yuan / kWh, κ ep =400 yuan / kW, κ0 = 120000 yuan.

[0064] The objective function of the capacity allocation model is constructed by combining the investment cost function of a multi-energy system.

[0065]

[0066] S4. Linearize the capacity configuration model of the multi-energy system, and then solve it through a solver to obtain the capacity configuration strategy of the multi-energy system.

[0067] S5.1, sum v of the daily operating costs under different scenarios of a multi-energy system. av (θ) can be converted to dual form as follows:

[0068]

[0069] Wherein, the coefficient matrix satisfy: x = [x1, x2, ..., x S ]; y is the optimal solution corresponding to θ;

[0070] S5.2, dual form of v av(θ) is added to the capacity configuration model to represent the cutting plane, resulting in the added capacity configuration model and its constraints:

[0071]

[0072] θ≥0

[0073] Where ζ is a variable replacing v av (θ), y i For different θ i The corresponding optimal solution;

[0074] In this embodiment, the cutting plane is added to the constraints of the planning model to narrow down the feasible region and facilitate the solution.

[0075] S5.3 Linearize the capacity configuration model with added cutting planes;

[0076] Let the variable Then the capacity configuration model is linearized as follows:

[0077]

[0078] z>0

[0079]

[0080] S5.4. Sample θ to obtain multiple θ values. i Then each θ i Substituting even form v av In (θ), multiple optimal solutions y are obtained. i Finally, each y i Substituting the linearized capacity allocation model, the variables are obtained by solving the problem using a solver.

[0081] S5.5, Based on variables Solve for the capacity configuration parameter θ;

[0082]

[0083] Finally, the capacity configuration strategy for the multi-energy system is obtained based on the optimal θ [C]. w C p E emax ;P e,max ].

[0084] In this embodiment, the commercial solver GUROBI is selected to solve the model, and the final configuration result is C. w =32.34kW, C w =32.34kW, E emax =26.09kWh, Pe,max =5.46kW.

[0085] In addition, we keep other parameters constant and adjust κ. w Different configuration results, such as Figure 4 As shown, in κ w When the value increases, the wind power configuration capacity decreases, indicating that excessively high investment costs when configuring wind power will reduce the economic benefits of the system. Therefore, the solution will reduce the wind power configuration capacity.

[0086] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A capacity allocation method for a multi-energy system based on fractional programming theory, characterized in that, Includes the following steps: (1) Construct an operational model for a multi-energy system; (2) Construct a capacity benefit evaluation function for a multi-energy system; ； in, Indicates the configured capacity is Capacity benefit evaluation function for multi-energy systems For the capacity to be configured, , For wind power installed capacity, For photovoltaic installed capacity, For energy storage capacity, Maximum energy storage capacity; This represents the sum of daily operating costs under different scenarios when the configured capacity is 0. Indicates the configured capacity is The sum of daily operating costs under different scenarios is expressed as: ； in, This indicates that the multi-energy system is in the first stage. The probability of each scenario , Indicates the number of scenes collected; Indicates the configured capacity is Time The daily operating cost for each scenario is expressed as: ； Among them, the superscript " " indicates transpose; For multi-energy systems in the first The runtime variables for each scenario are specifically represented as follows: ; Indicates the first The coefficient matrix for each scenario , The number of elements in the middle is equal, among which The coefficients corresponding to each time point are or At that moment During off-peak hours, the corresponding electricity price At that moment During peak hours, the corresponding electricity price The coefficients for all other positions are 0; , , These represent the multi-energy system in the first... The constant coefficient matrix corresponding to the model running in each scenario, and satisfying the following: ; (3) Construct a capacity configuration model for a multi-energy system; (4) The capacity configuration model of the multi-energy system is linearized, and then the capacity configuration strategy of the multi-energy system is obtained by solving the solution. The specific solution process is as follows: (4.1) The sum of daily operating costs under different scenarios of a multi-energy system Converted to dual form, it can be represented as: ； Wherein, the coefficient matrix , , , , , , satisfy: , ; for The corresponding optimal solution; (4.2) Dual Form Add the cutting plane to the capacity configuration model to obtain the added capacity configuration model and constraints: ； in, Substitute for variable , For different The corresponding optimal solution; (4.3) Linearize the capacity configuration model with added cutting planes; Let the variable Then, the capacity configuration model is linearized as follows: ； (4.4) Regarding Sampling was performed to obtain multiple Then each Substitution of dual forms In this process, multiple optimal solutions were obtained. Finally, each Substituting the linearized capacity allocation model, the variables are obtained by solving the problem using a solver. ; (4.5) Based on variables Solving for capacity configuration parameters ; ； Finally, based on the optimal... Obtain capacity configuration strategies for multi-energy systems .

2. The capacity allocation method for a multi-energy system based on fractional programming theory according to claim 1, characterized in that, The operation model of the multi-energy system includes: the power balance model of the multi-energy system, the output model of wind power and photovoltaic power, the operation model of energy storage devices, and the operation model of electric boilers. The power balance model of the multi-energy system is as follows: ； in, , Indicates the total number of sampling times. and Photovoltaic power plants and wind farms respectively Time of the first Output power in each scenario For the power grid Time of the first Output power in each scenario and For energy storage devices in Time of the first Discharge and charging power in various scenarios for Time of the first Electrical load power in each scenario For electric boilers Time of the first Output power in each scenario; The power output models for the wind farm and photovoltaic power station are as follows: ； ； in, and These represent the capacities of the wind farm and the photovoltaic power station being sampled, respectively. and These represent the required wind power capacity and photovoltaic capacity, respectively. The operating model of the energy storage device is as follows: ； ； ； ； in, Indicates the maximum power of the energy storage device. and These represent the charging and discharging efficiencies of the energy storage device, respectively. For energy storage devices in Time of the first The amount of electricity stored in each scenario Indicates the maximum capacity of the energy storage device. The sampling interval; The operating model of the electric boiler is as follows: ； ； ； in, This indicates the maximum power of the electric boiler. Indicates that the electric boiler is Time of the first Thermal power output in each scenario Indicates the electro-thermal conversion efficiency. express Time of the first The required heat load for each scenario.

3. The capacity allocation method for a multi-energy system based on fractional programming theory according to claim 1, characterized in that, The capacity configuration model for the multi-energy system is as follows: Investment cost function for constructing a multi-energy system; ； in, This represents the total investment cost of a multi-energy system. This represents the unit cost parameter. , These represent the unit capacity cost of wind farms, photovoltaic power plants, energy storage devices, and the unit cost of power devices, respectively. This represents the fixed cost of deploying wind power, solar power, and energy storage devices; The objective function of the capacity allocation model is constructed by combining the investment cost function of a multi-energy system. 。

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