A carbon emission flow constraint linearization method for low-carbon dispatch of power system

Abstract

The application belongs to the technical field of power systems, and relates to a carbon emission flow constraint linearization method for low-carbon scheduling of power systems. The method comprises the following steps: establishing a power carbon emission flow model based on power flow direction decomposition to obtain power flow direction constraints and node carbon flow balance constraints for coupling carbon flow calculation; introducing auxiliary state variables and processing the power flow direction constraints by using a large M method; constructing a carbon flow balance equation simplification model based on piecewise linearization and a large M relaxation method; based on the power flow direction constraint and node carbon flow balance constraint linearization method, establishing a low-carbon economic scheduling model of the power system coupled with carbon flow calculation, and converting the model into a linear optimization problem for solving. The application converts the original nonlinear problem into a linear optimization programming problem, improves the solving universality of the low-carbon economic scheduling method of the power system containing carbon flow calculation, can guarantee good carbon accounting accuracy, and significantly improves the model solving efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power systems, and in particular, relates to a carbon emission flow constraint set linearization method for low-carbon scheduling of power systems. BACKGROUND

[0002] In recent years, the research on low-carbon economic scheduling of power systems has gradually changed from a single generation-side carbon emission control mode to a refined scheduling mode focusing on the responsibility of user-side carbon emissions. The node carbon emission factor, as a key indicator for user-side carbon emission accounting, is usually calculated based on the carbon emission flow theory (CEF). Therefore, combining the carbon emission flow model with the optimization scheduling framework has become an effective means to improve the precision of carbon control in scheduling schemes. However, existing scheduling methods coupled with carbon flow calculation face severe solving challenges in practical applications, with the core problem being the high nonlinearity of the model.

[0003] The existing research on power system optimization scheduling models coupled with carbon flow calculation needs to satisfy two types of key constraints: the power flow direction constraint for determining the flow direction in the optimization process and ensuring that the carbon flow direction and the power flow direction are strictly matched, and the node carbon flow balance constraint for establishing the transmission relationship between direct carbon emissions of power generation and node carbon emission factors. Both of the above two types of constraints have significant nonlinearity characteristics: the power flow direction constraint needs to be described through binary variables and nonlinear complementary constraint conditions, and there is a multiplicative coupling relationship between power flow and carbon intensity in the node carbon flow balance equation. This strong nonlinearity leads to the non-convexity of the optimization problem, making it difficult to solve the optimization scheduling problem with the above constraints. SUMMARY

[0004] To solve the above technical problems, the application provides a carbon emission flow constraint set linearization method for low-carbon scheduling of power systems, comprising:

[0005] Establishing a power carbon emission flow model based on power flow direction decomposition, including node power balance equations and node carbon emission flow balance equations, obtaining power flow direction constraints and node carbon flow balance constraints for coupling carbon flow calculation;

[0006] Introducing auxiliary state variables and using the big M method to process the power flow direction constraints;

[0007] Constructing a carbon flow balance equation simplification model based on piecewise linearization and big M relaxation method, including: determining the number of segments of the node carbon emission factor and the upper and lower bounds of the node carbon emission factor; using piecewise linearization and big M relaxation method to process line carbon flow and load carbon flow; linearizing the node carbon flow balance constraint to obtain the carbon flow balance equation simplification model;

[0008] Based on the linearization method of power flow direction constraints and nodal carbon flow balance constraints, a low-carbon economic dispatch model of power system coupled with carbon flow calculation is established and then transformed into a linear optimization problem for solution.

[0009] Based on the above technical solution, the present invention can be further improved as follows.

[0010] Furthermore, an electricity carbon emission flow model based on power flow direction decomposition is established, including nodal power balance equations and nodal carbon emission flow balance equations.

[0011] set up , and Represents a node. Indicates load, Represents the set of all nodes in a power system. via a single line to the node The set of neighboring nodes to which the injected power is applied. Indicates that the node passes through a single line. The set of neighboring nodes from which power flows out. Represents a node The assembly of the generator sets, Represents a node The set of loads, Indicates from node Flow to Node power, Indicates from node Flow to Node power, Represents a node Up generator set Injection power, Represents a node On load The outflow power, Indicates from node Flow to Node carbon flow, Indicates from node Flow to Node carbon flow, Represents a node Up generator set Injected carbon flow, Represents a node On load Given the outflow of carbon and the fact that carbon emission flow follows the active power distribution law, the nodal power balance equation can be expressed as:

[0012] ;

[0013] The node carbon emission flow balance equation is expressed as:

[0014] ;

[0015] Let denote the node carbon emission factor of node , denote the node carbon emission factor of node , denote the fuel emission factor of generator ,According to the principle of fair mixing, all nodes have the same carbon emission factor, and the node carbon emission flow balance equation is expressed as:

[0016] Further, the power flow direction constraint and the node carbon flow balance constraint for coupling carbon flow calculation are obtained, including:

[0017] Let the actual power flow of line be , , and denote the node, denote the load, denote the line, for the start node and the end node of line , define the positive direction from to , and decompose the actual power flow of line into positive and negative directions, define as the positive flow component of line , as the negative flow component of line , then the power flow direction constraint is:

[0018] ;

[0019] ;

[0020] ;

[0021] Let denote the set of nodes adjacent to node , denote the variable belonging to node , denote the node carbon emission factor of node , denote the fuel emission factor of generator , denote the node Up generator set Injection power, Represents a node On load The outflow power, Indicates from node Flow to Node The weight of the trend, Indicates from node Flow to Node The tidal current components, after tidal current direction decomposition, are represented by the nodal carbon flow balance constraints used for coupled carbon flow calculation as follows:

[0022] .

[0023] Furthermore, auxiliary state variables are introduced, and the Big M method is used to handle power flow direction constraints, including:

[0024] set up Indicates the line The positive power flow state variables, Represents the reverse power flow state variable. It is an infinitely large positive number. For the line The positive trend weight, For the line The reverse current component, then the linearization of the current direction constraint is expressed as:

[0025] ;

[0026] .

[0027] Furthermore, the number of segments of the node carbon emission factor and the upper and lower bounds of the node carbon emission factor are determined, including:

[0028] Let the upper bound of the node carbon emission factor be The lower bound of the node carbon emission factor is The number of segments is , Represents a node. Indicates load, Indicates the first Each segment Variables that belong to a node. Represents the set of all nodes in a power system, segmented. The upper bound is Segmentation The lower bound is Segmentation The midpoint is , Represents a node the piecewise state variable of the nodal carbon emission factor of node is 1, it indicates that the piecewise state variable of the nodal carbon emission factor of node is 1, it indicates that the piecewise state variable of the nodal carbon emission factor of node For each node:

[0029] .

[0030] Further, the piecewise linearization and large M relaxation method are adopted to deal with the line carbon flow and load carbon flow, including:

[0031] Let and denote the node, denote the number of pieces, denote the th piece, denote the load, denote the variable belonging to node, denote the number of infinity, denote the carbon flow from node to node , denote the carbon flow component from node to node , denote the piecewise state variable of the nodal carbon emission factor of node , denote the midpoint of the piecewise state variable of the nodal carbon emission factor of node , denote the power flow component from node to node , denote the piecewise state variable of the nodal carbon emission factor of node , denote the midpoint of the piecewise state variable of the nodal carbon emission factor of node , denote the power flow component from node to node , denote the set of all nodes in the power system, denote the adjacent node set of node through which power is injected into node and from which power flows out, denote the set of loads on node , denote the outflow carbon flow of load on node , denote the set of nodes , denote the set of nodes On load The outflow power, Indicates generator set fuel emission factors, Represents a node Up generator set Injection power, Represents a node On load The outflow of carbon, Represents a node The node carbon emission factor in segments The lower bound above, Represents a node The node carbon emission factor in segments The lower bound above;

[0032] Line carbon current is represented as:

[0033] ;

[0034] The load carbon flow is expressed as:

[0035] ;

[0036] The nodal carbon flow balance equation is expressed as:

[0037] ;

[0038] The large M relaxation method is used to process the line carbon current and load carbon current, as follows:

[0039] ;

[0040] ;

[0041] ;

[0042] .

[0043] Furthermore, set and Represents a node. Indicates load, Variables that belong to a node. Indicates the route. Indicates from node Flow to Node carbon flow, Indicates generator set fuel emission factors, Represents a node Up generator set Injection power, Indicates from node Flow to Node The carbon flow component, Represents a node On load The outflow of carbon, To represent the set of all nodes in a power system, Indicates a route to the node via a single line. Injected power and nodes The set of neighboring nodes from which power flows out. Indicates a route to the node via a single line. Up generator set Injection power and nodes Up generator set The set of adjacent nodes of the outflow power, linearized by the node carbon flow balance constraint, yields a simplified model of the carbon flow balance equation as follows:

[0044] .

[0045] Furthermore, based on the linearization method of power flow direction constraints and nodal carbon flow balance constraints, a low-carbon economic dispatch model for the power system coupled with carbon flow calculation is established and transformed into a linear optimization problem for solution, including:

[0046] Constructing an economic dispatch model for traditional power systems;

[0047] The Big M method is used to handle power flow direction constraints and incorporated into the low-carbon economic dispatch model of the power system;

[0048] The linearized node carbon flow balance constraint is incorporated into the low-carbon economic dispatch model of the power system;

[0049] Construct a set of low-carbon dispatch constraints for the power system;

[0050] The low-carbon economic dispatch model of the power system coupled with carbon flow calculation is transformed into a mixed-integer linear optimization problem and solved.

[0051] Furthermore, constructing a traditional power system economic dispatch model includes determining the objective function of the traditional power system economic dispatch model, the power balance constraints of the system at different time periods, and the inequality constraints in the economic dispatch model; the inequality constraints in the economic dispatch model include line power flow constraints, unit output constraints, and unit ramping constraints.

[0052] Assume the number of nodes in the system is . Number of lines The number of generator sets is The number of fossil fuel units is The number of renewable energy units is , the number of dispatch periods is , is a vector matrix composed of , the dimension of , is a quoted cost column vector of generating units, , the dimension of , denotes a generating unit output column vector, , the dimension of , denotes a generating unit output column vector of time period , which is expanded as , denotes a dispatch step size, denotes a generating unit output operation matrix, , the dimension of , denotes , the dimension of is a is an all-1 column vector of denotes a Kronecker product in matrix operation, denotes a node load operation matrix, , the dimension of , denotes , the dimension of is an all-1 column vector of denotes a node load column vector, , the dimension of , denotes a node load column vector of time period , which is expanded as , denotes a renewable energy unit output column vector, , the dimension of , denotes a renewable energy unit output column vector of time period , which is expanded as is a line transmission capacity column vector, , the dimension of is a power flow transfer distribution factor matrix, , the dimension of ​​​​​​​is the node-generating unit association matrix, is the generating unit-fossil fuel generating unit association matrix, is the generating unit-renewable energy generating unit association matrix, is of dimension , is of dimension , is of dimension , is of dimension is an identity matrix of order is an identity matrix of order is an identity matrix of order is an identity matrix of order is a zero column vector of dimension is a maximum technical output column vector of fossil fuel generating units, is a minimum technical output column vector of fossil fuel generating units, and are of dimension , is a vector matrix composed of identity matrices of order is of dimension ; is the up ramp rate vector of generating units, is the down ramp rate vector of generating units, and are of dimension ; is the coefficient matrix , ,

[0053] , and is defined as: ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] The objective function of the traditional economic dispatch model of power systems is to minimize the system generation cost, which is expressed as:

[0060] ;​​

[0061] The power balance constraint of each period of the system is represented as:

[0062] ;

[0063] The inequality constraint in the economic dispatch model is represented as:

[0064] .

[0065] Further, the low-carbon dispatch constraint set of the power system includes a system-level carbon emission constraint and a node-level carbon emission constraint;

[0066] Let represent a fuel emission factor column vector of the generator set, the dimension of , represent the maximum carbon emission of the system within the dispatch period , represent a node load carbon flow matrix, the dimension of , is a full 1 column vector of , represent the maximum carbon emission column vector of the node within the dispatch period , the dimension of ;

[0067] The system-level carbon emission constraint is represented as:

[0068] ;

[0069] The node-level carbon emission constraint is represented as:

[0070] .

[0071] The beneficial effects of the present application are:

[0072] (1) The present application introduces auxiliary variables and M method to process the power flow direction constraint, and constructs a carbon flow balance equation simplified model based on piecewise linearization, so as to realize the linearization of the node carbon flow balance constraint. Through the linearization of the power flow direction constraint and the node carbon flow balance constraint, the original nonlinear problem can be converted into a linear optimization programming problem, and the solving universality of the low-carbon economic dispatch method of the power system containing carbon flow calculation is improved;

[0073] (2) The carbon emission flow constraint linearization method for general solving of the low-carbon optimization dispatch problem of the power system proposed in the present application can realize basically the same dispatch result as the nonlinear solving method, and can guarantee good carbon accounting accuracy;

[0074] (3) The carbon emission flow constraint set linearization method for the low-carbon optimal dispatching problem of the power system can significantly improve the model solving efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 A principle diagram of the carbon emission flow constraint set linearization method for the low-carbon dispatching of the power system is provided for the embodiment.

[0076] Figure 2 A flow chart of the specific implementation of the carbon emission flow constraint set linearization method for the low-carbon dispatching of the power system is provided for the embodiment.

[0077] Figure 3 A schematic diagram of the modified version of the PJM5 node system is provided for the embodiment. DETAILED DESCRIPTION

[0078] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings of the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0079] As an embodiment, as shown in the accompanying drawings, to solve the above technical problems, the embodiment provides a carbon emission flow constraint set linearization method for the low-carbon dispatching of the power system, which comprises: Figure 1

[0080] A power carbon emission flow model based on the power flow direction decomposition is established, including a node power balance equation and a node carbon emission flow balance equation, to obtain the power flow direction constraint and the node carbon flow balance constraint for coupling the carbon flow calculation;

[0081] An auxiliary state variable is introduced, and the power flow direction constraint is processed by using the big M method;

[0082] A carbon flow balance equation simplified model based on the piecewise linearization and the big M relaxation method is constructed, including: determining the piecewise number of the node carbon emission factor and the upper and lower bounds of the node carbon emission factor; processing the line carbon flow and the load carbon flow by using the piecewise linearization and the big M relaxation method; linearizing the node carbon flow balance constraint to obtain the carbon flow balance equation simplified model;

[0083] Based on the power flow direction constraint and the node carbon flow balance constraint linearization method, a low-carbon economic dispatching model of the power system coupling the carbon flow calculation is established, and is converted into a linear optimization problem for solving.

[0084] ​In order to make the low-carbon economic dispatch optimization model of the embedded carbon flow constrained power system be solved by most of the current commercial solvers, the application provides a carbon emission flow constraint set linearization method for general solving of low-carbon optimization dispatch problems. Through innovative modeling means: on the one hand, auxiliary variables and M method are introduced to process the power flow direction constraint; on the other hand, a carbon flow balance equation simplified model based on piecewise linearization is constructed, so that the linearization of the node carbon flow balance constraint is realized. The method converts the original nonlinear problem into a mixed integer linear programming problem which can be efficiently solved, reduces the difficulty of model solving under the premise of retaining the physical meaning of carbon emission flow, and makes the model be solved by most of the current commercial solvers. As shown in the accompanying Figure 2 Fig. 1 is a flow chart of a specific embodiment of the carbon emission flow constraint set linearization method for low-carbon dispatch of a power system.

[0085] Through linearization of the power flow direction constraint and the node carbon flow balance constraint, the application can convert the original nonlinear problem into a linear optimization programming problem, and improve the general solvability of the low-carbon economic dispatch method of the power system containing carbon flow calculation.

[0086] The carbon emission flow constraint set linearization method for general solving of low-carbon optimization dispatch problems of the power system provided by the application can realize basically the same dispatch result as the nonlinear solving method, and can guarantee good carbon accounting accuracy.

[0087] The carbon emission flow constraint set linearization method for general solving of low-carbon optimization dispatch problems of the power system provided by the application can significantly improve the model solving efficiency.

[0088] Since the carbon emission flow strictly follows the active power distribution rule, in order to improve the calculation efficiency, the power loss caused by network loss is ignored, and the node power balance equation and the node carbon emission flow balance equation are established.

[0089] Optionally, a power carbon emission flow model based on power flow direction decomposition is established, including a node power balance equation and a node carbon emission flow balance equation.

[0090] Let , and represent a node, represent a load, represent a set of all nodes in the power system, a set of adjacent nodes through which a single line injects power into the node , a set of adjacent nodes through which a single line flows out of the node , represent a set of generator units of the node , represent a node The set of loads, Indicates from node Flow to Node power, Indicates from node Flow to Node power, Represents a node Up generator set Injection power, Represents a node On load The outflow power, Indicates from node Flow to Node carbon flow, Indicates from node Flow to Node carbon flow, Represents a node Up generator set Injected carbon flow, Represents a node On load Given the outflow of carbon and the fact that carbon emission flow follows the active power distribution law, the nodal power balance equation can be expressed as:

[0091] ;

[0092] The node carbon emission flow balance equation is expressed as:

[0093] ;

[0094] set up Represents a node The node carbon emission factor, Represents a node The node carbon emission factor, Indicates generator set Given the fuel emission factor, and based on the principle of fair mixing, all nodes have the same carbon emission factor. Therefore, the node carbon emission flow balance equation is expressed as:

[0095] Optionally, obtain the power flow direction constraints and nodal carbon flow balance constraints used for coupled carbon flow calculations, including:

[0096] Set up the line The actual power flow is , , and Represents a node. Indicates load, Indicates the route, with the starting node as... With the end node The route , defined from arrive The current direction is positive, and the line Actual power flow Decompose in both forward and reverse directions, and define... For the line The positive trend weight, For the line If the reverse current component is a given component, then the current direction constraint is:

[0097] ;

[0098] ;

[0099] ;

[0100] set up Represents nodes The set of adjacent nodes, Variables that belong to a node. Represents a node The node carbon emission factor, Indicates generator set fuel emission factors, Represents a node Up generator set Injection power, Represents a node On load The outflow power, Indicates from node Flow to Node The weight of the trend, Indicates from node Flow to Node The tidal current components, after tidal current direction decomposition, are represented by the nodal carbon flow balance constraints used for coupled carbon flow calculation as follows:

[0101] .

[0102] Current flow direction constraints are crucial to ensuring a strict match between carbon flow calculations and current flow distribution. However, to guarantee that at least one of the forward and reverse current flow components is zero, The introduction of the product term of the forward and reverse power flow components in the previous model resulted in nonlinearity, making it difficult to solve. To address this, this invention introduces auxiliary state variables and employs the Big M method to linearize the power flow direction constraints.

[0103] Optionally, auxiliary state variables are introduced, and a large M method is used to process the power flow direction constraint, including:

[0104] Let represent the positive power flow state variable of the line , represent the reverse power flow state variable, be a positive number of infinity, be the positive power flow component of the line , be the reverse power flow component of the line , then the linearization processing of the power flow direction constraint is represented as:

[0105] ;

[0106] .

[0107] By introducing state variables, the linearization processing of the power flow direction constraint is equivalent to , and is completely linearized, and can be directly embedded into the power system optimization scheduling model to participate in solving.

[0108] The node carbon flow balance constraint obtained by power flow direction decomposition for coupling carbon flow calculation is used to establish the transmission relationship between direct carbon emission of power generation and node carbon emission factor, which includes three types of carbon flow calculation terms of power generation carbon flow, line carbon flow and load carbon flow. After considering the constraint for solving, the direct carbon emission of the generator set in the system, the carbon flow of each line, the carbon emission factor of each node and the indirect carbon emission of the load can be output. However, there are variable product items of node carbon emission factor and power flow component, which also bring nonlinearity problems to the model. In this regard, the invention adopts the processing mode of segmented linearization of the node carbon emission factor to realize the linearization of the node carbon flow balance constraint.

[0109] The physical meaning of the node carbon emission factor is the carbon dioxide emission corresponding to the use of unit electric quantity of a certain node. According to the carbon emission flow theory, the node carbon emission factor is essentially calculated by weighting all the direct carbon emission factors of the generator sets in the system according to the power flow distribution, so there is strict boundedness. Specifically, the upper and lower bounds of the node carbon emission factor can be determined by the maximum and minimum direct carbon emission factors of the generator sets in the system, and are usually between 0~0.8tCO2 / MWh, so the node carbon emission factor can be processed by limited segmented linearization.

[0110] Optionally, the number of segments of the node carbon emission factor and the upper and lower bounds of the node carbon emission factor are determined, including:

[0111] Let the upper bound of the node carbon emission factor be , and the lower bound of the node carbon emission factor be , the number of segments is , denotes a node, denotes a load, denotes the th segment, denotes a variable belonging to a node, denotes the set of all nodes in the power system, the upper bound of the th segment is , the lower bound of the th segment is , the midpoint of the th segment is , denotes the piecewise state variable of the node carbon emission factor of node , denotes that the node carbon emission factor of node is in the segment , for each node:

[0112] .

[0113] Optionally, the piecewise linearization and large M relaxation method are used to process the line carbon flow and load carbon flow, including:

[0114] Let and denote a node, denote the number of segments, denote the th segment, denote a load, denote a variable belonging to a node, denote a number that is infinite, denote the carbon flow from node to node , denote the carbon flow component from node to node , denote the piecewise state variable of the node carbon emission factor of node , denote the midpoint of the node carbon emission factor of node on the segment , denote the power flow component from node to node , denote the piecewise state variable of the node carbon emission factor of node , denote the midpoint of the node carbon emission factor of node on the segment , representing a node a component of the power flow to the node representing a set of all nodes in the power system, representing a set of adjacent nodes through which power is injected into the node and from which power is withdrawn by the node representing a set of loads at the node representing a withdrawal carbon flow of the load at the node representing a withdrawal power of the load at the node representing a withdrawal power of the load at the node representing a fuel emission factor of the generator unit representing an injection power of the generator unit at the node representing a withdrawal carbon flow of the load at the node representing a withdrawal carbon flow of the load at the node representing a lower bound of the node carbon emission factor of the node on a segment representing a lower bound of the node carbon emission factor of the node on a segment

[0115] The line carbon flow is represented as:

[0116]

[0117] The load carbon flow is represented as:

[0118]

[0119] The additional generation carbon flow (second term on the left side of the equation) in the node carbon flow balance constraint for coupling carbon flow calculation obtained through power flow direction decomposition is a linear calculation term and does not include the node carbon emission factor, without the need for change. Through the above segment processing, the calculation of each carbon flow in the node carbon flow balance equation does not have a non-linear problem.

[0120] The node carbon flow balance equation is represented as:

[0121]

[0122] ​​​​​​​​​​​​​​​In the above formula, because the node carbon emission factor is transformed from a variable to a constant, there is an imbalance on both sides of the original equation, and the equation constraint is difficult to satisfy. Therefore, the large M relaxation method is needed to process the line carbon flow and load carbon flow.

[0123] The large M relaxation method is used to process the line carbon current and load carbon current, as follows:

[0124] ;

[0125] ;

[0126] ;

[0127] .

[0128] Optional, set and Represents a node. Indicates load, Variables that belong to a node. Indicates the route. Indicates from node Flow to Node carbon flow, Indicates generator set fuel emission factors, Represents a node Up generator set Injection power, Indicates from node Flow to Node The carbon flow component, Represents a node On load The outflow of carbon, To represent the set of all nodes in a power system, Indicates a route to the node via a single line. Injected power and nodes The set of neighboring nodes from which power flows out. Indicates a route to the node via a single line. Up generator set Injection power and nodes Up generator set The set of adjacent nodes of the outflow power, linearized by the node carbon flow balance constraint, yields a simplified model of the carbon flow balance equation as follows:

[0129] .

[0130] Optionally, based on the linearization method of power flow direction constraint and node carbon flow balance constraint, a low-carbon economic dispatch model of power system coupled with carbon flow calculation is established, and is converted into a linear optimization problem for solving, including:

[0131] A traditional economic dispatch model of power system is constructed;

[0132] The power flow direction constraint is processed by using the big M method and is incorporated into the low-carbon economic dispatch model of power system;

[0133] The linearized node carbon flow balance constraint is incorporated into the low-carbon economic dispatch model of power system;

[0134] A constraint set of low-carbon dispatch of power system is constructed;

[0135] The low-carbon economic dispatch model of power system coupled with carbon flow calculation is converted into a mixed integer linear optimization problem and is solved.

[0136] Optionally, the construction of the traditional economic dispatch model of power system includes determining the objective function of the traditional economic dispatch model of power system, the power balance constraint of each time period of the system and the inequality constraint in the economic dispatch model; the inequality constraint in the economic dispatch model includes the line power flow constraint, the unit output constraint and the unit ramping constraint;

[0137] Let the number of nodes in the system be , the number of lines be , the number of generating units be , the number of fossil energy units be , the number of renewable energy units be , and the number of dispatch time periods be , is a vector matrix composed of unit matrices of order, the dimension of , is a quoted cost column vector of the generating units, the dimension of , denotes a generating unit output column vector, the dimension of , denotes a generating unit output column vector of time period, is expanded to , denotes a dispatch step, denotes a generating unit output operation matrix, the dimension of , denotes , for An identity matrix of order 1. for A column vector of all 1s This represents the Kronecker product in matrix operations. Represents the node load operation matrix. The dimension is , Represented as , for A column vector of all 1s Represents the column vector of node loads. The dimension is , express Time period node load column vector Expanded representation , This represents the column vector of output power from renewable energy units. The dimension is , express The output column vector of renewable energy units during a given time period, expanded as follows: , This is a column vector representing the transmission capacity of the power lines. The dimension is , The power flow transfer distribution factor matrix, The dimension is , This is the node-unit correlation matrix. The correlation matrix between generating units and fossil fuel generating units. For the unit-renewable energy unit correlation matrix, The dimension is , The dimension is , The dimension is , They are respectively An identity matrix of order 1. for An identity matrix of order 1. for An identity matrix of order 1. for A column vector of all zeros. The column vector representing the maximum technical output of fossil fuel units. The minimum technical output column vector for fossil fuel units. and All dimensions are , For the reason indivual A vector matrix composed of identity matrices of order 1. The dimension is ; Let this be the uphill speed vector of the generator set. This represents the downhill climbing rate vector of the generator set. and All dimensions are ;

[0138] coefficient matrix , , , and The definition of is:

[0139] ;

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] The objective function of the traditional power system economic dispatch model is to minimize the system generation cost, expressed as:

[0145] ;

[0146] The power balance constraints of the system at different time periods are expressed as follows:

[0147] ;

[0148] The inequality constraints in the economic scheduling model are expressed as:

[0149] .

[0150] Optionally, the set of low-carbon dispatch constraints for the power system includes system-level carbon emission constraints and node-level carbon emission constraints;

[0151] set up This represents the column vector of fuel emission factors for generator sets. The dimension is , Indicates the system during the scheduling period The maximum carbon emissions stipulated by the country. The carbon flow matrix representing the nodal load has dimensions of . , for A column vector of all 1s representing nodes at the dispatch period a maximum carbon emission column vector defined by the regulation, with dimension ;

[0152] The system-level carbon emission constraint is represented as:

[0153] ;

[0154] The node-level carbon emission constraint is represented as:

[0155] .

[0156] The power system low-carbon economic dispatch model coupled with the carbon flow calculation described above is a mixed integer linear optimization problem, which can be calculated and solved by using mature commercial optimization software, and finally the unit output plan, system power flow result and node carbon emission factor and other results are obtained.

[0157] Embodiments of the present application take a modified version of the PJM-5 (PJM Interconnection Power Grid 5-node test system, referred to as PJM-5) node system as the implementation object, and a schematic diagram of the modified version of the PJM-5 node system is shown in FIG. 1. The system contains 5 units in total, wherein G1 is a wind turbine unit, G2 is a photovoltaic turbine unit, G3 is a gas turbine unit, G4 and G5 are coal-fired turbine units, L1-L6 represent lines, B1-B5 represent nodes, and the parameters of the turbine units are shown in Tables 1 and 2. The system contains loads D1-D3, wherein D1 is an industrial high-energy consumption load. The system source load prediction data is shown in Table 3. Figure 3

[0158] Table 1: Generation cost and direct carbon emission factor table of turbine units

[0159]

[0160] Table 2: Generation cost and direct carbon emission factor table of turbine units

[0161]

[0162] Table 3: System source load prediction data table

[0163]

[0164] ​Six operation scenarios are set in the embodiments of the present application, scenarios A-C are solved based on the linearization model proposed in the present application, scenario A considers the low-carbon economic dispatch with node carbon emission constraint, the constraint node is D3, and the carbon emission reduction intensity is set to 5‰, 10‰ and 15‰ of the total carbon emission of the whole system; scenario B considers the low-carbon economic dispatch with the whole system carbon emission constraint, and the carbon emission reduction intensity is also set to 5‰, 10‰ and 15‰ of the total carbon emission of the whole system; scenario C is the benchmark scenario, that is, the traditional economic dispatch without considering the carbon emission constraint. Scenarios D-F are solved based on the nonlinear model, and the rest are one-to-one corresponding to scenarios A-C. The optimization model is written in Python language, and a mature commercial solver is used for optimization solving.

[0165] The optimization scheduling results of each scenario are shown in Table 4, and the absolute error and relative error of the carbon emission of loads 1-3 in each scenario are shown in Table 5. From Table 4, it can be seen that by setting different levels of carbon emission constraints, the linearization method for carbon emission flow constraint set for general solving of low-carbon optimization dispatching problem of power system proposed in the present application can realize synchronous calculation of power flow and carbon flow, thereby achieving the precise carbon control target.

[0166] Firstly, compare scenario A with scenario D from the perspective of solving results: when the same carbon emission reduction proportion of node carbon emission constraint is adopted, scenario A can adjust the output power of the generator unit to change the system power flow direction, re-direct the carbon flow of new energy originally flowing to load 2 to load 3, and avoid unnecessary cost increment. Therefore, the optimization scheduling result of scenario A remains unchanged at the carbon emission reduction proportion of 5‰-10‰, and only increases the total cost after 15‰. The optimization scheduling result of scenario D generally presents the trend of increasing total cost and reducing carbon emission, and the carbon emission reduction cost is significantly higher than that of scenario A.

[0167] Secondly, compare scenario A with scenario D from the perspective of solving time: under the same convergence condition, as the carbon emission reduction proportion gradually increases, the solving time of scenario A remains between 0.27s and 0.38s, with a small change range. The solving time of scenario D is significantly higher than that of scenario D, gradually increasing from 5.65s to 410.42s, with a large change range. It can be seen that by using the linearization method proposed in the present application to solve the dispatching problem considering node carbon emission constraint, on the one hand, the carbon reduction potential brought by power flow optimization can be tapped, and the economy of system carbon emission reduction can be improved, and on the other hand, the calculation efficiency of the model can be significantly improved, and the general solving performance is superior.

[0168] Table 4: Optimization scheduling results of each scenario

[0169]

[0170] Table 5 absolute error and relative error of load 1-3 carbon emission of each scenario

[0171]

[0172] After comparing scenario B and scenario E: when the same carbon emission reduction ratio is used for the whole system carbon emission constraint, the solving results of the two scenarios remain the same, the solving time of scenario B is less than 0.39s, and the solving time of scenario E is about 1.00s. Finally, comparing scenario C and scenario F: the obtained conclusion is similar to the comparison of scenario B and scenario E, and will not be repeated. As can be seen, the linearization method proposed in the application can be used to solve the scheduling problem considering the whole system carbon emission constraint or only coupled carbon flow calculation, and the same total cost and total carbon emission as the nonlinear solving method can be obtained, and the calculation efficiency is greatly improved.

[0173] From the data in Table 5, in scenario pairs A-D considering node carbon emission constraints, the absolute error of load 3 carbon emission is up to 9.63t, and the relative error is up to 0.15%. The carbon emission errors of load 1 and load 2 are relatively large, because the linearization solving method can fully utilize the carbon reduction space of power flow optimization, and the carbon emission of load 1 and load 2 has not been reduced under the corresponding carbon constraint condition. In addition, in scenario pairs B-E and scenario pairs C-F, the relative error of load carbon emission is up to 1.2% and down to 0.09%, and the overall error is within a reasonable range.

[0174] In summary, the linearization method proposed in the application can be used to solve the low-carbon economic dispatching problem of the power system coupled with carbon flow calculation, which can ensure high calculation accuracy.

[0175] The above is only a preferred embodiment of the application and is not intended to limit the application. For those skilled in the art, the application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A carbon emission flow constraint linearization method for low-carbon scheduling of a power system, characterized in that, The method comprises the following steps: A power carbon emission flow model based on power flow direction decomposition is established, including a node power balance equation and a node carbon emission flow balance equation, to obtain power flow direction constraints and node carbon flow balance constraints for coupling carbon flow calculation; Introduce auxiliary state variables, and use the big M method to deal with the power flow direction constraints, including: The positive power flow state variable of line , The reverse power flow state variable of line , is a positive number of infinity, The positive power flow component of line , The reverse power flow component of line , The linearization processing of the power flow direction constraint is represented as: ; A simplified model of the carbon flow balance equation based on piecewise linearization and a large M relaxation method is constructed, including determining the number of segments of the node carbon emission factor and the upper and lower bounds of the node carbon emission factor, processing line carbon flow and load carbon flow by using piecewise linearization and a large M relaxation method, and linearizing the node carbon flow balance constraint to obtain the simplified model of the carbon flow balance equation; Based on the linearization method of the power flow direction constraint and the node carbon flow balance constraint, a low-carbon economic dispatch model of the power system coupled with carbon flow calculation is established, and is converted into a linear optimization problem for solving.

2. The method of claim 1, wherein the method is a low-carbon dispatching oriented carbon emission flow constraint linearization method for power systems. A power carbon emission flow model based on power flow direction decomposition is established, including a node power balance equation and a node carbon emission flow balance equation; Let , and denote nodes, denote loads, denote the set of all nodes in the power system, denote the set of adjacent nodes that inject power to node through a single line, denote the set of adjacent nodes that inject power to node through a single line, denote the set of generators at node , denote the set of loads at node , denote the power flow from node to node , denote the power flow from node to node , denote the injection power of generators at node , denote the injection power of generators at node , denote the injection power of loads at node , denote the carbon flow from node to node , denote the carbon flow from node to node , denote the injection carbon flow of generators at node , denote the injection carbon flow of generators at node , denote the injection carbon flow of loads at node , and the carbon emission flow follows the active power flow, then the node power balance equation is represented as: ； The node carbon emission flow balance equation is expressed as: ； Let be the node carbon emission factor of node , be the node carbon emission factor of node , be the fuel emission factor of generator , and all nodes have the same carbon emission factor according to the principle of fair mixing, then the node carbon emission flow balance equation is represented as: 。 3. The method of claim 1, wherein, The power flow direction constraints and the node carbon flow balance constraints for coupling carbon flow calculation are obtained, including: Set up the line The actual power flow is , , and Represents a node. Indicates load, Indicates the route, with the starting node as... With the end node The route , defined from arrive The current direction is positive, and the line Actual power flow Decompose in both forward and reverse directions, and define... For the line The positive trend weight, For the line If the reverse current component is a given component, then the current direction constraint is: ； ； ； set up Represents nodes The set of adjacent nodes, Variables that belong to a node. Represents a node The node carbon emission factor, Indicates generator set fuel emission factors, Represents a node Up generator set Injection power, Represents a node On load The outflow power, Indicates from node Flow to Node The weight of the trend, Indicates from node Flow to Node The tidal current components, after tidal current direction decomposition, are represented by the nodal carbon flow balance constraints used for coupled carbon flow calculation as follows: 。 4. The method of claim 1, wherein, The number of segments of the node carbon emission factor and the upper and lower bounds of the node carbon emission factor are determined, including: Let the upper bound of the node carbon emission factor be The lower bound of the node carbon emission factor is The number of segments is , Represents a node. Indicates load, Indicates the first Each segment Variables that belong to a node. Represents the set of all nodes in a power system, segmented. The upper bound is Segmentation The lower bound is Segmentation The midpoint is , Represents a node Piecewise state variables of nodal carbon emission factors A value of 1 indicates a node The node carbon emission factors are in segments For each node: 。 5. The method of claim 1, wherein, Line carbon flow and load carbon flow are processed by using piecewise linearization and a large M relaxation method, including: Set and represent a node, represent the number of segments, represent the th segment, represent the load, represent the variable belonging to the node, represent the number infinity, represent the carbon flow from node to node , represent the carbon flow component from node to node , represent the segment state variable of the node carbon emission factor of node , represent the midpoint of the node carbon emission factor of node on the segment , represent the power flow component from node to node , represent the segment state variable of the node carbon emission factor of node , represent the midpoint of the node carbon emission factor of node on the segment , represent the power flow component from node to node , represent the set of all nodes in the power system, represent the adjacent node set that injects power into node and the node outflow power, represent the set of loads on node , represent the outflow carbon flow of load on node , represent the outflow power of load on node , represent the fuel emission factor of generator unit , represent the injection power of generator unit on node , represent the outflow carbon flow of load on node , represent the node carbon emission factor of node on the segment lower bound on the node carbon emission factor of the node representing a node lower bound on the node carbon emission factor of the node over the segment Line carbon flow is expressed as: ； Load carbon flow is expressed as: ； The node carbon flow balance equation is expressed as: ； The line carbon flow and the load carbon flow are processed by using a large M relaxation method, and are expressed as: ； ； ； 。 6. The method of claim 1, wherein, Let denote a node, denote a load, denote a variable belonging to a node, denote a line, denote a carbon flow from a node to a node , denote a carbon flow component from a node to a node , denote an injection power of a generator set on a node , denote an injection power of a generator set on a node , denote a carbon flow component from a node to a node , denote an outflow carbon flow of a load on a node , denote a set of all nodes in a power system, denote a set of adjacent nodes through which power is injected into a node and power is outflowed from a node , denote a set of adjacent nodes through which power is injected into a generator set on a node and power is outflowed from a generator set on a node , a linearization process of a node carbon flow balance constraint is performed, and a simplified model of a carbon flow balance equation obtained is represented as: 。 7. The method of claim 1, wherein, Based on the linearization method of the power flow direction constraint and the node carbon flow balance constraint, a low-carbon economic dispatch model of the power system coupled with carbon flow calculation is established, and is converted into a linear optimization problem for solving, including: A traditional economic dispatch model of the power system is constructed; The power flow direction constraint processed by using a large M method is incorporated into the low-carbon economic dispatch model of the power system; The node carbon flow balance constraint processed by linearization is incorporated into the low-carbon economic dispatch model of the power system; A low-carbon dispatch constraint set of the power system is constructed; The low-carbon economic dispatch model of the power system coupled with carbon flow calculation is converted into a mixed integer linear optimization problem and is solved.

8. The method of claim 7, wherein, The traditional economic dispatch model of the power system is constructed, including determining the objective function of the traditional economic dispatch model of the power system, the power balance constraint of each period of the system, and the inequality constraint in the economic dispatch model; the inequality constraint in the economic dispatch model includes line flow constraints, unit output constraints, and unit ramping constraints; Assume the number of nodes in the system is . Number of lines The number of generator sets is The number of fossil fuel units is The number of renewable energy units is The number of scheduling periods is , For the reason indivual A vector matrix composed of identity matrices of order 1. The dimension is , This is the column vector of the quoted cost of the generator set. The dimension is , This represents the column vector of generator output. The dimension is , express Time-period generator output column vector Expanded representation , Indicates the scheduling step size. This represents the generator set output calculation matrix. The dimension is , Represented as , for An identity matrix of order 1. for A column vector of all 1s This represents the Kronecker product in matrix operations. Represents the node load operation matrix. The dimension is , Represented as , for A column vector of all 1s Represents the column vector of node loads. The dimension is , express Time period node load column vector Expanded representation , This represents the column vector of output power from renewable energy units. The dimension is , express The output column vector of renewable energy units during a given time period, expanded as follows: , This is a column vector representing the transmission capacity of the power lines. The dimension is , The power flow transfer distribution factor matrix, The dimension is , This is the node-unit correlation matrix. The correlation matrix between generating units and fossil fuel generating units. For the unit-renewable energy unit correlation matrix, The dimension is , The dimension is , The dimension is , They are respectively An identity matrix of order 1. for An identity matrix of order 1. for An identity matrix of order 1. for A column vector of all zeros. The column vector representing the maximum technical output of fossil fuel units. The minimum technical output column vector for fossil fuel units. and All dimensions are , For the reason indivual A vector matrix composed of identity matrices of order 1. The dimension is ; Let this be the uphill speed vector of the generator set. This represents the downhill climbing rate vector of the generator set. and All dimensions are ; coefficient matrix , , , and are defined as: ； ； ； ； ； The objective function of the traditional economic dispatch model of the power system is to minimize the system generation cost, and is expressed as: ； The power balance constraint of each period of the system is expressed as: ； The inequality constraint in the economic dispatch model is expressed as: 。 9. The method of claim 7, wherein the method is a low-carbon dispatching of a power system oriented carbon emission flow constraint linearization method. The low-carbon dispatch constraint set of the power system includes system-level carbon emission constraints and node-level carbon emission constraints; Let denote the fuel emission factor column vector of the generator set, of dimension , denote the maximum carbon emission amount specified for the system within the dispatch period , denote the node load carbon flow matrix of dimension , be a column vector of all ones of dimension , denote the maximum carbon emission amount column vector specified for the nodes within the dispatch period , of dimension ; The system-level carbon emission constraint is expressed as: ； The node-level carbon emission constraint is expressed as: 。

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