CN111293686A - ARMAX system identification-based real-time evaluation method for inertia of power system - Google Patents
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- H—ELECTRICITY
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Abstract
The invention relates to a real-time evaluation method for inertia of an electric power system based on ARMAX system identification, which is based on the following steps: (1) obtaining active power and frequency fluctuation of each generator and an outlet side of a wind power plant when a power grid normally operates; (2) taking the active power change as input and the frequency change as output, and constructing an ARMAX identification model from the active power change to the frequency change; (3) calculating the frequency change rate of the ARMAX identification model after step response; (4) and substituting the frequency change rate after the step response into a swing equation to obtain an inertia time constant. Compared with the prior art, the method and the device can accurately reflect the dynamic changes of the inertia of the power system in different operation states, provide an auxiliary decision for the stable operation of the power grid and the new energy grid connection, update the evaluation result in real time according to the measured data, and are beneficial to knowing the potential unstable risk of the power system and the capability of keeping stable operation after an accident occurs.
Description
Technical Field
The invention relates to a real-time evaluation method for inertia of a power system, in particular to a real-time evaluation method for inertia of a power system based on ARMAX system identification.
Background
Inertia is an inherent property of a power system, is represented by an impedance effect of the system on frequency fluctuation caused by disturbance, and is a basic guarantee for safe and stable operation of the system. Inertia is a parameter that measures the ability of a power system to absorb or inject active power after being disturbed due to inertia. When the power system operates stably, the system frequency needs to be maintained within a certain range. When the system is disturbed by a certain magnitude, the frequency change of the system is influenced by the inertia time constant H of the system, the larger the H is, the smaller the frequency change rate of the system is, the slower the frequency of the system is reduced, more time is strived for primary frequency modulation, and the stronger the anti-disturbance capability of the system is. Therefore, H is an important parameter for representing the inertia of the system and representing the stability of the system.
Most of inertia is traditionally provided by the physical rotating mass of the synchronous generator, however, the increasing shortage of traditional energy sources promotes the development of new energy sources in various countries, wherein a large amount of wind power and photovoltaic power are connected to replace part of the synchronous generator in the power system. The continuous improvement of the wind power permeability greatly threatens the frequency stability of the power grid. Because wind driven generators are mostly connected to a power grid through power electronic equipment, the power generation side is decoupled from the power grid, and the frequency change of the power grid cannot be responded, so that the inertia time constant of the system is reduced, and the stability of the system is threatened.
Aiming at the problem of inertia loss caused by large-scale wind power integration to a traditional power grid, virtual inertia control is added to a fan integration converter, so that the fan changes the output power of the fan when the frequency of the power grid changes, and the equivalent inertia is expressed to the outside, and the method is an effective solution. The method has the advantages that the randomness and the time-varying property of wind power generation are considered, and the virtual inertia of the wind power generation can be changed according to the working condition state of each fan of the wind power plant. The research of the existing inertia estimation method focuses on the on-line evaluation of the inertia of a synchronous machine in a power grid, ignores the comprehensive evaluation of the actual effect of the virtual inertia control of a fan, lacks the real-time evaluation of the effective inertia represented by the control performance of the fan, and is difficult to quantify the support effect on the power grid in real time. In the auxiliary service market, a power grid company cannot give economic incentive according to the strength of frequency modulation auxiliary services provided by a wind power place. Therefore, the method has important practical significance and application value for online evaluation of the inertia of the wind power plant and the whole power system. However, the inertia of the actual output of the wind farm may not be consistent with the parameter settings in the controller. Therefore, it is very critical to identify the inertia of the power grid in real time according to the actual operation data of the power grid. The accurate measurement of the inertia time constant of the system is helpful for reflecting the dynamic change of inertia of the power system in different operation states, provides an auxiliary decision for stable operation of the power grid and new energy grid connection, and can update the evaluation result on line according to the measured data, thereby improving the accuracy and timeliness of judgment of the stability and disturbance resistance of the power grid.
The traditional inertia evaluation method generally adopts a generator swing equation to calculate an inertia time constant H. Although the traditional large-disturbance-based inertia online evaluation method is high in accuracy, excitation of large disturbance in a power grid, such as line short circuit, running quit of a generator set and the like, is needed, stable running of the power grid is not facilitated, real-time evaluation of inertia cannot be achieved, and the applicability is low.
The inertia evaluation method based on system identification utilizes active power and frequency fluctuation when a power grid normally operates, an ARMAX system identification method is used, a dynamic model from the active power change of a generator to the frequency change is established, and an inertia time constant H is obtained from the identified identification model. Compared with the traditional inertia evaluation method, the method can be used for evaluating the inertia only by utilizing the measured data of the power system in normal operation, large-disturbance excitation is not needed, and the inertia of the power system can be evaluated on line. The traditional evaluation method needs to determine the disturbance occurrence time, inertia response and primary frequency modulation response cannot be distinguished in the frequency modulation process, the method carries out inertia evaluation when a power system normally operates, and the primary frequency modulation does not participate in the frequency modulation process, so that the influence of the primary frequency modulation on the inertia evaluation can be avoided, and the inertia evaluation accuracy is improved.
Using system identification for online assessment of inertia entails assigning a specific order to the identification model, and although many studies have been made regarding identification model order selection, it is difficult to select a fixed model order. The synchronous generator comprises a plurality of complex frequency modulation control systems, specific orders cannot be determined for generator frequency modulation models, and the applicable model orders can change along with different system operation states. Therefore, the current method for online inertia evaluation based on system identification selects a proper order range, and calculates an inertia time constant and then calculates an average value for each order identification model in the range. This order range must be large enough to capture the main dynamics of the generator frequency modulation, but still small enough to not become too complex and computationally expensive. The evaluation result deviation of ARMAX identification models of different orders is very large, so that the error between the online inertia evaluation result and the true value is large. Therefore, for the conventional method of determining the inertia time constant by using the zero-time impulse response value, the order of the ARMAX recognition model has a great influence on the inertia evaluation accuracy.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a real-time evaluation method for the inertia of the power system based on ARMAX system identification.
The purpose of the invention can be realized by the following technical scheme:
a real-time evaluation method for inertia of an electric power system based on ARMAX system identification is based on the following steps:
(1) obtaining active power and frequency fluctuation of each generator and an outlet side of a wind power plant when a power grid normally operates;
(2) taking the active power change as input and the frequency change as output, and constructing an ARMAX identification model from the active power change to the frequency change by using an ARMAX system identification technology;
(3) calculating the frequency change rate of the ARMAX identification model after step response;
(4) and substituting the frequency change rate after the step response into a swing equation to obtain an inertia time constant.
And (2) constructing different-order ARMAX identification models, further calculating the frequency change rate of the ARMAX identification models with different orders after step response in the step (3), acquiring corresponding inertia time constants in the step (4), and finally averaging the inertia time constants to serve as the inertia time constant evaluation value of the generator or the wind power plant.
The frequency change rate in the step (3) is as follows: after the step response of the ARMAX identification model, the frequency change rate curve is subjected to low-pass filtering, and then the average value of the frequency change rate curve subjected to low-pass filtering within 0.2s is obtained.
The swing equation is as follows:
wherein H is the inertia time constant to be obtained and the unit is s, fsIs the rated frequency of the system, and the unit is Hz; sNFor the rated capacity of the generator or wind farm, the unit MVA, df (t)/dt is the frequency change rate at time t, in Hz/s, Pm(t) and Pe(t) mechanical and electromagnetic power, respectively, in units of MW, and Δ P (t) active power variation in units of MW.
And (1) acquiring active power and frequency fluctuation through a synchronous phasor measuring device of the power system.
The ARMAX identification model is as follows:
A(q)y(t)＝B(q)u(t-nk)+C(q)e(t)，
wherein A (q), B (q), C (q) are n for q, respectivelya、nb、ncPolynomial of degree u (t-n)k) Is the input of the recognition model, y (t) is the output of the recognition model, e (t) is the noise, nkFor input and output delays, na＝nb＝ncN is a constant, nk＝0。
Compared with the prior art, the invention has the following advantages:
(1) according to the method, the inertia is evaluated in real time through the step response of the ARMAX identification model, so that the error caused by the order of the identification model is reduced, and the accuracy of the real-time evaluation of the inertia of the power system is improved;
(2) according to the method, firstly, the ROOF curve is subjected to low-pass filtering, then the average value of the frequency change rate in the step response 0.2s is taken as the frequency change rate for calculating the inertia time constant, so that the fluctuation of the initial stage frequency after the step response of the identification model of partial orders is reduced, and the accuracy of real-time inertia evaluation is further improved;
(3) the method and the device can accurately reflect the dynamic changes of inertia of the power system in different operation states, provide auxiliary decisions for stable operation of a power grid and new energy grid connection, and update evaluation results on line according to measured data, thereby being beneficial to understanding potential unstable risks of the power system and the capability of keeping stable operation after accidents occur.
Drawings
FIG. 1 is a block flow diagram of a real-time evaluation method for inertia of an electric power system based on ARMAX system identification according to the present invention;
FIG. 2 is a schematic structural diagram of a simulation system according to an embodiment of the present invention;
FIG. 3 is a comparison graph of wind farm inertia estimation errors under a traditional impulse response method and a step response method in the embodiment of the invention;
fig. 4 is a comparison graph of the inertia estimation error of the generator G2 according to the step response method of the present invention and the conventional impulse response method in the embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. Note that the following description of the embodiments is merely a substantial example, and the present invention is not intended to be limited to the application or the use thereof, and is not limited to the following embodiments.
Examples
As shown in fig. 1, a real-time evaluation method for inertia of an electric power system based on ARMAX system identification is based on the following steps:
(1) acquiring active power and frequency fluctuation of each generator or an outlet side of a wind power plant when a power grid normally operates;
(2) taking the active power change as input and the frequency change as output, and constructing an ARMAX identification model from the active power change to the frequency change by using an ARMAX system identification technology;
(3) calculating the frequency change rate of the ARMAX identification model after step response;
(4) and substituting the frequency change rate after the step response into a swing equation to obtain an inertia time constant.
And (2) constructing different-order ARMAX identification models, further calculating the frequency change rate of the ARMAX identification models with different orders after step response in the step (3), acquiring corresponding inertia time constants in the step (4), and finally averaging the inertia time constants to serve as the inertia time constant evaluation value of the generator or the wind power plant. More specifically, the frequency change rate in step (3) is: after the step response of the ARMAX identification model, the frequency change rate curve is subjected to low-pass filtering, and then the average value of the frequency change rate curve subjected to low-pass filtering within 0.2s is obtained.
The step response of the ARMAX identification model can clearly show the response situation of the output (generator frequency deviation) along with the step change of the input (generator active power). When a step input is given to the ARMAX identification model, namely the active output of the generator generates a sudden change, the rotor of the generator accelerates or decelerates due to the imbalance between the electromagnetic power and the mechanical power, and the frequency fluctuation is externally shown, the process can be described by a swing equation, and the ARMAX identification model established between the active power change amount Δ P and the frequency change amount Δ f is related to the swing equation. The rate of change of frequency (ROCOF) can thus be calculated by identifying the output of the model after the step response, i.e. the value of the frequency change. Although the frequency of the different orders of the discriminative model after the step response have different deviations, their rates of change ROCOF are substantially equal for a short time after the step response. Because the frequency of the initial stage after the step response of the identification model of partial order fluctuates, the obtained ROOF curve is subjected to low-pass filtering, and the average value of the frequency change rate within 0.2s after the step response is taken as the frequency change rate in the step (4), so that the accuracy of the real-time inertia evaluation is improved.
The swing equation is as follows:
wherein H is the inertia time constant to be obtained and the unit is s, fsIs the rated frequency of the system, and the unit is Hz; sNFor the rated capacity of the generator or wind farm, the unit MVA, df (t)/dt is the frequency change rate at time t, in Hz/s, Pm(t) and Pe(t) mechanical and electromagnetic power, respectively, in units of MW, and Δ P (t) active power variation in units of MW.
And (1) acquiring active power and frequency fluctuation through a synchronous phasor measuring device of the power system.
The generator frequency control process is approximated as a linear control system. Considering a single generator, at the generator mechanical power PmWithin a constant time period, the active power output of the generator is changed by a variable quantity delta P (electromagnetic power change delta P)e) As input, the generator frequency deviation Δ f at the respective moment is taken as output. After determining the input and output of the system, a system identification method is applied to the input and output data. Model structure can be selected by comparing the fit percentages, using the best fit model for the extraction of inertia.
The ARMAX identification model is as follows:
A(q)y(t)＝B(q)u(t-nk)+C(q)e(t)，
wherein A (q), B (q), C (q) are n for q, respectivelya、nb、ncPolynomial of degree u (t-n)k) Is the input of the recognition model, y (t) is the output of the recognition model, e (t) is the noise, nkFor input and output delays, na＝nb＝ncN is a constant, nk＝0。
This embodiment performs simulation verification on the simulation system shown in fig. 2. To implement the identification method used herein, an identification model can be identified from the input and corresponding output data using a system identification method, assuming that there are a sufficient number of PMUs in the power system to measure enough measurement data. And acquiring inertia time constants H of corresponding generators and wind farms in the system from the identification model.
When the power system normally operates, PMU is utilized to measure active power and frequency fluctuation of a wind power plant and each synchronous generator, 60s of active power change delta P is taken as input, frequency change delta f is taken as output, and an ARMAX system identification method is used for identifying each data set by n-nmin，……，nmaxModels within the order range are fitted. To simplify the evaluation process, within each iteration order, an order equality is defined for the various variables of the model, i.e. na＝nb＝ncWith input-output delay of zero, i.e. nk＝0。
Since the identified ARMAX polynomial model is a discrete-time (i.e., Z-domain) linear system, the discrete-time ARMAX model is first converted to a continuous-time model using the d2c function in MATLAB, and the stability of the generated model is checked by the s-domain criterion (the real part of the poles should be less than zero). And then, inputting a unit step for each stage of ARMAX continuous time identification model, calculating the frequency change rate to obtain an ROOF curve, carrying out low-pass filtering on the ROOF curve, calculating the average value of the frequency change rate within 0.2s after step response, substituting the value into a formula swing equation, wherein delta P (t) is 1, and calculating the inertia time constant through the swing equation. The inertia evaluation is performed on the simulation system shown in fig. 2 by using the method.
The wind farm inertia evaluation result is shown in table 1, and fig. 3 is a comparison graph of wind farm inertia evaluation errors in a conventional impulse response method and a step response method of the invention.
TABLE 1 wind farm inertia assessment results
The inertia evaluation result of the generator G2 is shown in table 2, and fig. 4 is a comparison graph of the inertia evaluation error of the generator G2 under the conventional impulse response method and the step response method of the invention.
TABLE 2 Generator G2 inertia estimation results
The inertia evaluation results of the whole system obtained by the method of the invention are shown in table 3.
TABLE 3 System step response inertia evaluation results
The above embodiments are merely examples and do not limit the scope of the present invention. These embodiments may be implemented in other various manners, and various omissions, substitutions, and changes may be made without departing from the technical spirit of the present invention.
Claims (6)
1. A real-time evaluation method for inertia of an electric power system based on ARMAX system identification is characterized by comprising the following steps:
(1) obtaining active power and frequency fluctuation of each generator and an outlet side of a wind power plant when a power grid normally operates;
(2) taking the active power change as input and the frequency change as output, and constructing an ARMAX identification model from the active power change to the frequency change by using an ARMAX system identification technology;
(3) calculating the frequency change rate of the ARMAX identification model after step response;
(4) and substituting the frequency change rate after the step response into a swing equation to obtain an inertia time constant.
2. The real-time power system inertia evaluation method based on ARMAX system identification as claimed in claim 1, wherein the step (2) constructs ARMAX identification models of different orders, the step (3) calculates frequency change rates of the ARMAX identification models of different orders after step response, the step (4) obtains corresponding inertia time constants, and finally averages the inertia time constants to obtain the inertia time constant evaluation value of the generator or the wind power plant.
3. The ARMAX system identification-based real-time power system inertia evaluation method as claimed in claim 2, wherein the frequency change rate in step (3) is: after the step response of the ARMAX identification model, the frequency change rate curve is subjected to low-pass filtering, and then the average value of the frequency change rate curve subjected to low-pass filtering within 0.2s is obtained.
4. The method of claim 1, wherein the real-time estimation of the inertia of the power system based on the ARMAX system identification is performed according to the following equations:
wherein H is the inertia time constant to be obtained and the unit is s, fsIs the rated frequency of the system, and the unit is Hz; sNFor the rated capacity of the generator or wind farm, the unit MVA, df (t)/dt is the frequency change rate at time t, in Hz/s, Pm(t) and Pe(t) mechanical and electromagnetic power, respectively, in units of MW, and Δ P (t) active power variation in units of MW.
5. The method for real-time assessment of inertia of an electric power system based on ARMAX system identification as claimed in claim 1, wherein the active power and frequency fluctuation in step (1) are obtained by a synchronous phasor measurement device of the electric power system.
6. The method of claim 1, wherein the ARMAX system identification-based real-time power system inertia evaluation method is characterized in that an ARMAX identification model is as follows:
A(q)y(t)＝B(q)u(t-nk)+C(q)e(t)，
wherein A (q), B (q), C (q) are n for q, respectivelya、nb、ncPolynomial of degree u (t-n)k) Is the input of the recognition model, y (t) is the output of the recognition model, e (t) is the noise, nkFor input and output delays, na＝nb＝ncN is a constant, nk＝0。
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| CN114204579A (en) * | 2021-11-25 | 2022-03-18 | 湖北工业大学 | Energy storage output power shaping control method applied to power system frequency modulation |
| CN114204579B (en) * | 2021-11-25 | 2024-04-19 | 湖北工业大学 | Energy storage output power shaping control method applied to frequency modulation of power system |
| CN114498678A (en) * | 2022-01-29 | 2022-05-13 | 华北电力大学 | Power system inertia online evaluation method based on frequency space correlation |
| CN114498678B (en) * | 2022-01-29 | 2024-09-06 | 华北电力大学 | Online power system inertia assessment method based on frequency space correlation |
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