A two-stage regional comprehensive energy system distribution robust economic dispatch method

Abstract

The application discloses a two-stage regional comprehensive energy system distribution robust economic dispatching method, which is used for describing the uncertainty of wind power probability distribution, taking the Wasserstein distance as a measure between the experience distribution and the real distribution, and constructing a wind power probability distribution fuzzy set. In order to cope with the problems of possible line transmission overload and unit output out-of-limit, a joint opportunity constraint is applied to limit the influence of wind power on line transmission and unit output within a predetermined safety level. A linear decision rule and a linear incremental method are used to convert the model into a mixed integer linear programming problem. The application effectively improves the energy supply limitation of a single system in response to uncertain wind power through multi-energy complementation, solves the problem of low calculation efficiency caused by nonlinearity and non-convexity of the model, and can coordinate the economy and robustness, so that different risk schemes can be provided for decision makers by adjusting the distance and confidence.

Description

Technical Field

[0001] This invention relates to the field of power system technology, specifically to a two-stage regional integrated energy system distributed bar economic dispatch method. Background Technology

[0002] Integrated energy systems, through the interconnection and complementarity of multiple energy sources, break down barriers between different energy supply systems and achieve high-efficiency energy utilization, possessing immense practical value. However, the strong uncertainties following the large-scale integration of renewable energy sources such as wind power have brought unprecedented challenges to the economic dispatch of integrated energy systems.

[0003] Furthermore, in traditional optimization methods for addressing uncertainty, stochastic programming struggles to obtain accurate probability distribution information for wind power output, while robust optimization based on boundary information of uncertain variables can lead to overly conservative decisions or excessively high costs. Therefore, distributive robust optimization, which considers the probabilistic uncertainty of random variables, has gradually gained attention because it can effectively address the problem of overly optimistic or conservative decisions.

[0004] The construction of typical Kullback-Leibler divergence fuzzy sets relies on the first and second-order moment information (mean, covariance) and higher-order moment information of wind power. However, different distributions may share the same moment information, making it difficult to determine the worst-case probability distribution of wind power. In distance-based fuzzy sets, the widely used Kullback-Leibler divergence fuzzy set can only be derived from data if it supports the true distribution on a finite set, but the true distribution of wind power is continuous. In contrast, Wasserstein-based fuzzy sets, which encompass all (continuous or discrete) probability distributions sufficiently close to discrete empirical distributions, demonstrate good performance in terms of finite sample guarantees and confidence sets. Summary of the Invention

[0005] Based on the advantages of the sub-Bruker optimization method and joint opportunity constraints in handling the uncertainties of renewable energy sources such as wind power, this invention proposes a two-stage sub-Bruker economic dispatch method that takes into account joint opportunity constraints for the economic dispatch problem of regional integrated energy systems under wind power uncertainty, so as to ensure the economic and reliable operation of regional integrated energy systems.

[0006] The present invention adopts the following technical solution:

[0007] A two-stage regional integrated energy system distributed energy system economic dispatch method includes the following steps:

[0008] (1) Read integrated energy system data and wind power data;

[0009] (2) Construct a fuzzy set of probability distributions based on Wasserstein distance using historical wind power data;

[0010] (3) Construct the joint opportunity constraint of the sub-Bruker bar based on the Wasserstein fuzzy set, and apply the conditional value of risk approximation and the Bonferroni conservative approximation to transform it into a finite-dimensional deterministic constraint set;

[0011] (4) Establish a regional integrated energy supply day-ahead dispatch model that takes into account wind power forecasting errors;

[0012] (5) Establish a real-time dispatch model for the regional integrated energy system, and then form a two-stage sub-Bruker economic dispatch model that considers joint opportunity constraints;

[0013] (6) The model is transformed into a mixed-integer second-order cone programming problem using linear decision rules and linear incremental methods;

[0014] (7) Solve to obtain the economic dispatch scheme of the regional integrated energy system that takes into account both economy and robustness.

[0015] The integrated energy system includes a thermal system, an electric system, and a natural gas system.

[0016] Step (2) is achieved through the following method:

[0017] For an uncertain wind power deviation Its historical data is Uncertainty about wind power deviation The true distribution P can be approximated as in Represents historical samples of uncertain variables ζ k The Dirac measure; and as N→∞, P N The distribution P approaches the true distribution infinitely more closely, meaning that the larger the sample size of historical data, the better P becomes. N The distance between P and the true distribution becomes smaller and smaller; therefore, in order to introduce probability distribution information of uncertain variables, historical data can be used to establish a description of P. N A fuzzy set of distances to P;

[0018] Wasserstein distance d w :M(Ξ)×M(Ξ)→R + The definition is as follows:

[0019]

[0020] In the formula: d w (P1, P2) represents the distance between probability distributions P1 and P2; ||·|| represents the distance between probability distributions R. nAny possible norm form; Π is the joint probability distribution of uncertain random variables ζ1 and ζ2, P1 and P2 are the marginal distributions of uncertain random variables ζ1 and ζ2 respectively, and M(Ξ) represents the polyhedron set Ξ={ζ∈R W All probability measures of uncertain variables supported on :Hζ≤h};

[0021] Furthermore, the fuzzy set constructed based on the Wasserstein metric distance has the following form:

[0022]

[0023] In the formula: ρ represents the radius constant of the Wasserstein sphere;

[0024] The general form of the joint opportunity constraint in step (3) is as follows:

[0025]

[0026] In the formula: l represents the index of the energy device or transmission line, L is the total amount of the energy device or transmission line, and ε is the predefined confidence level;

[0027] Then, the joint chance constraint is divided into L independent chance constraints using the Bonferroni conservative approximation, with a confidence level of ε. l =ε / L:

[0028]

[0029] The above formula can be transformed using the worst-case conditional risk approximation method:

[0030]

[0031] Therefore, according to the theory of strong duality, we can obtain:

[0032]

[0033] The objective function of the day-ahead scheduling model in step (4) is as follows:

[0034]

[0035] In the formula: λ {·} The output cost of traditional generator sets, gas generator sets, and combined heat and power units; For natural gas costs; This indicates that each unit is scheduled to operate at its current capacity; G gas,t This represents the planned gas consumption for the day. These represent the unit's upper and lower reserve power, respectively, and their costs are respectively γc Adjusting the unit's output cost; To account for the unit adjustment amount under the probability distribution of wind power prediction deviation.

[0036] The objective function of the real-time scheduling model in step (5) is as follows:

[0037]

[0038] In the formula: To shed load; Represents the amount of wind curtailment; To contribute to the various units during the day.

[0039] Therefore, the two-stage regional integrated energy system distributed energy system economic dispatch model is as follows:

[0040]

[0041] st Ax'<b (2)

[0042]

[0043]

[0044]

[0045] st Ex+Fy+Gζ≤h (6)

[0046] In the formula: the objective function (1) is to minimize the operating cost of the first stage and the expected cost caused by energy adjustment. x is a decision variable including unit output and reserve capacity. D ζ Let f represent the fuzzy set containing the uncertain probability distribution P of wind power. Equations (2)-(4) give the constraints for the first stage. The real-time process is represented by equations (5) and (6), where f represents the variable coefficients in equation (5).

[0047] Step (5) transforms the model into a mixed-integer second-order cone programming problem using linear decision rules and the linear incremental method. The objective function of the transformed model is as follows:

[0048]

[0049] In the formula: λ o and s o It is an auxiliary variable.

[0050] The Weymouth equation for simulating gas flow under the constraints of the natural gas system is as follows:

[0051]

[0052] To improve computational speed, the gas flow equations are linearized using piecewise linear programming techniques as follows:

[0053]

[0054] The beneficial effects of this invention are: the method of this invention effectively overcomes the drawbacks of stochastic programming and robust optimization methods, takes into account the economy and robustness of the scheme, and the scheduling cost is adjustable and controllable according to the amount of wind power data and the confidence level; and under uncertain wind power grid connection, the coordinated use of multi-energy coupling and complementary technology effectively smooths the volatility of wind power and improves the flexibility and reliability of the economic dispatch scheme. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the model solution process of the present invention.

[0056] Figure 2 This is a typical regional integrated energy system structure diagram of electricity, gas and heat. Detailed Implementation

[0057] To better understand the above-mentioned objectives, features and advantages of the present invention, the technical solution of the present invention will be further described in a non-limiting detail below with reference to the accompanying drawings and specific embodiments.

[0058] A typical regional integrated energy system uses a constrained transmission network to coordinate power generation and natural gas resources, employing three different energy sources—electricity, natural gas, and heat—to meet local electricity, gas, and heat demands. The energy hub is equipped with energy conversion equipment including combined heat and power (CHP) units, gas turbine generators, and electric boilers. CHP simultaneously converts natural gas into electricity and heat. The gas turbine generators convert natural gas into electricity and are capable of responding quickly to power fluctuations. An electric boiler is also included to flexibly provide sufficient heat.

[0059] Step 1: Read integrated energy system data and wind power data;

[0060] Step 2: Construct a fuzzy set of probability distributions based on Wasserstein distance using historical wind power data; the specific process is as follows:

[0061] Using the Wasserstein distance as a measure between the empirical and actual distributions of wind power, a fuzzy set of the uncertain probability distribution of wind power is constructed.

[0062] For uncertain wind power deviation Its historical data is Uncertainty about wind power deviation The true distribution P can be approximated as in Represents historical samples of uncertain variables ζ k The Dirac measure. And as N→∞, P N The distribution P approaches the true distribution infinitely more closely, meaning that the larger the sample size of historical data, the better P becomes. N The distance from the true distribution P decreases over time. Therefore, to introduce probability distribution information of uncertain variables, historical data can be used to establish a description of P. N A fuzzy set of distances between P and P.

[0063] Wasserstein distance d w :M(Ξ)×M(Ξ)→R + The definition is as follows:

[0064]

[0065] In the formula: d w (P1, P2) represents the distance between probability distributions P1 and P2; ||·|| represents the distance between probability distributions R. n Any possible norm form; ∏ is the joint probability distribution of uncertain random variables ζ1 and ζ2, P1 and P2 are the marginal distributions of uncertain random variables ζ1 and ζ2 respectively, and M(Ξ) represents the polyhedron set Ξ={ζ∈R W All probability measures of uncertain variables supported on :Hζ≤h}.

[0066] Furthermore, the fuzzy set constructed based on the Wasserstein metric distance has the following form:

[0067]

[0068] In the formula: ρ represents the radius constant of the Wasserstein sphere.

[0069] At a certain acceptable confidence level, this fuzzy set contains the probability distributions of all possible uncertain variables in a Wasserstein sphere space with radius ρ.

[0070] Step 3: Construct joint opportunity constraints based on Wasserstein fuzzy sets, and apply conditional risk value approximation and Bonferroni conservative approximation to transform them into a finite-dimensional deterministic constraint set. The specific process is as follows: Based on Wasserstein distance fuzzy sets, construct joint opportunity constraints to limit the impact of wind power on line transmission, unit output, etc., within a predetermined safety level, and transform the infinite-dimensional joint opportunity constraints into finite-dimensional deterministic constraints using conditional risk value approximation and Bonferroni conservative approximation.

[0071] The general form of the joint opportunity constraint is shown below:

[0072]

[0073] In the formula: l represents the index of the energy device or transmission line, L is the total amount of the energy device or transmission line, and ε is the predefined confidence level.

[0074] Then, the joint chance constraint is divided into L independent chance constraints using the Bonferroni conservative approximation, with a confidence level of ε. l =ε / L:

[0075]

[0076] The above formula can be transformed using the worst-case conditional risk approximation method:

[0077]

[0078] Therefore, according to the theory of strong duality, we can obtain:

[0079]

[0080] Step 4: Establish a regional integrated energy supply system day-ahead dispatch model considering wind power forecasting errors: In the day-ahead phase, considering the probability distribution of uncertain wind power forecasting errors in historical data, the energy output and reserve capacity of multiple energy devices are dispatched. Therefore, the objective function is as follows:

[0081]

[0082] In the formula: λ {·} The output cost of traditional generator sets, gas generator sets, and combined heat and power units; For natural gas costs; This indicates that each unit is scheduled to operate at its current capacity; G gas,t This represents the planned gas consumption for the day. These represent the unit's upper and lower reserve power, respectively, and their costs are respectively γ c Adjusting the unit's output cost; To account for the unit adjustment amount under the probability distribution of wind power prediction deviation.

[0083] The constraints of the current scheduling model include:

[0084] 1) Power system constraints:

[0085] Reserve capacity of conventional generating units, gas-fired generating units, and combined heat and power units:

[0086]

[0087]

[0088] In the formula: These refer to the upper and lower standby capacities of the power generation equipment; These represent the maximum allowable standby capacity of the device at the top and bottom, respectively; {·}=i e ,gg,chp represents the node index of traditional generator sets, gas generator sets, and combined heat and power units in the power grid.

[0089] Output upper and lower limits and ramping constraints for conventional generating units, gas generator units, and combined heat and power units:

[0090]

[0091]

[0092]

[0093]

[0094] In the formula: The day-ahead output values ​​are for conventional generating units, gas generating units, and combined heat and power units. These are the upper and lower limits of the unit's output, respectively. These represent the maximum values ​​for the unit's uphill and downhill climbs, respectively.

[0095] Wind power forecasting deviations can lead to scheduling deviations in turbine output. Therefore, it is necessary to adjust the turbine output based on the wind power forecasting deviations and limit the adjustment amount to within the reserve capacity range.

[0096]

[0097] In the formula: This refers to the adjustment amount of unit power affected by wind power forecast deviations.

[0098] The transmission power of a line is constrained by its capacity as follows:

[0099]

[0100] In the formula: It is line l e The maximum transmission capacity; Q g Q w and Q d These are the coefficient matrices of generator sets (traditional units, gas generators, combined heat and power), wind turbines, and the lines where loads are located in the power subsystem.

[0101] Power system power balance constraints:

[0102]

[0103] In the formula: ζ j,t These represent the historical average and deviation of wind power output, respectively. Power flows into and out of power system nodes; conventional electrical loads and electric boiler loads are respectively determined by... express.

[0104] 2) Natural gas system constraints

[0105] The relationship between the gas pressures at the initial and terminal nodes of the gas compressor is as follows:

[0106]

[0107] In the formula: For node i in the gas network g j g The gas pressure at both ends of the active gas transmission pipeline; ρ c This indicates the compression ratio of the compressor.

[0108] The natural gas node flow balance constraint is:

[0109]

[0110] In the formula: This refers to the flow rate of the natural gas source. The natural gas flow rate in each natural gas pipeline; These represent the gas consumption of combined heat and power (CHP), gas generator sets, and conventional natural gas loads, respectively.

[0111] To prevent gas flow from two directions from existing simultaneously in the same gas pipe, the flow rate should be constrained:

[0112]

[0113] The constraint on the relationship between gas pressure and flow rate under steady-state conditions is expressed by the Weymouth gas flow rate equation as follows:

[0114]

[0115] In the formula: The coefficients in the Weymouth flow formula.

[0116] The gas pressure at each node and the gas flow rate in each gas pipeline are as follows:

[0117]

[0118]

[0119] In the formula: ψmin , ψ max , These represent the minimum / maximum node pressure and the minimum / maximum pipeline flow rate.

[0120] 3) Thermal system constraints

[0121] The output temperature of each node is equal to the temperature of the mixed water:

[0122]

[0123]

[0124]

[0125]

[0126] In the formula: This indicates the inlet and outlet temperatures of the return water pipe; This indicates the inlet and outlet temperatures of the hot water supply pipe. These represent the mass flow rates of the water supply pipe and the return pipe, respectively. This is the mixing temperature of the hot water supply pipe / return water pipe.

[0127] The relationship between the thermal power of each pipeline node in the heating system and the hot water temperature and mass flow rate is as follows:

[0128]

[0129] In the formula: For thermal load, C p This indicates the specific heat capacity of water.

[0130] The temperature relationship between the hot water flowing into and out of the hot water pipes is as follows:

[0131]

[0132] In the formula: Indicates the temperature at the end of the pipe; T represents the temperature at the beginning of the pipe. a Ambient temperature; L is the heat transfer coefficient of the hot water pipe. b This indicates the length of the hot water pipe.

[0133] The node thermal power balance is:

[0134]

[0135] In the formula: These represent the heat output of combined heat and power (CHP) and electric boilers, respectively. This represents the heat loss of each heating pipe.

[0136] 4) Constraints of energy coupling equipment

[0137]

[0138]

[0139]

[0140]

[0141] In the formula: Thermoelectric ratio represents the ratio between the output heat power and the output electrical power of a combined heat and power unit. This represents the power generation efficiency of a combined heat and power (CHP) unit. The power generation efficiency of the gas generator set; This represents the electro-thermal efficiency of an electric boiler.

[0142] Step 5: Establish a real-time dispatch model for the regional integrated energy system, thereby forming a two-stage partially robust economic dispatch model considering joint opportunity constraints. The specific process is as follows: In the real-time stage, adjust the power output according to the wind power output to achieve a balance between the economic efficiency and robustness of the regional integrated energy system. Therefore, the objective function is as follows:

[0143]

[0144] In the formula: To shed load; Represents the amount of wind curtailment; To contribute to the various units during the day.

[0145] In addition to the constraints that are the same as those for day-ahead scheduling, the following constraints also apply:

[0146]

[0147]

[0148]

[0149]

[0150] Therefore, a two-stage regional integrated energy system sub-Bluerg model is formed, which can be simplified as follows:

[0151]

[0152] st Ax'<b (2)

[0153]

[0154]

[0155]

[0156] st Ex+Fy+Gζ≤h (6)

[0157] The objective function (1) is to minimize the operating cost of the first stage and the expected cost caused by energy adjustment. x is a decision variable including unit output and reserve capacity. D ζ Let f represent the fuzzy set containing the uncertain probability distribution P of wind power. Equations (2)-(4) give the constraints for the first stage. The real-time process is represented by equations (5) and (6), where f represents the variable coefficients in equation (5).

[0158] Step 6: Transform the model into a mixed-integer second-order cone programming problem using linear decision rules and the linear incremental method. The specific process is as follows:

[0159] When decision variables are coupled with random variables, directly finding the exact solution to the sectional blue bar optimization problem is both complex and time-consuming. Therefore, the linear decision method is a typical approximation method that can handle the coupling relationship between decision variables and uncertain parameters. In this case, the expectation part of the objective function can be rewritten as follows:

[0160]

[0161] In the formula: λ o and s o It is an auxiliary variable.

[0162] In natural gas system scheduling models, the Weymouth flow-pressure equation is nonlinear and nonconvex. These characteristics make the optimization of natural gas system operation an NP-hard problem, which can be solved using piecewise linear programming techniques. In linearization techniques, piecewise linear functions describing nonlinearity and bivariate variables can avoid local optima caused by nonconvexity.

[0163] The Weymouth gas flow equation used to simulate gas flow is as follows:

[0164]

[0165] Assume gas flows from node i g Flowing to another node j g ,variable Replace with Indicates node i g The pressure is represented by a second-order conic section. Then, the Weymouth flow-pressure equation can be transformed into the following form:

[0166]

[0167] When the airflow direction is node i g To node j g At that time, airflow The range is 0 to This is the maximum flow rate in the pipe. (After conversion) The model is shown below:

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175] Finally, the Weymouth gas flow equation is transformed into the following form:

[0176]

[0177] Thus, a two-stage regional integrated energy system sub-bar economic dispatch model considering joint opportunity constraints has been established, and the effective transformation of the model has been achieved. The proposed model can be solved by running the Grobi solver on the Matlab platform to obtain the economic dispatch results of the two-stage regional integrated energy system.

Claims

1. A two-stage regional integrated energy system distributed bar economic dispatch method, characterized in that, Includes the following steps: (1) Read integrated energy system data and wind power data; (2) Construct a fuzzy set of probability distributions based on Wasserstein distance using historical wind power data; (3) Construct the joint chance constraint of the sub-Bruker bar based on the Wasserstein fuzzy set, and apply the conditional risk value approximation and Bonferroni conservative approximation to transform it into a finite-dimensional deterministic constraint set; (4) Establish a regional integrated energy dispatch model to the system that takes into account wind power forecasting errors; (5) Establish a real-time dispatch model for the regional integrated energy system, and then form a two-stage sub-Bruker economic dispatch model that considers joint opportunity constraints; (6) The model is transformed into a mixed-integer second-order cone programming problem using linear decision rules and linear incremental methods; (7) Solve to obtain the economic dispatch scheme of the regional integrated energy system that takes into account both economy and robustness; The general form of the joint opportunity constraint in step (3) is as follows: ， In the formula: An index indicating an energy device or transmission line. It refers to the total amount of energy devices or transmission lines. It is a predefined confidence level; Then, the joint chance constraint is divided into the following using the Bonferroni conservative approximation: Each independent opportunity constraint has a confidence level of 1. : ， The above formula can be transformed using the worst-case conditional risk approximation method: ， Therefore, according to the theory of strong duality, we can obtain: 。 2. The two-stage regional integrated energy system distributed economic dispatch method according to claim 1, characterized in that, The integrated energy system includes a thermal system, an electric system, and a natural gas system.

3. The two-stage regional integrated energy system distributed economic dispatch method according to claim 1, characterized in that, Step (2) is achieved through the following method: For an uncertain wind power deviation Its historical data is Then the uncertainty of wind power deviation The true distribution It can be approximated as ,in Historical samples representing uncertain variables The Dirac measure; and when hour, Infinitely close to the true distribution That is, the larger the historical data sample size, the better. With the true distribution The distance between them becomes smaller and smaller; therefore, in order to introduce the probability distribution information of uncertain variables, historical data can be used to establish a description. and A fuzzy set of distances between them; Wasserstein distance The definition is as follows: ， In the formula: Represents probability distribution and The distance between them; In order to be in Any possible norm form; For uncertain random variables and The joint probability distribution, and These are respectively uncertain random variables and marginal distribution, Represents a set of polyhedra All probability measures of uncertain variables supported above; Furthermore, the fuzzy set constructed based on the Wasserstein metric distance has the following form: ， In the formula: This represents the radius constant of the Wasserstein sphere.

4. The two-stage regional integrated energy system distributed economic dispatch method according to claim 1, characterized in that, The objective function of the day-ahead scheduling model in step (4) is as follows: ， In the formula: The output cost of traditional generator sets, gas generator sets, and combined heat and power units; For natural gas costs; This indicates that each unit is scheduled to operate at its current capacity. This represents the planned gas consumption for the day. , These represent the unit's upper and lower reserve power, respectively, and their costs are respectively , ; Adjusting the unit's output cost; To account for the unit adjustment amount under the probability distribution of wind power prediction deviation.

5. The two-stage regional integrated energy system distributed economic dispatch method according to claim 1, characterized in that, The objective function of the real-time scheduling model in step (5) is as follows: ， In the formula: To shed load; Represents the amount of wind curtailment; To provide support to all units during the day's operations; Therefore, the two-stage regional integrated energy system distributed energy system economic dispatch model is as follows: (1) (2) (3) (4) (5) (6)， In the formula: the objective function (1) is to minimize the operating cost of the first stage and the expected cost caused by energy adjustment; These are decision variables that include unit output and reserve capacity; This indicates the inclusion of an uncertain probability distribution for wind power. The fuzzy set; Equations (2)-(4) give the constraints for the first stage; The real-time process is represented by equations (5) and (6), where The variable coefficients of expression (5) are represented.

6. The two-stage regional integrated energy system distributed economic dispatch method according to claim 1, characterized in that, Step (5) transforms the model into a mixed-integer second-order cone programming problem using linear decision rules and the linear incremental method. The objective function of the transformed model is as follows: ， In the formula: , and It is an auxiliary variable.

7. The two-stage regional integrated energy system distributed economic dispatch method according to claim 2, characterized in that, The Weymouth equation for simulating gas flow under the constraints of the natural gas system is as follows: ， To improve computational speed, the gas flow equations are linearized using piecewise linear programming techniques as follows: 。

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