CN116316909A - Online power system inertia identification method and system based on ARMAX model - Google Patents
Online power system inertia identification method and system based on ARMAX model Download PDFInfo
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Abstract
The invention provides an online identification method and an online identification system for inertia of a power system based on an ARMAX model, which are based on common commutation failure and direct current blocking failure in the power system, decompose common failure of a power grid into pulse disturbance and step disturbance, and provide an inertia identification method based on impulse response and an inertia identification method based on step response. After parameter identification is performed based on the actually measured active power and frequency data, different orders (or reduction) are performed on the system model according to different disturbance forms: if the pulse disturbance is the pulse disturbance, judging whether the parameter can be reduced to 1 order by adopting a balance cut-off method, if so, reserving and applying an impulse response to further identify an inertia time constant, and if not, discarding a system model of the order; if the step disturbance is the step disturbance, the AIC fixed-order method is used for fixed-order, and inertia time constant identification is further carried out after the step disturbance is applied. The inertia identification method and the inertia identification device can be applied to inertia identification of synchronous generators and doubly-fed fans in an actual power system.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to an inertia identification technology of a power system, and particularly relates to an online inertia identification method and system of the power system based on an ARMAX model.
Background
Currently, the identification method based on power disturbance or energy function is essentially a method established based on the swing equation of the generator, and the premise of application of the methods is that larger disturbance is required to excite the frequency fluctuation of the system. However, because of the numerous synchronous generators present in the network to provide inertial support, it is often impractical if large disturbance events are required to excite the generator to cause sufficient frequency disturbances. Therefore, in order to ensure safe and stable operation of the system and guarantee of the quality of electric energy, a method for acquiring the inertia level of the electric power system through daily stable operation data of the electric network needs to be studied. Since measured data in the grid contains noise, it is difficult to use for mechanism modeling. However, if the relationship between the input and the output is focused on the external characteristics, a system identification method may be adopted. And the PMU equipment proportion in the system is increased, so that the power, frequency and other data of the system can be obtained easily and synchronously, and a data base is provided for online inertia evaluation of the system. The system can carry out on-line monitoring on inertia under the condition of stable frequency to provide safety precaution, and a strategy is formulated rapidly on the basis, so that the safe and stable operation of the system is ensured.
Disclosure of Invention
In view of the fact that the existing inertia identification method based on power disturbance and energy function is difficult to put into practice in an actual power system, and the proportion of PMU equipment is increased to provide a sufficient data basis, the invention aims to provide the inertia identification method based on the ARMAX model, which is characterized in that firstly, identification is carried out according to steady-state data, a system model is built, then the balance cut-off method is adopted for reducing the order of the model in the inertia identification method based on impulse response, the AIC criterion is adopted for order determination in the inertia identification method based on step response, then different types of disturbance (impulse disturbance and step disturbance) are added to the system model according to the disturbance types (impulse disturbance and step disturbance) in a power grid, response processes of the system model are observed, and finally the inertia on-line identification is realized according to the response processes.
According to a first aspect of the present invention, an online identification method for inertia of an electric power system based on an ARMAX model is provided, including:
step 1, collecting active power and frequency data of a generator grid connection point in a normal running state of a power grid;
and 7, taking the average value of the sum of the inertia time constants obtained by the corresponding steps of all continuous models capable of reducing the steps to 1 step as the identification value of the inertia time constant of the power system.
Wherein in said step 5, the inertia response of the power generation equipment in the power system is approximated as a linear process, the transfer function of which is expressed as:
wherein: Δf is the system frequency variation; ΔP is the system active power disturbance; d is system damping; t (T) J Is the inertia of the system;
the unit impulse response at unit impulse disturbance is expressed as:
the impulse response value of the generator first-order transfer function at zero time is the reciprocal of the inertia time constant, namely:
where H is the inertial time constant.
According to a second aspect of the present invention, there is provided an online power system inertia identification system based on an arax model, including: one or more processors; and a memory.
The memory is configured to store instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising the flow of the impulse response based power system inertia online identification method described above.
According to a third aspect of the present invention, there is provided an online identification method for inertia of an electric power system based on an ARMAX model, the method comprising the steps of:
step 1, collecting active power and frequency data of a generator grid connection point in a normal running state of a power grid;
and 8, determining an inertia time constant of the power system under step disturbance based on the reference value of the maximum value of the frequency change rate.
In the step 7, the first oscillation period of the output after the step response is selected as a time scale, and the average value of the frequency change rate in the time scale is selected as a reference value ROCOF the maximum value of the frequency change rate ref ：
Wherein in said step 8 ΔP in the step response L =1, thus based on ROCOFs ref And identifying the inertia time constant of the power system under the step disturbance:
wherein H is an inertial time constant.
According to a fourth aspect of the present invention, there is provided an online power system inertia identification system based on an arax model, including: one or more processors; and a memory.
The memory is configured to store instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising the flow of the step response based power system inertia online identification method described above.
According to the online power system inertia identification method based on the ARMAX model, based on the disturbance of the common pulse and step form in the system, an inertia identification method based on impulse response and an inertia identification method based on step response are provided, wherein the balance cut-off method is adopted for model reduction in the inertia identification method based on impulse response, and the AIC criterion is adopted for order determination in the inertia identification method based on step response, and the two methods can be applied to inertia identification of synchronous generators and doubly-fed fans in an actual power system. As the PMU equipment proportion in the system is increased, the power, frequency and other data of the system can be obtained easily and synchronously, and a data base is provided for online inertia evaluation of the system. Therefore, on-line inertia identification under the condition of stable frequency based on measured data can provide safety early warning for the system under a certain condition, so that a strategy is formulated rapidly, and safe and stable operation of the system is ensured.
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The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. Embodiments of various aspects of the invention will now be described, by way of example, with reference to the accompanying drawings.
FIG. 1 is a flow chart illustrating an online identification method of power system inertia based on an ARMAX model under unit pulse perturbation in accordance with certain embodiments of the present invention.
FIG. 2 is a flow chart illustrating an online identification method of power system inertia based on an ARMAX model under a step disturbance in accordance with certain embodiments of the present invention.
Fig. 3 and 4 are graphs illustrating PMU logs for commutation failure in an uhd system and PMU logs for unipolar latch-up in accordance with certain embodiments of the present invention.
Fig. 5 and 6 are diagrams illustrating the inertia recognition result of the synchronous generator under the pulse disturbance and the inertia recognition result of the synchronous generator under the step disturbance according to some embodiments of the present invention, respectively.
Fig. 7 and 8 are graphs illustrating the identification of the inertia of the doubly-fed wind turbine under a pulse disturbance and the identification of the inertia of the doubly-fed wind turbine under a step disturbance, respectively, according to some embodiments of the present invention.
Detailed Description
For a better understanding of the technical content of the present invention, specific examples are set forth below, along with the accompanying drawings.
Aspects of the invention are described in this disclosure with reference to the drawings, in which are shown a number of illustrative embodiments. The embodiments of the present disclosure are not necessarily intended to include all aspects of the invention. It should be understood that the various concepts and embodiments described above, as well as those described in more detail below, may be implemented in any of a number of ways, as the disclosed concepts and embodiments are not limited to any implementation. Additionally, some aspects of the disclosure may be used alone or in any suitable combination with other aspects of the disclosure.
According to the embodiment of the invention, an online identification method of the inertia of the power system based on an ARMAX model is provided, common faults of a power grid are decomposed into two types of disturbance including pulse disturbance (such as commutation failure) and step disturbance (such as monopole locking) according to a measured PMU wave recording curve based on common commutation failure and direct current locking faults in the power system, construction of an early model and later inertia identification are facilitated, and an inertia identification method based on impulse response and an inertia identification method based on step response are provided under two different disturbance forms.
After the system model is determined based on the measured active power and the frequency data through parameter identification, different orders (or reduction) are carried out on the system model according to different disturbance forms: (1) If the disturbance type is pulse disturbance, conventional parameter identification is carried out on the power system model to obtain models with different 2-9 steps. In order to utilize the acquired discrete data, the transfer function of the identified model is written out, so that the model is continuously changed through Laplace transformation. Then adopting a balance cut-off method to judge whether the system model can be reduced to 1 order, if so, reserving and applying impulse response to perform further inertia time constant identification, otherwise, discarding the system model of the order; (2) If the disturbance type is step disturbance, performing fixed-order by using an AIC fixed-order method, and performing further inertia time constant identification after the step disturbance is applied.
As an alternative embodiment, the overall implementation procedure of the online identification method of the inertia of the power system based on the ARMAX model includes:
firstly, according to a measured PMU wave recording curve, common faults of a power grid are decomposed into two types of pulse disturbance (such as phase change failure) and step disturbance (such as monopole locking), and the function forms of the common faults are mathematically simplified, so that construction of a front-stage model and later-stage inertia identification are facilitated;
secondly, collecting active power and frequency data of a generator grid connection point in a normal running state of the power grid (the oscillation amplitude of the data is required to be within a specified fluctuation amplitude, such as a + -5% fluctuation range) for later inertia identification; and the acquired data is subjected to per unit and filtering treatment (such as Butt Wo Siqi filtering), so that the influence of noise is reduced and the calculation is convenient;
then, the system model is subjected to different fixed orders (or reduced orders) according to different disturbance forms: if the pulse disturbance is the pulse disturbance, carrying out conventional parameter identification on the power system model to obtain models with different orders of 2-9, judging whether the power system model can be reduced to 1 order by a balance cut-off method, if so, reserving and applying an impulse response to carry out further inertia time constant identification, and if not, discarding the system model with the order; (2) If the disturbance type is step disturbance, performing fixed-order by using an AIC fixed-order method, and performing further inertia time constant identification after the step disturbance is applied.
Fig. 1 and 2 show exemplary implementation flows of the power system inertia online identification method provided by the invention under pulse disturbance and step disturbance.
As shown in the flow chart of fig. 1, the online identification method based on the inertia of the ARMAX power system under the pulse disturbance comprises the following steps:
step 1, collecting active power and frequency data of a generator grid connection point in a normal running state of a power grid;
and 7, taking the average value of the sum of the inertia time constants obtained by the corresponding steps of all continuous models capable of reducing the steps to 1 step as the identification value of the inertia time constant of the power system.
Alternatively, in step 2, the filtering process is performed by using a butterworth filter to filter noise in the acquired data.
Alternatively, in the step 4, the Laplace transformation is performed on each obtained system model, and the system model is converted into a continuous model.
Alternatively, in the step 3, the step of reducing the order of the system model by adopting a balanced cut-off method includes:
assume that
Stable, the controllable and observable gram matrices of the system are denoted by P and Q, respectively, wherein:
AP+PA T +BB T ＝0
A T Q+QA+C T C＝0
then there is a non-singular transformation
Such that:
after the non-singular transformation, the gram matrix also transforms accordingly:
simultaneously nonsingular transformed energy-controlled and energy-observed gram matrix
Satisfy->
If there is a diagonal matrix:
∑＝diag(σ 1 ,σ 2 ,…,σ n )
make the following steps
And at the same time satisfies pq=t -1 ∑ 2 T, balance is achieved;
arranging diagonal elements in order from large to small, sigma 1 ，σ 2 ，...，σ n Hankel singular values, sigma, called systems 1 ≥σ 2 ≥…≥σ n Not less than 0; if there is one r, so that sigma r ＞＞σ r+1 Then consider sigma r+1 ,…σ n The corresponding state is a system with poor controllability and observability, and the interception of the system can not cause information defect;
wherein, G represents an ARMAX-based power system model, and A, B, C and D respectively represent a system state matrix before interception;
the truncated r-order model is expressed as:
wherein: a is that r 、B r 、C r 、D r The system state matrix is the truncated system state matrix; u represents a system input.
P and Q are respectively the controllable and observable matrices of the system, transformed according to equations (7), (8), (9), and then transformed according to Sigma=diag (sigma) 1 ,σ 2 ,…,σ n ) And (3) reducing the order of the corresponding criteria to obtain a new system state matrix, and obtaining the simplified system.
Alternatively, in said step 5, the inertia response of the power generation equipment in the power system is approximated as a linear process, the transfer function of which is expressed as:
wherein: Δf is the system frequency variation; ΔP is the system active power disturbance; d is system damping; t (T) J Is the inertia of the system;
the unit impulse response at unit impulse disturbance is expressed as:
the impulse response value of the generator first-order transfer function at zero time is the reciprocal of the inertia time constant, namely:
where H is the inertial time constant.
Referring to fig. 2, under disturbance, the online identification method based on the inertia of the ARMAX power system comprises the following steps:
step 1, collecting active power and frequency data of a generator grid connection point in a normal running state of a power grid;
and 8, determining an inertia time constant of the power system under step disturbance based on the reference value of the maximum value of the frequency change rate.
Alternatively, in the step 7, the step-response post-output quantity is selectedAn oscillation period is taken as a time scale, and the average value of the frequency change rate in the time scale is taken as a reference value ROCOF of the maximum value of the frequency change rate ref ：
Alternatively, in step 8, ΔP in the step response L =1, thus based on ROCOFs ref And identifying the inertia time constant of the power system under the step disturbance:
wherein H is an inertial time constant.
The practice and/or effect of certain examples of the present invention will be described in more detail below in conjunction with the flowcharts shown in fig. 1 and 2 and some preferred or alternative examples of the present invention.
[ Online data acquisition and pretreatment ]
Referring to fig. 3 and 4, common faults in the power system are equivalent to applying a pulse disturbance or step disturbance.
The actual data of the power system is measured by the actual PMU system, and the PMU measurement unit is adopted to acquire the data and perform per unit. The data requirements are: active power and frequency data of the grid connection point of the generator in a normal running state of the power grid are collected, and the oscillation amplitude of the active power and the frequency data is required to be within a specified amplitude.
[ model mechanism of ARMAX ]
The general form of the system identification model is:
where each operator transfer function can be expressed as:
n a 、n b 、n c 、n d 、n f the orders of A (q), B (q), C (q), D (q) and F (q) are respectively shown; u represents an input; y represents the output; e represents an error; n is n k For the delay between input and output, typically 0 or 1 is taken; q represents a shift-back operator.
The ARMAX model is one of the system identification models, and the general structure of the ARMAX model is expressed as follows:
wherein: y (t) represents the output of the system at time t; u (t) represents the input of the system at time t; e (t) represents the noise of the system at time t; n is n β And n λ Are all equivalent orders.
It can be expressed briefly as:
A(q)y(t)＝B(q)u(t)+D(q)e(t) (4)
wherein: u (t) represents an input; y (t) represents an output; e (t) represents the average value of 0 and the variance of sigma e 2 Is a random white noise sequence of (1); q is the shift-back operator.
A (q) y (t) is the autoregressive portion of the "AR" system; d (q) e (t) is the "MA" moving average portion of the system; b (q) u (t) is the "X" part of the system external input.
The delivery system of the discrete system of formula (4) is shown below:
it can be seen from the transfer function that the ARMAX system consists of both deterministic and random parts.
Deterministic part is determined by transfer function
Representation of the response to a known deterministic signal。
The random part is composed of transfer functions
The manifestation, it represents the effect of noise.
In the system identification method of the invention, only a determined part is selected as a transfer function model of the system.
[ Balanced cut-off method reduced order ]
The order reduction method adopted in the embodiment of the invention is a balanced cut-off method, and mainly comprises two parts of 'state balance' and 'cut-off order reduction'.
For practical systems, the controllability and observability of the state variables are different, and state variables with strong controllability and weak observability exist, and if the variables are directly truncated, a large error is introduced in the reduction process. This problem can be solved by a balanced cut-off method.
The balance cut-off method firstly transforms the system through the energy-controllable gram matrix to enable each state to be energy-controllable and balanced, and then cuts off the state variables with poor energy controllability and energy observability to achieve the purpose of reducing the order. The emphasis of the balance cut-off model reduction is on singular value decomposition.
If it is
The controllable and observable gram matrices of the system are denoted by P and Q, respectively, wherein:
A. b, C and D are the original state matrix of the system, namely the state matrix of the system before truncation; a is that T 、B T And C T The transposes of A, B and C, respectively.
Then there is a non-singular transformation
Such that:
after the non-singular transformation, the gram matrix also transforms accordingly:
simultaneously nonsingular transformed energy-controlled and energy-observed gram matrix
Satisfy->
If there is a diagonal matrix:
∑＝diag(σ 1 ,σ 2 ,…,σ n ) (10)
make the following steps
And at the same time satisfies pq=t -1 ∑ 2 T, this implementation is referred to as a balanced implementation. Arranging diagonal elements in order from large to small, sigma 1 ≥σ 2 ≥…≥σ n 0 is called Hankel singular value (state variable) of the system. If there is one r, so that sigma r ＞＞σ r+1 Then it can be considered as σ r+1 ,…σ n The corresponding state is a system with poor controllability and observability, and the interception of the system can not cause a lot of information defects.
Then, the truncated r-order model can be expressed as:
wherein: a is that r 、B r 、C r 、D r The system state matrix is the truncated system state matrix;
and y is the output of the system.
In practical application, G depends on an adopted electric power system model (ARMAX system), P and Q are controllable and observable matrixes of the system respectively, transformation is carried out according to formulas (7), (8) and (9), and then reduction is carried out according to criteria corresponding to formula (10), so that a new system state matrix is obtained, and a simplified system is obtained.
[ AIC fixed-order method ]
In the implementation process of the invention, the AIC scaling method is used. The method of determining the order may employ a red-pool information content criterion (Akaike Information Criterion, AIC). The AIC order determining method can ensure higher fitting degree in the order determining process and avoid excessive fitting of the model.
The representation of AIC is as follows:
wherein:
for the parameter θ= [ θ ] 1 ,θ 2 ,……，θ N ]Maximum likelihood estimates of (a); />
Representing likelihood functions under certain conditions; />
Is an estimate of the model order or number of independent parameters.
The fixed order criterion of AIC isThe probability density estimated by the selected model is compared with the probability density of the real data. The performance index can be compatible with complexity and adaptability, and the Akaike criterion proves that when
When the value is the minimum value, the order of the model is relatively reasonable.
In practical application, θ is various parameters in the generator model of the electric power system, the number of parameters to be considered directly determines the order of the model, and the AIC criterion can be used for reducing the system to a low-order model or even a 1-order model.
[ inertia identification of ARMAX first-order model ]
In the embodiment of the invention, inertia identification is based on the following conditions: the inertia constant of the system is a constant value within the estimated time period and does not change with time.
Thus, we take the power at the outlet side of the unit as input and the frequency at the outlet side as output, then an ARMAX model between input and output can be built.
The inertial identification based on the ARMAX model is to change disturbance in physical sense into disturbance in mathematical sense after modeling is completed, observe the response of the equivalent model under the condition of mathematical disturbance to identify and obtain the inertial time constant.
The inertia response of a power plant in a system is approximately a linear process, and its transfer function is expressed as:
wherein: Δf is the system frequency variation; ΔP is the system active power disturbance; d is system damping; t (T) J Is the inertia of the system.
Whether the order is reduced based on the balanced cut-off method or the order is fixed based on the AIC criterion, the system is hoped to be reduced to 1 st order, and then the inertia identification can be carried out by adopting the formula of the formula (13).
Inertia calculation under pulse disturbance
To reduce errors, system identification uses an impulse response method to calculate the inertial time constant. First, a frequency modulation model needs to be obtained from the system identification, and since the system is a discrete sample, it needs to be converted into a continuous model, and its linear transfer function is as shown in equation (14).
The unit impulse response is as follows:
it can be seen that the impulse response value of the generator first order transfer function at zero time is the inverse of the inertial time constant, namely:
wherein: h is the power system inertia time constant.
And the inertia identification results of the synchronous generator and the doubly-fed fan under the system pulse disturbance after the step reduction by using the balance cut-off method are respectively shown in fig. 5 and 7.
Inertia calculation under step disturbance
Because the data are discretized, the identified model is also a discretized model, and the obtained model is obtained at the moment
It does not correspond exactly to the transfer function and therefore requires a continuous process first, then a step input to the model to simulate the change in frequency of the generator under known disturbances, and then an inertial time constant is calculated.
It is worth noting that the maximum value of the rate of change of frequency is required for calculation when calculating the inertial time constant.
Because of the large data bias at time zero, an approximation of rocofis generally required. Since it is generally considered that inertia response is mainly performed within 0.5s to 2s after disturbance occurs, and primary frequency modulation is not performed, the average value of the frequency change rate in the period of 0.5s to 2s after step response is used as the reference value of ROCOF.
However, due to different dynamic characteristics of different units, it is not reasonable to select the same time window. Through research on time windows, the time window with highest accuracy corresponding to inertia identification based on power disturbance is just a complete process of rising to the maximum value after the frequency is reduced to the minimum value, while the essence of parameter identification based on ARMAX is that disturbance occurs in a steady state by using a mathematical model and step response, so that the principle and thought are the same when the time window is selected, and the principle of selecting the maximum value of the frequency change rate is as follows: taking the first oscillation period of the output quantity after step response as a time scale, and selecting the average value of the frequency change rate in the time period as a reference value ROCOF of the maximum value of the frequency change rate ref 。
And also (b)
Whereas ΔP in step response L =1, and can therefore be based on ROCOFs ref Identifying the inertia time constant of the unit:
and the inertia identification results of the synchronous generator and the doubly-fed wind turbine under the system step disturbance after AIC (automatic identification) order determination are respectively shown in fig. 6 and 8.
The implementation of one or more embodiments of the present invention is to perform model order determination (or order reduction) according to the power and frequency data at steady state, and perform inertia identification under pulse disturbance and step disturbance based on the model after order determination (or order reduction), respectively.
According to an implementation of one or more of the foregoing embodiments of the present invention, the present invention further provides an online power system inertia identification system based on an ARMAX model, including: one or more processors; and a memory.
The memory is configured to store instructions that are operable, when executed by the one or more processors, to cause the one or more processors to perform operations including the aforementioned flow of a step response based power system inertia online identification method or the flow of an impulse response based power system inertia online identification method.
While the invention has been described with reference to preferred embodiments, it is not intended to be limiting. Those skilled in the art will appreciate that various modifications and adaptations can be made without departing from the spirit and scope of the present invention. Accordingly, the scope of the invention is defined by the appended claims.
Claims (10)
1. An online power system inertia identification method based on an ARMAX model is characterized by comprising the following steps:
step 1, collecting active power and frequency data of a generator grid connection point in a normal running state of a power grid;
step 2, preprocessing the collected active power and frequency data, including per unit processing and filtering processing;
step 3, aiming at pulse disturbance of the power system, carrying out parameter identification on an ARMAX-based power system model by using the preprocessed active power and frequency data to obtain 8 different system models from 2-order to 9-order;
step 4, converting the obtained 8 different system models into continuous models;
step 5, respectively performing reduced order processing on the 8 continuous models obtained in the step 4 based on a balance cut-off method, discarding any one of the 8 continuous models if the continuous model cannot be reduced to 1 order, and applying unit impulse response to the continuous model if the continuous model can be reduced to 1 order, and obtaining impulse response output;
step 6, inputting the model after the step reduction according to the impulse response output to obtain an inertia time constant;
and 7, taking the average value of the sum of the inertia time constants obtained by the corresponding steps of all continuous models capable of reducing the steps to 1 step as the identification value of the inertia time constant of the power system.
2. The online identification method of inertia of an electric power system based on an ARMAX model according to claim 1, wherein in the step 2, the filtering process adopts a Butterworth filter to perform the filtering process, and noise in the acquired data is filtered.
3. The online identification method of inertia of an electric power system based on an arax model according to claim 1, wherein in the step 4, the obtained system models are respectively subjected to Laplace transformation and converted into continuous models.
4. The online identification method of inertia of an electric power system based on an arax model according to claim 1, wherein in the step 3, a balance cut-off method is used to reduce the system model, comprising:
assume that
Stable, the controllable and observable gram matrices of the system are denoted by P and Q, respectively, wherein:
AP+PA T +BB T ＝0
A T Q+QA+C T C＝0
then there is a non-singular transformation
Such that:
after the non-singular transformation, the gram matrix also transforms accordingly:
simultaneously nonsingular transformed energy-controlled and energy-observed gram matrix
Satisfy->
If there is a diagonal matrix:
∑＝diag(σ 1 ,σ 2 ,…,σ n )
make the following steps
And at the same time satisfies pq=t -1 ∑ 2 T, balance is achieved;
arranging diagonal elements in order from large to small, sigma 1 ，σ 2 ，...，σ n Hankel singular values, sigma, called systems 1 ≥σ 2 ≥…≥σ n Not less than 0; if there is one r, so that sigma r ＞＞σ r+1 Then consider sigma r+1 ,…σ n The corresponding state is a system with poor controllability and observability, and the interception of the system can not cause information defect;
wherein, G represents an ARMAX-based power system model, and A, B, C and D respectively represent a system state matrix before interception;
the truncated r-order model is expressed as:
wherein: a is that r 、B r 、C r 、D r The system state matrix is the truncated system state matrix; u represents a system input.
P and Q are respectively the controllable and observable matrices of the system, transformed according to equations (7), (8), (9), and then transformed according to Sigma=diag (sigma) 1 ,σ 2 ,…,σ n ) And (3) reducing the order of the corresponding criteria to obtain a new system state matrix, and obtaining the simplified system.
5. The online identification method of inertia of an electric power system based on the ARMAX model according to claim 1, wherein in the step 5, the inertia response of the power generating equipment in the electric power system is approximated as a linear process, and the transfer function is expressed as:
wherein: Δf is the system frequency variation; ΔP is the system active power disturbance; d is system damping; t (T) J Is the inertia of the system;
the unit impulse response at unit impulse disturbance is expressed as:
the impulse response value of the generator first-order transfer function at zero time is the reciprocal of the inertia time constant, namely:
where H is the inertial time constant.
6. An online power system inertia identification system based on an ARMAX model is characterized by comprising:
one or more processors;
a memory storing instructions operable, when executed by the one or more processors, to cause the one or more processors to perform operations comprising the flow of the method of any of claims 1-5.
7. An online power system inertia identification method based on an ARMAX model is characterized by comprising the following steps:
step 1, collecting active power and frequency data of a generator grid connection point in a normal running state of a power grid;
step 2, preprocessing the collected active power and frequency data, including per unit processing and filtering processing;
step 3, determining a model order by using an AIC criterion aiming at step disturbance of the power system;
step 4, carrying out parameter identification on the ARMAX-based power system model by using the preprocessed active power and frequency data according to the order determined in the step 3 to obtain a system model;
step 5, converting the system model obtained in the step 4 into a continuous model by using Laplace transformation;
step 6, applying unit step disturbance to the continuous model obtained in the step 5, and obtaining step response output;
step 7, determining a reference value of the maximum value of the frequency change rate under unit step disturbance according to impulse response output;
and 8, determining an inertia time constant of the power system under step disturbance based on the reference value of the maximum value of the frequency change rate.
8. The online identification method of inertia of an electric power system based on an ARMAX model as claimed in claim 7, wherein in the step 7, a first oscillation period of the output after step response is selected as a time scale, and an average value of the frequency change rate in the time scale is selected as a reference value ROCOF of the maximum value of the frequency change rate ref ：
9. The online identification method of inertia of an electric power system based on an arax model as set forth in claim 8, wherein in said step 8, Δp in step response L =1, thus based on ROCOFs ref And identifying the inertia time constant of the power system under the step disturbance:
wherein H is an inertial time constant.
10. An online power system inertia identification system based on an ARMAX model is characterized by comprising:
one or more processors;
a memory storing instructions operable, when executed by the one or more processors, to cause the one or more processors to perform operations comprising the flow of the method of any of claims 7-9.
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