Power System Economic Dispatch Method Considering Line Dynamic Capacity Increase and Related Devices

Abstract

The present application provides a power system economic dispatch method and related device considering line dynamic capacity increase. The method establishes an objective function with the minimum operating cost of the units in the power system as the goal; determines the constraint conditions of the objective function according to the parameters of the power system; solves the economic dispatch model to obtain the square term of the current of each line in the power system; performs thermal stability verification on each line according to the square term of the current of each line to determine the over-limit lines; performs iterative solution on the power economic dispatch model to obtain the economic dispatch plan of the power system. The present application improves the calculation accuracy of the line temperature rise by determining the power adjustment rate constraint and considering the dynamic process of unit ramp-up in detail, and generates constraint iteration for the high-dimensional constraint set caused by considering the dynamic process of unit ramp-up by performing thermal stability verification on the solution result of the economic dispatch model, reducing the calculation complexity of the power system economic dispatch model and improving the solution speed and efficiency of the model.

Description

Technical Field

[0001] The present application relates to the technical field of electrical engineering, and particularly to an economic dispatch method and related devices for a power system considering line dynamic capacity increase. 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 on the premise of meeting the balance between supply and demand and various constraints.

[0003] Traditional economic dispatch methods usually use a conservative constant to specify the transmission capacity of a line, and this conservative constant 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, making the economic dispatch effect of the power system 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 and related devices for a power system considering line dynamic capacity increase, which can release the line transmission capacity. On the basis of ensuring safety, the economic dispatch model is optimized through line dynamic capacity increase, the power adjustment rate constraint considering the unit ramp dynamic is taken into account, and a constraint iteration generation strategy is adopted, which can improve the solution accuracy, solution speed and efficiency of the economic dispatch model considering dynamic capacity increase. The specific technical solutions are as follows:

[0005] 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:

[0006] Establish an objective function with the minimum operating cost of the units in the power system as the goal;

[0007] Determine the constraint conditions of the objective function according to the parameters of the power system, and the constraint conditions include unit constraints, network variable constraints, power adjustment rate constraints and linearized AC power flow constraints;

[0008] Solve the economic dispatch model to obtain the square terms of the currents of each line in the power system, and the economic dispatch model includes the objective function and the constraint conditions;

[0009] Perform thermal stability verification on each line according to the square terms of the currents of each line to determine the over-limit lines. The over-limit lines are the lines that do not pass the thermal stability verification, and the over-limit lines are used to determine the linearized line thermal stability constraints;

[0010] Iteratively solve the power economic dispatch model to obtain the economic dispatch plan of the power system, where the power economic dispatch model is obtained by adding the linearized line thermal stability constraint to the economic dispatch model.

[0011] In a possible implementation manner, the step of performing thermal stability verification on each line according to the square term of the current of each line to determine the over-limit line includes:

[0012] Perform steady-state thermal stability verification on each line according to the square term of the current of each line to obtain steady-state over-limit lines, where the steady-state over-limit lines are the lines that fail the steady-state thermal stability verification;

[0013] Use the square term of the current of the steady-state over-limit line to perform transient thermal balance calculation to obtain the final temperature of the line of the steady-state over-limit line;

[0014] Perform transient thermal stability verification on the steady-state over-limit line according to the final temperature of the line of the steady-state over-limit line to obtain the over-limit line.

[0015] In a possible implementation manner, determining the power adjustment rate constraint according to the parameters of the power system includes:

[0016] Construct a power adjustment rate equation for accounting for the ramp dynamic process according to the parameters of the power system;

[0017] Perform linearization processing on the power adjustment rate equation to obtain the power adjustment rate constraint.

[0018] In a possible implementation manner, determining the linearized line thermal stability constraint includes:

[0019] Calculate the linearized transient thermal balance equation based on the square term of the current of the over-limit line to obtain the linearized line thermal stability constraint, where the linearized transient thermal balance equation is constructed according to the parameters of the power system.

[0020] In a possible implementation manner, before performing thermal stability verification on each line according to the square term of the current of each line to determine the over-limit line, the method further includes:

[0021] Construct a transient thermal balance equation for accounting for the dynamic change of the line temperature according to the parameters of the power system;

[0022] Perform linearization processing on the transient thermal balance equation to obtain a linearized transient thermal balance equation.

[0023] In a second aspect, the present application further provides a power system economic dispatch device for accounting for line dynamic capacity increase, where the device includes:

[0024] A building module, configured to build an objective function with the minimum operating cost of the units in the power system as the objective;

[0025] A determination 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, power adjustment rate constraints, and linearized AC power flow constraints;

[0026] A model solving module, configured to solve the economic dispatch model to obtain the square term of the current of each line in the power system, where the economic dispatch model includes the objective function and the constraint conditions;

[0027] A verification module, configured to perform thermal stability verification on each line according to the square term of the current of each line, and determine the over-limit lines, where the over-limit lines are the lines that fail the thermal stability verification, and the over-limit lines are used to determine the linearized line thermal stability constraints;

[0028] An iterative solving module, configured to perform iterative solving on the power economic dispatch model to obtain the economic dispatch plan of the power system, where the power economic dispatch model is obtained by adding the linearized line thermal stability constraints to the economic dispatch model.

[0029] In a possible implementation manner, the verification module includes:

[0030] A steady-state verification unit, configured to perform steady-state thermal stability verification on each line according to the square term of the current of each line, and obtain the steady-state over-limit lines, where the steady-state over-limit lines are the lines that fail the steady-state thermal stability verification;

[0031] A transient calculation unit, configured to perform transient thermal balance calculation by using the square term of the current of the steady-state over-limit lines to obtain the final temperature of the lines of the steady-state over-limit lines;

[0032] A transient verification unit, configured to perform transient thermal stability verification on the steady-state over-limit lines according to the final temperature of the lines of the steady-state over-limit lines to obtain the over-limit lines.

[0033] In a possible implementation manner, the determination module includes:

[0034] A ramp dynamic construction unit, configured to construct a power adjustment rate equation for accounting for the ramp dynamic process according to the parameters of the power system;

[0035] A ramp dynamic linearization unit, configured to perform linearization processing on the power adjustment rate equation to obtain the power adjustment rate constraint.

[0036] In a third aspect, the present application further provides a computer device, including: a memory and a processor;

[0037] Among them, the memory is used to store computer programs;

[0038] The processor is used to execute the computer programs in the memory to implement the method described in the first aspect or any item of the first aspect above.

[0039] In a fourth aspect, the present application also provides a computer-readable storage medium storing instructions that, when run on a computer, cause the computer to execute the method described in the first aspect or any item of the first aspect above.

[0040] 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, power adjustment rate constraints, and linearized AC power flow constraints; the economic dispatch model is solved to obtain the square terms of the currents of each line in the power system, and the economic dispatch model includes the objective function and the constraint conditions; the thermal stability of each line is verified according to the square terms of the currents of each line to determine the over-limit lines, and the over-limit lines are the lines that fail the thermal stability verification, and the over-limit lines are used to determine the linearized line thermal stability constraints; the power economic dispatch model is iteratively solved to obtain the economic dispatch plan of the power system, and the power economic dispatch model is obtained by adding the linearized line thermal stability constraints to the economic dispatch model. By determining the power adjustment rate constraints and considering the dynamic process of unit ramp-up in detail, the present application can improve the calculation accuracy of line temperature rise. By constructing the power system economic dispatch model into a mixed-integer linear programming model and performing thermal stability verification on the solution results of the economic dispatch model, and generating constraint iterations for the high-dimensional constraint set caused by considering the dynamic process of unit ramp-up, the model solution can be accelerated. Description of the Drawings

[0041] 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. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0042] Figure 1 Shows a flowchart of a power system economic dispatch method considering line dynamic capacity increase provided by an embodiment of the present application;

[0043] Figure 2 Shows a schematic diagram of the unit ramp-up process provided by an embodiment of the present application;

[0044] Figure 3 Shows what is provided by an embodiment of the present application Schematic diagram of the piecewise linearization strategy of the function curve;

[0045] Figure 4 Shows a schematic diagram of the piecewise linearization strategy for the square term of the voltage squared difference provided by an embodiment of the present application;

[0046] Figure 5 Shows a schematic diagram of the line temperature curve obtained by the steady-state heat balance equation and the transient heat balance equation provided by an embodiment of the present application;

[0047] Figure 6 Shows a flowchart of the constraint iteration generation strategy provided by an embodiment of the present application;

[0048] Figure 7 Shows a schematic diagram of the network topology of the IEEE 39-bus system provided by an embodiment of the present application;

[0049] Figure 8 Shows a schematic diagram of the line temperature rise curves considering and not considering the ramping process provided by an embodiment of the present application;

[0050] Figure 9 Shows a schematic diagram of the structure of a power system economic dispatch device considering line dynamic rating provided by an embodiment of the present application. Detailed implementation manners

[0051] 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. Apparently, 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 of the present application without creative efforts shall fall within the protection scope of the present application.

[0052] Power system economic dispatch refers to a dispatch method that rationally utilizes energy and equipment to ensure reliable power supply to users at the lowest generation cost or fuel cost on the premise of meeting safety and power quality. Economic dispatch is a typical optimization problem that requires reasonable allocation of unit power under the conditions of meeting demand and various constraints to ensure the lowest operating cost.

[0053] 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 conservative constant only represents the safe transmission capacity under multiple typical working conditions. Under specific working 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 rating the line can optimize the economic dispatch strategy, which is of great significance for the safe, economic, and flexible operation of the power system.

[0054] The line dynamic capacity increase technology utilizes the thermal inertia effect of the transmission line. According to the meteorological data obtained by the micro-meteorological sensors and the actual operating conditions of the power system, the thermal 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. 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, optimize the economic dispatch strategy on the basis of ensuring safety, and enhance the operation flexibility of the power system.

[0055] In the prior art, an overload control strategy for an AC-DC hybrid power grid is proposed to ensure the operation economy and safety of the power grid and effectively avoid the occurrence of cascading tripping accidents in the hybrid power grid. The specific steps of the proposed control strategy are as follows:

[0056] Step 1: Judging the power flow over-limit and selecting the variables to be controlled, determining the set of power flow over-limit lines, and further determining the variables to be controlled for emergency control.

[0057] For the set of power flow over-limit lines, the line current over-limit index is introduced for judgment:

[0058] .

[0059] In the formula, is the active power of the line corresponding to nodes and after the accident, is the rated active power of the line. The larger the value, the more active power flows through the line. When , it indicates that the line current is over-limit.

[0060] According to , after the accident of the AC-DC hybrid power grid, by quickly estimating the power flow and comparing it with the upper limit value of the power flow, all the AC line sets in the power grid can be screened and divided into two types: the set of power flow over-limit lines SL1 and the non-over-limit line set SL0.

[0061] For the variables to be controlled, the following method is adopted for selection:

[0062] After the accident of the AC-DC hybrid power grid, the PQ decoupling algorithm can be used to quickly estimate the power flow after the accident:

[0063] ;

[0064] .

[0065] In the formula, is the unbalanced vector of the active power of the node, is the node voltage, is the coefficient matrix in the active power-phase angle (P-θ) iterative correction, is the correction vector of the node voltage phase angle, is the unbalanced vector of the reactive power of the node, is the coefficient matrix in the reactive power-voltage (Q-U) iterative correction, is the increment, is the correction vector of the node voltage amplitude. Since the DC injection power is independent of the phase angle of the node voltage, so is consistent with the calculation of the traditional AC system, but it will cause an increment and the specific increment can derive the calculation formula from different control methods of the DC system.

[0066] Furthermore, to improve the optimization efficiency of overload control, the power transmission distribution factors (PTDF) are introduced to reduce the control variables, and the generators and loads with good power flow control effects on the power flow over-limit line set SL1 are selected as control variables.

[0067] Then, the infinite norm set of the power transmission distribution factor vector is obtained. The nodes included in this set are the generator unit nodes and load nodes with the best power flow control effects on each over-limit line in the power flow over-limit line set SLl. The union of the infinite norm sets corresponding to multiple over-limit lines is taken to obtain the generator unit node set and the load shedding node set with the optimal control effects on all over-limit lines in the power flow over-limit line set SLl.

[0068] Step 2: Take the post-accident overload control as the research object and construct an overload control model for the AC-DC hybrid power grid.

[0069] The control objective is to take measures such as adjusting the active power of the generator sets, adjusting the sound DC power, and cooperating with load shedding if necessary after the accident to achieve power balance and finally block the power flow transfer. The objective function is divided into the active power control cost of the generator sets, the control cost of the sound DC participating in control, and the load shedding control cost.

[0070] Among them, the active power control cost of the generator sets is:

[0071] .

[0072] In the formula, is the set of generator unit nodes participating in overload control, is the generator unit at Active power output at a moment, is the constant term coefficient of the active power control cost of the generator unit, is the first-order term coefficient of the active power control cost of the generator unit, is the second-order term coefficient of the active power control cost of the generator unit, is the initial moment of control, is the end moment of control, , is the overload control time interval, is the differential of the time variable.

[0073] Sound DC participation control cost is:

[0074] .

[0075] In the formula, is the set of generator unit nodes included in the DC system that still operates soundly after the accident, is the active power output of the sound DC node or DC converter station at moment, is the control cost of the DC active power. Generally, the sound DC control cost should be less than the active power control cost of the generator unit .

[0076] Load shedding control cost is:

[0077] .

[0078] In the formula, is the set of load shedding nodes participating in the overload control, is the active power cut-off amount of the load node at moment, is the cut-off equivalent cost of different load shedding nodes , which can reflect the economic losses and liability compensation caused by load shedding. Load nodes refer to all nodes connected to loads, and load shedding nodes refer to the load nodes where load shedding measures are taken.

[0079] For the above multi-objective function, the weighted summation method is used to transform the multi-objective function into a single-objective function for processing, with the goal of minimizing the overall control cost, that is:

[0080] .

[0081] In the formula, represents the minimum value of the overall control cost, is the weight factor of the active power control cost of the generator unit, To improve the weight factor of the cost of DC participation in control, which is the weight factor of the cost of load shedding control. The judgment matrix method can be used to assign different weights to the active power control cost of generator units, the cost of sound DC participation in control, and the cost of load shedding control.

[0082] The constraint conditions of the objective function include equality constraints and inequality constraints. Among them, the equality constraints include the node power balance equation of the AC-DC hybrid power grid, the resistance-current equation considering the dynamic thermal characteristics of the transmission line, and the dynamic thermal balance state equation of the transmission line; the inequality constraints include the security constraints of the AC-DC hybrid power grid, the overload control quantity constraints, the safe operation constraints of the transmission line, and the power adjustment rate constraints.

[0083] By solving the optimization model composed of the objective function and the constraint conditions, the overload control strategy of the AC-DC hybrid power grid can be obtained, so that the line meets the thermal stability constraints.

[0084] Although the existing technology takes into account the power adjustment rate constraint, it does not consider the detailed dynamic process of unit ramp-up, and the calculation accuracy of line temperature rise needs to be improved; when considering the dynamic process of unit ramp-up, the constraint iteration generation strategy is not considered, so it is difficult to obtain an accurate solution with a fast solution speed. And the models constructed by the existing technology are mostly non-convex and non-linear models, and often use non-linear interior point methods, heuristic algorithms, etc. to solve, and it is difficult to obtain the global optimal solution.

[0085] Therefore, the embodiment of the present application provides an economic dispatch method for a power system. For short-time scale scenarios, the minute-level unit ramp-up dynamic process is considered in detail and modeled in a linear form, and constraint iteration generation is performed for the high-dimensional line transient thermal balance constraint set caused by considering the unit ramp-up dynamic, that is, the line thermal stability constraint is iteratively added to the economic dispatch model that does not consider the line thermal stability constraint. In this way, while improving the calculation accuracy of line temperature rise, the model solution is accelerated.

[0086] Please refer to Figure 1 , which shows the flowchart of an economic dispatch method for a power system considering line dynamic capacity increase provided by the embodiment of the present application. The embodiment of the present application at least includes the following steps:

[0087] S11. Establish an objective function with the minimum operating cost of the units in the power system as the goal.

[0088] In the embodiment 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.

[0089] The expression of the objective function is as follows:

[0090] (1)

[0091] In formula (1), is the scheduling discretization period, is the set of scheduling discretization periods, is the unit at the active power output at the moment, is the set of units, 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, is the discretization moment, which is used to divide the scheduling discretization period into finer time intervals. The discretization time interval of can be set according to the actual scenario. As an example, the discretization time interval of can be 15 minutes (min). If the discretization time interval of is 15 min, the discretization time interval of

[0092] In the embodiments of the present application, the objective function can be established according to the parameters of the power system. The , and corresponding to different units can be the same or different. The parameters of the power system can include the generator cost coefficients corresponding to different units (i.e., , and ).

[0093] In the embodiments 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 embodiments of the present application do not make limitations. It should be noted that the objective function in the economic dispatch model and the power economic dispatch model of the embodiments of the present application is the linearized objective function.

[0094] S12. Determine the constraint conditions of the objective function according to the parameters of the power system.

[0095] After establishing the objective function, the constraint conditions of the objective function can be determined according to the parameters of the power system. In the embodiments of the present application, the constraint conditions without considering the transient thermal stability constraints of the lines may include unit constraints, network variable constraints, power adjustment rate constraints, and linearized AC power flow constraints.

[0096] The parameters of the power system may include generator parameters, network parameters, and load parameters. The network parameters may include line parameters and node parameters. In a power system, nodes usually represent substations or load points, and these nodes are interconnected through transmission lines (i.e., lines) to jointly form the network structure of the power system.

[0097] The generator parameters may 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 may also include the generator cost coefficient corresponding to each generator.

[0098] The line parameters may 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).

[0099] The node parameters may include the upper limit of the square of the voltage and the lower limit of the square of the voltage of each node.

[0100] The load parameters may include active load and reactive load, both in MW.

[0101] As a possible implementation, the embodiments of the present application determine the constraint conditions of the objective function according to the parameters of the power system, which may include the following steps:

[0102] S121, determine the unit constraints.

[0103] 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:

[0104] (2)

[0105] (3)

[0106] In formulas (2) and (3), is the minimum active power output of the unit , is the active power output of the unit at time, is the maximum active power output of the unit , is the minimum reactive power output of the unit , is the unit The reactive power output at moment, is the maximum reactive power output of the unit .

[0107] S122, determine the network variable constraints.

[0108] 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:

[0109] (4)

[0110] (5)

[0111] In formulas (4) and (5), is the lower limit of the square of the voltage at node , is the voltage at node at moment, is the upper limit of the square of the voltage at node , is the lower limit of the phase angle difference from node to node , is the phase angle difference from node to node at moment, is the upper limit of the phase angle difference from node to node .

[0112] S123, determine the linearized AC power flow constraints.

[0113] The conventional power flow constraints are non-convex and non-linear constraints, making it difficult to directly obtain the global optimal solution. Therefore, the embodiments of the present application construct a linearized AC power flow model with the square of the voltage as the variable.

[0114] The expressions of the linearized AC power flow constraints are as follows:

[0115] (6)

[0116] (7)

[0117] In formulas (6) and (7), is the set of generators belonging to node , is the active power output of the unit at moment, is the load set subordinate to node . is the active power load of load d at time is the conductance of line . is the voltage of node at time is the voltage of node at time is the susceptance of line . is the phase angle difference from node to node at time is the reactive power output of unit at time is the reactive power load of load d at time is the total number of nodes, line is the line flowing from node to node . Node n is any node in the power system, and node i and node j are node pairs with a line connection in the power system.

[0118] S124, determine the power adjustment rate constraint.

[0119] For short-term real-time scheduling, a series of processes such as economic dispatch plan formulation, dispatch instruction issuance, unit output adjustment, and unit output maintenance are required. The time scale of each process is on the order of minutes. Generally speaking, the time constant of the line transient thermal balance equation is about 10 minutes, also on the order of minutes. Therefore, it is necessary to consider the specific ramping process of the unit to match the time scale of the line temperature rise.

[0120] In real-time scheduling, the specific ramping process of the unit is as shown in Figure 2 . For the real-time scheduling scenario, when the dynamic ramping process of the unit is not considered, at each dispatch instruction execution time, the unit output changes stepwise, which does not conform to the actual situation. Among them, the dispatch instruction execution time is as shown in Figure 2 in time. The dynamic ramping process of the unit refers to the process in which the unit changes from the starting output value to the given output value, and can also be understood as the process in which the unit transitions from one steady state to another steady state. In this process, the output power of the unit needs to increase gradually. When the dynamic ramping process of the unit is considered, the dynamic ramping process of the unit can be divided into the following two stages:

[0121] Output adjustment stage: After the scheduling instruction is issued and executed, the unit makes output adjustments. Due to the ramp rate limit, the unit needs a period of time to ramp up to the target output value set by the scheduling instruction.

[0122] Output holding stage: After the active power output of the unit is adjusted to the target output value, the unit enters the output steady state stage. At this time, the active power output of the unit no longer changes until the next scheduling instruction is issued.

[0123] Combining the output adjustment stage and the output holding stage, the power adjustment rate constraint can be determined, including:

[0124] S1241. Construct a power adjustment rate equation considering the ramp dynamic process according to the parameters of the power system.

[0125] The expression of the power adjustment rate equation considering the ramp dynamic process is as follows:

[0126] (8)

[0127] (9)

[0128] (10)

[0129] In equations (8) to (10), is the lower limit of the ramp slope of the unit, is the unit at the ramp slope during the period, is the upper limit of the ramp slope of the unit, is the unit at the active power output during the period, is the unit at the active power output during the period, is the unit at the active power output at the moment. can be understood as the target output value set in the scheduling instruction. In the embodiments of the present application, the ramp rate of each unit remains unchanged during the output adjustment stage in the period. Taking the discretization time interval of as 15 minutes for illustration, within the 15-minute output adjustment stage, the ramp rate of the unit is the same per minute.

[0130] For the real-time scheduling period , the total time experienced by the output adjustment stage is , and the total time experienced by the output holding stage is , if has a discretized time interval of 15 min, then take 15 min. Equation (8) is the constraint on the range of the unit ramp rate, Equation (9) is the constraint on the ramp power of the unit at each moment, and Equation (10) is the constraint on the critical moment between the output adjustment stage and the output holding stage.

[0131] S1242, linearize the power adjustment rate equation to obtain the power adjustment rate constraint.

[0132] Equations (9) and (10) of the power adjustment rate equation are non - linear terms. Therefore, it is necessary to linearize Equations (9) and (10).

[0133] Linearize Equation (9):

[0134] Transform the expression of Equation (9) into:

[0135] (11)

[0136] (12)

[0137] Introduce 0 - 1 auxiliary variables 、 、 into Equation (11), and introduce 0 - 1 auxiliary variables 、 、 into Equation (12) for equivalent transformation. , indicating that A is a sufficient condition for B.

[0138] Equation (11) is equivalently transformed into:

[0139] (13)

[0140] Equation (12) is equivalently transformed into:

[0141] (14)

[0142] Introduce minimum values, sufficiently large values, and sufficiently small values into Equations (13) and (14) for further equivalent transformation.

[0143] Equation (13) is further equivalently transformed into:

[0144] (15)

[0145] Equation (14) is further equivalently transformed into:

[0146] (16)

[0147] In formulas (15) and (16), is a minimum value used to transform the less-than sign into a less-than-or-equal-to sign and the greater-than sign into a greater-than-or-equal-to sign. The value of can be set according to the actual scenario. As an example, can be taken as . , , , are sufficiently large values. , , , are sufficiently small values. , , , , , , , The values of can be set according to the actual scenario. As an example, in the embodiments of the present application, the values of , , , , , , , are as follows:

[0148] (17)

[0149] Perform a linearization process on formula (10):

[0150] Transform the expression of formula (10) into:

[0151] (18)

[0152] In formula (18), is the product of two consecutive variables. There are definite upper and lower bounds. Therefore, perform a binary expansion approximation on :

[0153] (19)

[0154] In formula (19), are all 0-1 auxiliary variables used to perform a binary expansion approximation on . The value of can be set according to the actual scenario. As an example, in the embodiments of the present application, is taken as .

[0155] At this time, can be transformed into the sum of products of several 0-1 auxiliary variables ( ) and continuous variables ( ):

[0156] (20)

[0157] For the product of the 0-1 auxiliary variable and the continuous variable in Equation (20), taking as an example, it can be linearized using the following strategy:

[0158] (21)

[0159] In Equation (21), is a value large enough, is an auxiliary continuous variable introduced for linearization, The value of can be set according to the actual scenario. As an example, in the embodiments of the present application, is taken.

[0160] Combining the above process, the dynamic process of unit ramp can be modeled to reach the minute level, so as to reach the same time scale as the transient thermal balance equation. In addition, the relevant constraints of the unit ramp dynamics are all modeled as linear constraints. The finally obtained power adjustment rate constraints can include Equation (8), Equation (15), Equation (16), Equation (17), Equation (20) and Equation (21).

[0161] S13. Solve the economic dispatch model to obtain the square term of the current of each line in the power system.

[0162] After S11 and S12, the embodiments of the present application can obtain an economic dispatch model. The economic dispatch model can include an objective function and constraint conditions without considering the transient thermal stability constraints of the line, that is, the economic dispatch model of the embodiments of the present application can include Equation (1) to Equation (5), Equation (8), Equation (15) to Equation (17), Equation (20) and Equation (21).

[0163] By constructing the objective function and determining the constraint conditions, the economic dispatch model of the embodiments of the present application is a mixed-integer linear programming model (Mixed-Integer Linear Programming, MILP), which can handle complex problems that contain both continuous variables and integer variables, and can ensure that the solution satisfies the integer constraints, thereby improving the accuracy of decision-making.

[0164] The embodiments of the present application solve the economic dispatch model to obtain the square term of the current of the line in the power system , thereby obtaining the squared current term for each line. The solution method for the economic dispatch model can be set according to the actual scenario. As an example, embodiments of the present application can use an optimization solver to solve the economic dispatch model. The optimization solver can be Cplex, Gurobi, etc. Both Cplex and Gurobi can efficiently solve linear programming, mixed integer programming, quadratic programming, quadratically constrained programming, and constraint programming problems.

[0165] S14, performing thermal stability check on each circuit according to the square term of the current of each circuit, and determining the circuit that exceeds the limit.

[0166] After obtaining the squared current term for each circuit, embodiments of the present application can perform a thermal stability check on each circuit based on the squared current term to identify out-of-limit circuits. Out-of-limit circuits are circuits that fail the thermal stability check. The thermal stability check can include steady-state thermal stability check and transient thermal stability check. Out-of-limit circuits can be used to determine linearized thermal stability constraints.

[0167] In order to dynamically adjust the maximum transmission capacity of the line to adapt to real-time operating conditions, it is necessary to consider the dynamic capacity expansion of the line when generating the economic dispatch plan. To this end, the embodiment of the present application can use the transient heat balance equation to describe the dynamic temperature change process of the line. If the linearized transient heat balance equation is directly added to the constraints of the economic dispatch model, it will form a high-dimensional constraint set, which will slow down the solution of the economic dispatch model. Therefore, the embodiment of the present application provides a constraint iteration generation strategy to accelerate the solution of the economic dispatch model.

[0168] Next, we will introduce transient heat balance.

[0169] For lines , a transient heat balance equation can be constructed based on the parameters of the power system to take into account the dynamic changes in line temperature. The expression of the transient heat balance equation after forward difference is as follows:

[0170] (twenty two)

[0171] (twenty three)

[0172] In formula (22) and formula (23), for Timeline The line temperature, For the line The line quality, For the line The circuit specific heat capacity, is the differencing step size, for Timeline The radiation heat dissipation, is the convective heat dissipation of the line at time , is the solar heat absorption of the line is the heat generation of the line at time , is the line current of the line at time , is the AC resistance of the line is the upper limit of the line temperature. Equation (22) is the transient heat balance equation in forward difference form, and Equation (23) is the line temperature constraint.

[0173] The transient heat balance equation has a non - linear term. Therefore, it is necessary to linearize the transient heat balance equation to obtain a linearized transient heat balance equation. Further, the radiative heat dissipation, convective heat dissipation, solar heat absorption, and heat generation of the line are expanded, and the radiative heat dissipation, convective heat dissipation, and heat generation of the line are linearized, converting the transient heat balance equation in forward difference form into a first - order linear difference equation.

[0174] 1) Radiative heat dissipation

[0175] The expression of the radiative heat dissipation is as follows:

[0176] (24)

[0177] In Equation (24), is the outer diameter of the conductor of the line is the radiative heat dissipation coefficient of the conductor surface of the line is the line temperature of the line at time , is the ambient temperature. Generally speaking, the line models in the power system are the same. Therefore, it can be considered that the outer diameters of the conductors and the radiative heat dissipation coefficients of the conductor surfaces of each line are the same. It should be noted that within the scheduling period , the ambient temperature is a fixed value and can be set according to the actual scenario. In different scheduling periods, the ambient temperature may be the same or different.

[0178] When the external meteorological factors are given, the radiative heat dissipation is a quartic function of the conductor temperature, and the radiative heat dissipation can be linearly segmented. The external meteorological factors can include ambient temperature, solar radiation intensity, wind speed, and the angle between the wind and the conductor, etc.

[0179] The piecewise linearized expression of the radiative heat dissipation is as follows:

[0180] (25)

[0181] In Equation (25), is the line temperature of line at time is the lower limit of the line temperature of the line taken for piecewise linearization. In the embodiments of the present application, can be set according to the actual situation. Exemplarily, can be set to 0 , is the slope value of the th segment of the function curve, is the value of the temperature increment of the th segment of the function curve, is the 0-1 auxiliary variable introduced for the piecewise linearization of the th segment of the function curve, is the width of the segmentation interval of the th segment of the function curve, is the upper limit of the line temperature of the line taken for piecewise linearization. In the embodiments of the present application, can be set according to the actual situation. Exemplarily, can be set to 90 . is always greater than 0. Therefore, the function curve only takes the part where is greater than 0. The piecewise linearization strategy of the function curve is as shown in Figure 3 . 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 has symmetry, then the value of

[0182] 2) Convective heat dissipation

[0183] The expression of the convective heat dissipation is as follows:

[0184] (26)

[0185] (27) ​​​​

[0186] (28)

[0187] In Equations (26), (27), and (28), 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 Reynolds number, is the outer diameter of the wire, is the wind speed, is the line convective heat dissipation in a low wind speed environment, is the line convective heat dissipation in a high wind speed environment, is the line convective heat dissipation in a zero wind speed environment, is the line convective heat dissipation. Take , and the maximum value among them.

[0188] For in Equation (27), and , linearized approximations can be adopted, and the specific expressions are as follows:

[0189] (29)

[0190] In Equation (29), is the convective heat dissipation at low wind speed when the line temperature is taken as , is the convective heat dissipation at low wind speed when the line temperature is taken as , is the convective heat dissipation at high wind speed when the line temperature is taken as , is the convective heat dissipation at high wind speed when the line temperature is taken as , is the convective heat dissipation at zero wind speed when the line temperature is taken as , is the convective heat dissipation at zero wind speed when the line temperature is taken as . Further, for the maximum value constraint of Equation (28), the maximum value constraint can be linearized by introducing a 0-1 auxiliary variable, and the linearized expression of the maximum value constraint is as follows:

[0191] (30)

[0192] In formula (30), is an introduced 0-1 auxiliary variable, is a relatively large constant introduced for linearization.

[0193] 3) Heat absorption due to sunlight

[0194] The expression of the heat absorption due to sunlight is as follows:

[0195] (31)

[0196] In formula (31), is the heat absorption coefficient, is the sunlight intensity, is the outer diameter of the wire.

[0197] It can be seen from the expression of the heat absorption due to sunlight that the heat absorption due to sunlight is independent of the wire temperature. When the sunlight intensity is given, the heat absorption due to sunlight is a constant.

[0198] 4) Heat generation of the line

[0199] AC resistance The expression of

[0200] (32)

[0201] In formula (32), is the skin effect coefficient, is the conductor temperature effect coefficient, is the line at the line temperature at the moment, is the DC resistance of the wire.

[0202] Taking a conservative assumption for the expression of the AC resistance, let , then there is:

[0203] (33)

[0204] The square term of the current of the line The expression of

[0205] (34)

[0206] In formula (34), is the conductance of the line , is the line ​The electrical susceptance, For nodes exist The voltage at the moment, For nodes exist The voltage at the moment, For Time from node To Node The phase angle difference, for Time Node The phase angle, for Time Node The phase angle of . The conversion process is as follows:

[0207] (35)

[0208] Therefore, the expression of the circuit heat generation can be obtained: The expression is as follows:

[0209] (36)

[0210] There are two square terms of variables in formula (36), namely and The embodiment of the present application can use piecewise linearization processing and .by For example, the specific piecewise linearization strategy is as follows Figure 4 As shown, The voltage square term and Linear combination transformation.

[0211] Squared term of the voltage squared difference The piecewise linearization expression of is as follows:

[0212] (37)

[0213] In formula (37), For nodes exist The voltage at the moment, For nodes exist The voltage at the moment, For nodes The lower voltage limit, For nodes The upper voltage limit, For nodes The lower voltage limit, is the voltage upper limit for 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 th segment piecewise linearization 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 ; is the voltage of node

[0214] The squared term of the phase angle difference has the following piecewise linearization expression:

[0215] (38)

[0216] In Equation (38), is the lower limit of the phase angle difference from node to node ; is the phase angle difference from node to node at time ; 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 the 0-1 auxiliary variable introduced for the th segment piecewise linearization of the function curve; is the width of the segment interval of the th segment of the function curve. The piecewise linearization strategy of the function curve is similar to that of the function curve and can be referred to ; see Figure 4Understand.

[0217] Through the above process, the radiation heat dissipation, convection heat dissipation, and line heat generation are all converted to linear form, and the solar heat absorption is converted to a constant term. At this point, the transient heat balance equation in forward difference form is converted to a linearized difference equation. The embodiments of the present application linearize the transient heat balance equation in forward difference form, which can improve the convergence speed during solution to meet real-time requirements.

[0218] During the research process, it was found that steady-state thermal stability verification can be used as a pre-filtering method for transient thermal stability verification. Figure 5 The line temperature curves calculated using the steady-state heat balance equation and the transient heat balance equation are shown under the real-time scheduling time scale of 15 minutes. Figure 5 It can be seen that the line temperature obtained from the steady-state heat balance equation undergoes a step change at each scheduling moment, while the line temperature obtained from the transient heat balance equation can reflect the dynamic change process of the line temperature.

[0219] On the one hand, given environmental parameters and line current, the solution to the steady-state heat balance equation provides an upper bound for the transient heat balance equation during the line temperature rise process. That is, for a short time scale of 15 minutes, the temperature calculated by the steady-state heat balance equation is greater than or equal to the temperature calculated by the transient heat balance equation, where the temperature calculated by the transient heat balance equation is consistent with the actual situation. On the other hand, the steady-state heat balance equation is calculated faster than the transient heat balance equation. To this end, using steady-state thermal stability verification as a pre-filter for transient thermal stability verification can obtain a more conservative and rapid solution. This means that lines with high line temperatures can be quickly filtered out, avoiding the need to perform transient thermal stability verification on all lines, thereby improving the efficiency of thermal stability verification.

[0220] Therefore, in one possible implementation, performing thermal stability verification on each circuit based on the square term of the current of each circuit to determine the circuit that exceeds the limit may include:

[0221] S141, performing steady-state thermal stability verification on each line according to the square term of the current of each line to obtain a steady-state over-limit line.

[0222] After obtaining the squared term of the current of each circuit, the embodiment of the present application can perform a steady-state thermal stability check on each circuit to obtain a steady-state over-limit circuit. The steady-state over-limit circuit is a circuit that fails the steady-state thermal stability check.

[0223] First, the verification criteria for the steady-state thermal stability of the line are analyzed.

[0224] In the steady-state heat balance equation, the radiation heat dissipation, convection heat dissipation and AC resistance values are When the value of

[0225] (39)

[0226] In formula (39), is the maximum allowable current that the line can carry under given external meteorological conditions, is the line temperature of the line , is the upper limit of the line temperature, is when the radiant heat dissipation, is when the convective heat dissipation, is when the AC resistance value, is the solar heat absorption. External meteorological factors can include ambient temperature, solar radiation intensity, wind speed, and the angle between the wind and the conductor, etc.

[0227] Therefore, the steady-state thermal stability check of the line is as follows: When is satisfied, the line passes the steady-state heat balance equation check; otherwise, the line does not pass the steady-state heat balance equation check. That is to say, at any moment , the current flowing through the line is not greater than the maximum allowable current .

[0228] The above analyzes the check criterion of the steady-state heat balance equation. Further, during the dynamic process of unit ramp-up, the current of the line will change. Therefore, for a real-time scheduling period , the embodiments of the present application use the following expression as the check criterion for the steady-state thermal stability of the line:

[0229] (40)

[0230] Formula (40) means that for each moment in the scheduling period , the square term of the current of the line is calculated, and the maximum value is obtained. This maximum value is compared with the square term of the maximum allowable current of the steady-state heat balance equation. If is not greater than , then the line Through steady-state thermal stability verification, the steady-state current of the line does not exceed the limit at this time. If is greater than , then the line fails the steady-state thermal stability verification. At this time, the steady-state current of the line exceeds the limit, and the line is a steady-state over-limit line. After obtaining the steady-state over-limit line, add the steady-state over-limit line to the steady-state over-limit set .

[0231] S142, use the square term of the current of the steady-state over-limit line to perform transient thermal balance calculation to obtain the final temperature of the line of the steady-state over-limit line.

[0232] S143, perform transient thermal stability verification on the steady-state over-limit line according to the final temperature of the line of the steady-state over-limit line to obtain the over-limit line.

[0233] For the steady-state over-limit set that fails the steady-state thermal stability verification, perform transient thermal stability verification. Substitute the square term of the current of the steady-state over-limit line into the transient thermal balance equation, calculate the transient temperature rise process, and obtain the line temperature at the end of a dispatching period (such as 15 min) of the steady-state over-limit line, and compare it with the upper limit of the line temperature. Finally, add the temperature over-limit line to the transient over-limit set .

[0234] The criteria for transient thermal stability verification of the line include Equations (22) to (27), Equations (29) to (31), and Equations (36) to (38). Through the transient thermal balance equations (22), (24) to (27), (29) to (31), and (36) to (38) by forward difference method, calculate the temperature flowing through the line at each discretized time ; then through Equation (23), verify (such as 15 min) of the line temperature whether it exceeds the limit. If (such as 15 min) of the line temperature there is no temperature over-limit, then the line passes the transient thermal stability verification. If of the line temperature there is a temperature over-limit, it means that the line has a transient temperature over-limit and fails the transient thermal stability verification. Add the line to the transient over-limit set . The lines in the transient over-limit set are over-limit lines. The final temperature of the line is (such as 15 min) of the line temperature.

[0235] Compared with the transient thermal balance equation, the steady-state thermal balance equation has a simpler calculation method and a faster verification speed. Therefore, in the embodiments of the present application, for all lines in the power system, the steady-state thermal balance equation is first used for constraint and rapid pre-verification, and then for the lines that do not pass the steady-state thermal stability verification (i.e., the set ), the transient thermal balance equation is further used for strict verification, which can improve the line verification efficiency.

[0236] If the set and / or the set is empty, the solution result of the economic dispatch model is used as the economic dispatch plan of the power system.

[0237] If the set is not empty, the linearized line thermal stability constraints corresponding to each line in the set are added to the constraint conditions of the economic dispatch model. The linearized line thermal stability constraints corresponding to each line in the set are obtained by substituting the square terms of the current of each line in the set [[ID=--]]into equations (22) to (27), (29) to (31), and (36) to (38).

[0238] In the embodiments of the present application, by performing thermal stability verification on the lines, the over-limit situation of the lines can be determined. If a line fails the thermal stability verification, the linearized line thermal stability constraint corresponding to the line is added to the economic dispatch model to form an iteration until all lines pass the thermal stability verification. The constraint iteration generation strategy is as Figure 6 shown.

[0239] S15. Iteratively solve the power economic dispatch model to obtain the economic dispatch plan of the power system. The power economic dispatch model is obtained by adding the linearized line thermal stability constraint to the economic dispatch model.

[0240] It should be noted that there seems to be an error in the original text where the placeholder "[[ID=--]]" is used. It should probably be a correct ID number. Also, this translation is based on the best understanding of the context with the given text.After performing thermal stability verification on each line, if there are lines that fail the thermal stability verification, the linearized line thermal stability constraints of the lines that fail the thermal stability verification are added to the economic dispatch model to obtain the power economic dispatch model. The power economic dispatch model is solved to obtain the square terms of the currents of each line in the power system. Then, based on the square terms of the currents of each line, thermal stability verification is performed on each line to determine the over-limit lines. That is, after adding the linearized line thermal stability constraints of the over-limit lines to the economic dispatch model, steps S13 to S15 are repeatedly executed to obtain multiple power economic dispatch models. The linearized line thermal stability constraints of different power economic dispatch models are different until there are no over-limit lines, forming an iterative generation of constraint conditions, and the final power economic dispatch model is solved to obtain the economic dispatch plan of the power system. In the embodiments of the present application, the economic dispatch model including the linearized line thermal stability constraints is used as the power economic dispatch model. Among them, the linearized line thermal stability constraints are determined based on the over-limit lines. The linearized transient thermal balance equation is calculated based on the square terms of the currents of the over-limit lines, that is, the square terms of the currents of the over-limit lines are substituted into the linearized transient thermal balance equation to obtain the linearized line thermal stability constraints. The linearized transient thermal balance equation may include Equations (22) to (27), Equations (29) to (31), and Equations (36) to (38).

[0241] Obtain the square terms of the currents of each line from the economic dispatch plan of the power system, and execute S114 until the set and / or the set is empty, then the final economic dispatch plan of the power system is obtained.

[0242] The linearized line thermal stability constraints of the lines that fail the thermal stability verification are added to the economic dispatch model to obtain the power economic dispatch model. The power economic dispatch model is still a MILP. The solution method for the power economic dispatch model can be set according to the actual scenario. As an example, in the embodiments of the present application, an optimization solver can be used to solve the power economic dispatch model, and the optimization solver can be Cplex, Gurobi, etc.

[0243] In the embodiments of the present application, an objective function is established with the goal of minimizing the operating cost of the units in the power system; 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, power adjustment rate constraints, and linearized AC power flow constraints; the economic dispatch model is solved to obtain the square term of the current of each line in the power system, and the economic dispatch model includes the objective function and the constraint conditions; the thermal stability of each line is verified according to the square term of the current of each line, and the over-limit lines are determined. The over-limit lines are the lines that fail the thermal stability verification, and the over-limit lines are used to determine the linearized line thermal stability constraints; the power economic dispatch model is iteratively solved to obtain the economic dispatch plan of the power system. The power economic dispatch model is obtained by adding the linearized line thermal stability constraints to the economic dispatch model. In the embodiments of the present application, by determining the power adjustment rate constraints and considering the unit ramp-up dynamic process in detail, the calculation accuracy of the line temperature rise is improved. By constructing the power system economic dispatch model into a mixed-integer linear programming model and performing thermal stability verification on the solution results of the economic dispatch model, and performing constraint iteration generation for the high-dimensional constraint set caused by considering the unit ramp-up dynamic process, the model solution can be accelerated.

[0244] To facilitate further understanding of the advantages of the technical solutions provided in the embodiments of the present application, the power system economic dispatch method provided in the embodiments of the present application is 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.

[0245] In the embodiments of the present application, the IEEE 39-bus system is used as an example, which includes a total of 46 lines. Dynamic capacity increase is performed on all lines. The network topology diagram of the IEEE 39-bus system is as Figure 7 shown.

[0246] The specific settings of the example parameters are as follows:

[0247] For the real-time economic dispatch scenario, in a set of scheduling discretization time periods , the time interval of the scheduling instruction (i.e., the time interval of t) is 15 minutes, and the discretization time interval of the line transient thermal balance equation (i.e., 's time interval) is taken as 1 minute. The basic parameters of each generator, line, and load all adopt the example parameters provided by the MATPOWER 8.0 toolbox. In addition, for each generating unit, , are respectively set to 1% and 3% of the maximum capacity of the unit, with the unit of MW / min.

[0248] The line conductor parameters and environmental parameters are shown in Table 1.

[0249] Table 1 Line Conductor Parameters and Environmental Parameters

[0250]

[0251] First, to verify the necessity of considering the dynamic process of unit ramping, the load rate is set to suddenly increase to 1.15 times the initial value. Within 15 minutes, the transient heat balance equation is used to calculate the line temperature rise curve under two conditions: considering the unit ramping process and not considering the unit dynamic ramping process. Taking line L8 (head end node 4, terminal node 5) as an example, its temperature change curve is as follows Figure 8 shown.

[0252] according to Figure 8 It can be seen that the line temperature rise curves have significant differences between the two cases of considering the unit ramping process and not considering the unit ramping process. The line temperature rise curve considering the ramping process is lower than the temperature rise curve not considering the unit ramping process. In addition, at 15 minutes, the line temperatures calculated for the two cases are 36.7 and 36.7, respectively. , 34.2 , the relative error is 7.31%. This is because during the ramp adjustment process of the unit, the line current changes dynamically, and the line heat generation in the transient heat balance equation It can calculate more accurately, thereby improving the accuracy of the line temperature rise calculation curve.

[0253] Furthermore, in order to verify the solution speed and solution accuracy of the power economic dispatch model proposed in the embodiment of the present application, the following three different algorithms are designed for comparison, and the specific settings are shown in Table 2:

[0254] Table 2 Settings of three comparison algorithms

[0255]

[0256] The solution results and solution time of three different algorithms are shown in Table 3:

[0257] Table 3 Comparison of solution results and solution time of different algorithms

[0258]

[0259] Table 3 shows that for Algorithms 1 and 2, as the number of iterations increases, the number of lines exceeding the limits for both the steady-state and transient heat balance equations decreases. By the end of the iteration, all lines pass the transient heat balance equation. For the same number of iterations, the number of lines exceeding the limits for the steady-state heat balance equation is greater than or equal to the number exceeding the limits for the transient heat balance equation. This is because during the line temperature rise, the steady-state heat balance equation is more conservative in its line temperature prediction, while the transient heat balance equation is more accurate.

[0260] Comparing the objective function values, when the algorithm iteration converges, the objective function values obtained by Algorithm 1, Algorithm 2, and Algorithm 3 are the same, indicating that the constraint iteration generation strategy proposed in the embodiments of the present application can identify all temperature-limited lines and obtain the global optimal solution.

[0261] Comparing the solution times, the total solution times of Algorithm 1, Algorithm 2, and Algorithm 3 are 59.2 seconds (s), 67.2 s, and 164.8 s respectively. The solution time of Algorithm 1 is the shortest, which is 88.1% and 35.9% of Algorithm 2 and Algorithm 3 respectively. Comparing Algorithm 1 and Algorithm 3, the constraint iteration generation strategy designed by Algorithm 1 can identify the key bottleneck lines of thermal stability and iteratively add constraint conditions to improve the model solution efficiency. Comparing Algorithm 1 and Algorithm 2, Algorithm 1 first performs a quick pre-check through a steady-state thermal balance equation with a shorter time, and then uses a transient thermal balance equation with a longer time for strict verification, which can further accelerate the model verification speed and improve the solution efficiency.

[0262] Therefore, in the embodiments of the present application, for short-time scale scenarios, in the economic dispatch model considering the transient thermal balance equation of the line, the calculation accuracy of the line temperature rise is improved while ensuring the real-time nature of the solution. Specifically, the calculation accuracy of the line temperature rise is improved by considering the detailed ramp process of the unit, and the model solution speed is improved by the constraint iteration generation strategy, so that the solution speed meets the real-time requirements.

[0263] Next, a power system economic dispatch device considering line dynamic capacity increase provided by the embodiments of the present application is introduced. The power system economic dispatch device considering line dynamic capacity increase introduced below can be mutually corresponding and referred to with the power system economic dispatch method considering line dynamic capacity increase introduced above.

[0264] Please refer to Figure 9 , which shows a schematic structural diagram of a power system economic dispatch device provided by the embodiments of the present application. The device includes:

[0265] 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;

[0266] 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, power adjustment rate constraints, and linearized AC power flow constraints;

[0267] A model solution module 903, configured to solve the economic dispatch model to obtain the square term of the current of each line in the power system, where the economic dispatch model includes the objective function and the constraint conditions;

[0268] A checking module 904, configured to perform thermal stability checking on each of the lines according to the square term of the current of each line, determine the over-limit lines, where the over-limit lines are the lines that fail the thermal stability check, and the over-limit lines are used to determine the thermal stability constraints of the linearized lines;

[0269] An iterative solution module 905, configured to iteratively solve the power economic dispatch model to obtain the economic dispatch plan of the power system, where the power economic dispatch model is obtained by adding the thermal stability constraints of the linearized lines to the economic dispatch model.

[0270] In the embodiment of the present application, the checking module 904 includes:

[0271] A steady-state checking unit, configured to perform steady-state thermal stability checking on each of the lines according to the square term of the current of each line to obtain steady-state over-limit lines, where the steady-state over-limit lines are the lines that fail the steady-state thermal stability check;

[0272] A transient calculation unit, configured to perform transient thermal balance calculation by using the square term of the current of the steady-state over-limit lines to obtain the final temperature of the lines of the steady-state over-limit lines;

[0273] A transient checking unit, configured to perform transient thermal stability checking on the steady-state over-limit lines according to the final temperature of the lines of the steady-state over-limit lines to obtain the over-limit lines.

[0274] In the embodiment of the present application, the determination module 902 includes:

[0275] A ramp dynamic construction unit, configured to construct a power adjustment rate equation for accounting for the ramp dynamic process according to the parameters of the power system;

[0276] A ramp dynamic linearization unit, configured to perform linearization processing on the power adjustment rate equation to obtain the power adjustment rate constraint.

[0277] In the embodiment of the present application, the iterative solution module 905 includes:

[0278] A calculation unit, configured to calculate the linearized line thermal stability constraint based on the square term of the current of the over-limit lines for the linearized transient thermal balance equation, where the linearized transient thermal balance equation is constructed according to the parameters of the power system.

[0279] In the embodiment of the present application, the device further includes:

[0280] A transient construction module, configured to construct a transient thermal balance equation for accounting for the dynamic change of the line temperature according to the parameters of the power system;

[0281] A transient linearization module is used to linearize the transient heat balance equation to obtain a linearized transient heat balance equation.

[0282] An embodiment of the present application further provides a computer device, including: a memory and a processor;

[0283] Wherein, the memory is used to store a computer program;

[0284] The processor is used to execute the computer program in the memory to implement the method described in the above method embodiment.

[0285] 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 described in the above method embodiment.

[0286] In an embodiment of the present application, a building module builds an objective function with the minimum operating cost of the units in the power system as the goal; a determining module determines the constraint conditions of the objective function according to the parameters of the power system, and the constraint conditions include unit constraints, network variable constraints, power adjustment rate constraints, and linearized AC power flow constraints; a model solving module solves the economic dispatch model to obtain the square terms of the currents of each line in the power system, and the economic dispatch model includes the objective function and the constraint conditions; a verification module performs thermal stability verification on each line according to the square terms of the currents of each line to determine the over-limit lines, and the over-limit lines are the lines that do not pass the thermal stability verification, and the over-limit lines are used to determine the linearized line thermal stability constraints; an iterative solving module iteratively solves the power economic dispatch model to obtain the economic dispatch plan of the power system, and the power economic dispatch model is obtained by adding the linearized line thermal stability constraints to the economic dispatch model. In the embodiment of the present application, by determining the power adjustment rate constraints and considering the dynamic process of unit ramp-up in detail, the calculation accuracy of line temperature rise is improved. By constructing the power system economic dispatch model into a mixed integer linear programming model and performing thermal stability verification on the solution result of the economic dispatch model, it is possible to iteratively generate constraints for the high-dimensional constraint set caused by considering the dynamic process of unit ramp-up, which can accelerate model solving.

[0287] It should be noted that the same or similar parts between the various embodiments can be referred to each other. For the device embodiments and system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can refer to the partial description of the method embodiments.

[0288] For the foregoing embodiments, for the sake of simplicity of description, they are all described as a series of combinations of actions. However, those skilled in the art should be aware that this application is not limited by the described order of actions, 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 the specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0289] Finally, it should also be noted that in this text, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without more limitations, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element.

[0290] The above description of the disclosed embodiments enables those skilled in the art to implement or use this application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

[0291] The foregoing is only the preferred embodiment of this application. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of this application, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of this application.

Claims

1. An economic dispatch method for a power system considering line dynamic capacity increase, characterized in that, The method includes: Establishing an objective function with the minimum operating cost of the units in the power system as the goal; Determining 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, power adjustment rate constraints, and linearized AC power flow constraints; Solving the economic dispatch model to obtain the square terms of the currents of each line in the power system, where the economic dispatch model includes the objective function and the constraint conditions; Performing thermal stability verification on each line according to the square terms of the currents of each line to determine the over-limit lines, where the over-limit lines are the lines that fail the thermal stability verification, and the over-limit lines are used to determine the linearized line thermal stability constraints; Performing iterative solution on the power economic dispatch model to obtain the economic dispatch plan of the power system, where the power economic dispatch model is obtained by adding the linearized line thermal stability constraints to the economic dispatch model.

2. The method according to claim 1, wherein The performing thermal stability verification on each line according to the square terms of the currents of each line to determine the over-limit lines includes: Performing steady-state thermal stability verification on each line according to the square terms of the currents of each line to obtain steady-state over-limit lines, where the steady-state over-limit lines are the lines that fail the steady-state thermal stability verification; Performing transient thermal balance calculation using the square terms of the currents of the steady-state over-limit lines to obtain the final temperatures of the lines of the steady-state over-limit lines; Performing transient thermal stability verification on the steady-state over-limit lines according to the final temperatures of the lines of the steady-state over-limit lines to obtain the over-limit lines.

3. The method according to claim 1, wherein Determining the power adjustment rate constraints according to the parameters of the power system includes: Constructing a power adjustment rate equation for accounting for the ramp dynamic process according to the parameters of the power system; Performing linearization processing on the power adjustment rate equation to obtain the power adjustment rate constraints.

4. The method according to any one of claims 1 to 3, characterized in that Determining the linearized line thermal stability constraints includes: Calculating the linearized transient thermal balance equation based on the square terms of the currents of the over-limit lines to obtain the linearized line thermal stability constraints, where the linearized transient thermal balance equation is constructed according to the parameters of the power system.

5. The method according to any one of claims 1 to 3, characterized in that Before the performing thermal stability verification on each line according to the square terms of the currents of each line to determine the over-limit lines, the method further includes: Constructing a transient thermal balance equation for accounting for the dynamic change of the line temperature according to the parameters of the power system; Performing linearization processing on the transient thermal balance equation to obtain a linearized transient thermal balance equation.

6. An economic dispatch device for a power system considering line dynamic capacity increase, characterized in that, The device includes: An establishment module for establishing an objective function with the minimum operating cost of the units in the power system as the goal; A determination module for determining 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, power adjustment rate constraints, and linearized AC power flow constraints; A model solution module for solving the economic dispatch model to obtain the square terms of the currents of each line in the power system, where the economic dispatch model includes the objective function and the constraint conditions; A checking module, configured to perform thermal stability checking on each of the lines according to the square term of the current of each line, determine the over-limit lines, where the over-limit lines are the lines that fail the thermal stability checking, and the over-limit lines are used to determine the thermal stability constraints of the linearized lines; An iterative solution module, configured to perform iterative solution on the power economic dispatch model to obtain the economic dispatch plan of the power system, where the power economic dispatch model is obtained by adding the thermal stability constraints of the linearized lines to the economic dispatch model.

7. The device according to claim 6, characterized in that, The checking module includes: A steady-state checking unit, configured to perform steady-state thermal stability checking on each of the lines according to the square term of the current of each line to obtain steady-state over-limit lines, where the steady-state over-limit lines are the lines that fail the steady-state thermal stability checking; A transient calculation unit, configured to perform transient thermal balance calculation by using the square term of the current of the steady-state over-limit lines to obtain the final temperature of the lines of the steady-state over-limit lines; A transient checking unit, configured to perform transient thermal stability checking on the steady-state over-limit lines according to the final temperature of the lines of the steady-state over-limit lines to obtain the over-limit lines.

8. The device according to claim 6, characterized in that The determination module includes: A ramp dynamic construction unit, configured to construct a power adjustment rate equation for considering the ramp dynamic process according to the parameters of the power system; A ramp dynamic linearization unit, configured to perform linearization processing on the power adjustment rate equation to obtain the power adjustment rate constraint.

9. A computer device, characterized in that, It includes: A memory and a processor; 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 according to any one of claims 1 to 5.

10. A computer-readable storage medium, characterized in that, Instructions are stored, which, when running on a computer, cause the computer to execute the method according to any one of claims 1 to 5.

Images