Method for participation of temperature controlled load in frequency response reduction of power system based on routh approximation

Abstract

The application provides a model reduction method for temperature control load participating in power system demand response control based on Ljapunov approximation, comprising the following steps: proposing an application scenario and a model reduction processing method of Ljapunov approximation in temperature control load demand response; establishing a power system frequency response reduction model integrated with temperature control load clusters; and obtaining an analytical expression of system frequency response frequency key information, including a system frequency deviation maximum drop value, a steady-state frequency deviation and a maximum frequency change rate. The temperature control load frequency response reduction model obtained by the method retains the main frequency band accuracy of the original high-order system and the stability characteristics of the original high-order system, and the analytical expression of the system frequency key information derived from the reduction system model has a certain guiding significance for frequency regulation analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and particularly relates to an application scenario of Routh approximation in frequency response model order reduction of a power system integrating a temperature-controlled load cluster. Background Art

[0002] When a power system is disturbed, its frequency changes. Traditional power systems primarily achieve real-time power balance by regulating the output of thermal, hydropower, and other generators. While the proportion of power electronic power sources connected has continued to increase in recent years, their generation is subject to significant uncertainty and intermittency, which can easily lead to instability in the safe operation of the power system. Furthermore, their increasing proportion further compresses the system's regulation capacity. Therefore, exploring new regulation resources to provide the system with regulation capabilities to resist disturbances is of great practical significance. The rapid development of load-side demand response technology has provided a new approach to regulating system frequency response.

[0003] The potential of loads, particularly large-scale, distributed, and micro-loads, in supporting power system frequency response has received less attention. With significant improvements in living standards and the frequent occurrence of extreme high and low temperatures, the proportion of temperature-controlled loads during periods of peak grid load operation continues to rise. In economically developed regions like Shanghai and Beijing, temperature-controlled loads account for over 50% of peak summer electricity demand, posing significant potential for frequency regulation. To mitigate the increasing pressure on supply-side frequency regulation, the flexible regulation of large-scale temperature-controlled loads to participate in grid frequency regulation has become an emerging research area within the field of power system frequency security.

[0004] The system frequency response model based on the single-unit equivalent method reduces the power system to a second-order linear model and is capable of calculating analytical expressions for key system frequency characteristics. There are two main types of frequency response models based on the single-unit equivalent method: the average system frequency (ASF) model and the system frequency response (SFR) model. The ASF model aggregates the rotor motion equations of each generator and equates the load cluster to a single concentrated load, retaining the prime mover and speed regulator models of the generator sets while simplifying the transmission lines. The SFR model builds on the ASF model by further equating the prime mover and speed regulator of the generator sets to single units, thereby simplifying the power system frequency response to a second-order linear model. After a system disturbance occurs, the system frequency response model can be used to derive analytical expressions for the power system frequency deviation, frequency change rate, time to reach the lowest point, frequency lowest point, and steady-state frequency value. This allows for quantitative analysis of the impact of system parameters on frequency dynamic characteristics, effectively improving the analysis speed of the system frequency response and providing a fast and intuitive tool for frequency stability analysis.

[0005] When considering the demand response of load clusters on the power consumption side, the load cluster can be made equivalent to a traditional generator set through appropriate control strategies, equating the load cluster to a centralized load. A power system model integrating temperature-controlled load clusters can be established to achieve source-load interaction. However, the frequency response model for this power system has high-order characteristics, making it difficult to directly solve for the time-domain analytical expression of key frequency information.

[0006] Therefore, how to reduce the order of the high-order model of the system frequency response and make the resulting simplified model take into account the approximate accuracy of both high-frequency and low-frequency bands, laying the foundation for the quantitative analysis of frequency response control parameters, is a technical problem that technicians in this field urgently need to solve. Summary of the Invention

[0007] The purpose of this invention is to propose a method for applying the Routh approximation to reduce the frequency response model order of a power system in which temperature-controlled loads participate, thereby achieving second-order equivalence of the power system frequency response model. This method also derives a time-domain analytical expression for the key frequency information of the power system frequency response model for an integrated temperature-controlled load cluster, providing a quantitative analysis tool for the design of temperature-controlled load frequency response control parameters.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] The method for applying Routh approximation to a power system frequency response model integrating a temperature-controlled load cluster includes the following steps:

[0010] (1) Establish a demand response control model for temperature control loads:

[0011] a. Define the frequency response regulation power provided by the single temperature control load as:

[0012]

[0013] b. Temperature control load cluster frequency response control adopts PD control:

[0014] b1. Total delay Δt of load terminal demand response execution d is the delay Δt based on 5G communication 5G and load side sampling control period Δt con The superposition of Δt d =Δt con +Δt 5G ;

[0015] b2. The virtual inertia control link of temperature control load is:

[0016]

[0017] b3. The temperature control load droop control link is:

[0018]

[0019] b4. The total power of the temperature control load cluster demand response is:

[0020]

[0021] (2) Establish an equivalent model of the system frequency response of the integrated temperature control load;

[0022] a. Use the single-machine equivalent method to model the frequency response of traditional power systems.

[0023] a1. Simplify the power system into a single synchronous motor and equate the grid frequency to the frequency of a single synchronous generator;

[0024] a2. Perform single-machine equivalence on the synchronous generator set, its prime mover and speed control system, simplify the entire system into a second-order linear model, and establish the system frequency response model SFR model.

[0025] b. When the load cluster on the electricity consumption side responds to demand, the load cluster is made equivalent to a traditional generator set through the demand response control strategy, and the load cluster is equivalent to a centralized load, and a power system model with integrated temperature-controlled load cluster is established.

[0026] (3) The frequency response model of the power system with integrated temperature-controlled load cluster is reduced based on Routh approximation.

[0027] a. Equivalent the response delay to the first-order inertia link to obtain the transfer function of the system frequency response model;

[0028] b. Use Routh approximation to obtain a second-order approximation for the system's high-order transfer function;

[0029] c. The system disturbance power is in step form, and the frequency domain expression of the system frequency information of the reduced-order model is obtained. Using the inverse Laplace transform, the time domain analytical expression of the system frequency key information is obtained.

[0030] Routh approximation is a method for reducing the frequency response model of high-order power systems, which includes the following steps:

[0031] (1) Using the Pade approximation principle, we take the first-order approximation for the temperature control load demand response delay link:

[0032]

[0033] (2) The transfer function of the power system frequency response model is derived as a rational fraction:

[0034]

[0035] (3) Using the intermediate variable p, a second-order approximation is taken for the high-order transfer function:

[0036]

[0037] Where α1, α2, β1, and β2 are calculated from the high-order transfer function parameters according to the Routh approximation table.

[0038] (4) Perform parameter reduction s = 1 / p on the second-order approximate transfer function to obtain the second-order transfer function of the power system frequency response:

[0039]

[0040] The parameters in the formula are all derived from the parameters of the high-order transfer function.

[0041] The present invention provides a method for applying Routh's approximation to a power system frequency response model for an integrated temperature-controlled load cluster. This method utilizes a single-machine equivalent method to establish a power system SFR model, with the load cluster being treated as a concentrated load. This model then establishes a power system model for the integrated temperature-controlled load cluster, achieving source-load interaction. The Routh's approximation reduces the order of the system frequency response to a second-order equivalent, thereby deriving analytical expressions for the power system's frequency deviation, frequency rate of change, time to reach the lowest point, frequency lowest point, and steady-state frequency value. This method effectively speeds up the analysis of the system's frequency response and provides a fast and intuitive tool for frequency stability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 A schematic diagram of a demand response control method for a temperature control load provided in an embodiment;

[0044] Figure 2 A schematic diagram of a power system frequency response model for an integrated temperature-controlled load cluster provided in an embodiment;

[0045] Figure 3 A flow chart of a method for applying Routh approximation to a power system frequency response model integrating a temperature-controlled load cluster provided in an embodiment;

[0046] Figure 4 The frequency response model of the power system with integrated temperature-controlled load cluster is used to calculate the system frequency deviation curve before and after order reduction using Routh approximation;

[0047] Figure 5 The zero-pole distribution diagram of the power system frequency response model before and after order reduction using Routh approximation for the integrated temperature-controlled load cluster;

[0048] Figure 6 The dominant pole distribution diagram of the system before and after the Routh approximation is used to reduce the frequency response model of the power system with integrated temperature-controlled load clusters;

[0049] Figure 7 The Bode diagram of the power system frequency response model with integrated temperature-controlled load clusters before and after order reduction using Routh approximation. DETAILED DESCRIPTION

[0050] The embodiments of the present invention are implemented based on the technical solutions and provide detailed implementation methods, but the protection scope of the present invention is not limited to the following embodiments.

[0051] The method for applying Routh's approximation proposed in the present invention to the frequency response model of a power system integrating a temperature-controlled load cluster comprises the following steps:

[0052] (1) Establish a demand response control model for temperature control loads;

[0053] like Figure 1 As shown, the temperature control load demand response control variable is defined as S AC，i , i=1,2,…,N,N is the total number of load clusters. When a demand response control instruction is issued, S AC，i Set to 1. In addition, set the temperature control load temperature control state variable to S T，i , i=1,2,…,N,when the temperature control load indoor temperature T in Exceeding the user comfort constraint range [T up , T down ], S T，i Set to 0, the load will exit the response, and normal temperature control operation will resume the indoor temperature.

[0054] Therefore, the load cluster demand response state variable S DR Set to S DR =S AC，i &S T，i ,When the demand response control variables and temperature ,control variables meet the requirements, the load cluster is activated and participates in the ,demand response of the power system and provides regulation ,capabilities for the system.

[0055]

[0056] At time t, the frequency response regulation power that a single temperature control load can provide to the power system is shown in the following formula:

[0057]

[0058] In response to system frequency changes, the temperature-controlled load cluster demand response adopts integrated inertia control, and the control center controller adopts PD control.

[0059] When the power on the power generation side and the power consumption side is unbalanced, the system will have a frequency deviation Δf. When the frequency deviation exceeds the stability threshold, the load-side control center calculates and determines the temperature control load cluster response power instruction, and issues the control instruction to the large-scale distributed temperature control load. Due to the limitations of the communication system and hardware facilities, the delays in the strategy calculation of each control layer, network communication, and load terminal execution still exist objectively. The total delay Δt of the load terminal demand response execution d is the delay Δt based on 5G communication 5G and load side sampling control period Δt con The superposition of Δt d =Δt con +Δt 5G ;

[0060] The virtual inertia control link of temperature control load is:

[0061]

[0062] The temperature control load droop control link is:

[0063]

[0064] The total power of the temperature control load cluster demand response is:

[0065]

[0066] Among them, K vi is the virtual inertia control parameter of the temperature control load, K dr are droop control parameters, Δf(t), f rate (t) are the frequency deviation and frequency change rate of the power system at time t respectively.

[0067] (2) Establish an equivalent model of the system frequency response of the integrated temperature control load:

[0068] The frequency response of traditional power systems is modeled using the single-machine equivalent method. The power system is simplified to a single synchronous motor, and the grid frequency is equivalent to the frequency of a single synchronous generator. The synchronous generator set, its prime mover, and speed control system are equivalent to a single machine, and the system frequency response model (SFR) is established.

[0069] The system power-speed relationship can be expressed as:

[0070]

[0071] Where M is the system inertia time constant, D is the system damping, Δω is the system equivalent synchronous motor rotor speed deviation, ΔP m is the mechanical power output deviation of the prime mover, ΔP e is the electromagnetic power deviation of the generator.

[0072] After Laplace transform, the frequency domain relationship between frequency change and power imbalance is:

[0073]

[0074] When the load cluster demand response is implemented on the power consumption side, the load cluster is made equivalent to a traditional generator set through the demand response control strategy, and the load cluster is made equivalent to a centralized load, and a power system model with integrated temperature control load cluster is established. Figure 2 As shown in the figure, the conventional units of the power system are set as hydropower units, and the temperature control load cluster is integrated into the power system frequency response model as a fast frequency response resource.

[0075] The turbine transfer function is:

[0076]

[0077] Among them, T w is the time constant of water hammer effect.

[0078] The turbine speed control system adopts PID speed regulator, and its transfer function is:

[0079]

[0080] Among them, K P , K I and K D are the proportional, integral and differential coefficients of the turbine PID governor, b p is the adjustment coefficient, T y is the servo system time constant.

[0081] (3) The frequency response model of the power system with integrated temperature-controlled load cluster is reduced based on Routh approximation.

[0082] Routh approximation is a method for reducing the frequency response model of high-order power systems, such as Figure 3 As shown, the following steps are included:

[0083] a. Using the Pade approximation principle, the temperature control load demand response delay link is approximated to the first-order inertia link:

[0084]

[0085] The transfer function of the system frequency response model is obtained as follows:

[0086]

[0087] The coefficients m0~m4, n0~n5 are determined by the following formula:

[0088]

[0089]

[0090] b. Using the intermediate variable p, let p = 1 / s, and take a second-order approximation for the high-order transfer function R(s):

[0091]

[0092] Where α1, α2, β1, and β2 are calculated from the high-order transfer function parameters according to the Routh approximation table.

[0093]

[0094] c. Perform parameter reduction s = 1 / p on the second-order approximate transfer function to obtain the second-order transfer function of the power system frequency response:

[0095]

[0096] The parameters x0, x1, y0, y1, and y2 are all derived from the parameters of the high-order transfer function.

[0097]

[0098] (3) Using the second-order power system frequency response model to derive the analytical formula of key system frequency information

[0099] System disturbance power ΔP D In step form, the frequency domain expression of the system frequency deviation of the reduced-order model is:

[0100]

[0101] Perform inverse Laplace transform on the frequency domain expression of the system frequency deviation to obtain the time domain analytical expression of the system frequency deviation:

[0102]

[0103] The derivation results of the parameters in the formula are as follows:

[0104]

[0105] By differentiating the frequency deviation, we can obtain the time domain analytical expression of the frequency change rate:

[0106]

[0107] Let the frequency change rate f rate =0, find the time t when the frequency reaches the maximum value nadir ,

[0108]

[0109] Substituting the time to reach the maximum value into the frequency deviation analytical formula, the maximum value of the system frequency deviation Δf can be obtained nadir ,

[0110]

[0111] System steady-state frequency deviation Δf stb and maximum frequency change rate It can be obtained from the frequency domain expression (29) of the system frequency deviation through the Laplace transform final value theorem and initial value theorem.

[0112]

[0113] The scenario of temperature-controlled load clusters participating in the power system frequency response model reduction based on Routh approximation is analyzed as an example.

[0114] At t=0.5s, the system was subjected to a 0.2pu power disturbance, and the frequency exceeded the limit. The hydropower units and the temperature control load cluster responded to the system frequency change and provided power support for system frequency recovery.

[0115] The system frequency deviation curves before and after order reduction using the improved Routh approximation are as follows: Figure 4 As shown. Maximum drop value of high-order system frequency deviation Time to reach the lowest point The maximum frequency deviation of the second-order system obtained by Routh approximation reduction The relative error of the maximum system frequency deviation before and after order reduction is 8.24%, indicating that the improved Routh approximation can ensure the approximate accuracy of the system frequency response process. The analytical expression of key system frequency information derived from the reduced-order system model has certain guiding significance for frequency regulation analysis.

[0116] Further verify the effect of the improved Routh approximation on system stability, Figure 5 、 6 The distribution diagrams of the system zeros and poles before and after order reduction and the distribution diagrams of the system dominant poles are given. The results show that before and after order reduction using the improved Routh approximation, the dominant pole of the system shifts slightly to the right, but the zeros and poles of the system are still distributed in the left half plane, and the system remains stable.

[0117] Figure 7The Bode plots for the system before and after order reduction are shown. The results show that the reduced-order model maintains the accuracy of the main frequency band and the stability characteristics of the original high-order system, which can be used for subsequent analysis of the system's amplitude and phase stability. For the system frequency response model of the integrated temperature-controlled load cluster, the Routh approximation method was used to achieve model order reduction, achieving high approximation accuracy without compromising the stability characteristics of the model before and after order reduction.

[0118] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for applying Routh approximation to a power system frequency response model integrating a temperature-controlled load cluster includes the following steps: (1) Establish a frequency response control model for temperature control load: a. Define the frequency response regulation power provided by the single temperature control load for: Where, and are the operating power of the single temperature control load at time t and t+1 respectively; S DR (t) is the load cluster demand response state variable at time t; b. Temperature control load cluster frequency response control adopts PD control: b1. Total time delay Δt of the temperature control load terminal frequency response execution d is the delay Δt based on 5G communication 5G and load side sampling control period Δt con The superposition of Δt d =Δt con +Δt 5G ; b2. The virtual inertia control link of temperature control load is: Where K vi It is the virtual inertia control parameter of temperature control load; b3. The temperature control load droop control link is: Where K dr is the temperature control load droop control parameter; b4. The total regulation power of the temperature control load cluster frequency response is: Where, Δf(t), f rate (t) are the power system frequency deviation and frequency change rate at time t respectively; (2) Establish a power system frequency response model integrating temperature-controlled load clusters; a. Use the single-machine equivalent method to model the frequency response of the power system; a1. Simplify the power system into a single synchronous motor and equate the power system frequency to the frequency of a single synchronous generator; a2. Perform single-machine equivalence on the synchronous generator set, its prime mover, and speed control system, simplify the entire system into a second-order linear model, and establish a system frequency response model (SFR); b. When the temperature-controlled load cluster on the power consumption side responds to frequency, the load cluster is made equivalent to a traditional generator set through a frequency response control strategy, and the load cluster is regarded as a centralized load. A power system frequency response model integrating the temperature-controlled load cluster is established. (3) Reduce the frequency response model of the power system with integrated temperature-controlled load clusters based on Routh approximation; a. Equivalent the response delay to the first-order inertia link to obtain the transfer function of the system frequency response model; b. Use Routh approximation to obtain a second-order approximation for the system's high-order transfer function; c. The system disturbance power is in step form, and the frequency domain expression of the system frequency information of the reduced-order model is obtained. Using the inverse Laplace transform, the time domain analytical expression of the system frequency key information is obtained.

2. The method for applying Routh approximation according to claim 1 to a power system frequency response model integrating a temperature-controlled load cluster is characterized by: Establish a single-machine equivalent model of the power system and a temperature-controlled load frequency response control model to conduct source-load interaction; The frequency response of the temperature-controlled load cluster adopts virtual inertia control and droop control to provide frequency response regulation power for the power system; Routh approximation is used to reduce the order of the high-order frequency response model of the power system, and the time domain analytical expression of the key frequency information of the system is obtained.

3. The method for applying Routh approximation to a power system frequency response model of an integrated temperature-controlled load cluster according to claim 1, wherein the Routh approximation is a method for reducing the order of a high-order power system frequency response model, comprising the following steps: (1) Using the Pade approximation principle, we take the first-order approximation for the temperature control load response delay link: (2) The transfer function of the power system frequency response model is derived as a rational fraction: The parameters m0~m4, n0~n5 are determined by the following formula: Where M is the inertia time constant of the power system, D is the power system damping, K P , K I and K D are the proportional, integral and differential coefficients of the turbine PID governor, b p is the adjustment coefficient, T y is the servo system time constant, T w is the time constant of water hammer effect; (3) Using the intermediate variable p, let p = 1 / s, take the second-order approximation of the high-order transfer function, and obtain the second-order approximate transfer function of the system with p as the variable. Where, the parameters α1, α2, β1, and β2 are calculated from the high-order transfer function parameters according to the Routh approximation table; (4) Perform parameter reduction s = 1 / p on the system’s second-order approximate transfer function to obtain the power system frequency response second-order transfer function R (2) (s): Where the parameters x0, x1, y0, y1, and y2 are derived from the parameters of the higher-order transfer function.

4. The method for applying Routh approximation to a power system frequency response model for an integrated temperature-controlled load cluster according to claim 1, wherein the Routh approximation is an order reduction method for a high-order power system frequency response model, characterized in that: The response delay link is equivalent to the first-order inertia link, and the transfer function of the power system frequency response model is a rational fraction; The Routh formula is processed using intermediate variables, taking into account the approximate effects of both high and low frequency bands; Based on Routh's second-order approximate transfer function, the time-domain analytical expression of the key frequency information of the power system can be further derived.

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