Method for evaluating frequency response performance of doubly-fed variable-speed pumped storage unit

Abstract

The invention belongs to the technical field of primary frequency modulation control of doubly-fed variable-speed pumped storage units, and particularly discloses a method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit. Establishing a linear model of the doubly-fed variable-speed pumped storage unit participating in primary frequency regulation, and further constructing a system frequency response full-order model containing the doubly-fed variable-speed pumped storage unit; performing order reduction on the system frequency response full-order model containing the doubly-fed variable-speed pumped storage unit to obtain a system equivalent second-order frequency response equation containing the doubly-fed variable-speed pumped storage unit, and performing analysis to obtain a time domain function containing the doubly-fed variable-speed pumped storage unit system frequency response and a typical frequency modulation dynamic performance index; and further analyzing key parameters and influence rules which influence the frequency response performance of the doubly-fed variable-speed pumped storage system. The method solves the problem that the accuracy of the frequency modulation model and the analytic and quantitative performance of the frequency modulation mechanism cannot be considered in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of primary frequency modulation control of double-fed variable-speed pumped storage units, and particularly relates to a frequency response performance evaluation method for double-fed variable-speed pumped storage units. BACKGROUND

[0002] In recent years, with the continuous development of renewable energy such as wind and light, large-scale renewable energy access to the power system has become an inevitable trend of future power system development. However, due to the strong randomness and uncertainty of renewable energy such as wind and light, it has brought great challenges to the stable operation of the system. In order to further improve the proportion of renewable energy access and improve the stability of the system, energy storage has been developed vigorously, among which double-fed variable-speed pumped storage has become a new development trend due to its wider regulation range, higher operation efficiency and greater flexibility. In order to alleviate the increasingly deteriorating frequency problem of the new power system, it has great research and practical value to study the frequency response performance of double-fed variable-speed pumped storage system.

[0003] At present, the methods for researching the frequency response model of variable-speed pumped storage can be divided into three categories: the first category is the time-domain simulation full characteristic model, which obtains the characteristics of each element in the variable-speed pumped storage unit through time-domain simulation; the second category is the advanced model, which obtains the frequency response characteristics of the variable-speed pumped storage unit through advanced technologies such as big data and intelligent algorithms; the third category is the low-order model method, which equivalent the variable-speed pumped storage to the traditional hydroelectric generating set to analyze the system response characteristics after the pumped storage participates in frequency modulation.

[0004] However, in the first method, the response characteristics of the system are obtained through time-domain simulation, which is difficult to analyze and express the frequency modulation mechanism, and the response model established when the system or control parameters change will be invalid; the second method blurs the physical nature of frequency modulation, and it is difficult to explain the frequency modulation mechanism, and a large amount of experimental data is needed as the basis; the third method can reveal and analyze the frequency modulation mechanism to some extent, but the double-fed variable-speed pumped storage unit has a wider frequency modulation space than the traditional hydroelectric generating set due to the adjustable guide vane and speed. SUMMARY

[0005] The purpose of the present application is to solve the problem that the prior art cannot balance the accuracy of the frequency modulation model and the analysis and quantification of the frequency modulation mechanism, and a frequency response performance evaluation method for double-fed variable-speed pumped storage units is proposed.

[0006] The technical scheme of the present application is: a frequency response performance evaluation method for double-fed variable-speed pumped storage units, comprising the following steps: Based on the actual physical structure of the double-fed variable-speed pumped storage unit, a linear model of the double-fed variable-speed pumped storage unit participating in primary frequency regulation is established; Based on the linear model of the doubly-fed variable speed pumped storage unit participating in primary frequency regulation, a full-order model of system frequency response containing the doubly-fed variable speed pumped storage unit is constructed; The full-order model of system frequency response containing the doubly-fed variable speed pumped storage unit is reduced by the Routh reduction method to obtain an equivalent two-order frequency response equation of the system containing the doubly-fed variable speed pumped storage unit; Based on the equivalent two-order frequency response equation of the system containing the doubly-fed variable speed pumped storage unit, a time domain function of the system frequency response containing the doubly-fed variable speed pumped storage unit is obtained; According to the time domain function of the system frequency response containing the doubly-fed variable speed pumped storage unit, typical frequency modulation dynamic performance indexes are obtained; Based on the typical frequency modulation dynamic performance indexes, key parameters affecting the frequency response performance of the doubly-fed variable speed pumped storage system and the influence law are obtained, and the frequency response performance evaluation of the doubly-fed variable speed pumped storage unit is completed.

[0007] As preferred, the linear model of the doubly-fed variable speed pumped storage unit participating in primary frequency regulation is:

[0008]

[0009]

[0010]

[0011] wherein, represents the electromagnetic power of the doubly-fed variable speed pumped storage unit, represents the mechanical power of the doubly-fed variable speed pumped storage unit, represents the mechanical guide vane opening of the doubly-fed variable speed pumped storage unit, represents the electromagnetic guide vane opening of the doubly-fed variable speed pumped storage unit, represents the rotor speed deviation of the doubly-fed variable speed pumped storage unit, represents the linearized transfer function of the electromagnetic power of the doubly-fed variable speed pumped storage unit to the mechanical guide vane opening, represents the linearized transfer function of the mechanical guide vane opening of the doubly-fed variable speed pumped storage unit to the electromagnetic guide vane opening, represents the linearized transfer function of the electromagnetic power of the doubly-fed variable speed pumped storage unit to the rotor speed deviation, represents the linearized transfer function of the rotor speed deviation of the doubly-fed variable speed pumped storage unit to the mechanical power, represents the linearized transfer function of the mechanical power of the doubly-fed variable speed pumped storage unit to the rotor speed deviation, represents the water hammer time constant, denotes Laplace operator, denotes the time constant of the governing system of the guide vane, denotes the droop coefficient of the pumped storage unit, denotes the inertia coefficient of the pumped storage unit.

[0012] As preferred, the system frequency response full order model of the pumped storage unit with double-fed variable speed is:

[0013] wherein, denotes the frequency response transfer function of the pumped storage unit with double-fed variable speed system, denotes the inertia time constant of the pumped storage unit with double-fed variable speed system, denotes Laplace operator, denotes the damping of the pumped storage unit with double-fed variable speed system, , and is a linearized transfer function of the electromagnetic power of the double-fed variable speed pumped storage unit to the rotor speed deviation is an auxiliary variable constructed, denotes a linearized transfer function of the electromagnetic power of the double-fed variable speed pumped storage unit to the mechanical guide vane opening, denotes a linearized transfer function of the mechanical guide vane opening of the double-fed variable speed pumped storage unit to the electromagnetic guide vane opening, denotes the reset time of the double-fed variable speed pumped storage unit, denotes the time constant of the synchronous machine governor, denotes the reheating time constant of the synchronous machine, denotes the transient droop coefficient of the pumped storage unit, denotes the permanent droop coefficient of the pumped storage unit, denotes the turbine droop coefficient, denotes the reheating coefficient of the synchronous machine, denotes the proportion of renewable energy access, denotes the proportion of pumped storage access, denotes the proportion of synchronous machine access, denotes the droop coefficient of clean energy, denotes the inertia coefficient of clean energy, denotes the droop coefficient of the pumped storage unit, denotes the inertia coefficient of the pumped storage unit.

[0014] As preferred, the system frequency response full order model of the pumped storage unit with double-fed variable speed is reduced by the Routh reduction method, and the system equivalent second order frequency response equation of the pumped storage unit with double-fed variable speed is obtained, which is specifically: The full-order model of the system frequency response containing the doubly-fed variable-speed pumped storage unit is reorganized to obtain the higher-order form of the full-order model of the system frequency response containing the doubly-fed variable-speed pumped storage unit. make And substitute it into the higher-order form of the full-order model of the system frequency response containing the doubly-fed variable-speed pumped storage unit. ; Using the Routh reduction method, Take a second-order approximation, and then... Restore to The equivalent second-order frequency response equation of the system containing the doubly-fed variable-speed pumped storage unit is obtained as follows:

[0015] in, This represents the equivalent second-order frequency response transfer function of a system containing a doubly-fed variable-speed pumped storage unit. , , , and The coefficients of the second-order frequency response transfer function of a system containing a doubly fed variable-speed pumped storage unit after order reduction are represented.

[0016] As a preferred embodiment, based on the equivalent second-order frequency response equation of the system containing the doubly-fed variable-speed pumped storage unit, the time-domain function of the system frequency response containing the doubly-fed variable-speed pumped storage unit is obtained, specifically as follows: Based on the system equivalent second-order frequency response equation of the doubly-fed variable-speed pumped storage unit, the system frequency response containing the doubly-fed variable-speed pumped storage unit is obtained. :

[0017] in, This indicates the disturbance power of a system including doubly-fed variable-speed pumped storage units. Let represent the system equivalent second-order frequency response transfer function of a doubly-fed variable-speed pumped storage unit. Represents the Laplace operator; frequency response of a system containing doubly-fed variable-speed pumped storage units. Performing an inverse Laplace transform, we obtain the time-domain function of the frequency response of the system containing the doubly-fed variable-speed pumped storage unit:

[0018] in, The time-domain function representing the frequency response of a system containing a doubly-fed variable-speed pumped storage unit. This represents the amplitude of the system response, including the doubly-fed variable-speed pumped storage unit. Represents the natural base. Represents the cosine function. φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, ω(ω) represents the angular frequency of the response of the system with doubly-fed variable speed pumped storage units, Δφ(ω) represents the phase difference of the response of the system with doubly-fed variable speed pumped storage units,

[0019] wherein, , , , and φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, ω(ω) represents the angular frequency of the response of the system with doubly-fed variable speed pumped storage units, Δφ(ω) represents the phase difference of the response of the system with doubly-fed variable speed pumped storage units,

[0020] as preferred, the typical frequency modulation dynamic performance indicators include: initial frequency change rate, frequency minimum point time, quasi-steady state frequency deviation and maximum frequency deviation.

[0021] as preferred, the analytical expression of the initial frequency change rate is:

[0022] wherein, φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, ω(ω) represents the angular frequency of the response of the system with doubly-fed variable speed pumped storage units, Δφ(ω) represents the phase difference of the response of the system with doubly-fed variable speed pumped storage units, φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, ω(ω) represents the angular frequency of the response of the system with doubly-fed variable speed pumped storage units, Δφ(ω) represents the phase difference of the response of the system with doubly-fed variable speed pumped storage units, φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, ω(ω) represents the angular frequency of the response of the system with doubly-fed variable speed pumped storage units, Δφ(ω) represents the phase difference of the response of the system with doubly-fed variable speed pumped storage units, and φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units,

[0023] as preferred, the analytical expression of the quasi-steady state frequency deviation is:

[0024] wherein, φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, φ(ω) represents the phase angle of the response of the system with doubly-fed variable speed pumped storage units, ω(ω) represents the angular frequency of the response of the system with doubly-fed variable speed pumped storage units, and denotes the second-order frequency response transfer function coefficient of the reduced-order system of the doubly-fed variable-speed pumped storage unit system.

[0025] As preferred, the analytical expression of the maximum frequency deviation is:

[0026] wherein, denotes the maximum frequency deviation, denotes the disturbance power of the doubly-fed variable-speed pumped storage unit system, denotes the response amplitude of the doubly-fed variable-speed pumped storage unit system, denotes the natural base, denotes the cosine function, denotes the phase angle of the response of the doubly-fed variable-speed pumped storage unit system, denotes the angular frequency of the response of the doubly-fed variable-speed pumped storage unit system, denotes the phase difference of the response of the doubly-fed variable-speed pumped storage unit system, denotes the frequency minimum point time.

[0027] As preferred, the analytical expression of the frequency minimum point time is:

[0028] wherein, denotes the inverse tangent function, denotes the enumeration of all time point numbers satisfying that the frequency deviation reaches the maximum value, , , , and denotes the second-order frequency response transfer function coefficient of the reduced-order system of the doubly-fed variable-speed pumped storage unit system.

[0029] The beneficial effects of the present application are: The doubly-fed variable-speed pumped storage unit frequency response performance evaluation method of the present application takes into account the accuracy of the frequency modulation model and reveals the frequency modulation mechanism, analytically expresses the frequency modulation performance of the doubly-fed variable-speed pumped storage unit, deeply analyzes the key factors and influence law of the frequency modulation capacity, and as a by-product of production, can deeply mine and improve the frequency modulation capacity of the doubly-fed variable-speed pumped storage unit, and ensure the safety and stability of the new power system. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 Fig. 1 shows a doubly-fed variable-speed pumped storage unit frequency response performance evaluation method flowchart provided by Embodiment 1 of the present application.

[0031] Figure 2 The diagram shown is a power control block diagram of a doubly-fed variable-speed pumped storage unit provided in Embodiment 1 of the present invention.

[0032] Figure 3 The figure shown is the maximum power tracking curve of the doubly fed variable speed pumped storage unit provided in Embodiment 1 of the present invention.

[0033] Figure 4 The figure shows the linearized frequency response model of the doubly fed variable speed pumped storage unit provided in Embodiment 1 of the present invention.

[0034] Figure 5 The figure shows the frequency response model of a power system containing a doubly fed variable speed pumped storage unit provided in Embodiment 2 of the present invention.

[0035] Figure 6 The figure shows a comparison of the response curves of the full-order model and the reduced-order second-order equivalent model of the doubly-fed variable-speed pumped storage unit provided in Embodiment 2 of the present invention.

[0036] Figure 7 The figure shows the water hammer time constant of the doubly-fed variable-speed pumped storage unit provided in Embodiment 2 of the present invention. The dynamic response diagram of the system under change.

[0037] Figure 8 The figure shows the permanent inertia droop coefficient of the governor for the doubly-fed variable-speed pumped storage unit provided in Embodiment 2 of the present invention. The dynamic response diagram of the system under change.

[0038] Figure 9 The figure shows the droop coefficient of the electromagnetic power control circuit for the doubly-fed variable-speed pumped storage unit provided in Embodiment 2 of the present invention. The dynamic response diagram of the system under change.

[0039] Figure 10 The figure shows the inertia coefficient of the electromagnetic power control element of the doubly-fed variable-speed pumped storage unit provided in Embodiment 2 of the present invention. The dynamic response diagram of the system under change. Detailed Implementation

[0040] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0041] Example 1: like Figure 1 As shown, a method for evaluating the frequency response performance of a doubly-fed variable-speed pumped storage unit includes the following steps: S1. Based on the actual physical structure of the double-fed variable-speed pumped storage unit, a linear model of the double-fed variable-speed pumped storage unit participating in primary frequency regulation is established; S2. Based on the linear model of the double-fed variable-speed pumped storage unit participating in primary frequency regulation, a full-order model of the system frequency response containing the double-fed variable-speed pumped storage unit is constructed; S3. The full-order model of the system frequency response containing the double-fed variable-speed pumped storage unit is reduced by the Routh reduction method, and an equivalent two-order frequency response equation of the system containing the double-fed variable-speed pumped storage unit is obtained; S4. Based on the equivalent two-order frequency response equation of the system containing the double-fed variable-speed pumped storage unit, a time domain function of the system frequency response containing the double-fed variable-speed pumped storage unit is obtained; S5. According to the time domain function of the system frequency response containing the double-fed variable-speed pumped storage unit, a typical frequency modulation dynamic performance index is obtained; S6. Based on the typical frequency modulation dynamic performance index, the key parameters affecting the frequency response performance of the double-fed variable-speed pumped storage system and the influence law are obtained, and the frequency response performance evaluation of the double-fed variable-speed pumped storage unit is completed.

[0042] In this embodiment, step S1 is specifically: The control block diagram of the double-fed variable-speed pumped storage unit in the power generation condition is as shown in Figure 2 , which can be divided into a mechanical link and an electromagnetic link; In the mechanical link, the mechanical power obtained by the pumped storage unit from the water is expressed as:

[0043]

[0044]

[0045]

[0046] wherein, P represents a power coefficient, P represents a double-fed variable-speed pumped storage operating condition characteristic parameter, Q represents a flow of the double-fed variable-speed pumped storage unit, H represents an effective water head of the double-fed variable-speed pumped storage unit, is an intermediate calculation variable, R represents a radius of a turbine blade, A represents an area of the turbine blade, ω represents a rotor speed of the double-fed variable-speed pumped storage unit, , , , 、 、 、 、 and represent the fitting coefficients of the mechanical power curve; Further, the effective power of the pumped storage unit is mainly related to the guide vane opening and the rotating speed of the unit. The linear model of the pumped storage unit is obtained by small signal analysis method as follows:

[0047] wherein, represents the mechanical power of the doubly-fed variable-speed pumped storage unit, represents the water hammer time constant, represents the Laplace operator, represents the time constant of the governor, represents the electromagnetic guide vane opening of the doubly-fed variable-speed pumped storage unit, represents the rotor rotating speed deviation of the doubly-fed variable-speed pumped storage unit.

[0048] In the electromagnetic link, the maximum power point tracking curve of the doubly-fed variable-speed pumped storage unit is shown in Figure 3 , and the linear expression of the output electromagnetic power of the unit when the unit is at the maximum power point tracking is as follows:

[0049] wherein, represents the transfer function of the electromagnetic power of the doubly-fed variable-speed pumped storage unit to the rotor rotating speed, and represent the fitting parameters of the maximum power tracking curve, represents the initial rotor speed of the doubly-fed variable-speed pumped storage unit; Thus, the linear model of the doubly-fed variable-speed pumped storage unit participating in the primary frequency regulation can be obtained as follows:

[0050]

[0051]

[0052]

[0053] wherein, represents the electromagnetic power of the doubly-fed variable-speed pumped storage unit, represents the mechanical power of the doubly-fed variable-speed pumped storage unit, represents the mechanical guide vane opening of the doubly-fed variable-speed pumped storage unit, represents the electromagnetic guide vane opening degree of the doubly-fed variable-speed pumped storage unit, represents the rotor speed deviation of the doubly-fed variable-speed pumped storage unit, represents the linearized transfer function of the electromagnetic power to the mechanical guide vane opening degree of the doubly-fed variable-speed pumped storage unit, represents the linearized transfer function of the mechanical guide vane opening degree to the electromagnetic guide vane opening degree of the doubly-fed variable-speed pumped storage unit, represents the linearized transfer function of the electromagnetic power to the rotor speed deviation of the doubly-fed variable-speed pumped storage unit, represents the linearized transfer function of the rotor speed deviation to the mechanical power of the doubly-fed variable-speed pumped storage unit, represents the linearized transfer function of the mechanical power to the rotor speed deviation of the doubly-fed variable-speed pumped storage unit, represents the water hammer time constant, represents the Laplace operator, represents the delay time constant of the guide vane servo system, represents the droop coefficient of the pumped storage unit, represents the inertia coefficient of the pumped storage unit.

[0054] Further, by introducing auxiliary variables , , , a pumped storage unit linearized frequency response model for decoupling analysis of the mechanical link and the electromagnetic link is established, as shown in Figure 4 , wherein the auxiliary variables are represented as:

[0055]

[0056]

[0057] wherein, represents the damping coefficient of the doubly-fed variable-speed pumped storage unit, represents the transfer function of the mechanical power to the rotor speed of the doubly-fed variable-speed pumped storage unit, represents the inertia coefficient of the doubly-fed variable-speed pumped storage unit.

[0058] The linearized model of the frequency regulation of the doubly-fed variable-speed pumped storage unit established by the embodiment of the application realizes decoupling analysis of the guide vane opening degree control and the rotor speed control, and is beneficial to subsequent construction of a system frequency response full-order model containing the doubly-fed variable-speed pumped storage unit.

[0059] In the embodiment, the system full-order frequency response model containing the doubly-fed variable-speed pumped storage unit is as shown in Figure 5 , and the system frequency response full-order model containing the doubly-fed variable-speed pumped storage unit is:

[0060] wherein, represents a frequency response transfer function of a system containing a doubly-fed variable-speed pumped storage unit, represents an inertia time constant of a system containing a doubly-fed variable-speed pumped storage unit, represents a Laplace operator, represents a damping of a system containing a doubly-fed variable-speed pumped storage unit, , and is an auxiliary variable, represents a water hammer time constant, represents a linearized transfer function of an electromagnetic power of a doubly-fed variable-speed pumped storage unit to a mechanical guide vane opening degree, represents a linearized transfer function of a mechanical guide vane opening degree of a doubly-fed variable-speed pumped storage unit to an electromagnetic guide vane opening degree, represents a reset time of a doubly-fed variable-speed pumped storage unit, represents a governor time constant of a synchronous machine, represents a reheating time constant of a synchronous machine, represents a pumped storage transient droop coefficient, represents a pumped storage permanent droop coefficient, represents a turbine droop coefficient, represents a reheating coefficient of a synchronous machine, represents a renewable energy access ratio, represents a pumped storage access ratio, represents a synchronous machine access ratio, represents a clean energy droop coefficient, represents a clean energy inertia coefficient, represents a pumped storage unit droop coefficient, represents a pumped storage unit inertia coefficient.

[0061] The above system frequency response full-order model containing a doubly-fed variable-speed pumped storage unit is arranged to obtain a high-order expression of the system frequency response full-order model containing a doubly-fed variable-speed pumped storage unit:

[0062] wherein, , , , and represent polynomial coefficients after simplification of a transfer function numerator term;

[0063] wherein, , and denotes the intermediate calculation coefficient of the system response function of the double-fed variable speed pumped storage unit system, , , , denotes the droop coefficient of the synchronous machine, denotes the reheating time constant of the synchronous machine;

[0064] wherein, , , , , and denotes the polynomial coefficient of the simplified denominator of the transfer function, and denotes the intermediate calculation constant, , , denotes the damping of the double-fed variable speed pumped storage unit system, denotes the reheating coefficient of the synchronous machine.

[0065] Substituting into the high-order expression of the full-order model of the system frequency response of the double-fed variable speed pumped storage unit, we obtain:

[0066] By the Routh reduction method, we obtain a second-order approximation:

[0067] wherein, and denote the calculation coefficients of the denominator part in the Routh reduction method, and denote the calculation coefficients of the numerator part in the Routh reduction method, and we have:

[0068] Substituting back to we obtain:

[0069] wherein, , , , and denote the second-order frequency response transfer function coefficients of the double-fed variable speed pumped storage unit system after reduction, which are calculated by the following formula:

[0070] The second-order frequency response transfer function of the double-fed variable speed pumped storage unit system derived by the embodiment of the application can accurately reflect the frequency response characteristics of the system, and lays a foundation for subsequent research on the frequency response performance and key influencing factors of the system.

[0071] In the embodiment, step S3 is specifically: Considering that the step form of disturbance is the most common and has the greatest impact in the power system, such as generator tripping, load surge, etc., it is assumed that the disturbance power of the double-fed variable speed pumped storage unit system is represented by The frequency response of the system is The expression is:

[0072] The frequency response of the double-fed variable speed pumped storage unit system The time domain expression of the frequency response of the double-fed variable speed pumped storage unit system is obtained by inverse Laplace transform of the expression :

[0073] Wherein, represents the amplitude of the response of the double-fed variable speed pumped storage unit system, represents the natural base, represents the cosine function, represents the phase angle of the response of the double-fed variable speed pumped storage unit system, represents the angular frequency of the response of the double-fed variable speed pumped storage unit system, represents the phase difference of the response of the double-fed variable speed pumped storage unit system, and has:

[0074] The time domain expression of the frequency response of the double-fed variable speed pumped storage unit system quantifies the frequency dynamic response behavior of the system after the disturbance, and based on this, the analytical expression of the typical frequency modulation dynamic performance index can be further derived. Common typical frequency modulation dynamic performance indexes include initial frequency change rate, quasi-steady state frequency deviation and maximum frequency deviation. These frequency response typical parameters can be obtained by the time domain expression of the system frequency response. The time domain expression of the system frequency response The derivative of time is obtained as:

[0075] The maximum value of the system frequency occurs at the initial time of the disturbance, and The maximum value of the frequency change rate is obtained by substituting into the expression of the system frequency change rate.

[0076] When the frequency rate of change is 0, the system frequency reaches a minimum point, the maximum frequency deviation The expression is as follows:

[0077] Wherein, the time to reach the minimum point of frequency is:

[0078] The steady-state frequency of the system refers to the limit value of the frequency deviation after the system reaches a stable state, the frequency deviation when the time tends to infinity will be brought into the expression of the system frequency rate of change, to obtain the expression of the quasi-steady-state frequency deviation The expression is as follows:

[0079] From the analysis of the typical frequency modulation dynamic performance indicators, it can be seen that the key control parameters affecting the frequency modulation characteristics of the double-fed variable speed pumped storage unit include the water hammer coefficient , the permanent droop coefficient of the speed regulator , the droop control coefficient of the electromagnetic link and the inertia control coefficient . Example 2 On the basis of example 1, the accuracy of the reduced second-order system response function and the influence law of the key control parameters on the frequency modulation characteristics of the double-fed variable speed pumped storage unit are verified. Based on the linearization model of the variable speed pumped storage unit, the power system frequency response model of the double-fed variable speed pumped storage unit is constructed as shown in Figure 5 , and the frequency response curves of the double-fed variable speed pumped storage unit full characteristic model and the reduced second-order system under the generating condition are compared as shown in Figure 6 .

[0080] Table 1 power system parameters

[0081] Table 2 double-fed variable speed pumped storage unit parameters

[0082] Figure 6 As shown in the figure, when a 0.1 p.u. load disturbance occurs at t=0, the full characteristic model response curve and the reduced second-order equivalent system response curve. From the figure, it can be seen that the maximum frequency deviation before and after reduction is-7.45×10 -2The change in PU is -7.62 × 10⁻⁶. -2 pu, with an error of 0.17×10 -2 The time to reach the lowest frequency point changed from 5.2s to 6s, while the steady-state deviation and the rate of change of the initial frequency were almost equal before and after the order reduction. Therefore, from the perspective of frequency regulation performance indicators, the accuracy of the model can be measured as follows: the established second-order equivalent frequency response model of the doubly-fed variable-speed pumped storage unit basically matches the simulation results of the full-characteristic model, thus verifying the correctness and accuracy of the established model.

[0083] Furthermore, in order to verify the correctness of the derived frequency modulation performance index and to explore its influence on frequency modulation characteristics, the response curves of the system frequency under different control parameters were compared.

[0084] Figure 7 To apply a load disturbance of 0.1 pu at t=1s, adjust the water hammer time constant of the doubly-fed variable-speed pumped storage unit. The system frequency response curves are shown for different values ​​(0.5s, 1s, 5s, and 10s). Simulation results show that the water hammer time constant mainly affects the maximum frequency deviation. As the water hammer time constant increases, the system frequency deviation increases, and the time to reach the minimum frequency also gradually increases, but the effect on the maximum frequency deviation gradually decreases. Changes in the water hammer time constant have almost no effect on the rate of frequency change or the steady-state frequency deviation.

[0085] Figure 8 To apply a load disturbance of 0.1 pu at t=1s, adjust the permanent droop coefficient of the governor of the doubly-fed variable-speed pumped storage unit. The system frequency response curves are shown for values ​​of 0.03, 0.05, 0.07, and 0.09. Simulation results indicate that the permanent droop coefficient of the governor in the variable-speed pumped-storage unit primarily affects the maximum frequency deviation, the time to reach the minimum frequency, and the steady-state frequency deviation, while having little impact on the rate of frequency change. Furthermore, the permanent droop coefficient increases with increasing frequency. As the droop coefficient increases, the maximum frequency deviation of the system will increase, as will the time to reach the minimum frequency and the steady-state frequency deviation. However, the effect gradually decreases as the permanent droop coefficient increases, which is consistent with the aforementioned theoretical analysis results and verifies the correctness of the derived expression for the typical frequency response index.

[0086] Figure 9 To apply a load disturbance of 0.1 pu at t=1s, adjust the droop control coefficient of the electromagnetic link of the doubly-fed variable-speed pumped storage unit. The system frequency response curves are shown in (1, 2, 3, and 4). Simulation results show that the droop control coefficient of the electromagnetic link in the variable-speed pumped-storage unit mainly affects the maximum frequency deviation, the time to reach the minimum frequency, and the steady-state frequency deviation, while having little effect on the rate of frequency change. Furthermore, with the droop control coefficient... As the value of increases, the maximum value of the system frequency deviation decreases, as does the time to reach the lowest frequency and the steady-state frequency deviation. However, the effect gradually increases with the increase of the permanent droop coefficient, which is consistent with the aforementioned theoretical analysis results and verifies the correctness of the derived expression for the typical frequency response index.

[0087] Figure 10 To apply a load disturbance of 0.1 pu at t=1s, adjust the inertia control coefficient of the electromagnetic link of the doubly-fed variable-speed pumped storage unit. The system frequency response curves are shown in (2, 4, 6, and 8). Simulation results indicate that the inertia control coefficient of the electromagnetic link in the variable-speed pumped-storage unit mainly affects the maximum frequency deviation and the time to reach the minimum frequency, while having little impact on the rate of frequency change and steady-state frequency deviation. Furthermore, with the increase in the inertia control coefficient... As the coefficient of permanent droop increases, the maximum value of the system frequency deviation will decrease, but it mainly affects the steady-state recovery time. However, as the permanent droop coefficient increases, the effect gradually decreases, which is consistent with the aforementioned theoretical analysis results and verifies the correctness of the derived expression for the typical frequency response index.

[0088] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit, characterized by, The method comprises the following steps: A linear model of the double-fed variable-speed pumped storage unit participating in primary frequency regulation is established based on the actual physical structure of the double-fed variable-speed pumped storage unit; A full-order model of system frequency response containing the double-fed variable-speed pumped storage unit is constructed based on the linear model of the double-fed variable-speed pumped storage unit participating in primary frequency regulation; The full-order model of system frequency response containing the double-fed variable-speed pumped storage unit is reduced by the Routh reduction method to obtain an equivalent two-order frequency response equation of the system containing the double-fed variable-speed pumped storage unit; A time-domain function of the system frequency response containing the double-fed variable-speed pumped storage unit is obtained based on the equivalent two-order frequency response equation of the system containing the double-fed variable-speed pumped storage unit; Typical frequency modulation dynamic performance indexes are obtained according to the time-domain function of the system frequency response containing the double-fed variable-speed pumped storage unit; Based on the typical frequency modulation dynamic performance indexes, key parameters affecting the frequency response performance of the double-fed variable-speed pumped storage system and the influence law are obtained, and the frequency response performance evaluation of the double-fed variable-speed pumped storage unit is completed.

2. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 1, characterized in that, The linear model of the double-fed variable-speed pumped storage unit participating in primary frequency regulation is: wherein, represents an electromagnetic power of the doubly-fed variable-speed pumped storage unit, represents a mechanical power of the doubly-fed variable-speed pumped storage unit, represents a mechanical guide vane opening degree of the doubly-fed variable-speed pumped storage unit, represents an electromagnetic guide vane opening degree of the doubly-fed variable-speed pumped storage unit, represents a rotor speed deviation of the doubly-fed variable-speed pumped storage unit, represents a linearized transfer function of the electromagnetic power of the doubly-fed variable-speed pumped storage unit with respect to the mechanical guide vane opening degree, represents a linearized transfer function of the mechanical guide vane opening degree of the doubly-fed variable-speed pumped storage unit with respect to the electromagnetic guide vane opening degree, represents a linearized transfer function of the electromagnetic power of the doubly-fed variable-speed pumped storage unit with respect to the rotor speed deviation, represents a linearized transfer function of the rotor speed deviation of the doubly-fed variable-speed pumped storage unit with respect to the mechanical power, represents a linearized transfer function of the mechanical power of the doubly-fed variable-speed pumped storage unit with respect to the rotor speed deviation, represents a water hammer time constant, represents a Laplace operator, represents a delay time constant of a guide vane servo system, represents a droop coefficient of the pumped storage unit, represents an inertia coefficient of the pumped storage unit.

3. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 1, characterized by, The full-order model of system frequency response containing the double-fed variable-speed pumped storage unit is: wherein, represents the frequency response transfer function of the doubly-fed variable speed pumped hydro unit system, represents the inertia time constant of the doubly-fed variable speed pumped hydro unit system, represents the Laplace operator, represents the damping of the doubly-fed variable speed pumped hydro unit system, , and is the linearized transfer function of the electromagnetic power of the doubly-fed variable speed pumped hydro unit to the rotor speed deviation is the auxiliary variable constructed according to the linearized transfer function of the electromagnetic power of the doubly-fed variable speed pumped hydro unit to the rotor speed deviation represents the water hammer time constant, represents the linearized transfer function of the electromagnetic power of the doubly-fed variable speed pumped hydro unit to the mechanical guide vane opening, represents the linearized transfer function of the mechanical guide vane opening of the doubly-fed variable speed pumped hydro unit to the electromagnetic guide vane opening, represents the reset time of the doubly-fed variable speed pumped hydro unit, represents the governor time constant of the synchronous machine, represents the reheating time constant of the synchronous machine, represents the pumped hydro transient droop coefficient, represents the pumped hydro permanent droop coefficient, represents the turbine droop coefficient, represents the reheating coefficient of the synchronous machine, represents the renewable energy access ratio, represents the pumped hydro access ratio, represents the synchronous machine access ratio, represents the clean energy droop coefficient, represents the clean energy inertia coefficient, represents the pumped hydro unit droop coefficient, represents the pumped hydro unit inertia coefficient.

4. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 3, characterized by, The full-order model of system frequency response containing the double-fed variable-speed pumped storage unit is reduced by the Routh reduction method to obtain an equivalent two-order frequency response equation of the system containing the double-fed variable-speed pumped storage unit, which is specifically: The full-order model of system frequency response containing the double-fed variable-speed pumped storage unit is arranged to obtain a high-order form of the full-order model of system frequency response containing the double-fed variable-speed pumped storage unit; Let and substituting into the high-order form of the full-order model of the system frequency response containing the doubly-fed variable-speed pumped storage unit ; By using the Routh reduction method, the system equation is reduced to the second order approximation, and the system equation is further reduced to the second order approximation, and the system equation is further reduced to the second order approximation, and the system equation is further reduced to wherein, represents the equivalent second-order frequency response transfer function of the system with doubly-fed variable-speed pumped storage units, , , , and represents the second-order frequency response transfer function coefficients of the reduced-order system with doubly-fed variable-speed pumped storage units.

5. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 1, characterized by, The time-domain function of the system frequency response containing the double-fed variable-speed pumped storage unit is obtained based on the equivalent two-order frequency response equation of the system containing the double-fed variable-speed pumped storage unit, which is specifically: Based on the second order frequency response equation of the system equivalent of the doubly-fed variable speed pumped storage unit, the frequency response of the system containing the doubly-fed variable speed pumped storage unit is obtained : wherein, represents the disturbance power of the system with doubly-fed variable speed pumped storage unit, represents the system equivalent second-order frequency response transfer function of the doubly-fed variable speed pumped storage unit, represents the Laplace operator; the frequency response of the system with doubly-fed variable speed pumped storage unit the Laplace inverse transform is performed to obtain the time-domain function of the frequency response of the system with doubly-fed variable speed pumped storage unit: wherein, denotes a time-domain function representing frequency response of the doubly-fed variable speed pumped storage unit system, denotes a response amplitude magnitude of the doubly-fed variable speed pumped storage unit system, denotes a natural base number, denotes a cosine function, denotes a phase angle of the response of the doubly-fed variable speed pumped storage unit system, denotes an angular frequency of the response of the doubly-fed variable speed pumped storage unit system, denotes a phase difference of the response of the doubly-fed variable speed pumped storage unit system, wherein , , , and denote the reduced-order frequency response transfer function coefficients of the doubly-fed variable speed pumped storage unit system, denotes the inverse tangent function.

6. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 1, characterized in that, The typical frequency modulation dynamic performance indexes include: initial frequency change rate, frequency minimum point time, quasi-steady-state frequency deviation, and maximum frequency deviation.

7. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 6, characterized in that, The analytical expression of the initial frequency change rate is: wherein, denotes a time-domain function representing frequency response of the doubly-fed variable speed pumped storage unit system to time derivative, denotes a perturbation power of the doubly-fed variable speed pumped storage unit system, denotes a response amplitude of the doubly-fed variable speed pumped storage unit system, denotes a natural base, denotes a cosine function, denotes a phase angle of the response of the doubly-fed variable speed pumped storage unit system, denotes an angular frequency of the response of the doubly-fed variable speed pumped storage unit system, denotes a phase difference of the response of the doubly-fed variable speed pumped storage unit system, and denotes a second-order frequency response transfer function coefficient of the doubly-fed variable speed pumped storage unit system after order reduction.

8. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 6, characterized in that, The analytical expression of the quasi-steady-state frequency deviation is: wherein, denotes the quasi-steady frequency deviation, denotes the time-domain function of the frequency response of the system with doubly-fed variable-speed pumped storage units, denotes the disturbance power of the system with doubly-fed variable-speed pumped storage units, and denotes the second-order frequency response transfer function coefficient of the reduced-order system with doubly-fed variable-speed pumped storage units.

9. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 6, characterized in that, The analytical expression of the maximum frequency deviation is: wherein, denotes the maximum frequency deviation, denotes the disturbance power of the doubly-fed variable speed pumped storage unit system, denotes the response amplitude of the doubly-fed variable speed pumped storage unit system, denotes the natural base number, denotes the cosine function, denotes the phase angle of the response of the doubly-fed variable speed pumped storage unit system, denotes the angular frequency of the response of the doubly-fed variable speed pumped storage unit system, denotes the phase difference of the response of the doubly-fed variable speed pumped storage unit system, denotes the frequency minimum point time.

10. The method for evaluating frequency response performance of a doubly-fed variable-speed pumped storage unit according to claim 6, characterized in that, frequency minimum time The analytical expression for the frequency minimum time is: wherein, denotes the inverse tangent function, denotes enumerating all time point numbers for which the frequency deviation reaches a maximum value, , , , and denote the second-order frequency response transfer function coefficients of the reduced-order system of the doubly-fed variable-speed pumped storage unit system.

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