Power system economic dispatching method considering line dynamic capacity increase and related device

Abstract

The invention provides a power system economic dispatching method considering dynamic capacity increase of a line and a related device. The method comprises the following steps: establishing a target function taking the minimum unit operation cost of a power system as a target; determining constraint conditions of the target function according to the parameters of the power system, wherein the constraint conditions comprise unit constraint, network variable constraint, linearized alternating current power flow constraint and linearized line thermal stability constraint; the economic dispatching model of the power system is solved, an economic dispatching scheme of the power system is obtained, and the economic dispatching model of the power system comprises a target function and constraint conditions. According to the method, the temperature change of the line is tracked by using the linearized line thermal stability constraint, so that the transmission capacity of the line can be improved on the basis of meeting the thermal stability constraint, an economic dispatching strategy is optimized, and the economic dispatching efficiency is improved by linearizing the alternating current power flow constraint and the line thermal stability constraint. The power system economic dispatching model is constructed into a mixed integer linear programming model, so that the solving speed and efficiency of the model can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of electrical engineering, and particularly to an economic dispatch method for a power system considering line dynamic capacity increase and related devices. Background Art

[0002] The economic dispatch problem is one of the basic problems in the operation of a power system. Its goal is to dispatch units to meet the total demand at the minimum cost under the premise of meeting the supply-demand balance and various constraints.

[0003] In traditional economic dispatch methods, the transmission capacity of a line is usually specified by a conservative constant, which only represents the safe transmission capacity under multiple typical operating conditions. Under actual operating conditions, there is room for improvement in the transmission capacity of the line, that is, the transmission capacity of the line has not been fully exploited. If the power system is economically dispatched according to a fixed transmission capacity, the actual situation of the power system is not considered, and the role of each line in the power system cannot be fully exerted. The economic dispatch result of the power system needs to be further optimized. Summary of the Invention

[0004] In view of this, the purpose of the present application is to provide an economic dispatch method for a power system considering line dynamic capacity increase and related devices. For the economic dispatch scenario on a short time scale, a linearized transient thermal balance equation is used to describe the temperature rise change of the line, which can improve the transmission capacity of the transmission line on the basis of ensuring safety, and also improve the solution speed and efficiency of the economic dispatch model. The specific technical solutions are as follows: In a first aspect, the present application provides an economic dispatch method for a power system considering line dynamic capacity increase, and the method includes: Establish an objective function with the minimum operating cost of the units in the power system as the goal; Determine the constraint conditions of the objective function according to the parameters of the power system. The constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints. The linearized line thermal stability constraints take into account the dynamic change of the line temperature; Solve the economic dispatch model of the power system to obtain the economic dispatch plan of the power system. The economic dispatch model of the power system includes the objective function and the constraint conditions.

[0005] In a possible implementation manner, determining the linearized AC power flow constraint according to the parameters of the power system includes: Construct an AC power flow model according to the parameters of the power system. The AC power flow model includes line power flow constraints considering network losses; Perform linearization processing on the line power flow constraint to obtain the linearized AC power flow constraint.

[0006] In a possible implementation, determining the linearized line thermal stability constraint according to the parameters of the power system includes: Constructing a transient thermal balance equation for accounting for the dynamic change of line temperature according to the parameters of the power system; Performing linearization processing on the transient thermal balance equation to obtain the linearized line thermal stability constraint.

[0007] In a possible implementation, the performing linearization processing on the transient thermal balance equation to obtain the linearized line thermal stability constraint includes: Discretizing the transient thermal balance equation by using a forward difference algorithm; Performing linearization processing on the radiative heat dissipation amount, convective heat dissipation amount, and line heat generation amount in the transient thermal balance equation respectively to obtain the linearized line thermal stability constraint.

[0008] In a possible implementation, the solving the economic dispatch model of the power system to obtain the economic dispatch plan of the power system includes: Solving the economic dispatch model of the power system by using an optimization solver to obtain the economic dispatch plan of the power system.

[0009] In a second aspect, the present application further provides an economic dispatch device of a power system considering line dynamic capacity increase, and the device includes: A establishing module, configured to establish an objective function with the minimum operating cost of the units of the power system as the objective; A determining module, configured to determine the constraint conditions of the objective function according to the parameters of the power system, where the constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, and the linearized line thermal stability constraints account for the dynamic change of line temperature; A solving module, configured to solve the economic dispatch model of the power system to obtain the economic dispatch plan of the power system, where the economic dispatch model of the power system includes the objective function and the constraint conditions.

[0010] In a possible implementation, the determining module includes: An AC power flow constructing unit, configured to construct an AC power flow model according to the parameters of the power system, where the AC power flow model includes line power flow constraints considering network losses; A power flow linearization unit, configured to perform linearization processing on the line power flow constraints to obtain the linearized AC power flow constraints.

[0011] In a possible implementation, the determining module includes: A thermal equilibrium construction unit for constructing a transient thermal equilibrium equation considering the dynamic change of line temperature according to the parameters of the power system; A thermal equilibrium linearization unit for linearizing the transient thermal equilibrium equation to obtain the linearized line thermal stability constraint.

[0012] In a third aspect, the present application also provides a computer device, including: a memory and a processor; wherein, the memory is used for storing a computer program; the processor is used for executing the computer program in the memory to implement the method described in the first aspect or any item of the first aspect above.

[0013] In a fourth aspect, the present application also provides a computer-readable storage medium storing instructions, which when running on a computer, cause the computer to execute the method described in the first aspect or any item of the first aspect above.

[0014] In the present application, an objective function is established with the minimum operating cost of the units in the power system as the goal; the constraint conditions of the objective function are determined according to the parameters of the power system, and the constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints and linearized line thermal stability constraints, and the linearized line thermal stability constraints take into account the dynamic change of line temperature; the economic dispatch model of the power system is solved to obtain the economic dispatch plan of the power system, and the economic dispatch model of the power system includes the objective function and the constraint conditions. The present application uses the linearized line thermal stability constraint to describe and track the temperature change of the line, which can ensure the expansion of the actual transmission capacity of the line on the basis of meeting the thermal stability constraint, release the potential of the line transmission capacity, improve the availability of the line on the basis of ensuring safety, so as to optimize the economic dispatch strategy. By linearizing the non-linear constraints in the constraint conditions, the linearized AC power flow constraints and the linearized line thermal stability constraints are obtained, and the economic dispatch model of the power system considering the line thermal stability constraint is constructed into a mixed integer linear programming model, which can make the mathematical form of the economic dispatch model of the power system simpler, reduce the computational complexity of the model, and improve the solution speed and efficiency of the model. Description of the Drawings

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present application, and those of ordinary skill in the art can also obtain other drawings according to these drawings.

[0016] Figure 1 Shows a flowchart of an economic dispatch method for a power system considering line dynamic capacity increase provided by an embodiment of the present application; Figure 2 Shows a schematic diagram of the piecewise linearization strategy for the square term of the voltage square difference provided by an embodiment of the present application; Figure 3 Shows a flowchart of the linearization of the transient heat balance equation provided by an embodiment of the present application; Figure 4 Shows what is provided by an embodiment of the present application Schematic diagram of the piecewise linearization strategy of the function curve; Figure 5(a) shows a schematic diagram of the change curve of the convective heat dissipation in an environment with a wind speed of 0 m / s provided by an embodiment of the present application; Figure 5(b) shows a schematic diagram of the change curve of the convective heat dissipation in an environment with a wind speed of 2 m / s provided by an embodiment of the present application; Figure 5(c) shows a schematic diagram of the change curve of the convective heat dissipation in an environment with a wind speed of 4 m / s provided by an embodiment of the present application; Figure 6 Shows a schematic diagram of the network topology of the IEEE 39-node system provided by an embodiment of the present application; Figure 7(a) shows a schematic diagram of the change curve of the line temperature calculated based on two heat balance equations when the line current is 100 A provided by an embodiment of the present application; Figure 7(b) shows a schematic diagram of the change curve of the line temperature calculated based on two heat balance equations when the line current is 400 A provided by an embodiment of the present application; Figure 7(c) shows a schematic diagram of the change curve of the line temperature calculated based on two heat balance equations when the line current is 700 A provided by an embodiment of the present application; Figure 8 Shows a schematic diagram of the change curve of the temperature for solving the transient heat balance by two methods provided by an embodiment of the present application; Figure 9 Shows a schematic diagram of the structure of a power system economic dispatch device considering line dynamic capacity increase provided by an embodiment of the present application. Detailed implementation manners

[0017] 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 clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application fall within the scope of protection of the present application.

[0018] Power system economic dispatch refers to a dispatch method that, on the premise of meeting safety and power quality requirements, rationally utilizes energy and equipment to ensure reliable power supply to users at the lowest generation cost or fuel cost. Economic dispatch is a typical optimization problem that requires reasonable distribution of unit power under the conditions of meeting demand and various constraints to ensure the lowest operating cost.

[0019] During the operation of the power system, the system operating state often fluctuates and changes strongly, and the line transmission capacity limit will affect the position of the system operating point. However, in existing economic dispatch methods, the transmission capacity limit of the line is usually specified by a conservative constant, and the value of the conservative constant only represents the safe transmission capacity under multiple typical operating conditions. Under specific operating conditions, there is still room for improvement in the transmission capacity limit, that is, the transmission capacity of the line has not been fully exploited. Therefore, dynamically increasing the transmission capacity of the line can optimize the economic dispatch strategy, which is of great significance for the safe, economic, and flexible operation of the power system.

[0020] The line dynamic capacity increase technology mainly utilizes the thermal inertia effect of the transmission line. According to the meteorological data obtained by the micro-meteorological sensor and the actual operating conditions of the power system, the heat balance equation is used to describe and track the temperature change of the transmission line, and the transmission capacity of the transmission line is set on the basis of ensuring that the transmission line meets the thermal stability constraint. Therefore, applying the line dynamic capacity increase technology to power system operation scenarios such as economic dispatch can release the potential of the line transmission capacity and explore the availability of the line on the basis of ensuring safety.

[0021] Traditionally, the mathematical model of this optimization problem of economic dispatch is an optimization problem with a quadratic cost function and linear constraint conditions. However, when considering the thermal inertia effect of the line, the constraint conditions of the economic dispatch model become non-linear and non-convex functions, making the optimization problem difficult to solve. Many classic mathematical algorithms, such as linear programming, quadratic programming, and dynamic programming, have been applied to solve traditional economic dispatch problems. However, these algorithms have great limitations in dealing with non-convex constraint condition problems, so the solution results are not ideal.

[0022] In view of the above problems, in the prior art, an optimal power flow model considering security constraints is proposed, and the transmission line dynamic capacity increase technology is used to describe the line thermal stability limit to ensure the operating economy and security of the power grid. The specific steps of the proposed method are as follows: Step 1, construct an enhanced security-constrained optimal power flow model. The objective function of the model is to be economically optimal (that is, the minimum unit generation cost), and the constraint conditions of the model include power balance constraint, unit output upper and lower limit constraints, DC power flow constraint, N-1 unit output upper and lower limit constraints, N-1 fault state DC power flow constraint, and line temperature limit constraint.

[0023] Step 2: Regarding the line temperature limit constraint, it is described by the transient heat balance equation, which is a first-order nonlinear differential equation about the line temperature: .

[0024] In the formula, is the line mass, is the specific heat capacity of the line, is the line temperature, is the differential with respect to the time variable, is the line current, is the AC resistance, is the solar heat absorption, is the radiative heat dissipation, is the convective heat dissipation.

[0025] Adopt a conservative assumption to linearize the nonlinear terms in the transient heat balance equation and transform it into a first-order linear differential equation form about the line temperature, which is abbreviated as follows: .

[0026] In the formula, is the ambient temperature, and are equivalent constants, and are determined by the line conductor parameters and the surrounding environmental conditions.

[0027] For the above formula, its solution function can be obtained, which is a nonlinear convex function: .

[0028] In the formula, is the line temperature at time is the initial temperature of the conductor, is the steady-state final temperature that the conductor can reach during the dynamic rating process, e is the base of the exponential function in the natural state, is the time constant of the conductor heat process, is determined by the line conductor characteristic parameters.

[0029] Step 3: Regarding the above enhanced security-constrained optimal power flow model, decompose the enhanced security-constrained optimal power flow model into a preventive control main problem, a dynamic rating verification sub-problem, and a corrective control feasibility verification sub-problem, and use the Benders decomposition algorithm to solve it iteratively until the algorithm meets the convergence condition to obtain the optimization model result.

[0030] Although the existing technologies introduce the line dynamic capacity increase technology into the optimal power flow (dispatching operation) problem of the power system to release the potential of line capacity, the existing technologies use the transient thermal balance equation to describe the dynamic thermal limit of the line, which transforms the transient thermal balance equation into a non-linear form, and there are often problems with slow convergence speed during solution, and the requirements for real-time performance are not well met.

[0031] In addition, some existing technologies use the steady-state thermal balance equation to describe the dynamic thermal limit of the line, specifically by taking the differential term of the transient thermal balance as 0: .

[0032] Taking the temperature as the upper limit of the allowable temperature of the line , then there is: .

[0033] In the formula, is the maximum value of the line current, is the maximum value of the line temperature, is the radiative heat dissipation when the line temperature is the maximum value of the line temperature, is the convective heat dissipation when the line temperature is the maximum value of the line temperature, is the solar radiation heat absorption when the line temperature is the maximum value of the line temperature, is the AC resistance when the line temperature is the maximum value of the line temperature.

[0034] According to the formula of the steady-state thermal balance equation, the steady-state thermal balance equation can be embedded in a linear form. However, the steady-state thermal balance constraint is difficult to account for the dynamic change process of the line temperature rise. For temperature rise scenarios with a short time scale such as 15-minute (min) real-time dispatching, there is a problem of insufficient description fineness.

[0035] Therefore, the embodiments of the present application provide an economic dispatching method for a power system considering line dynamic capacity increase. For short-time scale dispatching scenarios, the transient thermal balance equation can be used to describe the temperature rise change of the line, and an economic dispatching model considering the transient thermal balance equation of the line is constructed into a mixed-integer linear programming model, making the mathematical form of the model simple and the solution efficiency high.

[0036] Please refer to Figure 1 , which shows the flowchart of an economic dispatching method for a power system considering line dynamic capacity increase provided by the embodiments of the present application. The embodiments of the present application at least include the following steps: S11, establish an objective function with the minimum operating cost of the units in the power system as the goal.

[0037] In the embodiments of the present application, an objective function with the minimum operating cost of the units in the power system as the goal can be established.

[0038] The expression of the objective function is as follows: (1) In formula (1), is the scheduling period, is the set of scheduling periods, is the generator at the active power output during the period, is the set of generators, is the quadratic term coefficient of the objective function, is the linear term coefficient of the objective function, is the constant term coefficient of the objective function. The discretization time interval of can be set according to the specific scenario. As an example, the discretization time interval of can be 15 minutes (min). In the embodiment of the present application, the active power output of each generator remains unchanged during the period. Taking the discretization time interval of

[0039] as 15 min for illustration, within this 15 min, the active power output of generator , and can be the same or different. The parameters of the power system may include the generator cost coefficients corresponding to different generators (i.e., , and ).

[0040] In the embodiment of the present application, a piecewise linearization strategy can be adopted to linearize the quadratic function curve of the objective function. The piecewise linearization strategy for the objective function can be set according to the actual scenario, and the embodiment of the present application does not make any limitation. It should be noted that the objective function in the economic dispatch model of the power system in the embodiment of the present application is a linearized objective function.

[0041] S12. Determine the constraint conditions of the objective function according to the parameters of the power system.

[0042] After establishing the objective function, the constraint conditions of the objective function can be determined according to the parameters of the power system. The constraint conditions in the embodiment of the present application may include generator constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints. Among them, the linearized AC power flow constraints take into account the network losses, and the linearized line thermal stability constraints take into account the dynamic changes of the line temperature.

[0043] The parameters of the power system can include generator parameters, network parameters, and load parameters. The network parameters can include line parameters and node parameters. In a power system, nodes usually represent substations or load points, and these nodes are interconnected by transmission lines (i.e., lines) to jointly form the network structure of the power system.

[0044] The generator parameters can include the maximum active power output, minimum active power output, maximum reactive power output, and minimum reactive power output of each generator, all in megawatts (MW). The generator parameters can also include the generator cost coefficient corresponding to each generator.

[0045] The line parameters can include the conductance, susceptance, upper limit of phase angle difference, and lower limit of phase angle difference of each line. The units of conductance and susceptance are Siemens (S), and the units of the upper limit of phase angle difference and the lower limit of phase angle difference are radians (rad).

[0046] The node parameters can include the upper limit and lower limit of the square of the voltage of each node.

[0047] The load parameters can include active load and reactive load, both in MW.

[0048] S121. Determine the unit constraints according to the parameters of the power system.

[0049] The unit constraints involve the upper and lower limit constraints of the active power output and reactive power output of the unit. The expressions of the unit constraints are as follows: (2) (3) In formulas (2) and (3), is the lower limit of the active power output of unit , is the active power output of unit at time , is the upper limit of the active power output of unit , is the reactive power output of unit at time , is the lower limit of the reactive power output of unit , is the upper limit of the reactive power output of unit . In the embodiment of the present application, the active and reactive power outputs of each unit remain unchanged during time .

[0050] S122. Determine the network variable constraints according to the parameters of the power system.

[0051] The network variable constraints involve voltage constraints and phase angle (hereinafter referred to as phase angle) constraints. The expressions of the network variable constraints are as follows: (4) (5) In equations (4) and (5), is the voltage of node at time period, is the lower voltage limit of node , is the upper voltage limit of node , is from node to node at time period, is the phase angle difference from node to node , is the lower limit of the phase angle difference from node to node , is the upper limit of the phase angle difference from node

[0052] S123. Determine the linearized AC power flow constraints according to the parameters of the power system.

[0053] Conventional power flow constraints are non-convex and non-linear constraints, making it difficult to directly obtain the global optimal solution. Therefore, in this embodiment of the present application, a linearized AC power flow model with the square of the voltage as the variable is constructed.

[0054] In a possible implementation manner, determining the linearized AC power flow constraints may include: S31. Construct an AC power flow model according to the parameters of the power system. The AC power flow model includes line power flow constraints and node power balance constraints.

[0055] S32. Linearize the line power flow constraints to obtain the linearized AC power flow constraints.

[0056] The expression of the line power flow constraint is as follows: (6) (7) In equations (6) and (7), is the active power of line at time period, is the reactive power of line at time period, is the conductance of line , is the susceptance of line , is the voltage of node at time period, is the voltage of node at time period, is the phase angle difference from node to node at time period, is the active power network loss of line at time period, is the reactive power network loss of line at time period. Line is the line flowing from node to node .

[0057] At time period, the expressions of the active power network loss and reactive power network loss of line are as follows: (8) (9) It can be seen from equations (8) and (9) that both the active power network loss and the reactive power network loss have square terms as variables, that is and , which will lead to the non-linearity of the AC power flow model. Therefore, the embodiments of the present application can adopt piecewise linearization processing and . Taking as an example, the specific piecewise linearization strategy is as Figure 2 shown, where can be converted by the linear combination of the voltage square terms and .

[0058] The piecewise linearization expression of the square term of the voltage square difference is as follows: (10) In equation (10), is the voltage of node at time period, is the voltage of node at time period, is the lower voltage limit of node ​ is the upper voltage limit of node . is the lower voltage limit of node . is the upper voltage limit of node . is the slope value of the -th segment of the function curve. is the value of the squared voltage difference of the -th segment of the function curve. is the 0-1 auxiliary variable introduced for the linearization of the -th segment of the function curve. is the width of the segment interval of the -th segment of the function curve. is the minimum value of . is the maximum value of . is the voltage of node . The value of can be set according to the actual situation. Generally speaking, the larger the value of

[0059] the better the approximation effect, but the longer the solution time. If the function curve has symmetry, then the value of (11) In formula (11), is the phase angle difference from node to node during the time period, is the lower limit of the phase angle difference from node to node , is the upper limit of the phase angle difference from node to node . is the slope value of the -th segment of the function curve, is the value of the phase angle difference of the -th segment of the function curve, is for the -th segment of the function curve The 0-1 auxiliary variables introduced by piecewise linearization of the segment For The width of the piecewise interval of the function curve. The piecewise linearization strategy of the function curve is the same as that of the function curve and can be understood with reference to Figure 2 it.

[0060] The expressions of the node power balance constraint are as follows: (12) (13) In equations (12) and (13), is the set of generators affiliated with node , is the active power output of unit at time , is the set of loads affiliated with node , is the set of node pairs connected by lines to node , is the active load of load d at time , is the line active power of line at time , is the conductance of line , is the voltage of node at time , is the reactive power output of unit at time , is the reactive load of load d at time , is the line reactive power of line at time , is the susceptance of line , is the total number of nodes. Node n is any node in the power system, and nodes i and j are node pairs connected by lines in the power system.

[0061] S124. Determine the linearized line thermal stability constraint according to the parameters of the power system.

[0062] The embodiment of the present application considers the dynamic change of the line temperature and determines the linearized line thermal stability constraint.

[0063] The linearization process of the transient thermal balance equation is as follows Figure 3 As shown. In a possible implementation, determining the linearized line thermal stability constraint may include: S41. Construct a transient thermal balance equation considering the dynamic change of line temperature according to the parameters of the power system.

[0064] Line The dynamic change process of the temperature can be described by the transient thermal balance equation. The expression of the transient thermal balance equation in the embodiments of the present application is as follows: (14) In Equation (14), is the radiation heat dissipation when the line temperature is , is the convective heat dissipation when the line temperature is , is the solar radiation heat absorption, is the line heat generation, is the line temperature, is the line at the current during the time period, is the AC resistance, is the line line mass, is the line specific heat capacity of the line. In the embodiments of the present application, the current of each line remains unchanged during the time period.

[0065] The transient thermal balance equation describes the change process of temperature over time under the action of the external environment and line current. To meet the line thermal stability, the line temperature should not exceed the set upper limit value: (15) In Equation (15), is the upper limit of the line temperature.

[0066] S42. Linearize the transient thermal balance equation to obtain the linearized line thermal stability constraint.

[0067] The above transient thermal balance equation is a first-order nonlinear differential equation and is difficult to solve directly. Therefore, in the embodiments of the present application, the transient thermal balance equation is discretized by the forward difference algorithm. The expression of the discretized transient thermal balance equation is as follows: (16) In Equation (16), is the discrete time after the differential equation is differenced, represents the line temperature at the discrete time, denote the radiative heat dissipation at discrete moments, denote the convective heat dissipation at discrete moments, is the differential step size. The discretized time interval of can be set according to the actual scenario. As an example, the discretized time interval of can be 1 min. If the discretized time interval of is 15 min, and

[0068]

[0069] 1) Radiative heat dissipation The radiative heat dissipation has the following expression: (17) In Equation (17), is the pi, is the outer diameter of the wire of line is the radiative heat dissipation coefficient of the wire surface of line is the Stefan - Boltzmann constant, is the environmental temperature. Generally speaking, the models of each line in the power system are the same. Therefore, it can be considered that the outer diameter of the wire and the radiative heat dissipation coefficient of the wire surface of each line are the same. It should be noted that during

[0070] the environmental temperature is a fixed value and can be set according to the actual scenario. In different dispatching periods, the environmental temperature may be the same or different.

[0071] When the external meteorological factors are given, the radiative heat dissipation is a quartic function of the wire temperature, and the radiative heat dissipation can be piece - wise linearized. The external meteorological factors can include environmental temperature, sunshine intensity, wind speed and the angle between the wind and the wire, etc. The piece - wise linearized expression of in the radiative heat dissipation is as follows: (18) In Equation (18), is The slope value of the segment of the function curve, is the lower temperature limit of the line taken for piecewise linearization. In the embodiments of the present application, it can be set according to the actual situation. Exemplarily, it can be set to 0 , is the value of the temperature increment of the segment of the function curve, is the 0-1 auxiliary variable introduced for the piecewise linearization of the segment of the function curve, is the width of the segmentation interval of the segment of the function curve, is the upper temperature limit of the line taken for piecewise linearization. In the embodiments of the present application, it can be set according to the actual situation. Exemplarily, it can be set to 90 . is always greater than 0. Therefore, only the part of the function curve where is greater than 0 is taken. The piecewise linearization strategy of the function curve is as Figure 4 shown.

[0072] 2) Convective heat dissipation The expression of the convective heat dissipation is as follows: (19) (20) (21) In equations (19), (20) and (21), is the introduced intermediate temperature variable, is the air thermal conductivity, is the wind direction factor, is the wind direction angle, is the air density, is the altitude of the area where the power system is located, is the air dynamic viscosity, is the outer diameter of the wire, is the wind speed, is the convective heat dissipation of the line in a low wind speed environment, is the convective heat dissipation of the line in a high wind speed environment.​​ For the line the convective heat dissipation in a zero-wind speed environment, For the line the convective heat dissipation, Take , and the maximum value in.

[0073] In the embodiments of the present application, images of the convective heat dissipation with respect to temperature are made when the wind speeds are 0, 2, and 4 meters per second (m / s), as shown in FIGS. 5(a), 5(b), and 5(c). When the wind speed is low, high, and zero, the curves are all quasi-linear. Therefore, , and can be approximately linearized, and their specific expressions are as follows: (22) In formula (22), is the low-wind speed convective heat dissipation when the line temperature is taken as , is the low-wind speed convective heat dissipation when the line temperature is taken as , is the high-wind speed convective heat dissipation when the line temperature is taken as , is the high-wind speed convective heat dissipation when the line temperature is taken as , is the zero-wind speed convective heat dissipation when the line temperature is taken as , is the zero-wind speed convective heat dissipation when the line temperature is taken as .

[0074] Furthermore, for the maximum value constraint of formula (21), the maximum value constraint can be linearized by introducing a 0-1 auxiliary variable. The linearized expression of the maximum value constraint is as follows: (23) In formula (23), is the introduced 0-1 auxiliary variable, is a relatively large constant introduced for linearization.

[0075] 3) Solar radiation heat absorption The expression of the solar radiation heat absorption is as follows: (24) In formula (24), is the heat absorption coefficient, is the solar radiation intensity, is the outer diameter of the wire.

[0076] It can be seen from the expression of the heat absorption from sunshine that the heat absorption from sunshine is independent of the conductor temperature. When the sunshine intensity is given, the heat absorption from sunshine is a constant value.

[0077] 4) Heat generation of the line AC resistance The expression is as follows: (25) In formula (25), is the skin effect coefficient, is the conductor temperature effect coefficient, is the line temperature at discrete moments, and is the DC resistance of the conductor.

[0078] Taking a conservative assumption for the expression of the AC resistance, let , then we have: (26) Furthermore, the square term of the line current has the following expression: (27) In formula (27), is the conductance of the line , is the susceptance of the line , is the voltage of node at time period, is the voltage of node at time period, is the phase angle difference from node to node at time period, is the phase angle of node at time period, is the phase angle of node The conversion process of is as follows: (28) Therefore, the expression of the heat generation of the line can be obtained. The expression of the heat generation of the line is as follows: (29) There are square terms of two variables in formula (29), that is and . The same can be done by piecewise linearization and , and The piecewise linearization expression of can refer to equation (10) and equation (11).

[0079] Through the above process, the radiation heat dissipation, convection heat dissipation and line heat generation are all transformed into linear forms, and the solar heat absorption is in the form of a constant term. At this point, the transient heat balance equation is transformed into a linearized difference equation form. The embodiment of the present application linearizes the transient heat balance equation, which can improve the convergence speed when solving it.

[0080] The thermal stability constraint of the linearized circuit in the embodiment of the present application may include equation (10), equation (11), equation (15) to equation (20), equation (22) to equation (24) and equation (29). The specific expression of the thermal stability constraint of the linearized circuit is as follows: (16) (15) (17) (18) (19) (20) (twenty two) (twenty three) (twenty four) (29) (10) (11) S13, solving the economic dispatch model of the power system to obtain an economic dispatch plan for the power system.

[0081] After S11 and S12, the embodiment of the present application can obtain an economic dispatch model of the power system, and the economic dispatch model of the power system includes an objective function and constraints.

[0082] The power system economic dispatch model of the embodiment of the present application may include equations (1) to (13), equations (15) to (20), equations (22) to (24) and equation (29).

[0083] After obtaining the economic dispatch model of the power system, the economic dispatch solution of the power system can be obtained by solving the economic dispatch model of the power system. As an example, the embodiments of the present application can use an optimization solver to solve the economic dispatch model of the power system according to the parameters of the power system, such as Cplex, Gurobi, etc. Both Cplex and Gurobi can efficiently solve problems such as linear programming, mixed integer programming, quadratic programming, quadratic constraint programming, and constraint programming.

[0084] It should be noted that the embodiments of the present application can also solve the economic dispatch model of the power system in other ways, and the embodiments of the present application do not limit the solution methods.

[0085] In the embodiments of the present application, an objective function with the minimum operating cost of the units in the power system as the objective is established; the constraint conditions of the objective function are determined according to the parameters of the power system, and the constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints; the economic dispatch model of the power system is solved to obtain the economic dispatch solution of the power system. The economic dispatch model of the power system includes an objective function and constraint conditions. The embodiments of the present application use linearized line thermal stability constraints to characterize and track the temperature changes of the lines, which can ensure the expansion of the actual transmission capacity of the lines on the basis of meeting the thermal stability constraints, release the potential of the line transmission capacity, improve the availability of the lines on the basis of ensuring safety, so as to optimize the economic dispatch strategy. By linearizing the non-linear constraints in the constraint conditions, linearized AC power flow constraints and linearized line thermal stability constraints are obtained, and the economic dispatch model of the power system considering thermal stability constraints is constructed into a mixed integer linear programming model, which can make the mathematical form of the economic dispatch model of the power system simpler, reduce the computational complexity of the model, and improve the solution speed and efficiency of the model.

[0086] To facilitate further understanding of the advantages of the technical solutions provided by the embodiments of the present application, the following takes the economic dispatch method of the power system provided by the embodiments of the present application applied to the IEEE 39-bus system as an example for an overall exemplary introduction. The IEEE 39-bus system is a regional transmission system network in the field of power systems.

[0087] The embodiments of the present application use the IEEE 39-bus system as an example, which includes a total of 46 lines, and dynamic capacity increase is performed on all lines. The network topology diagram of the IEEE 39-bus system is as Figure 6 shown.

[0088] The specific settings of the example parameters are as follows: Considering the real-time economic dispatch scenario, the time scale is 15 minutes, and the discretization time interval of the discretized transient heat balance equation is 1 minute, is 5000.

[0089] Generator, line and load parameters: based on the calculation example parameters provided by MATPOWER 8.0 toolbox.

[0090] The line conductor parameters and environmental parameters are shown in Table 1.

[0091] Table 1 Line conductor parameters and environmental parameters

[0092] In order to verify the necessity of applying the transient heat balance equation proposed in this embodiment to short-time scale scenarios, taking line L8 (i.e., the head-end node 4 and the terminal node 5) as an example, the line currents are set to 100 A, 400 A, and 700 A, respectively. The transient heat balance equation and the steady-state heat balance equation are used to calculate the line temperature rise process, respectively. The simulation time is 90 minutes. The results are shown in Figures 7(a), 7(b), and 7(c). Table 2 gives the comparison of temperature values ​​at 15 minutes.

[0093] Table 2 Comparison of transient heat balance equation and steady-state heat balance data of line L8

[0094] According to Figure 7 (a), Figure 7 (b) and Figure 7 (c), during the line temperature rise process, the temperature obtained by the steady-state heat balance equation is the upper limit of the temperature obtained by the transient heat balance equation, and the transient heat balance curve will be consistent with the steady-state heat balance curve after more than 40 minutes. According to Table 2, the errors in the three current cases are all above 5%, and as the line current increases, the relative error of the temperature obtained at 15 minutes continues to increase, indicating that for short-time scale scenarios, the transient heat balance equation has a higher precision in describing the line temperature rise and can obtain more accurate temperature calculation results.

[0095] Furthermore, in order to verify the accuracy and safety of the temperature change curve simulated by the method proposed in the embodiment of the present application, the line current is set to 700A, and the transient thermal balance equation, that is, the transient thermal balance equation, equation (14) is solved by the Runge-Kutta numerical calculation method. The discretization time step of the numerical calculation is 30 seconds (s), and compared with the method proposed in the embodiment of the present application, the total simulation time is 90 minutes. The method proposed in the embodiment of the present application is to substitute the line current of 700A into the linearized line thermal stability constraint for temperature calculation. Taking line L8 as an example, Figure 8 The temperature curves calculated by two different methods are shown. The temperature values ​​of the two methods at 15 minutes are calculated for each of the 46 lines, and the results are obtained in Table 3.

[0096] Table 3 Two methods to calculate the temperature rise of each line at 15 minutes Line number First section node End node Temperature obtained by the method proposed in the embodiment of the present application at 15 min (°C) Temperature obtained by the Runge-Kutta method at 15 min (°C) Relative error (%) L1 1 2 69.3 68.1 1.76 L2 1 39 55.7 55.0 1.27 L3 2 3 63.5 62.6 1.40 L4 2 25 66.5 65.4 1.68 L5 2 30 32.0 31.8 0.50 L6 3 4 63.5 62.6 1.40 L7 3 18 58.3 57.5 1.32 L8 4 5 50.4 49.8 1.16 L9 4 14 50.4 49.8 1.16 L10 5 6 34.6 34.4 0.64 L11 5 8 50.4 49.8 1.16 L12 6 7 45.2 44.7 1.03 L13 6 11 47.8 47.3 1.10 L14 6 31 32.0 31.8 0.50 L15 7 8 39.9 39.5 0.86 L16 8 9 69.5 68.3 1.76 L17 9 39 55.7 55.0 1.27 L18 10 11 39.9 39.5 0.86 L19 10 13 39.9 39.5 0.86 L20 10 32 32.0 31.8 0.50 L21 12 11 71.3 70.3 1.50 L22 12 13 71.3 70.3 1.50 L23 13 14 53.0 52.4 1.22 L24 14 15 76.6 75.4 1.55 L25 15 16 53.0 52.4 1.22 L26 16 17 47.8 47.3 1.10 L27 16 19 71.3 70.3 1.50 L28 16 21 50.4 49.8 1.16 L29 16 24 37.2 37.0 0.76 L30 17 18 47.8 47.3 1.10 L31 17 27 63.5 62.6 1.40 L32 19 20 47.8 47.3 1.10 L33 19 33 47.8 47.3 1.10 L34 20 34 53.0 52.4 1.22 L35 21 22 50.4 49.8 1.16 L36 22 23 45.2 44.7 1.03 L37 22 35 32.0 31.8 0.50 L38 23 24 86.9 85.5 1.64 L39 23 36 42.5 42.1 0.95 L40 25 26 62.6 61.6 1.62 L41 25 37 45.2 44.7 1.03 L42 26 27 66.1 65.2 1.43 L43 26 28 69.5 68.2 1.91 L44 26 29 65.2 64.1 1.71 L45 28 29 66.1 65.2 1.43 L46 29 38 50.4 49.8 1.16 As can be seen from Figure 8 Figure 8 , in the embodiment of the present application, the temperature simulated by the linearized line thermal stability constraint is slightly higher than the temperature obtained by numerical calculation using the Runge-Kutta method. This error is mainly caused by the linearization error of the transient thermal equilibrium equation. On the one hand, for conductor heating, the temperature is taken as a conservative term, and the conductor heating estimation is more conservative. On the other hand, for the radiant heat dissipation and convective heat dissipation, a piecewise linearization strategy is adopted, and at the same temperature, their values are also more conservative. Therefore, the temperature calculated by the linearized line thermal stability constraint in the embodiment of the present application is slightly higher than the actual value, which can ensure the safety of line thermal stability.

[0097] According to Table 3, on the one hand, for all lines, the temperature obtained by the method proposed in the embodiment of the present application at 15 minutes is higher than the temperature obtained by the Runge-Kutta method, and the temperature calculation has a certain degree of conservativeness. On the other hand, among all lines, the maximum relative error is 1.91%, which is within an acceptable range. In summary, the verification results show that: based on the linearized line thermal stability constraint proposed in the embodiment of the present application, the operating temperature error of the line conductor is within an acceptable range, and the temperature calculation is more conservative, further ensuring safety.

[0098] Furthermore, in order to verify the solution speed of the power system economic dispatch model in the embodiment of the present application, the following several algorithms are designed for comparison: Algorithm 1: The power system economic dispatch model in the embodiment of the present application.

[0099] Algorithm 2: The same as Algorithm 1, but using the steady-state thermal equilibrium equation to model the line thermal stability constraint.

[0100] Algorithm 3: The same as Algorithm 1, but using the transient thermal stability equation mentioned in the prior art to model the line thermal stability constraint.

[0101] The solution results and solution times obtained by the three algorithms are shown in Table 4: Table 4 Comparison of solution results and solution times of different algorithms

[0102] As can be seen from Table 4: Regarding the objective function value: The objective function values obtained by Algorithm 1 and Algorithm 3 are basically the same, with a relative error of 0.054%, indicating that the transient thermal balance equation approximation method proposed in the embodiments of the present application and the existing transient thermal balance equation processing methods can obtain similar results; the relative error between the objective function values obtained by Algorithm 1 and Algorithm 2 is 6.36%. The relative error mainly stems from the different processing of the line temperature rise process. For short-time scale scenarios, the line temperature rise will not reach the steady-state value, and the constraints given by the steady-state thermal balance equation are too conservative. However, the linearized line thermal stability constraint proposed in the embodiments of the present application can calculate a more accurate line temperature, thereby improving the calculation accuracy of the economic dispatch results.

[0103] Regarding the solution time: Comparing Algorithm 1 and Algorithm 2, the solution time of Algorithm 2 is shorter than that of Algorithm 1, and its form is simpler. However, for a short time scale (such as 15 minutes), the solution speed of the embodiments of the present application can also meet the real-time requirements; in addition, comparing Algorithm 1 and Algorithm 3, the solution time of Algorithm 1 is only 42.8% of that of Algorithm 3, indicating that the power system economic dispatch model of the embodiments of the present application can significantly shorten the solution time. This is because the power system economic dispatch model of the embodiments of the present application is a mixed-integer linear programming, and the line transient temperature rise process constraint is modeled as a linear constraint, while the non-linear constraint of Algorithm 3 will significantly extend the solution time.

[0104] For short-time scale scenarios, in order to make the mathematical form of the model simple and have a low computational complexity, the embodiments of the present application construct an economic dispatch model considering the line transient thermal balance equation, specifically, a mixed-integer linear programming model. In the prior art, the line transient thermal balance equation is often embedded in a non-linear form. Through comparison with examples, it is found that the power system economic dispatch model proposed in the embodiments of the present application has the significant advantage of high solution efficiency, and the calculation accuracy is within a reasonable range.

[0105] Next, an economic dispatch device for a power system considering line dynamic capacity increase provided by the embodiments of the present application will be introduced. The economic dispatch device for a power system considering line dynamic capacity increase introduced below can be correspondingly referred to the economic dispatch method for a power system considering line dynamic capacity increase introduced above.

[0106] Please refer to Figure 9 , which shows a schematic structural diagram of an economic dispatch device for a power system provided by the embodiments of the present application. The device includes: A building module 901, configured to build an objective function with the minimum operating cost of the units in the power system as the objective; A determination module 902, configured to determine the constraint conditions of the objective function according to the parameters of the power system, where the constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, and the linearized line thermal stability constraints take into account the dynamic change of the line temperature; A solution module 903, configured to solve the economic dispatch model of the power system to obtain the economic dispatch plan of the power system, where the economic dispatch model of the power system includes the objective function and the constraint conditions.

[0107] In an embodiment of the present application, the determination module 902 includes: An AC power flow construction unit, configured to construct an AC power flow model according to the parameters of the power system, where the AC power flow model includes line power flow constraints considering network losses; A power flow linearization unit, configured to perform linearization processing on the line power flow constraints to obtain the linearized AC power flow constraints.

[0108] In an embodiment of the present application, the determination module 902 includes: A thermal balance construction unit, configured to construct a transient thermal balance equation for taking into account the dynamic change of the line temperature according to the parameters of the power system; A thermal balance linearization unit, configured to perform linearization processing on the transient thermal balance equation to obtain the linearized line thermal stability constraints.

[0109] In an embodiment of the present application, the thermal balance linearization unit is specifically configured to: Discretize the transient thermal balance equation by forward difference; Perform linearization processing on the radiative heat dissipation, convective heat dissipation, and line heat generation in the transient thermal balance equation respectively to obtain the linearized line thermal stability constraints.

[0110] In an embodiment of the present application, the solution module 903 is specifically configured to: Use an optimization solver to solve the economic dispatch model of the power system to obtain the economic dispatch plan of the power system.

[0111] An embodiment of the present application further provides a computer device, including: a memory and a processor; Wherein, the memory is used to store a computer program; The processor is used to execute the computer program in the memory to implement the method as described in the above method embodiment.

[0112] An embodiment of the present application further provides a computer-readable storage medium, storing instructions, which when running on a computer, cause the computer to execute the method as described in the above method embodiment.

[0113] In an embodiment of the present application, an establishment module establishes an objective function with the goal of minimizing the unit operating cost of the power system; a determination module determines the constraints of the objective function, and the constraints include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints; a solution module solves the power system economic dispatch model to obtain an economic dispatch plan for the power system, and the power system economic dispatch model includes the objective function and the constraints. The embodiment of the present application uses the line thermal stability equation to characterize and track the temperature changes of the line, which can ensure that the line satisfies the thermal stability constraints on the basis of the expansion of the actual transmission capacity of the line, release the potential of the line transmission capacity, and improve the availability of the line on the basis of ensuring safety, so as to optimize the economic dispatch strategy, and obtain the linearized AC power flow constraints and the linearized line thermal stability constraints by linearizing the nonlinear constraints in the constraints, and constructing the power system economic dispatch model taking into account the thermal stability constraints into a mixed integer linear programming model, which can make the mathematical form of the power system economic dispatch model simpler, reduce the computational complexity of the model, and improve the solution speed and efficiency of the model.

[0114] It should be noted that the same or similar parts between the various embodiments can be referred to each other. As for the device embodiment and the system embodiment, since they are basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0115] For the above-mentioned embodiments, for the sake of simplicity, they are all described as a series of action combinations, but those skilled in the art should know that the present application is not limited by the order of the actions described, because according to the present application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0116] Finally, it should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0117] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

[0118] The above is only a preferred implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for economic dispatching of a power system taking into account dynamic capacity increase of lines, characterized in that: The method comprises: Establish an objective function with the goal of minimizing the unit operating cost of the power system; Determining the constraint conditions of the objective function according to the parameters of the power system, the constraint conditions including unit constraint, network variable constraint, linearized AC power flow constraint and linearized line thermal stability constraint, the linearized line thermal stability constraint taking into account the dynamic change of line temperature; The economic dispatch model of the power system is solved to obtain an economic dispatch plan of the power system, wherein the economic dispatch model of the power system includes the objective function and the constraint conditions.

2. The method according to claim 1, characterized in that Determining the linearized AC power flow constraint according to the parameters of the power system includes: Constructing an AC power flow model according to the parameters of the power system, wherein the AC power flow model includes line power flow constraints taking into account network losses; The line power flow constraint is linearized to obtain the linearized AC power flow constraint.

3. The method according to claim 1, characterized in that: Determining the thermal stability constraint of the linearized line according to the parameters of the power system includes: Constructing a transient heat balance equation for taking into account the dynamic change of line temperature according to the parameters of the power system; The transient heat balance equation is linearized to obtain the linearized circuit thermal stability constraint.

4. The method according to claim 3, characterized in that The linearizing the transient heat balance equation to obtain the linearized circuit thermal stability constraint includes: Discretizing the transient heat balance equation by a forward difference algorithm; The radiation heat dissipation, convection heat dissipation and line heat generation in the transient heat balance equation are linearized respectively to obtain the linearized line thermal stability constraint.

5. The method according to any one of claims 1 to 4, characterized in that: The solving of the power system economic dispatch model to obtain the economic dispatch plan of the power system includes: The economic dispatch model of the power system is solved by using an optimization solver to obtain an economic dispatch plan for the power system.

6. An economic dispatching device for a power system taking into account dynamic capacity increase of lines, characterized in that: The device comprises: Establishing a module for establishing an objective function with the goal of minimizing the unit operation cost of the power system; A determination module, used for determining the constraint conditions of the objective function according to the parameters of the power system, wherein the constraint conditions include unit constraint, network variable constraint, linearized AC power flow constraint and linearized line thermal stability constraint, wherein the linearized line thermal stability constraint takes into account the dynamic change of line temperature; The solution module is used to solve the power system economic dispatch model to obtain the economic dispatch plan of the power system. The power system economic dispatch model includes the objective function and the constraint conditions.

7. The device according to claim 6, characterized in that The determining module comprises: An AC power flow construction unit, configured to construct an AC power flow model according to the parameters of the power system, wherein the AC power flow model includes line power flow constraints taking into account network losses; The power flow linearization unit is used to perform linearization processing on the line power flow constraint to obtain the linearized AC power flow constraint.

8. The device according to claim 6, characterized in that The determining module comprises: A heat balance construction unit, used to construct a transient heat balance equation for taking into account the dynamic change of line temperature according to the parameters of the power system; The heat balance linearization unit is used to linearize the transient heat balance equation to obtain the thermal stability constraint of the linearized circuit.

9. A computer device, characterized in that: include: Memory and processor; The memory is used to store computer programs; The processor is configured to execute the computer program in the memory to implement the method according to any one of claims 1 to 5.

10. A computer-readable storage medium, characterized in that: The device stores instructions which, when executed on a computer, cause the computer to execute the method according to any one of claims 1 to 5.

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