Power system low-frequency load shedding optimal distribution method considering system security constraints

Abstract

The invention discloses a power system low-frequency load shedding optimal distribution method considering system security constraints, which comprehensively considers the system security constraints and aims to realize minimization of power system line change before and after a low-frequency load shedding event so as to keep system operation points as close as possible before and after load shedding. And the stability of the system operation state is maintained. According to the method, a mixed integer programming (MIP) model is adopted, the low-frequency load shedding amount is distributed to each load point of the power system, and the system security constraint is met to the maximum extent under the condition of multiple credible events. According to the method, the non-linear objective function is converted into a linear form through introduction of the auxiliary variable and linear processing, so that the problem solving process is simplified. According to the method, the stability and the reliability of the power system in the case of low-frequency events are effectively improved, and the risks of line overload and system collapse caused by improper load shedding are reduced.

Description

Technical Field

[0001] The invention relates to an optimal distribution method for low-frequency load shedding in an electric power system taking into account system safety constraints, and belongs to the technical field of electric power system safety and stability. Background Art

[0002] In power systems, underfrequency load shedding is an important safety measure used to prevent system collapse when a large-scale power generation loss occurs in the system. From the perspective of frequency stability, the total load shedding amount and its distribution over time are the main decision variables when designing underfrequency load shedding schemes. However, these load shedding amounts need to be reasonably distributed among the underfrequency load shedding relays installed on the substation outgoing distribution feeders. Due to the complexity and dynamics of the power system, the allocation strategy of underfrequency load shedding needs to accurately respond to changes in the system state to ensure that the system can maintain stability during the load shedding process. In existing power system underfrequency load shedding (UFLS) schemes, static or simple dynamic methods are usually used to determine the load shedding amount and its distribution in the system. These methods often do not fully consider the dynamic response and safety constraints of the system after an underfrequency event, which may lead to problems such as line overload and reduced system stability in practical applications. Therefore, it is particularly important to propose a method to optimize the load shedding distribution while meeting the safety constraints of the power system. Summary of the invention

[0003] The purpose of the present invention is to provide an optimal allocation method for under-frequency load shedding in an electric power system taking into account system safety constraints. In view of the technical bottlenecks faced by the above-mentioned existing under-frequency load shedding (UFLS) allocation in the electric power system, the method of the present invention can dynamically respond to changes in the system state and achieve optimal load allocation while satisfying the system safety constraints.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] The core of the technical solution of the present invention is to establish an optimization model to allocate load shedding when a low-frequency event occurs in the system. The model goal is to minimize the power flow change of the power transmission line before and after load shedding, thereby reducing the risk of system operation.

[0006] The optimal allocation method for low-frequency load shedding in a power system considering system safety constraints of the present invention comprises the following steps:

[0007] 1) Constructing DC power flow model: Applicable to a node set k=1,...,n k , transmission line set I l =1,··,l,··,n l , and the set I representing the number of specific power outage events j =1,··,j··,n cThe power network is composed of low-frequency load shedding relays according to the frequency step (s = 1, ···, n s ) disconnects a specific load block; where k and n k Respectively represent the node number and quantity in the power system, l and n l They represent the number and quantity of transmission lines connecting each node in the power system; j represents the number of specific power outage events, n c Represents the total number of specific generation failures or outages that may occur in the system; n s represents the total number of frequency steps, i.e., the total number of load shedding stages that the under-frequency load shedding relay may take; subscripts g and d are used to indicate the generation and demand at the node, respectively;

[0008] 2) With the goal of minimizing the line power change after a low-frequency event occurs in the system, an objective function is constructed. The mathematical expression of the objective function is:

[0009]

[0010] Among them, the superscripts BE and AE represent before and after the event, respectively; represents the power flow on line l before event j occurs; represents the power flow on line l after event j occurs and at load shedding step s; s d is the final deployment step of the load shedding relay; the semicolon in the formula indicates that when s=s d When , the current equation is established;

[0011] 3) Objective function linearization: Convert the absolute value operation in the objective function into a linear expression, as follows:

[0012]

[0013] Where ΔP jsl is an auxiliary positive continuous variable, which indicates the power flow change on line l before and after event j occurs. To simulate the absolute value removal operation, it can be further written as:

[0014] 4) The node power balance equation constructed before the load shedding event occurs is:

[0015]

[0016] In the formula, I dk ,I gk ,I lk denote the set of loads, generators and lines at node k respectively, represents the power generated by generator g before event j occurs; represents the power consumption of load d before event j occurs;

[0017] 5) Calculate the power generation of each node after load reduction: If a power outage occurs on node k, the number of power outages of the node engine is proportionally reduced according to the network load factor; if no power outage occurs, the power generation should be equal to the corresponding value before the event occurs, as shown in the following formula:

[0018]

[0019] in, represents the power generated by generator g after event j occurs; Ld j represents the network load factor under event j, GO jk Represents the power reduction caused by power generation interruption at node k; since the DC power flow model does not take into account heat loss, the total power generation interruption should be equal to the sum of the total load reduction and the load response value to frequency change, expressed as follows:

[0020]

[0021] Among them, TLS s , D j denote the total load reduction and load reduction factor under event j, Δf s and f 0 Respectively represent the frequency deviation from the nominal value and the nominal frequency; GOP jk represents the amount of power generation interruption at each node under event j;

[0022] 6) Calculate the total load of each node after load reduction: Considering that the change of the total load of each node is affected by two factors: (1) the effect of frequency reduction on the load damping coefficient; (2) the cumulative total load reduction from the initial stage to the sth stage; therefore, the mathematical expression is as follows:

[0023]

[0024] in, represents the power consumption of load d after event j occurs and at load reduction step s; LS s′k represents the load reduction amount on node k at load reduction step s;

[0025] 7) Constructing the node power balance equation after the load shedding event: Add the transient power gain (PGA) to the node power balance equation after the event, which is valid for all load shedding steps; the output power of the in-service generators varies due to the frequency response characteristics. According to the load shedding steps and distribution, the power consumption on the demand side should be reduced to below the level before the event:

[0026]

[0027] In the formula, represents the power consumption of load d after event j occurs and at load reduction step s; PGA jsk represents the transient power gain of node k after event j occurs and at load reduction step s, which is proportional to the inertia constant H and is calculated as:

[0028]

[0029] 8) Add power system line flow constraints;

[0030] 9) Add total load reduction constraints;

[0031] 10) Mathematically solve the mixed integer programming (MIP) problem to obtain the optimal load shedding allocation plan.

[0032] The purpose of the present invention can also be further achieved by the following technical measures:

[0033] Furthermore, the line power flow before and after the load shedding event is as follows:

[0034]

[0035] The power flow constraint is as follows:

[0036]

[0037] In the formula, B l represents the susceptance of line l, are the voltage angles at the sending and receiving ends of line l after event j occurs, are the voltage angles at the sending and receiving ends of line l after event j occurs and at load shedding step s; represents the maximum power flow limit of line l; s = s d Indicates the last step of load shedding.

[0038] Furthermore, when a low-frequency event occurs, the total amount of load reduction at each node should be equal to the required total load reduction TLS s :

[0039]

[0040] Where TL represents the total system load under event j.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention comprehensively considers the system safety constraints, aiming to minimize the changes in the power system lines before and after the low-frequency load shedding event, so as to keep the system operating point as close as possible before and after the load shedding, and maintain the stability of the system operation state. The method adopts a mixed integer programming (MIP) model to distribute the low-frequency load shedding amount to each load point of the power system, ensuring that the system safety constraints are met to the maximum extent under various credible event conditions. The present invention converts the nonlinear objective function into a linear form by introducing auxiliary variables and linearization processing, thereby simplifying the problem-solving process. The present invention effectively improves the stability and reliability of the power system in the face of low-frequency events, and reduces the risk of line overload and system collapse caused by improper load shedding. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a modeling flow chart of the present invention. DETAILED DESCRIPTION

[0043] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0044] The core of the present invention is an optimization model, such as Figure 1 As shown in Figure 1, the model is used to allocate load shedding when a low-frequency event occurs in the system. The model objective is to minimize the power flow changes of the power transmission line before and after load shedding, thereby reducing the risk of system operation. The specific construction of the optimization model includes the following steps:

[0045] 1) Constructing DC power flow model: Applicable to a node set k=1,...,n k , transmission line set I l =1,··,l,··,n l , and the set I representing the number of specific power outage events j =1,··,j··,n c The power network is composed of low-frequency load shedding relays according to the frequency step (s = 1, ···, n s ) disconnects a specific load block; where k and n k Respectively represent the node number and quantity in the power system, l and n l They represent the number and quantity of transmission lines connecting each node in the power system; j represents the number of specific power outage events, n c Represents the total number of specific generation failures or outages that may occur in the system; n s represents the total number of frequency steps, i.e., the total number of load shedding stages that the under-frequency load shedding relay may take; subscripts g and d are used to indicate the generation and demand at the node, respectively.

[0046] 2) The objective function is constructed with the goal of minimizing the line power change after the low-frequency event occurs in the system. Although the low-frequency load reduction scheme generally includes multiple unloading steps (the unloading step depends on the lowest frequency point), here we only focus on the line flow related to the last step as the final state after load unloading, that is, s = s d When; the mathematical expression of the objective function is:

[0047]

[0048] Among them, the superscripts BE and AE represent before and after the event, respectively; represents the power flow on line l before event j occurs; represents the power flow on line l after event j occurs and at load shedding step s; s d is the final deployment step of the load shedding relay; the semicolon in the formula indicates that when s=s d , the current equation holds.

[0049] 3) Linearization of the objective function: Since the objective function contains absolute value operations, it presents nonlinear characteristics. In order to facilitate the solution, this method introduces auxiliary variables to convert the absolute value operations in the objective function into linear expressions, which are as follows:

[0050]

[0051] Among them, ΔP jsl is an auxiliary positive continuous variable, which indicates the power flow change on line l before and after event j occurs. To simulate the absolute value removal operation, it can be further written as:

[0052] 4) The node power balance equation constructed before the load shedding event occurs is:

[0053]

[0054] In the formula, I dk ,I gk ,I lk denote the set of loads, generators and lines at node k respectively, represents the power generated by generator g before event j occurs; It represents the power consumption of load d before event j occurs.

[0055] 5) Calculate the power generation of each node after load reduction: If a power outage occurs on node k, the number of power outages of the node engine is proportionally reduced according to the network load factor; if no power outage occurs, the power generation should be equal to the corresponding value before the event occurs, as shown in the following formula:

[0056]

[0057] in, represents the power generated by generator g after event j occurs; Ld j represents the network load factor under event j, GO jk Represents the power reduction caused by power generation interruption at node k; since the DC power flow model does not take into account heat loss, the total power generation interruption should be equal to the sum of the total load reduction and the load response value to frequency change, expressed as follows:

[0058]

[0059] Among them, TLS s , D j denote the total load reduction and load reduction factor under event j, Δf s and f 0 Respectively represent the frequency deviation from the nominal value and the nominal frequency; GOP jk Represents the amount of power interruption at each node under event j.

[0060] 6) Calculate the total load of each node after load reduction: Considering that the change of the total load of each node is affected by two factors: (1) the effect of frequency reduction on the load damping coefficient; (2) the cumulative total load reduction from the initial stage to the sth stage; therefore, the mathematical expression is as follows:

[0061]

[0062] in, represents the power consumption of load d after event j occurs and at load reduction step s; LS s′k It represents the load reduction amount on node k in load reduction step s.

[0063] 7) Constructing the node power balance equation in the post-load shedding event stage: When a generator fails, the power imbalance is compensated by releasing the stored kinetic energy. To simulate this phenomenon, consider adding the transient power gain (PGA) to the post-event node power balance equation, as shown below, which is valid for all load shedding steps. Among them, the output power of the in-service generators varies due to the frequency response characteristics. According to the load shedding steps and distribution, the power consumption on the demand side should be reduced to below the level before the event:

[0064]

[0065] In the formula, represents the power consumption of load d after event j occurs and at load reduction step s; PGA jsk represents the transient power gain of node k after event j occurs and at load reduction step s, which is proportional to the inertia constant H and is calculated as:

[0066]

[0067] 8) Consider power system line flow constraints:

[0068] The line flow before and after the load shedding event is shown as follows:

[0069]

[0070]

[0071] The power flow constraint is as follows:

[0072]

[0073] In the formula, B l represents the susceptance of line l, are the voltage angles at the sending and receiving ends of line l after event j occurs, are the voltage angles at the sending and receiving ends of line l after event j occurs and at load shedding step s; represents the maximum power flow limit of line l; s = s d Indicates the last step of load shedding.

[0074] 9) Consider the total load reduction constraint: When a low-frequency event occurs, the total amount of load reduction at each node should be equal to the required total load reduction TLS s :

[0075]

[0076] Where TL represents the total system load under event j.

[0077] 10) Mathematical solution: The optimization problem is formalized as a mixed integer programming (MIP) problem, which can be solved by the SCIP solver to obtain the optimal load shedding allocation solution.

[0078] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solutions formed by equivalent replacement or equivalent transformation shall fall within the protection scope required by the present invention.

Claims

1. An optimal allocation method for low-frequency load shedding in a power system considering system security constraints, characterized in that: The following steps are involved: 1) Constructing DC power flow model: Applicable to a node set k=1,...,n k , transmission line set I l =1,··,l,··,n l , and the set I representing the number of specific power outage events j =1,··,j··,n c The power network is composed of low-frequency load shedding relays according to the frequency step s=1,···,n s ) disconnects a specific load block; where k and n k Respectively represent the node number and quantity in the power system, l and n l They represent the number and quantity of transmission lines connecting each node in the power system; j represents the number of specific power outage events, n c Represents the total number of specific generation failures or outages that may occur in the system; n s represents the total number of frequency steps, i.e., the total number of load shedding stages that the under-frequency load shedding relay may take; subscripts g and d are used to indicate the generation and demand at the node, respectively; 2) With the goal of minimizing the line power change after a low-frequency event occurs in the system, an objective function is constructed. The mathematical expression of the objective function is: Among them, the superscripts BE and AE represent before and after the event, respectively; represents the power flow on line l before event j occurs; represents the power flow on line l after event j occurs and at load shedding step s; s d is the final deployment step of the load shedding relay; the semicolon in the formula indicates that when s=s d When , the current equation is established; 3) Objective function linearization: Convert the absolute value operation in the objective function into a linear expression as follows: Among them, ΔP jsl is an auxiliary positive continuous variable, which indicates the power flow change on line l before and after event j occurs. To simulate the absolute value removal operation, it can be further written as: 4) The node power balance equation constructed before the load shedding event occurs is: In the formula, I dk ,I gk ,I lk denote the set of loads, generators and lines at node k respectively, represents the power generated by generator g before event j occurs; represents the power consumption of load d before event j occurs; 5) Calculate the power generation of each node after load reduction: If a power outage occurs on node k, the number of power outages of the node engine is proportionally reduced according to the network load factor; if no power outage occurs, the power generation should be equal to the corresponding value before the event occurs, as shown in the following formula: in, represents the power generated by generator g after event j occurs; Ld j represents the network load factor under event j, GO jk Represents the power reduction caused by power generation interruption at node k; since the DC power flow model does not take into account heat loss, the total power generation interruption should be equal to the sum of the total load reduction and the load response value to frequency change, expressed as follows: Among them, TLS s , D j denote the total load reduction and load reduction factor under event j, Δf s and f0 represent the frequency deviation from the nominal value and the nominal frequency respectively; GOP jk represents the amount of power generation interruption at each node under event j; 6) Calculate the total load of each node after load reduction: Considering that the change of the total load of each node is affected by two factors: (1) the effect of frequency reduction on the load damping coefficient; (2) the cumulative total load reduction from the initial stage to the sth stage; therefore, the mathematical expression is as follows: in, represents the power consumption of load d after event j occurs and at load reduction step s; LS s′k represents the load reduction amount on node k at load reduction step s; 7) Constructing the node power balance equation after the load shedding event: The transient power gain is added to the node power balance equation after the event, which is valid for all load shedding steps; the output power of the in-service generators varies due to the frequency response characteristics. According to the load shedding steps and distribution, the power consumption on the demand side should be reduced to below the level before the event: In the formula, represents the power consumption of load d after event j occurs and at load reduction step s; PGA jsk represents the transient power gain of node k after event j occurs and at load reduction step s, which is proportional to the inertia constant H and is calculated as: 8) Add power system line flow constraints; 9) Add total load reduction constraints; 10) Mathematically solve the mixed integer programming problem to obtain the optimal load shedding allocation plan.

2. The optimal allocation method for low-frequency load shedding in a power system considering system safety constraints according to claim 1, characterized in that: The line flow before and after the load shedding event in step 8) is as follows: The power flow constraint is as follows: In the formula, B l represents the susceptance of line l, are the voltage angles at the sending and receiving ends of line l after event j occurs, are the voltage angles at the sending and receiving ends of line l after event j occurs and at load shedding step s; represents the maximum power flow limit of line l; s = s d Indicates the last step of load shedding.

3. The optimal allocation method for low-frequency load shedding in a power system considering system safety constraints according to claim 1, characterized in that: In step 9), when a low-frequency event occurs, the total amount of load reduction at each node should be equal to the required total load reduction TLS s : Where TL represents the total system load under event j.

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