Power system bearing capacity determination method and device, computer equipment, readable storage medium and program product

Abstract

The invention relates to a power system bearing capacity determination method and device, computer equipment, a computer readable storage medium and a computer program product. The method comprises the steps that an optimization model of the power system is acquired, the optimization model comprises an objective function and constraint conditions, and the objective function is determined based on a loadable coefficient of the power system; the constraint conditions comprise a first constraint condition and a second constraint condition, the first constraint condition is determined based on system power flow constraint, and the second constraint condition is determined based on harmonic distortion; solving the optimization model, and determining a bearing capacity evaluation index; and determining the bearing capacity of the power system based on the bearing capacity evaluation index. By adopting the method, the accuracy of determining the bearing capacity of the power system can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of load-carrying capacity assessment and harmonic analysis of power systems, and particularly to a method, device, computer equipment, computer-readable storage medium, and computer program product for determining the load-carrying capacity of a power system. Background Art

[0002] With the rapid development of new loads such as electric vehicles, energy storage batteries, and various power electronic devices, the determination of voltage capacity margin poses a severe challenge to power system operators. At the same time, the continuous increase of nonlinear loads such as various power electronic devices poses a huge challenge to the stable and safe operation of the power system, resulting in various power quality problems.

[0003] In the aspect of power system load-carrying capacity assessment, static techniques based on power flow are widely applied. The traditional continuation power flow method can be used to detect sensitive areas affected by voltage instability and determine the maximum load capacity and voltage stability margin of the system by assuming a predetermined power consumption of the load bus. The modal analysis method uses the eigenvalues and eigenvectors of the power flow Jacobian matrix of the power system to determine the critical buses of the system and calculate the influencing factors of voltage instability phenomena.

[0004] However, the current methods for determining and assessing the load-carrying capacity of power systems have the problem of insufficient accuracy. Summary of the Invention

[0005] Based on this, it is necessary to provide a method, device, computer equipment, computer-readable storage medium, and computer program product for determining the load-carrying capacity of a power system that can improve accuracy in view of the above technical problems.

[0006] In a first aspect, the present application provides a method for determining the load-carrying capacity of a power system, the method comprising:

[0007] Obtain an optimization model of the power system, wherein the optimization model includes an objective function and constraint conditions, the objective function is determined based on the load factor of the power system; the constraint conditions include a first constraint condition and a second constraint condition, the first constraint condition is determined based on system power flow constraints, and the second constraint condition is determined based on harmonic distortion;

[0008] Solve the optimization model to determine a load-carrying capacity assessment index;

[0009] Based on the load-carrying capacity assessment index, determine the load-carrying capacity of the power system.

[0010] In one embodiment, the solving the optimization model to determine a load-carrying capacity assessment index includes:

[0011] Determine a new objective function according to the objective function, the number of the second constraint conditions, and the slack variables;

[0012] Convert the new objective function into a Lagrangian objective function;

[0013] Determine new constraint conditions according to the first constraint condition, the second constraint condition, and the slack variables;

[0014] Determine the bearing capacity evaluation index under the condition that the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality condition.

[0015] In one embodiment, the bearing capacity evaluation index includes a voltage stability index, a harmonic distortion index, and a reactive power support index; determining the bearing capacity evaluation index under the condition that the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality condition includes:

[0016] Under the condition that the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality condition, obtain the Lagrangian multiplier related to the voltage amplitude, the Lagrangian multiplier of the active power constraint related to the total harmonic distortion, and the maximum Lagrangian multiplier related to the reactive power;

[0017] Determine the voltage stability index based on the Lagrangian multiplier related to the voltage amplitude;

[0018] Determine the harmonic distortion index based on the Lagrangian multiplier of the active power constraint related to the total harmonic distortion;

[0019] Determine the reactive power support index based on the maximum Lagrangian multiplier related to the reactive power.

[0020] In one embodiment, determining the power system bearing capacity based on the bearing capacity evaluation index includes:

[0021] When any one of the voltage stability index, the harmonic distortion index, and the reactive power support index approaches a preset threshold, the upper limit of the power system bearing capacity is reached.

[0022] In one embodiment, the system power flow constraint includes a fundamental wave power flow constraint and a harmonic power flow constraint, and the determination method of the first constraint condition includes:

[0023] Determine the fundamental wave power flow constraint according to the total number of load buses obtained, the active power and reactive power of each bus in the power system, the planned active power output and reactive power output on the bus, and the active power load and reactive power load on the bus;

[0024] Determine the harmonic power flow constraint according to the obtained harmonic phase voltage vector, harmonic current vector and power system harmonic admittance matrix;

[0025] Based on the fundamental power flow constraint and the harmonic power flow constraint, determine the first constraint condition.

[0026] In one embodiment, the method for determining the second constraint condition includes:

[0027] Determine the fundamental voltage constraint according to the obtained fundamental voltage amplitude, the upper limit of the fundamental voltage amplitude and the lower limit of the fundamental voltage amplitude;

[0028] Determine the active power constraint according to the obtained active power generated on the bus and the maximum capacity of the corresponding generator;

[0029] Determine the reactive power constraint according to the obtained reactive power generated on the bus, the maximum value of the reactive power and the minimum value of the reactive power;

[0030] Determine the harmonic voltage constraint according to the obtained total harmonic distortion rate of voltage, the maximum limit value of the total harmonic distortion rate of voltage, the single - harmonic distortion rate of voltage and the maximum limit value of the single - harmonic distortion rate of voltage;

[0031] Determine the harmonic current constraint according to the obtained total harmonic distortion rate of current, the maximum limit value of the total harmonic distortion rate of current, the single - harmonic distortion rate of current and the maximum limit value of the single - harmonic distortion rate of current;

[0032] Determine the second constraint condition according to the fundamental voltage constraint, the active power constraint, the reactive power constraint, the harmonic voltage constraint and the harmonic current constraint.

[0033] In a second aspect, the present application further provides a device for determining the carrying capacity of a power system, where the device includes:

[0034] An acquisition module, configured to acquire an optimization model of a power system, where the optimization model includes an objective function and constraint conditions, the objective function is determined based on the load - carrying coefficient of the power system; the constraint conditions include a first constraint condition and a second constraint condition, the first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on harmonic distortion;

[0035] A solving module, configured to solve the optimization model to determine a carrying capacity evaluation index;

[0036] A determining module, configured to determine the carrying capacity of the power system based on the carrying capacity evaluation index.

[0037] In a third aspect, the present application further provides a computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the above method are implemented.

[0038] In a fourth aspect, the present application further provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0039] In a fifth aspect, the present application further provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0040] For the above power system carrying capacity determination method, device, computer device, computer-readable storage medium, and computer program product, first, an optimization model of the power system is obtained. The optimization model includes an objective function and constraint conditions. The objective function is determined based on the load factor of the power system. The constraint conditions include a first constraint condition and a second constraint condition. The first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on the harmonic distortion. The harmonic distortion problem is considered in the power system, and an optimization model is established. Secondly, the optimization model is solved to determine the carrying capacity evaluation index. Finally, based on the carrying capacity evaluation index, the power system carrying capacity is determined. By incorporating the harmonic distortion factor into the optimization model, the carrying capacity evaluation index obtained by solving the optimization model also takes into account the harmonic distortion. Based on the carrying capacity evaluation index considering the harmonic distortion, the power system carrying capacity is determined. Compared with the traditional solution that does not consider the impact of harmonic distortion in the power system on the evaluation of the power system carrying capacity, the accuracy of the power system carrying capacity evaluation is improved. Description of the Drawings

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following will briefly introduce the drawings required for use in the description of the embodiments of the present application or related technologies. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0042] Figure 1 It is an application environment diagram of the power system carrying capacity determination method in an embodiment;

[0043] Figure 2 It is a flowchart of the power system carrying capacity determination method in an embodiment;

[0044] Figure 3 It is a flowchart of determining the carrying capacity evaluation index in an embodiment;

[0045] Figure 4 Flow chart for determining the bearing capacity evaluation index for another embodiment;

[0046] Figure 5 Flow chart for determining the first constraint condition in one embodiment;

[0047] Figure 6 Flow chart for determining the second constraint condition in one embodiment;

[0048] Figure 7 Block diagram of the power system bearing capacity determination device in one embodiment;

[0049] Figure 8 Internal structure diagram of a computer device in one embodiment. Detailed implementation manners

[0050] In order to make the objectives, technical solutions and advantages of the present application more clear and understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0051] The power system bearing capacity determination method provided by the embodiments of the present application can be applied to an application environment as shown in Figure 1 . Among them, the power system terminal 102 communicates with the server 104 through a network. The data storage system can store the data that the server 104 needs to process. The data storage system can be integrated on the server 104, or can be placed in the cloud or on other network servers. The server 104 obtains an optimization model of the power system, where the optimization model includes an objective function and constraint conditions. The objective function is determined based on the load factor of the power system. The constraint conditions include a first constraint condition and a second constraint condition. The first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on the harmonic distortion. Solve the optimization model to determine the bearing capacity evaluation index. Based on the bearing capacity evaluation index, determine the bearing capacity of the power system. The server 104 can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server providing cloud computing services.

[0052] In an exemplary embodiment, as shown in Figure 2 , a power system bearing capacity determination method is provided. Taking the method applied to the server in Figure 1 as an example, the method includes the following steps S202 to step S206. Among them:

[0053] Step S202, obtain an optimization model of the power system.

[0054] Among them, the optimization model includes an objective function and constraint conditions. The objective function is determined based on the loadability factor of the power system. The constraint conditions include a first constraint condition and a second constraint condition. The first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on the harmonic distortion.

[0055] Optionally, the optimization model includes a linear programming model composed of an objective function and constraint conditions. The objective function is determined based on the loadability factor of the power system. The objective function can be denoted as f(x), as shown in formula (1).

[0056] Formula (1)

[0057] In the formula, λ represents the loadability factor of the power system assuming that the increments of all system load buses are equal.

[0058] The constraint conditions include a first constraint condition and a second constraint condition. The constraint conditions are as shown in formula (2).

[0059] Formula (2)

[0060] Among them, the first constraint condition is an equality constraint g(x) determined based on the system power flow constraint, and the second constraint condition is an inequality constraint h(x) determined based on the harmonic distortion.

[0061] Step S204: Solve the optimization model to determine the bearing capacity evaluation index.

[0062] Optionally, the server solves the optimization model by the interior point method. By introducing a slack variable s, the inequality constraint (i.e., the second constraint condition) can be transformed into an equality constraint, and the original first constraint condition, the equality constraint transformed from the second constraint condition, and the slack variable are used as new constraint conditions. By introducing the slack variable s, a new objective function is determined. The optimization model determined by the new constraint conditions and the new objective function is solved by the interior point method to determine the bearing capacity evaluation index.

[0063] Step S206: Determine the bearing capacity of the power system based on the bearing capacity evaluation index.

[0064] Optionally, the server determines the upper limit of the bearing capacity of the power system based on the bearing capacity evaluation index. The upper limit of the bearing capacity of the power system is also the grid critical point. The area exceeding the upper limit of the bearing capacity of the power system or exceeding the grid critical point can be called a sensitive area.

[0065] In the above method for determining the power system carrying capacity, first, an optimization model of the power system is obtained. The optimization model includes an objective function and constraint conditions. The objective function is determined based on the load factor of the power system. The constraint conditions include a first constraint condition and a second constraint condition. The first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on harmonic distortion. The harmonic distortion problem is considered in the power system, and an optimization model is established. Secondly, the optimization model is solved to determine the carrying capacity evaluation index. Finally, based on the carrying capacity evaluation index, the power system carrying capacity is determined. By incorporating the harmonic distortion factor into the optimization model, the carrying capacity evaluation index obtained by solving the optimization model also takes into account harmonic distortion. Determining the power system carrying capacity based on the carrying capacity evaluation index considering harmonic distortion improves the accuracy of the power system carrying capacity evaluation compared to the traditional solution that does not consider the impact of harmonic distortion in the power system on the power system carrying capacity evaluation.

[0066] In an exemplary embodiment, as Figure 3 shown, solving the optimization model to determine the carrying capacity evaluation index includes steps S302 to S308. Among them:

[0067] Step S302, determine a new objective function according to the objective function, the number of second constraint conditions, and the slack variable.

[0068] Optionally, the server obtains the objective function f(x), the number n ineq of the second constraint conditions, and the slack variable s, and determines a new objective function. The new objective function is as shown in formula (3).

[0069] Formula (3)

[0070] Among them, μ represents the damping coefficient, n ineq represents the number of inequality constraints, x represents the variable vector; f(x) represents the objective function to be maximized.

[0071] Step S304, convert the new objective function into a Lagrangian objective function.

[0072] Optionally, the server converts the new objective function into a Lagrangian objective function L (x,δ,π,μ) , as shown in formula (4).

[0073] Formula (4)

[0074] Among them, L (x,δ,π,μ) represents the Lagrangian objective function; δ j represents the Lagrangian multiplier related to the first constraint condition; π jDenote the Lagrange multiplier related to the second constraint condition, and the meanings of other letters are as shown in the above formula.

[0075] Step S306: Determine a new constraint condition according to the first constraint condition, the second constraint condition, and the slack variable.

[0076] Optionally, the server determines a new constraint condition according to the first constraint condition, the second constraint condition, and the slack variable, and the new constraint condition is as shown in formula (5).

[0077] Formula (5)

[0078] Among them, g(x) represents the equality constraint condition; h(x) represents the inequality constraint condition; s represents the introduced slack variable.

[0079] Step S308: Determine the bearing capacity evaluation index under the condition that the Lagrangian objective function and the new constraint condition satisfy the first-order optimality condition.

[0080] Optionally, according to the Karush-Kuhn-Tucker first-order optimality condition, that is, under the condition that the Lagrangian objective function and the new constraint condition satisfy the first-order optimality condition, the derivative of L (x,δ,π,μ) with respect to the state variable x, and the Lagrange multipliers related to the equality constraint δ j and the inequality constraint π j can be calculated, and they are expressed as:

[0081] Formula (6)

[0082] Since the derivative is set to 0, the Newton-Raphson iteration method can be used for calculation. It should be noted that the constraint condition (such as h(x*) = 0) at the local maximum (x*) is related to a relatively large Lagrange multiplier, which can be used to identify the inequality constraints reaching the relevant boundary values. The boundary settings of these inequality constraints have a great impact on the objective function value and can provide key boundary limits when formulating the constraint optimization problem of power system analysis and operation.

[0083] The interior point method provides the Lagrange multiplier value, which is closely related to the system loadability and can indicate the most critical system buses. In this case, even if it cannot be guaranteed to find the global minimum or maximum, the KKT first-order optimality condition must be satisfied to find the optimal solution.

[0084] In voltage stability assessment, relatively large Lagrange multipliers are usually associated with the most critical buses. In addition, when the load increases from the rated load factor (λ = 1) to the maximum load rate, the Lagrange multiplier related to the maximum reactive power generation decreases as the power system approaches the maximum load rate (λ = λ max ) at the critical point.

[0085] Optionally, the server determines the bearing capacity evaluation index according to the Lagrange multiplier.

[0086] In this embodiment, the new optimization model is solved by the interior point method, and when the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality, the bearing capacity evaluation index can be determined, and the bearing capacity evaluation index takes into account the harmonic distortion factor, so the accuracy can be improved.

[0087] In an exemplary embodiment, as Figure 4 shown, the bearing capacity evaluation index includes a voltage stability index, a harmonic distortion index, and a reactive power support index; when the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality, determining the bearing capacity evaluation index includes steps S402 to S408. Among them:

[0088] Step S402, when the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality, obtain the Lagrange multiplier related to the voltage amplitude, the Lagrange multiplier of the active power constraint related to the total harmonic distortion, and the maximum Lagrange multiplier related to the reactive power.

[0089] Optionally, when the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality, the Lagrange multiplier related to the voltage amplitude can be calculated and denoted as , the Lagrange multiplier of the active power constraint related to the total harmonic distortion and the maximum Lagrange multiplier related to the reactive power .

[0090] Step S404, determine the voltage stability index based on the Lagrange multiplier related to the voltage amplitude.

[0091] Step S406, determine the harmonic distortion index based on the Lagrange multiplier of the active power constraint related to the total harmonic distortion.

[0092] Step S408, determine the reactive power support index based on the maximum Lagrange multiplier related to the reactive power.

[0093] Optionally, the server determines the voltage stability index based on the Lagrange multiplier related to the voltage amplitude, denoted as ; as shown in formula (7). Determine the harmonic distortion index based on the Lagrange multiplier of the active power constraint related to the total harmonic distortion, denoted as ; as shown in formula (7). Determine the reactive power support index based on the maximum Lagrange multiplier related to the reactive power, denoted as ; as shown in formula (7). Since all Lagrange multipliers are approximately equal to 0 when the power system approaches the critical point, the above index tends to 1 during calculation. Therefore, the loadability factor λ is added.

[0094] Formula (7)

[0095] In this embodiment, through the Lagrange multiplier, the corresponding index can be determined, and through the voltage stability index, harmonic distortion index, and reactive power support index, the upper limit of the power system's carrying capacity can be determined subsequently to facilitate the determination of the sensitive area of the power system.

[0096] In an exemplary embodiment, determining the power system carrying capacity based on the carrying capacity evaluation index includes: when any one of the voltage stability index, harmonic distortion index, and reactive power support index approaches a preset threshold, the upper limit of the power system carrying capacity is reached.

[0097] Optionally, use the voltage stability index and the harmonic distortion index to evaluate the maximum Lagrange multiplier related to the voltage amplitude and total harmonic distortion constraint of the fundamental voltage constraint and harmonic voltage constraint, which can evaluate the deterioration of power quality in different situations and point out the buses most sensitive to undervoltage and their harmonic distortion limits. When the system voltage is stable, and the values of the two indexes are low. When the system approaches the maximum load capacity margin, and the two indexes will approach the unit value 1 to determine whether the system load is close to the maximum load capacity margin. In addition, the sensitivity between the reactive power injection and voltage amplitude of each bus k can be used to identify the key buses of the network. When the system approaches the critical point, calculate the reactive power support index of each load bus , to determine which buses need additional reactive power support. When approaches 1, it indicates that the area needs additional reactive power support.

[0098] In this embodiment, when any one of the voltage stability index, harmonic distortion index, and reactive power support index approaches a preset threshold, the upper limit of the power system carrying capacity is reached, that is, the sensitive area of the power system.

[0099] In an exemplary embodiment, as Figure 5 shown, the system power flow constraint includes the fundamental power flow constraint and the harmonic power flow constraint. The determination method of the first constraint condition includes steps S502 to S506. Among them:

[0100] Step S502: Determine the fundamental power flow constraints based on the total number of load buses obtained, the active and reactive powers of each bus in the power system, the active and reactive power planned outputs on the bus, and the active and reactive power loads on the bus.

[0101] Optionally, the server determines the fundamental power flow constraints according to the total number of load buses obtained, the active and reactive powers of each bus in the power system, the active and reactive power planned outputs on the bus, and the active and reactive power loads on the bus, as shown in Equation (8).

[0102] Equation (8)

[0103] Where, N L represents the total number of load buses; and respectively represent the active and reactive powers of each bus k in the system calculated according to the state variables; P1 g,k and Q1 g,k respectively represent the active and reactive power planned outputs on the given bus k; and respectively represent the active and reactive power loads on the given bus k.

[0104] According to the power flow equation, and The calculation formulas are as shown in Equation (9).

[0105] Equation (9)

[0106] In the formula, K represents the bus directly connected to the given bus k; and respectively represent the susceptance and conductance between the fundamental frequency bus k and the bus m; represents the phase angle difference between the bus k and the bus m.

[0107] Step S504: Determine the harmonic power flow constraints based on the obtained harmonic phase voltage vector, harmonic current vector, and the harmonic admittance matrix of the power system.

[0108] Optionally, the server obtains the harmonic phase voltage vector, harmonic current vector, and the harmonic admittance matrix of the power system. Among them, the harmonic phase voltage vector refers to the h -th harmonic phase voltage vector; the harmonic current vector refers to the h -th harmonic current vector. The harmonic power flow constraints are as shown in Equation (10).

[0109] Equation (10)

[0110] Where, and respectively represent the h - th harmonic phase voltage vector and the h - th harmonic current vector, represents the system harmonic admittance matrix.

[0111] Step S506, based on the fundamental power flow constraint and the harmonic power flow constraint, determine the first constraint condition.

[0112] Optionally, the server determines the first constraint condition, that is, the equality constraint condition, based on the fundamental power flow constraint formula (9) and the harmonic power flow constraint formula (10).

[0113] In this embodiment, through the above parameters, the equality constraint condition can be determined to facilitate the subsequent determination of the optimization model.

[0114] In an exemplary embodiment, as Figure 6 shown, the determination method of the second constraint condition includes steps S602 to S612. Among them:

[0115] Step S602, according to the obtained fundamental voltage amplitude, the upper limit of the fundamental voltage amplitude, and the lower limit of the fundamental voltage amplitude, determine the fundamental voltage constraint.

[0116] Optionally, the server determines the fundamental voltage constraint according to the obtained fundamental voltage amplitude, the upper limit of the fundamental voltage amplitude, and the lower limit of the fundamental voltage amplitude, as shown in formula (11).

[0117] Fundamental voltage constraint:

[0118] Formula (11)

[0119] Among them, represents the fundamental voltage amplitude, and respectively represent the upper limit and the lower limit of the fundamental voltage amplitude.

[0120] Step S604, according to the obtained active power generated on the bus and the maximum capacity of the corresponding generator, determine the active power constraint.

[0121] Optionally, the server determines the active power constraint according to the obtained active power generated on the bus and the maximum capacity of the corresponding generator, as shown in formula (12).

[0122] Active power constraint:

[0123] Formula (12)

[0124] In the formula, represents the active power generated on bus i; represents the maximum capacity of the corresponding generator, and Ng represents the total number of generators.

[0125] Step S606: Determine the reactive power constraint based on the reactive power generated on the bus, the maximum value of the reactive power, and the minimum value of the reactive power obtained.

[0126] Optionally, the server determines the reactive power constraint based on the reactive power generated on the bus, the maximum value of the reactive power, and the minimum value of the reactive power obtained, as shown in Equation (13).

[0127] Reactive power constraint:

[0128] Equation (13)

[0129] In the formula, represents the reactive power generated on bus i; and represent the maximum value and the minimum value of the reactive power respectively.

[0130] Step S608: Determine the harmonic voltage constraint based on the total harmonic distortion rate of the voltage, the maximum limit of the total harmonic distortion rate of the voltage, the single - harmonic distortion rate of the voltage, and the maximum limit of the single - harmonic distortion rate of the voltage obtained.

[0131] Optionally, the server determines the harmonic voltage constraint based on the total harmonic distortion rate of the voltage, the maximum limit of the total harmonic distortion rate of the voltage, the single - harmonic distortion rate of the voltage, and the maximum limit of the single - harmonic distortion rate of the voltage obtained, as shown in Equation (14).

[0132] Harmonic voltage constraint:

[0133] Equation (14)

[0134] In the formula, and represent the total harmonic distortion rate of the voltage and its maximum limit respectively; and represent the single - harmonic distortion rate of the voltage and its maximum limit respectively. and The calculation formula is as shown in Equation (15).

[0135] Equation (15)

[0136] In the formula, represents the effective value of the h - th harmonic voltage, represents the maximum harmonic order considered, represents the effective value of the fundamental voltage.

[0137] Step S610: Determine the harmonic current constraint according to the obtained total harmonic distortion rate of current, the maximum limit value of the total harmonic distortion rate of current, the single - harmonic distortion rate of current, and the maximum limit value of the single - harmonic distortion rate of current.

[0138] Optionally, determine the harmonic current constraint according to the obtained total harmonic distortion rate of current, the maximum limit value of the total harmonic distortion rate of current, the single - harmonic distortion rate of current, and the maximum limit value of the single - harmonic distortion rate of current, as shown in formula (16).

[0139] Harmonic current constraint:

[0140] Formula (16)

[0141] In the formula, and respectively represent the total harmonic distortion rate of current and its maximum limit value; and respectively represent the single - harmonic distortion rate of current and its maximum limit value. and The calculation formula is as shown in formula (17).

[0142] Formula (17)

[0143] In the formula, represents the effective value of the h - th harmonic current, represents the effective value of the fundamental current.

[0144] Step S612: Determine the second constraint condition according to the fundamental voltage constraint, active power constraint, reactive power constraint, harmonic voltage constraint, and harmonic current constraint.

[0145] Optionally, the server determines the second constraint condition, that is, the inequality constraint condition, according to the fundamental voltage constraint formula (11), active power constraint formula (12), reactive power constraint formula (13), harmonic voltage constraint formula (14), and harmonic current constraint formula (16).

[0146] In this embodiment, through the above parameters, the inequality constraint condition can be determined to facilitate the subsequent determination of the optimization model.

[0147] In an exemplary embodiment, the server obtains the optimization model of the power system, where the optimization model includes an objective function, a first constraint condition, and a second constraint condition.

[0148] Objective function:

[0149] Formula (1)

[0150] In the formula, λ represents the loadability factor of the power system assuming equal increments of all system load buses.

[0151] The constraint conditions include the first constraint condition and the second constraint condition.

[0152] Among them, the first constraint condition includes:

[0153] Fundamental power flow constraint: Equation (8)

[0154] Among them, N L represents the total number of load buses; and respectively represent the active power and reactive power of each bus k of the system calculated according to the state variables; P1 g,k and Q1 g,k respectively represent the active and reactive power planned outputs on the given bus k; and respectively represent the active and reactive power loads on the given bus k.

[0155] According to the power flow equation, and The calculation formula is as shown in Equation (9).

[0156] Equation (9)

[0157] In the formula, K represents the bus directly connected to the given bus k; and respectively represent the susceptance and conductance between the fundamental frequency bus k and the bus m; represents the phase angle difference between the bus k and the bus m.

[0158] Harmonic power flow constraint:

[0159] Equation (10)

[0160] Among them, and respectively represent the h - th harmonic phase voltage vector and the h - th harmonic current vector, represents the system harmonic admittance matrix.

[0161] The second constraint condition includes:

[0162] Fundamental voltage constraint:

[0163] Equation (11)

[0164] Among them, represents the fundamental voltage amplitude, and respectively represent the upper and lower limits of the fundamental voltage amplitude.

[0165] Active power constraint:

[0166] Formula (12)

[0167] Wherein, represents the active power generated on bus i; represents the maximum capacity of the corresponding generator, and Ng represents the total number of generators.

[0168] Reactive power constraint:

[0169] Formula (13)

[0170] Wherein, represents the reactive power generated on bus i; and respectively represent the maximum and minimum values of reactive power.

[0171] Harmonic voltage constraint:

[0172] Formula (14)

[0173] Wherein, and respectively represent the total harmonic distortion rate of voltage and its maximum limit value; and respectively represent the single - harmonic distortion rate of voltage and its maximum limit value. and The calculation formula is as shown in Formula (15).

[0174] Formula (15)

[0175] Wherein, represents the effective value of the h - th harmonic voltage, represents the maximum harmonic order considered, represents the effective value of the fundamental voltage.

[0176] Harmonic current constraint:

[0177] Formula (16)

[0178] Wherein, and respectively represent the total harmonic distortion rate of current and its maximum limit value; and respectively represent the single - harmonic distortion rate of current and its maximum limit value. and The calculation formula is as shown in Formula (17).

[0179] Formula (17)

[0180] Wherein, represents the effective value of the h - th harmonic current, represents the effective value of the fundamental current.

[0181] The server obtains the objective function f(x), the number n of the second constraint conditions ineq and the slack variable s, and determines a new objective function. The new objective function is as shown in Formula (3).

[0182] Formula (3)

[0183] where μ represents the damping coefficient, n ineq represents the number of inequality constraints, x represents the variable vector; f(x) represents the objective function to be maximized.

[0184] The server transforms the new objective function into a Lagrangian objective function L (x,δ,π,μ) , as shown in Formula (4).

[0185] Formula (4)

[0186] where L (x,δ,π,μ) represents the Lagrangian objective function; δ j represents the Lagrangian multiplier related to the first constraint; π j represents the Lagrangian multiplier related to the second constraint, and the meanings of other letters are as shown in the above formula.

[0187] The server determines new constraint conditions according to the first constraint condition, the second constraint condition and the slack variable. The new constraint conditions are as shown in Formula (5).

[0188] Formula (5)

[0189] where g(x) represents the equality constraint condition; h(x) represents the inequality constraint condition; s represents the introduced slack variable.

[0190] According to the Karush - Kuhn - Tucker first - order optimality conditions, that is, under the condition that the Lagrangian objective function and the new constraint conditions satisfy the first - order optimality, the derivative of L (x,δ,π,μ) with respect to the state variable x, and the Lagrangian multipliers related to the equality constraint δ j and the inequality constraint π j can be calculated, and it is expressed as:

[0191] Formula (6)

[0192] Since the derivative is set to 0, the Newton-Raphson iteration method can be used for calculation. It should be noted that the constraint conditions (such as h(x*) = 0) at the local maximum (x*) are related to relatively large Lagrange multipliers, which can be used to identify the inequality constraints that reach the relevant boundary values. The boundary settings of these inequality constraints have a great impact on the objective function value and can provide key boundary limits when formulating the constrained optimization problem for power system analysis and operation.

[0193] In voltage stability assessment, relatively large Lagrange multipliers are usually associated with the most critical buses. In addition, when the load increases from the rated load factor (λ = 1) to the maximum load rate, the Lagrange multiplier related to the maximum reactive power generation decreases as the power system approaches the maximum load rate (λ = λ max ) at the critical point.

[0194] The bearing capacity assessment indicators include voltage stability indicators, harmonic distortion indicators, and reactive power support indicators; under the condition that the Lagrangian objective function and the new constraint conditions satisfy the first-order optimality, the Lagrange multiplier related to the voltage amplitude can be calculated and denoted as , the Lagrange multiplier of the active power constraint related to the total harmonic distortion and the maximum Lagrange multiplier related to reactive power .

[0195] The server determines the voltage stability indicator, denoted as ; as shown in formula (7). Based on the Lagrange multiplier of the active power constraint related to the total harmonic distortion, the harmonic distortion indicator is determined and denoted as ; as shown in formula (7). Based on the maximum Lagrange multiplier related to reactive power, the reactive power support indicator is determined and denoted as ; as shown in formula (7). Since all Lagrange multipliers are approximately equal to 0 when the power system approaches the critical point and the above indicators tend to 1 in calculation, the load factor λ is added.

[0196] Formula (7)

[0197] Using the voltage stability indicator and the harmonic distortion indicator two indicators to evaluate the maximum Lagrange multipliers related to the voltage amplitude and the total harmonic distortion of the voltage, which are represented by the fundamental voltage constraint and the harmonic voltage constraint, can evaluate the deterioration of power quality in different situations and point out the buses most sensitive to undervoltage and their harmonic distortion limits. When the system voltage is stable, and the values of the two indicators are low. When the system approaches the maximum load capacity margin, and Two indicators will approach the unit value of 1 to determine whether the system load is close to the maximum load capacity margin. In addition, the sensitivity between the reactive power injection and the voltage magnitude of each bus k can be used to identify the critical buses of the network. When the system approaches the critical point, the reactive power support index of each load bus is calculated , to determine which buses require additional reactive power support. When approaches 1, it indicates that the area requires additional reactive power support.

[0198] It should be understood that although the steps in the flowcharts involved in the above-described embodiments are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear description in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-described embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily executed at the same moment, but can be executed at different moments. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or alternately with at least a part of other steps or steps in other steps.

[0199] Based on the same inventive concept, the embodiments of the present application also provide a device for determining the carrying capacity of a power system for implementing the method for determining the carrying capacity of the power system involved above. The implementation solutions provided by this device to solve problems are similar to the implementation solutions described in the above method. Therefore, the specific limitations in one or more embodiments of the device for determining the carrying capacity of the power system provided below can refer to the limitations on the method for determining the carrying capacity of the power system in the above text, and will not be repeated here.

[0200] In an exemplary embodiment, as Figure 7 shown, a device for determining the carrying capacity of a power system is provided, including: an acquisition module 701, a solution module 702, and a determination module 703, where:

[0201] The acquisition module 702 is used to acquire the optimization model of the power system, where the optimization model includes an objective function and constraint conditions. The objective function is determined based on the loadability factor of the power system; the constraint conditions include a first constraint condition and a second constraint condition. The first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on the harmonic distortion.

[0202] The solution module 702 is used to solve the optimization model and determine the carrying capacity evaluation index.

[0203] A determination module 703, configured to determine the power system carrying capacity based on a carrying capacity evaluation index.

[0204] In an exemplary embodiment, the solving module 702 is further configured to determine a new objective function according to the objective function, the number of second constraint conditions, and the slack variables; convert the new objective function into a Lagrangian objective function; determine new constraint conditions according to the first constraint condition, the second constraint condition, and the slack variables; and determine the carrying capacity evaluation index when the Lagrangian objective function and the new constraint conditions meet the first-order optimality condition.

[0205] In an exemplary embodiment, the carrying capacity evaluation index includes a voltage stability index, a harmonic distortion index, and a reactive power support index; the solving module 702 is further configured to obtain the Lagrangian multiplier related to the voltage amplitude, the Lagrangian multiplier of the active power constraint related to the total harmonic distortion, and the maximum Lagrangian multiplier related to the reactive power when the Lagrangian objective function and the new constraint conditions meet the first-order optimality condition; determine the voltage stability index based on the Lagrangian multiplier related to the voltage amplitude; determine the harmonic distortion index based on the Lagrangian multiplier of the active power constraint related to the total harmonic distortion; and determine the reactive power support index based on the maximum Lagrangian multiplier related to the reactive power.

[0206] In an exemplary embodiment, the determination module 703 is configured to reach the upper limit of the power system carrying capacity when any one of the voltage stability index, the harmonic distortion index, and the reactive power support index approaches a preset threshold.

[0207] In an exemplary embodiment, the system power flow constraint includes a fundamental power flow constraint and a harmonic power flow constraint, and the device further includes a first constraint condition determination module, configured to determine the fundamental power flow constraint according to the total number of load buses obtained, the active power and reactive power of each bus in the power system, the planned active power output and reactive power output on the bus, and the active power load and reactive power load on the bus; determine the harmonic power flow constraint according to the obtained harmonic phase voltage vector, harmonic current vector, and power system harmonic admittance matrix; and determine the first constraint condition based on the fundamental power flow constraint and the harmonic power flow constraint.

[0208] In an exemplary embodiment, the device further includes a second constraint condition determination module, configured to determine a fundamental voltage constraint according to the acquired fundamental voltage amplitude, the upper limit of the fundamental voltage amplitude, and the lower limit of the fundamental voltage amplitude; determine an active power constraint according to the acquired active power generated on the bus and the maximum capacity of the corresponding generator; determine a reactive power constraint according to the acquired reactive power generated on the bus, the maximum value of the reactive power, and the minimum value of the reactive power; determine a harmonic voltage constraint according to the acquired total harmonic distortion rate of the voltage, the maximum limit value of the total harmonic distortion rate of the voltage, the single harmonic distortion rate of the voltage, and the maximum limit value of the single harmonic distortion rate of the voltage; determine a harmonic current constraint according to the acquired total harmonic distortion rate of the current, the maximum limit value of the total harmonic distortion rate of the current, the single harmonic distortion rate of the current, and the maximum limit value of the single harmonic distortion rate of the current; and determine a second constraint condition according to the fundamental voltage constraint, the active power constraint, the reactive power constraint, the harmonic voltage constraint, and the harmonic current constraint.

[0209] Each module in the above power system carrying capacity determination device can be implemented in whole or in part by software, hardware, and their combination. Each of the above modules can be embedded in or independent of a processor in a computer device in the form of hardware, or stored in a memory in the computer device in the form of software, so as to facilitate the processor to call and execute the operations corresponding to the above respective modules.

[0210] In an exemplary embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as Figure 8 shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store power system related data. The input / output interface of the computer device is used for the processor to exchange information with external devices. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it implements a power system carrying capacity determination method.

[0211] Those skilled in the art can understand that Figure 8The structure shown is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have a different component layout.

[0212] In one embodiment, a computer device is further provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0213] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0214] In one embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0215] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc. The databases involved in the embodiments provided in this application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in this application can be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, data processing logics based on quantum computing, artificial intelligence (AI) processors, etc., without limitation.

[0216] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this application.

[0217] The above-described embodiments merely represent several implementation manners of the present application. The description thereof is relatively specific and detailed, but it should not be construed as a limitation on the patent scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all fall within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims

1. A method for determining the carrying capacity of a power system, characterized in that: The method comprises: Acquire an optimization model of the power system, wherein the optimization model includes an objective function and a constraint condition, wherein the objective function is determined based on the load factor of the power system; the constraint condition includes a first constraint condition and a second constraint condition, wherein the first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on the harmonic distortion; Solving the optimization model to determine a load-bearing capacity evaluation index; Based on the carrying capacity evaluation index, the carrying capacity of the power system is determined.

2. The method according to claim 1, characterized in that: The step of solving the optimization model and determining the load-bearing capacity evaluation index includes: Determine a new objective function according to the objective function, the number of the second constraints and the slack variables; Converting the new objective function into a Lagrangian objective function; Determine a new constraint condition according to the first constraint condition, the second constraint condition and the slack variable; Under the condition that the Lagrangian objective function and the new constraint condition satisfy the first-order optimum, the carrying capacity evaluation index is determined.

3. The method according to claim 2, characterized in that The carrying capacity evaluation index includes a voltage stability index, a harmonic distortion index and a reactive power support index; the carrying capacity evaluation index is determined under the condition that the Lagrangian objective function and the new constraint condition meet the first-order optimality, including: Under the condition that the Lagrangian objective function and the new constraint condition satisfy the first-order optimum, a Lagrangian multiplier related to the voltage amplitude, a Lagrangian multiplier of active power constraint related to the total harmonic distortion, and a maximum Lagrangian multiplier related to reactive power are obtained; determining the voltage stability index based on a Lagrange multiplier associated with the voltage amplitude; Determining the harmonic distortion index based on the Lagrange multiplier of the active power constraint related to the total harmonic distortion; Based on the reactive power-related maximum Lagrangian multiplier, a reactive power support indicator is determined.

4. The method according to claim 3, characterized in that Determining the power system carrying capacity based on the carrying capacity evaluation index includes: When any one of the voltage stability index, the harmonic distortion index and the reactive power support index approaches a preset threshold, the upper limit of the power system carrying capacity is reached.

5. The method according to claim 1, characterized in that The system power flow constraint includes a fundamental power flow constraint and a harmonic power flow constraint, and the first constraint condition is determined in a manner including: Determine the fundamental power flow constraint according to the total number of load buses obtained, the active power and reactive power of each bus of the power system, the planned active output and reactive output on the bus, and the active power load and reactive power load on the bus; Determining the harmonic power flow constraint according to the acquired harmonic phase voltage vector, harmonic current vector and power system harmonic admittance matrix; The first constraint condition is determined based on the fundamental power flow constraint and the harmonic power flow constraint.

6. The method according to claim 1, characterized in that The method for determining the second constraint condition includes: Determining a fundamental voltage constraint according to the acquired fundamental voltage amplitude, an upper limit of the fundamental voltage amplitude, and a lower limit of the fundamental voltage amplitude; Determine active power constraints according to the acquired active power generated on the bus and the maximum capacity of the corresponding generator; Determine a reactive power constraint according to the acquired reactive power generated on the bus, the maximum value of the reactive power and the minimum value of the reactive power; Determining harmonic voltage constraints according to the acquired voltage total harmonic distortion rate, the maximum limit of the voltage total harmonic distortion rate, the voltage single harmonic distortion rate, and the maximum limit of the voltage single harmonic distortion rate; Determining harmonic current constraints according to the acquired total harmonic distortion rate of the current, the maximum limit of the total harmonic distortion rate of the current, the single harmonic distortion rate of the current, and the maximum limit of the single harmonic distortion rate of the current; The second constraint condition is determined according to the fundamental voltage constraint, the active power constraint, the reactive power constraint, the harmonic voltage constraint and the harmonic current constraint.

7. A device for determining the carrying capacity of a power system, characterized in that: The device comprises: An acquisition module is used to acquire an optimization model of the power system, wherein the optimization model includes an objective function and a constraint condition, wherein the objective function is determined based on the load factor of the power system; the constraint condition includes a first constraint condition and a second constraint condition, wherein the first constraint condition is determined based on the system power flow constraint, and the second constraint condition is determined based on harmonic distortion; A solution module, used for solving the optimization model and determining a bearing capacity evaluation index; The determination module is used to determine the carrying capacity of the power system based on the carrying capacity evaluation index.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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