Power system economic dispatch method and related device considering dynamic capacity increase of lines

Abstract

The present application provides a method and related apparatus for economic dispatch of an electric power system taking into account dynamic capacity expansion of lines. The method comprises: establishing an objective function with the goal of minimizing the operating cost of the units in the electric power system; determining the constraints of the objective function based on the parameters of the electric power system, the constraints including unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints; solving the economic dispatch model of the electric power system to obtain an economic dispatch plan for the electric power system, the economic dispatch model of the electric power system including the objective function and the constraints. The present application utilizes linearized line thermal stability constraints to track the temperature changes of the line, which can ensure that the line improves its transmission capacity on the basis of satisfying the thermal stability constraints, thereby optimizing the economic dispatch strategy. By linearizing the AC power flow constraints and the line thermal stability constraints, the economic dispatch model of the electric power system is constructed as a mixed integer linear programming model, which can improve the solution speed and efficiency of the model.

Description

Technical Field

[0001] The present application relates to the field of electrical engineering technology, and in particular to a method and related apparatus for economic dispatching of a power system taking into account dynamic capacity expansion of lines. Background Art

[0002] The economic dispatch problem is one of the basic problems in the operation of power systems. Its goal is to dispatch units to meet total demand at the lowest cost while satisfying the supply and demand balance and various constraints.

[0003] Traditional economic dispatch methods typically use a conservative constant to determine the transmission capacity of a line. This conservative constant only represents the safe transmission capacity under multiple typical operating conditions. Under actual operating conditions, the transmission capacity of a line has room for improvement, meaning that its transmission capacity is not fully utilized. Economic dispatch of the power system based on a fixed transmission capacity fails to take into account the actual conditions of the power system and cannot fully utilize the role of each line in the power system. Consequently, the results of economic dispatch of the power system need further optimization. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a power system economic dispatch method and related devices that take into account the dynamic capacity expansion of the line. For short-time-scale economic dispatch scenarios, a linearized transient heat balance equation is used to characterize the temperature rise changes of the line. This can improve the transmission capacity of the transmission line while ensuring safety, and also improve the speed and efficiency of solving the economic dispatch model. The specific technical solution is as follows:

[0005] In a first aspect, the present application provides a method for economic dispatch of a power system taking into account dynamic capacity expansion of lines, the method comprising:

[0006] Establish an objective function with the goal of minimizing the unit operating cost of the power system;

[0007] Determining constraints of the objective function based on parameters of the power system, wherein the constraints include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, wherein the linearized line thermal stability constraints take into account dynamic changes in line temperature;

[0008] 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.

[0009] In a possible implementation, determining the linearized AC power flow constraint according to the parameters of the power system includes:

[0010] constructing an AC power flow model based on the parameters of the power system, wherein the AC power flow model includes line power flow constraints taking into account network losses;

[0011] The line power flow constraint is linearized to obtain the linearized AC power flow constraint.

[0012] In a possible implementation, determining the linearized line thermal stability constraint according to the parameters of the power system includes:

[0013] Constructing a transient heat balance equation for taking into account the dynamic change of line temperature according to the parameters of the power system;

[0014] The transient heat balance equation is linearized to obtain the linearized circuit thermal stability constraint.

[0015] In a possible implementation, linearizing the transient heat balance equation to obtain the linearized circuit thermal stability constraint includes:

[0016] Discretizing the transient heat balance equation by a forward difference algorithm;

[0017] The radiation heat dissipation, convection heat dissipation and circuit heating value in the transient heat balance equation are linearized respectively to obtain the linearized circuit thermal stability constraint.

[0018] In one possible implementation, solving the power system economic dispatch model to obtain the power system economic dispatch plan includes:

[0019] The power system economic dispatch model is solved using an optimization solver to obtain an economic dispatch plan for the power system.

[0020] In a second aspect, the present application further provides a power system economic dispatching device taking into account dynamic line capacity expansion, the device comprising:

[0021] Establishing a module for establishing an objective function with the goal of minimizing the unit operating cost of the power system;

[0022] a determination module, configured to determine the constraint conditions of the objective function according to the parameters of the power system, wherein the constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, wherein the linearized line thermal stability constraints take into account dynamic changes in line temperature;

[0023] 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.

[0024] In a possible implementation, the determining module includes:

[0025] 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;

[0026] 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.

[0027] In a possible implementation, the determining module includes:

[0028] a heat balance construction unit, configured to construct a transient heat balance equation for taking into account dynamic changes in line temperature according to parameters of the power system;

[0029] The heat balance linearization unit is used to linearize the transient heat balance equation to obtain the thermal stability constraint of the linearized circuit.

[0030] In a third aspect, the present application further provides a computer device, comprising: a memory and a processor;

[0031] Wherein, the memory is used to store computer programs;

[0032] The processor is configured to execute the computer program in the memory to implement the first aspect or the method described in any one of the first aspects.

[0033] In a fourth aspect, the present application further provides a computer-readable storage medium storing instructions, which, when executed on a computer, enables the computer to execute the method described in the first aspect or any one of the first aspects.

[0034] In this application, an objective function is established with the goal of minimizing the unit operating cost of the power system; the constraints of the objective function are determined based on the parameters of the power system, and the constraints 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 changes in line temperature; the power system economic dispatch model is solved to obtain an economic dispatch plan for the power system. The power system economic dispatch model includes the objective function and the constraints. This application uses linearized line thermal stability constraints to characterize and track the temperature changes of the line, which can ensure that the line can expand its actual transmission capacity on the basis of satisfying the thermal stability constraints, release the line transmission capacity potential, and improve the line availability on the basis of ensuring safety, so as to optimize the economic dispatch strategy. By linearizing the nonlinear constraints in the constraints, linearized AC power flow constraints and linearized line thermal stability constraints are obtained. The power system economic dispatch model taking into account the line thermal stability constraints is constructed 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0036] Figure 1 A flow chart of a method for economic dispatch of a power system taking into account dynamic capacity expansion of lines provided in an embodiment of the present application is shown;

[0037] Figure 2 A schematic diagram of a piecewise linearization strategy for the square term of the voltage square difference provided by an embodiment of the present application is shown;

[0038] Figure 3 A flow chart of linearization of transient heat balance equations provided in an embodiment of the present application is shown;

[0039] Figure 4 The embodiment of the present application provides Schematic diagram of the piecewise linearization strategy of the function curve;

[0040] FIG5 (a) shows a schematic diagram of a curve showing a change in convective heat dissipation in an environment with a wind speed of 0 m / s provided by an embodiment of the present application;

[0041] FIG5( b ) shows a schematic diagram of a curve showing a change in convective heat dissipation in an environment with a wind speed of 2 m / s provided by an embodiment of the present application;

[0042] FIG5 (c) shows a schematic diagram of a curve showing a change in convective heat dissipation in an environment with a wind speed of 4 m / s provided by an embodiment of the present application;

[0043] Figure 6 A schematic diagram of the network topology of the IEEE 39-node system provided in an embodiment of the present application is shown;

[0044] FIG7 (a) shows a schematic diagram of a line temperature variation curve calculated based on two heat balance equations when the line current is 100 A provided in an embodiment of the present application;

[0045] FIG7( b ) shows a schematic diagram of a line temperature variation curve calculated based on two heat balance equations when the line current is 400 A according to an embodiment of the present application;

[0046] FIG7( c ) shows a schematic diagram of a line temperature variation curve calculated based on two heat balance equations when the line current is 700 A according to an embodiment of the present application;

[0047] Figure 8Schematic diagram of temperature change curves for solving transient thermal equilibrium using two methods provided in embodiments of the present application;

[0048] Figure 9 A structural schematic diagram of an economic dispatching device for an electric power system taking into account dynamic capacity expansion of lines provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0049] To make the purpose, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments in the present application are within the scope of protection of this application.

[0050] Economic dispatch of power systems refers to a scheduling method that rationally utilizes energy and equipment to ensure reliable power supply to users at the lowest generation cost or fuel expense, while ensuring safety and power quality. Economic dispatch is a typical optimization problem, requiring the rational allocation of unit power while meeting demand and various constraints to ensure the lowest operating cost.

[0051] During power system operation, the system's operating state often experiences significant fluctuations and changes, and the transmission capacity limit of a line can affect the location of the system's operating point. However, existing economic dispatch methods typically use a conservative constant to determine the transmission capacity limit of a line. The value of this conservative constant only represents the safe transmission capacity under multiple typical operating conditions. Under specific operating conditions, the transmission capacity limit still has room for improvement, meaning that the transmission capacity of the line has not yet been fully explored. Therefore, dynamically increasing the transmission capacity of a line can optimize economic dispatch strategies and is of great significance to the safe, economical, and flexible operation of the power system.

[0052] Dynamic line capacity expansion technology primarily leverages the thermal inertia effect of transmission lines. Based on meteorological data from micrometeorological sensors and the actual operating conditions of the power system, it uses heat balance equations to characterize and track temperature changes along the transmission lines. The technology then adjusts the transmission capacity of the transmission lines while ensuring that the lines meet thermal stability constraints. Therefore, applying dynamic line capacity expansion technology to power system operation scenarios such as economic dispatch can unlock the potential of line transmission capacity and maximize line utilization while ensuring safety.

[0053] Traditionally, the mathematical model for the optimization problem of economic dispatch involves optimizing a quadratic cost function and linear constraints. However, when considering line thermal inertia, the constraints in the economic dispatch model become nonlinear and non-convex, 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 significant limitations in handling problems with non-convex constraints, resulting in unsatisfactory results.

[0054] To address the above issues, an optimal power flow model that takes security constraints into account has been proposed in the prior art. Dynamic capacity expansion technology for transmission lines is used to characterize the thermal stability limits of the lines to ensure the economical and safe operation of the power grid. The specific steps of the proposed method are as follows:

[0055] Step 1: Construct an enhanced safety-constrained optimal power flow model. The objective function of the model is economic optimization (i.e., minimizing the unit power generation cost). The model constraints include power balance constraints, unit output upper and lower limit constraints, DC power flow constraints, N-1 unit output upper and lower limit constraints, N-1 fault state DC power flow constraints, and line temperature limit constraints.

[0056] Step 2: For the line temperature limit constraint, a transient heat balance equation is used to describe it. The transient heat balance equation is a first-order nonlinear differential equation about the line temperature:

[0057] .

[0058] Where, For line quality, is the circuit specific heat capacity, is the line temperature, is the differential with respect to the time variable, is the line current, is the AC resistance, To absorb heat from sunlight, For radiation heat dissipation, Convection cooling.

[0059] Taking conservative assumptions, the nonlinear terms in the transient heat balance equation are linearized and converted into a first-order linear differential equation about the line temperature, which can be abbreviated as follows:

[0060] .

[0061] Where, is the ambient temperature, and is an equivalent constant, and Determined by the line conductor parameters and surrounding environmental conditions.

[0062] For the above formula, its solution function can be obtained, which is a nonlinear convex function:

[0063] .

[0064] Where, for The line temperature at the time, is the initial temperature of the conductor, is the steady-state final temperature that the conductor can reach during the dynamic capacity expansion process, e is the base of the exponential function under the natural state, is the time constant of the conductor thermal process, Determined by the characteristic parameters of the line conductor.

[0065] Step 3: For the enhanced safety-constrained optimal power flow model mentioned above, decompose the enhanced safety-constrained optimal power flow model into the preventive control main problem, the dynamic capacity expansion check subproblem, and the corrective control feasibility check subproblem. Use the Benders decomposition algorithm to iteratively solve it until the algorithm meets the convergence conditions and obtains the optimization model result.

[0066] Although existing technologies introduce dynamic line capacity expansion technology into the optimal power flow (dispatching operation) problem of power systems to release the capacity potential of lines, existing technologies use transient heat balance equations to characterize the dynamic thermal limits of lines. This converts the transient heat balance equations into a nonlinear form, which often results in slow convergence when solving them, and does not meet the real-time requirements well.

[0067] In addition, some existing technologies use a steady-state heat balance equation to characterize the dynamic thermal limit of the line, specifically by setting the differential term of the transient heat balance to 0:

[0068] .

[0069] Take the temperature as the upper limit of the allowable temperature of the circuit , then:

[0070] .

[0071] Where, is the maximum value of the line current, is the maximum line temperature, is the radiation heat dissipation when the line temperature is the maximum line temperature, is the convection heat dissipation when the circuit temperature is the maximum circuit temperature, is the solar heat absorption when the line temperature is the maximum line temperature, is the AC resistance when the circuit temperature is the maximum circuit temperature.

[0072] The steady-state heat balance equation can be embedded in a linear form, as shown in the formula. However, the steady-state heat balance constraint makes it difficult to account for the dynamic changes in line temperature rise. For temperature rise scenarios with short timescales, such as 15-minute real-time scheduling, the characterization is insufficiently detailed.

[0073] Therefore, an embodiment of the present application provides an economic dispatch method for an electric power system that takes into account the dynamic capacity expansion of lines. For dispatching scenarios with a short time scale, the transient thermal balance equation can be used to characterize the temperature rise changes of the lines, and the economic dispatch model that takes into account the transient thermal balance equation of the lines can be constructed into a mixed integer linear programming model, so that the mathematical form of the model is simple and the solution efficiency is high.

[0074] See Figure 1 , shows a flow chart of a method for economic dispatch of a power system taking into account dynamic capacity expansion of lines provided in an embodiment of the present application, and the embodiment of the present application includes at least the following steps:

[0075] S11, establish an objective function with the goal of minimizing the unit operating cost of the power system.

[0076] In an embodiment of the present application, an objective function may be established with the goal of minimizing the unit operating cost of the power system.

[0077] The expression of the objective function is as follows:

[0078] (1)

[0079] In formula (1), For the scheduling period, is the scheduling period set, For the crew exist The active power output of the time period, For the crew collection, is the quadratic term coefficient of the objective function, is the linear coefficient of the objective function, is the constant coefficient of the objective function. The discretization time interval can be set according to the specific scenario. As an example, The discretization time interval of can be 15 minutes (min). The active power output of each unit remains unchanged during the period. The discretization time interval is 15 minutes. In this 15 minutes, the unit The active output per minute is the same.

[0080] In the embodiment of the present application, the objective function can be established based on the parameters of the power system, and the corresponding parameters of different units are as follows: , and The parameters of the power system may include the generator cost coefficients corresponding to different units (i.e. , and ).

[0081] The embodiment of the present application can adopt a piecewise linearization strategy to linearize the quadratic function curve of the objective function. The piecewise linearization strategy of the objective function can be set according to the actual scenario and is not limited by the embodiment of the present application. It should be noted that the objective function in the power system economic dispatch model of the embodiment of the present application is a linearized objective function.

[0082] S12, determining the constraint conditions of the objective function according to the parameters of the power system.

[0083] After establishing the objective function, the constraints of the objective function can be determined based on the parameters of the power system. The constraints in this embodiment of the application may include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints. The linearized AC power flow constraints take into account network losses, and the linearized line thermal stability constraints take into account dynamic changes in line temperature.

[0084] Power system parameters can include generator parameters, network parameters, and load parameters. Network parameters can include line parameters and node parameters. In a power system, a node usually represents a substation or load point. These nodes are interconnected by transmission lines (i.e., lines), together forming the network structure of the power system.

[0085] Generator parameters may include the maximum active output, minimum active output, maximum reactive output, and minimum reactive output of each generator, all in megawatts (MW). Generator parameters may also include a generator cost coefficient corresponding to each generator.

[0086] Line parameters include the conductance, susceptance, and phase angle difference upper and lower limits of each line. The units of conductance and susceptance are Siemens (S), and the units of phase angle difference upper and lower limits are radians (rad).

[0087] The node parameters may include an upper voltage square limit and a lower voltage square limit of each node.

[0088] Load parameters may include active load and reactive load, both in MW.

[0089] S121, determining unit constraints according to power system parameters.

[0090] The unit constraints involve the upper and lower limits of the unit's active and reactive outputs. The unit constraints are expressed as follows:

[0091] (2)

[0092] (3)

[0093] In formula (2) and formula (3), For the crew The lower limit of active output, For the crew exist The active power output of the time period, For the crew The active output limit of For the crew exist Reactive power output during the period, For the crew The lower limit of reactive power output, For the crew The reactive power output limit of this application embodiment is The active and reactive outputs of each unit remain unchanged during the period.

[0094] S122: Determine network variable constraints based on power system parameters.

[0095] Network variable constraints involve voltage constraints and phase angle (hereinafter referred to as phase angle) constraints. The expressions for network variable constraints are as follows:

[0096] (4)

[0097] (5)

[0098] In formula (4) and formula (5), For nodes exist The voltage during the time period, For nodes The lower voltage limit, For nodes The upper voltage limit, For Time period slave node To Node The phase angle difference, For slave nodes To Node The lower limit of the phase angle difference, For slave nodes To Node The upper limit of the phase angle difference. The voltage of each node remains unchanged during the time period, and the phase angle difference between each node pair remains unchanged. Two nodes connected by a line are called a node pair.

[0099] S123: Determine linearized AC power flow constraints according to the parameters of the power system.

[0100] Conventional power flow constraints are non-convex nonlinear constraints, which makes it difficult to directly obtain the global optimal solution. Therefore, the embodiment of the present application constructs a square voltage constraint. Linearized AC power flow model with variables.

[0101] In one possible implementation, determining the linearized AC power flow constraints may include:

[0102] S31, constructing an AC power flow model according to the parameters of the power system, where the AC power flow model includes line power flow constraints and node power balance constraints.

[0103] S32, linearizing the line power flow constraint to obtain a linearized AC power flow constraint.

[0104] The expression of line power flow constraint is as follows:

[0105] (6)

[0106] (7)

[0107] In formula (6) and formula (7), For the line exist The line active power of the period, For the line exist Line reactive power during the period, For the line The conductivity, For the line The electrical susceptance, For nodes exist The voltage during the time period, For nodes exist The voltage during the time period, For Time period slave node To Node The phase angle difference, For the line exist Active network loss during the period, For the line exist Reactive network loss in the period, line For slave nodes Flow Node line.

[0108] exist Time Route The expressions of active network loss and reactive network loss are as follows:

[0109] (8)

[0110] (9)

[0111] From equations (8) and (9), we can see that both active network loss and reactive network loss have square terms as variables, namely and , which will lead to nonlinear AC power flow model. To this end, the embodiment of the present application can adopt piecewise linearization processing and .by For example, the specific piecewise linearization strategy is as follows Figure 2 As shown, The voltage square term and Linear combination transformation.

[0112] Squared term of the voltage squared difference The piecewise linearization expression of is as follows:

[0113] (10)

[0114] In formula (10), For nodes exist The voltage during the time period, For nodes exist The voltage during the time period, For nodes The lower voltage limit, For nodes The upper voltage limit, For nodes The lower voltage limit, For nodes The upper voltage limit, for Function curve The slope value of the segment, for Function curve The value of the square difference of the voltage of the segment, For Function curve The 0-1 auxiliary variable introduced by the piecewise linearization, for Function curve The width of the segment interval, for The minimum value of for The maximum value of For nodes The voltage, For nodes voltage. The value of can be set according to the actual situation. Generally speaking, The larger the value of , the better the approximation effect, but the longer the solution time. If the function curve is symmetrical, then The value of is an even number.

[0115] Squared term of phase angle difference The piecewise linearization expression of is as follows:

[0116] (11)

[0117] In formula (11), For Time period slave node To Node The phase angle difference, For slave nodes To Node The lower limit of the phase angle difference, For slave nodes To Node The upper limit of the phase angle difference, for Function curve The slope value of the segment, for Function curve The value of the phase angle difference between the segments, For Function curve The 0-1 auxiliary variable introduced by the piecewise linearization, For Function curve The width of the segment interval. Piecewise linearization strategy of function curve and The function curve is similar, you can refer to Figure 2 Understand.

[0118] The expression of the node power balance constraint is as follows:

[0119] (12)

[0120] (13)

[0121] In formula (12) and formula (13), Belong to the node A collection of generators, For the crew exist The active power output of the time period, Belong to the node The load collection, For nodes There are node pairs connected by lines gather, For load d Active load during the period, For the line exist The line active power of the period, For the line The conductivity, For nodes exist The voltage during the time period, For the crew exist Reactive power output during the period, For load d Reactive load during the period, For the line exist Line reactive power during the period, For the line The electrical susceptance, is the total number of nodes. Node n is any node in the power system, and node i and node j are pairs of nodes connected by a line in the power system.

[0122] S124: Determine linearized line thermal stability constraints based on power system parameters.

[0123] The embodiment of the present application considers the dynamic change of the circuit temperature and determines the thermal stability constraint of the linearized circuit.

[0124] The linearization process of transient heat balance equation is as follows Figure 3 In one possible implementation, determining the thermal stability constraint of the linearized circuit may include:

[0125] S41, constructing a transient heat balance equation for taking into account the dynamic change of line temperature according to the parameters of the power system.

[0126] line The dynamic temperature change process can be described by the transient heat balance equation. The transient heat balance equation of the embodiment of the present application is expressed as follows:

[0127] (14)

[0128] In formula (14), The line temperature is The radiation heat dissipation when The line temperature is The convective heat dissipation when To absorb heat from the sun, Heat generated by the circuit, is the line temperature, For the line exist The current of the time period, is the AC resistance, For the line The line quality, For the line The circuit specific heat capacity of the present application embodiment is The current in each line remains unchanged during the period.

[0129] The transient heat balance equation describes how the temperature changes over time under the influence of the external environment and line current. To ensure line thermal stability, the line temperature should not exceed the set upper limit:

[0130] (15)

[0131] In formula (15), The upper limit of the circuit temperature.

[0132] S42, linearize the transient heat balance equation to obtain the linearized line thermal stability constraint.

[0133] The above transient heat balance equation is a first-order nonlinear differential equation and is difficult to solve directly. Therefore, the embodiment of the present application discretizes the transient heat balance equation through a forward difference algorithm. The expression of the discretized transient heat balance equation is as follows:

[0134] (16)

[0135] In formula (16), is the discrete moment after the differential equation is differentiated, express The line temperature at a discrete moment, express The amount of heat dissipated by radiation at discrete moments, express Convective heat dissipation at discrete moments, is the differencing step size. The discretization time interval can be set according to the actual scenario. As an example, The discretization time interval of can be 1 minute. The discretization time interval is 15 minutes. The discretization time interval is 1 minute, then During the period, there are 15 Discrete moments.

[0136] Furthermore, the radiation heat dissipation, convection heat dissipation, solar heat absorption and line heat generation are expanded and represented, and the radiation heat dissipation, convection heat dissipation and line heat generation are linearized. The discretized transient heat balance equation is converted into a first-order linear difference equation to obtain the linearized line thermal stability constraint.

[0137] 1) Radiative heat dissipation

[0138] Radiant heat dissipation The expression is as follows:

[0139] (17)

[0140] In formula (17), is pi, For the line The outer diameter of the wire, For the line The radiation heat dissipation coefficient of the conductor surface, is the Stefan-Boltzmann constant, is the ambient temperature. Generally speaking, the models of the various lines in the power system are the same, so it can be assumed that the outer diameter of the wires of each line and the radiation heat dissipation coefficient of the wire surface are the same. It should be noted that The ambient temperature is fixed within the time period and can be set according to the actual scenario. The ambient temperature may be the same or different in different scheduling periods.

[0141] When external meteorological factors are given, the radiative heat dissipation is a quartic function of the conductor temperature, which can be piecewise linearized. External meteorological factors can include ambient temperature, sunlight intensity, wind speed, and the angle between the wind and the conductor.

[0142] Radiative heat dissipation The piecewise linearization expression of is as follows:

[0143] (18)

[0144] In formula (18), for Function curve The slope value of the segment, The circuit taken for piecewise linearization The lower limit of temperature of the embodiment of the present application It can be set according to the actual situation. For example, Can be set to 0 , for Function curve The value of the temperature increment of each segment, For Function curve The 0-1 auxiliary variable introduced by the piecewise linearization, for Function curve The width of the segment interval, The circuit taken for piecewise linearization The upper temperature limit of the embodiment of the present application It can be set according to the actual situation. For example, Can be set to 90 . is always greater than 0, so Function curve only takes The part greater than 0, The piecewise linearization strategy of the function curve is as follows Figure 4 shown.

[0145] 2) Convective heat dissipation

[0146] Convection heat dissipation The expression is as follows:

[0147] (19)

[0148] (20)

[0149] (twenty one)

[0150] In formula (19), formula (20) and formula (21), is the introduced intermediate temperature variable, is the thermal conductivity of air, 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 dynamic viscosity of air, is the outer diameter of the wire, is the wind speed, For the line Convective heat dissipation in low wind speed environment, For the line Convective heat dissipation in high wind speed environment, For the line Convective heat dissipation in zero wind speed environment, For the line The convective heat dissipation, Pick , and The maximum value in .

[0151] The embodiment of the present application makes images of the convective heat dissipation with respect to temperature when the wind speed is 0, 2, and 4 meters per second (m / s), as shown in Figures 5(a), 5(b), and 5(c). When the wind speed is low, high, and zero, the curves are quasi-linear, so the curves can be respectively calculated. , and Perform approximate linearization processing, and its specific expression is as follows:

[0152] (twenty two)

[0153] In formula (22), The line temperature is taken as Low wind speed convection heat dissipation, The line temperature is taken as Low wind speed convection heat dissipation, The line temperature is taken as High wind speed convection heat dissipation, The line temperature is taken as High wind speed convection heat dissipation, The line temperature is taken as The zero wind speed convection heat dissipation, The line temperature is taken as Zero wind speed convection heat dissipation.

[0154] Furthermore, for the maximum constraint of formula (21), the maximum constraint can be linearized by introducing a 0-1 auxiliary variable. The linearized expression of the maximum constraint is as follows:

[0155] (twenty three)

[0156] In formula (23), is the introduced 0-1 auxiliary variable, A large constant introduced for linearization.

[0157] 3) Heat absorption from sunlight

[0158] Heat absorbed by sunlight The expression is as follows:

[0159] (twenty four)

[0160] In formula (24), is the heat absorption coefficient, is the sunlight intensity, is the outer diameter of the wire.

[0161] From the expression of solar heat absorption, we can see that solar heat absorption is independent of the conductor temperature. When the solar intensity is given, the solar heat absorption is constant.

[0162] 4) Circuit heat generation

[0163] AC resistance The expression is as follows:

[0164] (25)

[0165] In formula (25), is the skin effect coefficient, is the conductor temperature effect coefficient, for The line temperature at a discrete moment, is the DC resistance of the wire.

[0166] A conservative assumption is made for the expression of AC resistance, , then:

[0167] (26)

[0168] Furthermore, the line The square term of the current The expression is as follows:

[0169] (27)

[0170] In formula (27), For the line The conductivity, For the line The electrical susceptance, For nodes exist The voltage during the time period, For nodes exist The voltage during the time period, For Time period slave node To Node The phase angle difference, for Time period node The phase angle, for Time period node The phase angle of . The conversion process is as follows:

[0171] (28)

[0172] Therefore, the expression of the circuit heat generation can be obtained: The expression is as follows:

[0173] (29)

[0174] There are two square terms of variables in formula (29), namely and . The same can be done using piecewise linearization and , and The piecewise linearization expression of can refer to Equation (10) and Equation (11).

[0175] Through the above process, the radiation heat dissipation, convection heat dissipation, and circuit heat generation are all converted to linear form, and the solar heat absorption is a constant term. At this point, the transient heat balance equation is transformed into a linearized difference equation. The embodiments of the present application linearize the transient heat balance equation, which can improve the convergence speed when solving it.

[0176] The thermal stability constraints of the linearized circuit in the embodiment of the present application may include equations (10), (11), (15) to (20), (22) to (24), and (29). The specific expressions of the thermal stability constraints of the linearized circuit are as follows:

[0177] (16)

[0178] (15)

[0179] (17)

[0180] (18)

[0181] (19)

[0182] (20)

[0183] (twenty two)

[0184] (twenty three)

[0185] (twenty four)

[0186] (29)

[0187] (10)

[0188] (11)

[0189] S13, solving the power system economic dispatch model to obtain the power system economic dispatch plan.

[0190] After S11 and S12, the embodiment of the present application can obtain the power system economic dispatch model, which includes an objective function and constraints.

[0191] 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).

[0192] After obtaining the power system economic dispatch model, the power system economic dispatch plan can be obtained by solving the power system economic dispatch model. As an example, embodiments of the present application can use an optimization solver, such as Cplex or Gurobi, to solve the power system economic dispatch model based on power system parameters. Cplex and Gurobi can both efficiently solve linear programming, mixed integer programming, quadratic programming, quadratically constrained programming, and constraint programming problems.

[0193] It should be noted that the embodiments of the present application may also solve the power system economic dispatch model in other ways, and the embodiments of the present application do not limit the solution method.

[0194] In an embodiment of the present application, an objective function is established with the goal of minimizing the unit operating cost of the power system; the constraints of the objective function are determined based on the parameters of the power system, and the constraints include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints; the power system economic dispatch model is solved 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 linearized line thermal stability constraints to characterize and track the temperature changes of the line, which can ensure that the line meets the thermal stability constraints on the basis of expanding the actual transmission capacity of the line, releasing the line transmission capacity potential, and improving the line availability on the basis of ensuring safety, so as to optimize the economic dispatch strategy. By linearizing the nonlinear constraints in the constraints, linearized AC power flow constraints and linearized line thermal stability constraints are obtained, and the power system economic dispatch model taking into account the thermal stability constraints is constructed 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.

[0195] To further understand the advantages of the technical solutions provided by the embodiments of the present application, the following is an overall illustrative introduction using the power system economic dispatch method provided by the embodiments of the present application applied to the IEEE 39-bus system. The IEEE 39-bus system is a regional transmission system network in the power system field.

[0196] The embodiment of this application uses IEEE 39 nodes as an example, which contains 46 lines in total. Dynamic capacity expansion is performed on all lines. The network topology diagram of the IEEE 39-node system is as follows: Figure 6 shown.

[0197] The specific settings of the calculation parameters are as follows:

[0198] 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.

[0199] Generator, line, and load parameters: Based on the calculation parameters provided by the MATPOWER 8.0 toolbox.

[0200] The line conductor parameters and environmental parameters are shown in Table 1.

[0201] Table 1 Line conductor parameters and environmental parameters

[0202]

[0203] To verify the necessity of applying the transient heat balance equation proposed in this embodiment to short-timescale scenarios, line L8 (i.e., head-end node 4 and terminal node 5) is taken 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. The simulation lasts for 90 minutes. The results are shown in Figures 7(a), 7(b), and 7(c). Table 2 shows the temperature comparison at 15 minutes.

[0204] Table 2 Comparison of transient heat balance equation and steady-state heat balance data of line L8

[0205]

[0206] Figures 7(a), 7(b), and 7(c) show that during the line temperature rise, the temperature calculated by the steady-state heat balance equation is the upper bound of the temperature calculated by the transient heat balance equation. The transient heat balance curves converge with the steady-state heat balance curves only after more than 40 minutes. Table 2 shows that the errors are all above 5% for all three current scenarios, and the relative error of the temperature calculated at 15 minutes increases continuously as the line current rises. This indicates that for short-timescale scenarios, the transient heat balance equation provides a more precise description of line temperature rise and can produce more accurate temperature calculation results.

[0207] 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 heat balance equation, i.e., the transient heat balance equation, formula (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 using the two different methods are shown. The temperature values ​​calculated for each of the 46 lines after 15 minutes using the two methods are shown in Table 3.

[0208] Table 3 Calculation of temperature rise of each line in 15 minutes by two methods

[0209] Line number First segment node End Node At 15 minutes, the temperature (°C) was obtained by the method proposed in the embodiment of the present application. The temperature at 15 minutes was obtained by the Runge-Kutta method (℃) 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

[0210] Depend on Figure 8 It can be seen that the temperature simulated by the linearized circuit thermal stability constraint in the embodiment of the present application is slightly higher than the temperature numerically calculated by the Runge-Kutta method. This error is mainly caused by the linearization error of the transient heat balance equation. On the one hand, for conductor heat generation, the temperature is taken as a conservative term, and the conductor heat generation estimate is more conservative; on the other hand, for radiation heat dissipation and convection 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 circuit thermal stability constraint in the embodiment of the present application is slightly higher than the actual value, which can ensure the safety of circuit thermal stability.

[0211] As can be seen from 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 is conservative to a certain extent. On the other hand, the maximum relative error in all lines is 1.91%, which is within an acceptable range. In summary, the verification results show that: based on the linearized circuit thermal stability constraints 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, and safety is further guaranteed.

[0212] Furthermore, in order to verify the solution speed of the power system economic dispatch model of the embodiment of the present application, the following algorithms are designed for comparison:

[0213] Algorithm 1: The power system economic dispatch model of the embodiment of the present application.

[0214] Algorithm 2: Other operations are the same as Algorithm 1, but the steady-state thermal balance equation is used to model the circuit thermal stability constraint.

[0215] Algorithm 3: Other steps are the same as Algorithm 1, but the transient thermal stability equation mentioned in the prior art is used to model the line thermal stability constraint.

[0216] The solution results and solution time of the three algorithms are shown in Table 4:

[0217] Table 4 Comparison of solution results and solution time of different algorithms

[0218]

[0219] From Table 4 we can see that:

[0220] 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 heat balance equation approximation method proposed in the embodiment of the present application and the existing transient heat balance equation processing method can obtain similar results; the relative error of the objective function values ​​obtained by Algorithm 1 and Algorithm 2 is 6.36%. The relative error is mainly due to the different treatment of the line temperature rise process. For short time scales, the line temperature rise will not reach the steady-state value, and the restrictions given by the steady-state heat balance equation are too conservative. The linearized line thermal stability constraint proposed in the embodiment of the present application can calculate a more accurate line temperature, thereby improving the calculation accuracy of the economic dispatch results.

[0221] Regarding solution time: Comparing Algorithms 1 and 2, Algorithm 2 takes less time to solve than Algorithm 1. Its form is simpler, but for shorter time scales (e.g., 15 minutes), the solution speed of the embodiment of the present application can also meet real-time requirements. Furthermore, comparing Algorithms 1 and 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 embodiment of the present application can significantly shorten the solution time. This is because the power system economic dispatch model of the embodiment of the present application is a mixed integer linear programming, and its line transient temperature rise process constraints are modeled as linear constraints, while the nonlinear constraints of Algorithm 3 significantly extend the solution time.

[0222] For short-timescale scenarios, in order to simplify the mathematical form of the model and reduce computational complexity, the present embodiment constructs an economic dispatch model that takes into account the transient heat balance equation of the line. Specifically, a mixed-integer linear programming model is constructed. In the prior art, the transient heat balance equation of the line is often constructed and embedded in a nonlinear form. Through comparative calculations, it is found that the power system economic dispatch model proposed in the present embodiment has the significant advantage of high solution efficiency and the calculation accuracy is within a reasonable range.

[0223] Next, an economic dispatching device for an electric power system taking into account dynamic capacity expansion of lines provided in an embodiment of the present application is introduced. The economic dispatching device for an electric power system taking into account dynamic capacity expansion of lines introduced below and the economic dispatching method for an electric power system taking into account dynamic capacity expansion of lines introduced above can refer to each other.

[0224] See Figure 9 , shows a schematic structural diagram of a power system economic dispatching device provided in an embodiment of the present application, the device comprising:

[0225] Establishing module 901, for establishing an objective function with the goal of minimizing the unit operating cost of the power system;

[0226] a determination module 902 for determining constraints of the objective function based on parameters of the power system, wherein the constraints include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, wherein the linearized line thermal stability constraints take into account dynamic changes in line temperature;

[0227] The solving module 903 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.

[0228] In the embodiment of the present application, the determining module 902 includes:

[0229] 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;

[0230] 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.

[0231] In the embodiment of the present application, the determining module 902 includes:

[0232] a heat balance construction unit, configured to construct a transient heat balance equation for taking into account dynamic changes in line temperature according to parameters of the power system;

[0233] The heat balance linearization unit is used to linearize the transient heat balance equation to obtain the thermal stability constraint of the linearized circuit.

[0234] In the embodiment of the present application, the thermal balance linearization unit is specifically used to:

[0235] discretizing the transient heat balance equation by forward difference;

[0236] The radiation heat dissipation, convection heat dissipation and circuit heating value in the transient heat balance equation are linearized respectively to obtain the linearized circuit thermal stability constraint.

[0237] In the embodiment of the present application, the solution module 903 is specifically configured to:

[0238] The power system economic dispatch model is solved using an optimization solver to obtain an economic dispatch plan for the power system.

[0239] The embodiment of the present application further provides a computer device, comprising: a memory and a processor;

[0240] Wherein, the memory is used to store computer programs;

[0241] The processor is configured to execute the computer program in the memory to implement the method described in the above method embodiment.

[0242] An embodiment of the present application further provides a computer-readable storage medium storing instructions, which, when executed on a computer, enables the computer to execute the method described in the above method embodiment.

[0243] 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 meets the thermal stability constraints on the basis of expanding the actual transmission capacity of the line, releasing the line transmission capacity potential, and improving the line availability on the basis of ensuring safety, so as to optimize the economic dispatch strategy. By linearizing the nonlinear constraints in the constraints, linearized AC power flow constraints and linearized line thermal stability constraints are obtained, and the power system economic dispatch model taking into account the thermal stability constraints is constructed 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.

[0244] It should be noted that the same or similar parts between the various embodiments can be referred to each other. As for the device and system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0245] For the sake of simplicity, the aforementioned embodiments are described as a series of action combinations. However, those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily required by this application.

[0246] Finally, it should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0247] The above description of the disclosed embodiments will enable one skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily apparent to one 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 is not limited to the embodiments shown herein, but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

[0248] The above is only a preferred embodiment 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 dispatch of power systems taking into account dynamic capacity expansion of power 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 constraints of the objective function based on parameters of the power system, wherein the constraints include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, wherein the linearized line thermal stability constraints take into account dynamic changes in line temperature; Solving a power system economic dispatch model to obtain an economic dispatch plan for the power system, wherein the power system economic dispatch model includes the objective function and the constraint conditions; 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; Discretizing the transient heat balance equation by a forward difference algorithm; The radiation heat dissipation, convection heat dissipation and circuit heating value in the transient heat balance equation are linearized respectively to obtain the linearized circuit thermal stability constraint.

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 based on 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 or 2, characterized in that Solving the power system economic dispatch model to obtain the power system economic dispatch plan includes: The power system economic dispatch model is solved using an optimization solver to obtain an economic dispatch plan for the power system.

4. An economic dispatching device for a power system taking into account dynamic capacity expansion of lines, characterized in that: The device comprises: Establishing a module for establishing an objective function with the goal of minimizing the unit operating cost of the power system; a determination module, configured to determine the constraint conditions of the objective function according to the parameters of the power system, wherein the constraint conditions include unit constraints, network variable constraints, linearized AC power flow constraints, and linearized line thermal stability constraints, wherein the linearized line thermal stability constraints take into account dynamic changes in line temperature; A solution module, configured to solve a power system economic dispatch model to obtain an economic dispatch plan for the power system, wherein the power system economic dispatch model includes the objective function and the constraint conditions; The determining module includes: a heat balance construction unit, configured to construct a transient heat balance equation for taking into account dynamic changes in line temperature according to parameters of the power system; The heat balance linearization unit is used to discretize the transient heat balance equation through a forward difference algorithm; linearize the radiation heat dissipation, convection heat dissipation and circuit heat generation in the transient heat balance equation respectively to obtain the linearized circuit thermal stability constraint.

5. The device according to claim 4, characterized in that The determining module includes: 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.

6. 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 3.

7. 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 3.

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