Routh approximation-based temperature control load participation power system frequency response reduction method

Abstract

The invention provides a model reduction method for a temperature control load to participate in demand response control of a power system based on Routh approximation. Comprising the following steps: proposing an application scene and a model order reduction processing method of Routh approximation in temperature control load demand response; establishing a power system frequency response reduced-order model of the integrated temperature control load cluster; and obtaining an analytic expression of the system frequency response frequency key information, wherein the analytic expression comprises a system frequency deviation maximum drop value, a steady-state frequency deviation and a maximum frequency change rate. The temperature control load frequency response reduced-order model obtained through the method keeps the main frequency band precision of an original high-order system and keeps the stable characteristics of the original high-order system, and a system frequency key information analytic expression obtained through deduction of the reduced-order system model has certain guiding significance for frequency adjustment analysis.

Description

Technical Field

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

[0002] When the power system is disturbed, the system frequency changes. The traditional power system mainly achieves real-time power balance by adjusting the output of thermal, hydropower and other generators. In recent years, the proportion of power electronic power supply access has continued to increase, but due to the large uncertainty and intermittency of its power generation, it is easy to bring instability to the safe operation of the power system, and its increase in proportion will further compress the system's regulation capacity. Therefore, it is of great practical significance to explore new regulation resources and provide regulation capabilities for the system to resist disturbances. The rapid development of load-side demand response technology provides a new regulation idea for system frequency response.

[0003] The load side, especially the large-scale decentralized distribution of small and micro loads, has received less attention in terms of its potential to provide frequency response support for the power system. With the significant improvement in residents' living standards and the frequent occurrence of extreme high / low temperature weather, the proportion of temperature-controlled loads during the high-load operation of the power grid has continued to rise. In economically developed regions such as Shanghai and Beijing, the proportion of temperature-controlled loads during peak electricity consumption in summer exceeds 50%, and the potential for frequency regulation is huge. In order to hedge the increasing pressure on frequency regulation on the supply side, flexible regulation of large-scale temperature-controlled loads to participate in grid frequency regulation has become an emerging research field under the frequency safety control of power systems.

[0004] The system frequency response model based on the single-machine equivalent method reduces the order of the power system to a second-order linear model, and has the ability to calculate the analytical expression of the key characteristics of the system frequency. The frequency response model based on the single-machine equivalent method is mainly divided into two types: 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 at the same time equates the load cluster to a concentrated load, retains the prime mover and speed regulator model of the generator set, and simplifies the transmission line. On the basis of the former, the SFR model further equates the prime mover and speed regulator of the generator set to a single machine, thereby simplifying the power system frequency response to a second-order linear model. After the system is disturbed, the system frequency response model can be used to derive the analytical expressions of the power system frequency deviation, frequency change rate, time to reach the lowest point, frequency lowest point, and steady-state frequency value, quantitatively analyze the influence of system parameters on the dynamic characteristics of frequency, effectively improve the analysis speed of system frequency response, and provide a fast and intuitive tool for frequency stability analysis.

[0005] When considering the demand response of the load cluster on the power consumption side, the load cluster can be made equivalent to the traditional generator set through the corresponding control strategy, and the load cluster can be equivalent to a centralized load. The power system model of the integrated temperature-controlled load cluster is established to realize source-load interaction. However, the power system frequency response model of the integrated temperature-controlled load cluster has high-order characteristics, and it is difficult to directly solve the time-domain analytical expression of the 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 to lay the foundation for quantitative analysis of frequency response control parameters is a technical problem that technical personnel in this field urgently need to solve. Summary of the invention

[0007] The purpose of the present invention is to propose an application method of Routh approximation in the frequency response model reduction of the power system in which the temperature control load participates, so as to realize the second-order equivalence of the frequency response model of the power system. The time domain analytical expression of the frequency key information of the frequency response model of the power system integrating the temperature control load cluster is derived, and a quantitative analysis tool is provided for the design of the frequency response control parameters of the temperature control load.

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

[0009] The method for applying Routh approximation in the frequency response model of a power system 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. The frequency response control of the temperature control load cluster 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 the 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. 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 system frequency response of 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 make the grid frequency equivalent 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 the traditional generator set through the demand response control strategy, and the load cluster is equivalent to a centralized load, and a power system model of the 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 take 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 a high-order power system, 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] Wherein 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 an application method of Routh approximation in a power system frequency response model of an integrated temperature-controlled load cluster, using a single-machine equivalent method to establish a power system SFR model, with the load cluster equivalent to a concentrated load, to establish a power system model of an integrated temperature-controlled load cluster, and to achieve source-load interaction. The Routh approximation order reduction method performs a second-order equivalent on a high-order model of the system frequency response, thereby being able 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, effectively improving the analysis speed of the system frequency response, and providing a fast and intuitive tool for frequency stability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying 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 in 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 clusters is used to generate the system frequency deviation curve before and after the reduction of the order using Routh approximation;

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

[0048] Figure 6 The dominant pole distribution diagram of the system before and after the reduction of the frequency response model of the power system with integrated temperature-controlled load cluster using Routh approximation;

[0049] Figure 7 The Bode diagram of the system before and after order reduction using Routh approximation for the frequency response model of the power system with integrated temperature-controlled load cluster. 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 approximation proposed in the present invention to the frequency response model of the power system integrated with the temperature control 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 command 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 When set to 0, the load exits the response and normal temperature control operation is performed to restore 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 the single temperature control load can provide to the power system is as follows:

[0057]

[0058] In response to system frequency changes, the temperature control load cluster demand response adopts comprehensive 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 command, and issues the control command 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, network communication, and load terminal execution of each control layer 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 the 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 power system frequency deviation and frequency change rate at time t respectively.

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

[0068] The frequency response modeling of the traditional power system is carried out using the single machine equivalent method. The power system is simplified into a single synchronous motor, and the grid frequency is equivalent to the frequency of a single synchronous generator; the synchronous generator set and its prime mover and speed control system are equivalent to a single machine, and the system frequency response model SFR model 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 on the power consumption side responds to demand, the load cluster is made equivalent to the 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 control load cluster is established. Figure 2 As shown, 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 taken as a first-order approximation, which is equivalent to a 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 the second-order approximation for the high-order transfer function R(s):

[0091]

[0092] Wherein 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 in the formula are all derived from the parameters of the high-order transfer function.

[0097]

[0098] (3) Using the second-order model of power system frequency response 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 parameter derivation results are as follows:

[0104]

[0105] By differentiating the frequency deviation, we can obtain the time domain analytical formula 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 cluster participating in the power system frequency response model reduction based on Routh approximation is taken as an example for analysis.

[0114] The system was subjected to a 0.2pu power disturbance at t=0.5s, 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 value of the system frequency deviation before and after order reduction is 8.24%, so the improved Routh approximation can ensure the approximate accuracy of the system frequency response process. The analytical formula of the key information of the system frequency derived from the reduced-order system model has certain guiding significance for frequency regulation analysis.

[0116] Further verify the impact of the improved Routh approximation on system stability. Figure 5 , 6 The distribution diagrams of the system zero poles and the dominant poles before and after order reduction are given. From the results, it can be seen that the dominant poles of the system move slightly to the right before and after order reduction using the improved Routh approximation, but the system zero poles are still distributed in the left half plane, and the system remains stable.

[0117] Figure 7The Bode diagrams of the system before and after order reduction are shown in Figure 2. The results show that the reduced-order model maintains the main frequency band accuracy of the original high-order system and the stability characteristics of the original high-order system, which can be used for subsequent analysis of the amplitude and phase stability of the system. For the system frequency response model of the integrated temperature control load cluster, the Routh approximation method is used to achieve model order reduction, which has high approximation accuracy and does not affect the stability characteristics of the model before and after order reduction.

[0118] The embodiments described above 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, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. The application method of Routh approximation in the frequency response model of the power system integrating the temperature control load cluster includes the following steps: (1) Establish a demand response control model for temperature control loads: a. Define the frequency response regulation power provided by the single temperature control load as: b. The frequency response control of the temperature control load cluster adopts PD control: b1. Total delay Δt of load terminal demand response execution d is the delay Δt based on 5G communication 5G And the 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: b3. Temperature control load droop control link is: b4. The total power of the temperature control load cluster demand response is: (2) Establish an equivalent model of system frequency response of integrated temperature control load; a. Use the single-machine equivalent method to model the frequency response of traditional power systems. a1. Simplify the power system into a single synchronous motor and make the grid frequency equivalent 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 (System Frequency Response, SFR) model; b. When the load cluster on the electricity consumption side responds to demand, the load cluster is made equivalent to the traditional generator set through the demand response control strategy, and the load cluster is equivalent to a centralized load, and a power system model of the integrated temperature-controlled load cluster is established. (3) The frequency response model of the power system with integrated temperature-controlled load cluster is reduced 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 take 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 application of Routh approximation according to claim 1 in the frequency response model of the power system integrating the temperature control load cluster is characterized by: Establish a single-machine equivalent model of the power system and a temperature-controlled load demand 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 regulation power for the power system; The 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. Routh approximation is a method for reducing the frequency response model of a high-order power system, including the following steps: (1) Using the Pade approximation principle, we take the first-order approximation for the temperature control load demand response delay link: (2) The transfer function of the power system frequency response model is derived as a rational fraction: (3) Using the intermediate variable p, a second-order approximation is taken for the high-order transfer function: Wherein 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 second-order approximate transfer function to obtain the second-order transfer function of the power system frequency response: The parameters in the formula are all derived from the parameters of the high-order transfer function.

4. The method for reducing the frequency response model of a high-order power system using Routh approximation according to claim 3 is characterized in that: The delay link is equivalent to the first-order inertia link, and the power system frequency response transfer function is a rational fraction; The Routh formula is processed using intermediate variables, taking into account the approximate effects of both high-frequency and low-frequency bands; Based on Routh's approximate second-order transfer function, the time-domain analytical expression of the key frequency information of the power system can be further derived.

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