Pmu optimization deployment method for monitoring power system inertia center frequency under limited measurement

Abstract

The application discloses a PMU optimization deployment method for monitoring an inertial center frequency of a power system under limited measurement, and the method is characterized in that: a linear mapping relationship between the inertial center frequency and bus frequencies of the system is established, a linear combination of the bus frequencies is constructed under the condition that the number of PMUs is limited, and the estimation of the inertial center frequency is realized; further, a monitoring accuracy evaluation index based on a fitting error of a normalized inertial time constant is introduced, different PMU deployment schemes are compared and screened, and thus the optimal deployment position and the minimum number of PMUs meeting the monitoring accuracy requirement are determined. The application does not need to configure a measuring device at a synchronous generator end, and can realize the effective monitoring of the dynamic process of the inertial center frequency by using only a small number of bus PMUs, thereby reducing the measurement and communication costs and improving the practicability and engineering feasibility of the frequency monitoring.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of power system operation monitoring and analysis, and particularly relates to a PMU optimization deployment method for monitoring the inertial center frequency of a power system under limited measurement. BACKGROUND

[0002] With the large-scale grid connection of new energy power generation, the structure of the traditional power system mainly based on synchronous generators has changed significantly, the equivalent inertia level of the system is continuously reduced, the dynamic response characteristics of the system frequency after disturbance are significantly deteriorated, and the frequency security problem is increasingly prominent. In the analysis and control of power system frequency stability, the inertial center frequency, as a key indicator reflecting the overall frequency dynamic characteristics of the system, is widely used in power imbalance estimation, low-frequency load shedding criterion formulation, and system transient analysis scenarios. However, the definition of the inertial center frequency depends on the weighted average of the frequency and inertia parameters of each synchronous generator, and in actual engineering, the following problems exist:

[0003] The existing problems in the operation monitoring of the power system are as follows: on the one hand, the definition of the inertial center frequency depends on the frequency and inertia parameters of each synchronous generator, and in actual engineering, the frequency measurement points of the synchronous generator are scattered, the measurement device configuration is incomplete, and there are problems such as high cost and poor communication reliability in centralized collection; on the other hand, with the large-scale access of new energy power sources, the equivalent inertia level of the system is continuously reduced, and the frequency dynamic characteristics are more complex, making it difficult for traditional methods based on local frequency or fixed measurement points to ensure the monitoring accuracy of the inertial center frequency in complex systems.

[0004] With the development of phasor measurement unit (PMU) technology, PMU deployment at the system busbar side is increasingly popular, and busbar frequency measurement has become a feasible frequency monitoring method. Existing research has shown that under certain conditions, the busbar frequency can be expressed as a linear combination of the frequency of synchronous generators, thereby providing a theoretical basis for estimating the inertial center frequency based on busbar frequency. However, existing technologies mostly assume sufficient PMU quantity or fixed deployment location, and in the case of limited PMU quantity, how to select appropriate busbar deployment PMU, how to quantify the monitoring accuracy of different deployment schemes, and how to determine the minimum PMU quantity that meets the monitoring accuracy requirements, still lack systematic and implementable solutions. SUMMARY

[0005] Invention purposes: The purpose of the present application is to provide a PMU optimized deployment method for monitoring the inertia center frequency of a power system under limited measurement. By establishing a linear relationship model between the inertia center frequency and the bus frequency, a monitoring accuracy evaluation index is constructed, and the system is compared between different PMU deployment schemes, so as to realize high-precision dynamic monitoring of the inertia center frequency under the condition of limited PMU quantity.

[0006] Technical scheme: The PMU optimized deployment method for monitoring the inertia center frequency of a power system under limited measurement comprises the following steps:

[0007] Step 1, a linear relationship model between the inertia center frequency of a synchronous generator and the bus frequency is constructed;

[0008] Step 2, based on the linear relationship model, for a given combination of phasor measurement unit (PMU) quantity and candidate deployment location, a monitoring accuracy evaluation index is constructed and the corresponding linear combination coefficient is solved;

[0009] Step 3, comparison and screening are carried out between different PMU deployment location combinations to determine the optimal deployment scheme under the given PMU quantity;

[0010] Step 4, the minimum PMU quantity meeting the requirements is determined based on the monitoring accuracy threshold, and the recommended deployment scheme is given accordingly;

[0011] Step 5, the bus frequency collected by the optimal deployment scheme is used to estimate and dynamically monitor the inertia center frequency in real time.

[0012] Further, step 1 specifically comprises the following steps:

[0013] Step 1.1, the number of synchronous generators in the system is obtained , the frequency of each synchronous generator is , the inertia constant is , and the normalized inertia time constant is calculated, wherein:

[0014] ;

[0015] Step 1.2, the definition formula of the inertia center frequency is constructed according to the normalized inertia time constant:

[0016] ;

[0017] Step 1.3, a linear mapping relationship between the bus frequency of any bus j and the synchronous generator frequency is established based on the frequency divider theory:

[0018] ;

[0019] where, is the influence coefficient of synchronous generator i on bus j frequency, which is calculated based on the augmented admittance matrix reflecting the system network topology and line parameters;

[0020] Step 1.4, when selecting the frequency of the bus where PMU is deployed for estimating the inertia center frequency, the linear combination of bus frequency is constructed as:

[0021] ;

[0022] where, is the linear combination coefficient of the corresponding bus frequency;

[0023] Step 1.5, compare the consistency of the coefficients of each synchronous generator frequency , and get the matrix relationship:

[0024] ;

[0025] where, is the matrix composed of the corresponding of the selected bus combination, is the normalized inertia time constant vector of each synchronous generator in the system, where represents the normalized inertia time constant of the th synchronous generator, which is used to represent the relative weight of the generator in the overall inertia of the system; is the linear coefficient vector of bus frequency; when the relationship is satisfied, the inertia center frequency is represented by the bus frequency in real time as:

[0026] .

[0027] Further, step 2 specifically includes the following steps:

[0028] Step 2.1, for a given number of PMUs and a certain bus combination , based on and k, the estimated vector of normalized inertia time constant is obtained;

[0029] Step 2.2, define the absolute percentage error of the normalized inertia time constant of the i th synchronous generator:

[0030] ;

[0031] Step 2.3, construct the relative error vector , and define the monitoring accuracy evaluation index based on the two-norm:

[0032] ;

[0033] wherein, is a normalized bus frequency mapping matrix, wherein is a diagonal matrix composed of normalized inertia time constants of each synchronous generator, which is used to describe the mapping relationship of bus frequency linear combination to the frequency of each synchronous generator in the sense of normalized inertia weight; and matrix then depicts the information completeness and numerical distinguishability of bus combination in the fitting of overall system inertia parameters; is a full 1 vector with dimension, and ‖·‖2 represents the two-norm of a vector;

[0034] Step 2.4, under the constraint condition , solve the linear combination coefficient that minimizes the evaluation index, and construct an optimization model:

[0035] .

[0036] Further, in step 2.3, when the matrix is invertible, the closed-form solution of the linear combination coefficient is:

[0037] ;

[0038] wherein, , and .

[0039] Further, when the matrix is not invertible or the condition number exceeds a threshold, by introducing a regularization coefficient to enhance numerical stability, the linear combination coefficient is solved in the following way:

[0040] ;

[0041] wherein, I is a unit matrix, which is obtained by replacing the matrix A with and calculating in the corresponding way.

[0042] Further, step 3 specifically includes the following steps:

[0043] Step 3.1, for a given PMU number N, enumerate all bus combinations in the system candidate buses, obtaining the combination set , and the total number of combinations is , wherein represents the number of combinations from the system under the condition that the given PMU number is N The number of different combinations of N busbars selected from N candidate busbars; The symbol represents a combination number, whose mathematical meaning is from... The number of combinations that can be formed by randomly selecting N elements from n elements;

[0044] Step 3.2, for the set Each busbar combination Calculate its minimum evaluation index ;

[0045] Step 3.3: Select the bus combination that minimizes the evaluation index as the optimal deployment scheme using the following optimization criteria:

[0046] ;

[0047] Furthermore, step 4 specifically includes the following steps:

[0048] Step 4.1: Set the monitoring accuracy threshold as follows And calculate the number of different PMUs. The optimal evaluation index ;

[0049] Step 4.2: Using the square root of the evaluation index as the monitoring error index, determine the criteria that meet the requirements. Minimum number of PMUs ,in:

[0050] ;

[0051] Furthermore, step 5 specifically includes the following steps:

[0052] Step 5.1: Collect bus frequency at the optimal bus deployment location. ;

[0053] Step 5.2: Use the linear combination coefficients corresponding to the optimal deployment scheme. The inertial center frequency is estimated by weighted summation of the bus frequencies.

[0054] Step 5.3: Output the estimated inertial center frequency as the dynamic monitoring result of the system's inertial center frequency.

[0055] Furthermore, when the line impedance and generator inertia time constant of the monitored power system are uncertain or change during disturbance, linear combination coefficients are calculated for multiple sampling operating conditions, and the obtained linear combination coefficients are averaged. The averaged linear combination coefficients are then used for inertial center frequency monitoring.

[0056] The application further discloses a PMU optimization deployment system for monitoring an inertial center frequency of a power system under limited measurement, comprising:

[0057] a modeling unit configured to construct a linear relationship model between the inertial center frequency of the synchronous generator and the bus frequency; a calculation unit configured to construct a monitoring accuracy evaluation index and solve corresponding linear combination coefficients for a given PMU number and candidate deployment position combination; a screening unit configured to compare and screen among different PMU deployment position combinations to determine an optimal deployment scheme under the given PMU number; a determination unit configured to determine a minimum PMU number meeting a requirement and recommend a deployment scheme accordingly; and a monitoring unit configured to use the bus frequency collected by the optimal deployment scheme to perform real-time estimation and dynamic monitoring on the inertial center frequency.

[0058] Advantages: Compared with the prior art, the application has the following remarkable advantages:

[0059] 1. Under the condition that the number of PMUs is limited, the linear combination of the bus frequency is used to realize real-time monitoring on the COI frequency in a full dynamic process, and the dependence on the frequency measurement of all synchronous generators is avoided.

[0060] 2. A monitoring accuracy evaluation index based on the two-norm is proposed, and the monitoring accuracy of the PMU deployment schemes with different numbers and different positions can be quantitatively compared.

[0061] 3. A closed-form solution of the linear combination coefficients is derived, and a regularized stable solving method is given, so that the optimal coefficients can be obtained under each deployment combination and the stability of the engineering solving is improved.

[0062] 4. The optimal deployment position and the minimum PMU number meeting the accuracy requirement are determined systematically through enumeration combination and threshold criterion, and explicit and executable planning basis is provided for actual deployment.

[0063] 5. When the IEEE 39 bus system is taken as a test object and the monitoring error threshold is set to 10%, only 4 PMUs need to be deployed to realize high-precision monitoring on the inertial center frequency. Under typical load disturbance, generator tripping and other scenes, the inertial center frequency curve monitored is consistent with the real inertial center frequency calculated directly from the synchronous generator frequency, which verifies the effectiveness of the application in a medium-scale system.

[0064] 6. In large-scale complex systems such as the IEEE 118 bus system, the application can still accurately track the dynamic process of the inertial center frequency under the condition of limited PMU number. Simulation results show that although the system scale is significantly increased, the monitoring error of the application method can still be controlled within the preset threshold range, indicating that the method has good scalability and engineering applicability. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 The topological structure schematic diagram of the IEEE 39-node system in Example 1 is shown, in which the 39 buses are marked with numbers, 1-29 are load nodes, 30-39 are generator nodes, the PMU deployment bus position is marked with magenta, and the photovoltaic access position is marked with blue;

[0066] Figure 2 The distribution of the square root of the inertia center frequency monitoring error index under different PMU numbers and different PMU deployment position combination conditions in Example 1 is shown, in which the connecting line represents the optimal deployment combination under each PMU number;

[0067] Figure 3 The comparison of the inertia center frequency monitoring results of the method of the application and other bus frequency-based methods when the system is subjected to load disturbance in Example 1 is shown;

[0068] Figure 4 The comparison of the inertia center frequency monitored by the method of the application and the real inertia center frequency under different generator outage disturbance scenarios in Example 1 is shown, in which (a) is the generator outage diagram at node 34, and (b) is the generator outage diagram at node 39;

[0069] Figure 5 The comparison of the inertia center frequency monitoring error index when different linear combination coefficients are used under the condition that the system parameters have uncertainties in Example 1 is shown;

[0070] Figure 6 The comparison of the inertia center frequency monitoring effect when different linear combination coefficients are used when the synchronous generator inertia parameter changes during the disturbance process in Example 1 is shown;

[0071] Figure 7 The comparison of the inertia center frequency dynamic process monitored by the method of the application and other methods in the IEEE 118 bus system in Example 2 is shown;

[0072] Figure 8 The flowchart of the application. DETAILED DESCRIPTION

[0073] The technical solutions of the application will be further described below with reference to the accompanying drawings.

[0074] The application establishes a linear mapping relationship model between the inertial center frequency and the bus frequency, and under the condition of limited PMU quantity, the bus frequency signal is collected by a small number of PMUs arranged at the system bus, and the real-time reconstruction of the inertial center frequency is realized by constructing a linear combination of the bus frequency; further, the application proposes a monitoring accuracy evaluation index based on the normalized inertial time constant fitting error, and on this basis, the monitoring accuracy of different PMU deployment position combinations is systematically compared, the optimal linear combination coefficient corresponding to each deployment scheme is derived, so as to determine the optimal deployment scheme under the given PMU quantity, and further determine the minimum PMU quantity meeting the monitoring accuracy requirement.

[0075] Compared with the existing inertial center frequency monitoring method relying on synchronous generator terminal frequency measurement or assuming sufficient PMU quantity, the application does not need to configure a measuring device at all synchronous generators, and while reducing the number of PMU deployment and communication burden, it can still realize high-precision monitoring of the inertial center frequency in the whole dynamic process; at the same time, the application solves the linear combination coefficient by closed-form solution and regularization method, which ensures the numerical stability of the solving process under different deployment schemes, and has good engineering implementability and popularization and application value. Embodiment

[0076] The embodiment provides a PMU optimization deployment method for monitoring the inertial center frequency of a power system under limited measurement, and verifies and analyzes the effectiveness and feasibility of the method based on typical multi-machine power systems (such as IEEE 39 bus system and IEEE 118 bus system).

[0077] The inertial center frequency monitoring method described in the embodiment is implemented on the basis of the linear relationship model between the inertial center frequency and the bus frequency, the monitoring accuracy evaluation index, the linear combination coefficient optimization model and the closed-form / regularization solution thereof established in the foregoing specific embodiments, as shown in Figure 8 The method comprises the following steps:

[0078] Step 1: Establish a linear mapping model between the inertial center frequency and the bus frequency, and construct a linear combination expression of the bus frequency;

[0079] Step 2: For a given PMU quantity and different deployment position combinations, construct a monitoring accuracy evaluation index based on the normalized inertial time constant fitting error, and solve the corresponding optimal linear combination coefficient;

[0080] Step 3: Enumerate and compare different PMU deployment position combinations to determine the optimal PMU deployment scheme under the given PMU quantity;

[0081] Step four: In the typical disturbance and parameter uncertainty scenario, the inertia center frequency is dynamically monitored by using the optimal deployment scheme, and the accuracy and robustness of the method are verified.

[0082] In an implementation scenario, the test system adopted is a power transmission system including multiple synchronous generators, and the bus thereof includes both generator buses and load buses. The network topology and line parameters of the system are used to calculate the influence coefficient matrix between the bus frequencies and the synchronous generator frequencies. The inertia constant of each synchronous generator can be obtained according to the system model or operation data. The system topology is shown in Figure 1 .

[0083] The system used for research in this embodiment is an IEEE-39 bus system, and the system topology is shown in Figure 1 . Taking the deployment of four PMUs as an example, the system has kinds of bus deployment combinations, and the optimal deployment combination position is marked in purple in Figure 1 . In order to be close to the engineering operation and verify the robustness of the method, the following settings are further adopted in this embodiment:

[0084] Disturbance setting: a 700 MW load increase is applied at bus 23 as a typical load disturbance scenario, and the differences in the inertia center frequency monitoring effects of the optimal deployment combination and other deployment combinations are compared;

[0085] Measurement noise setting: in order to simulate the PMU measurement error, Gaussian random noise is superimposed on the bus frequency measurement value, the noise mean value is 0, and the standard deviation is 10% of the maximum state change amount, which is used to test the monitoring performance of the present application in the presence of noise;

[0086] Uncertainty setting: it is assumed that the inertia constant of the synchronous generator and the line impedance both have Gaussian variation, and the uncertainty level is 5%; by generating 100 groups of different operating conditions, the evaluation indexes under different linear combination coefficients are compared, and it is verified that the average of the linear coefficients obtained under multiple operating conditions can improve the robustness.

[0087] The specific steps in step one are as follows:

[0088] 1) Define the inertia center frequency and establish the linear mapping of bus frequencies

[0089] In this embodiment, first, the frequencies of kinds of synchronous generators in the system are weighted by inertia, and the definition formula of the inertia center frequency is obtained:

[0090]

[0091] Subsequently, according to the frequency divider theory, the frequency of any bus j ​The bus frequency is expressed as a linear combination of the frequencies of the synchronous generators, with coefficients The augmented admittance matrix reflecting the topology and line parameters can be used to calculate the coefficients

[0092]

[0093] 2) Construct a linear combination of bus frequencies to reconstruct the inertia center frequency

[0094] When PMUs are deployed at N busbars in the system and the bus frequencies are collected, the collected bus frequencies are linearly combined:

[0095]

[0096] The matrix relationship is satisfied, where is the normalized inertia time constant vector of the synchronous generators in the system. is the linear coefficient vector of the bus frequencies, and the inertia center frequency is expressed in real time as:

[0097]

[0098] The specific steps in step two are as follows:

[0099] 1) Construct the normalized inertia time constant fitting error and define the evaluation index

[0100] When the number of PMUs is limited, different disturbance locations will have different effects on the frequency responses of different synchronous generators, showing a distribution characteristic. Therefore, the errors of all synchronous generators need to be considered to adapt to various disturbances.

[0101] In this embodiment, the normalized inertia time constant estimated value reconstructed by the linear combination of bus frequencies is compared with the true value, and the first i absolute percentage error of the normalized inertia time constant of the

[0102]

[0103] The two-norm of the error vector is further used as a monitoring accuracy evaluation index:

[0104]

[0105] where , the smaller the index, the more accurate the fitting of h , and the higher the monitoring accuracy of the inertia center frequency. And comprehensively depicts the information completeness and numerical distinguishability of the bus combination in the overall system inertia parameter fitting. is a full one vector with dimension, and ||·||2 represents the two-norm of a vector. 2) Solve the optimal linear combination coefficients under the steady-state consistency constraint

[0106] 2) To ensure that the steady-state value of the linear combination of the center-of-inertia frequency and the bus frequency is consistent at steady state, introduce a constraint when solving the linear combination coefficients and construct the optimization model:

[0107]

[0108] When is reversible, a closed-form solution is obtained;

[0109]

[0110] When the matrix is ill-conditioned due to a large condition number, introduce a regularization coefficient to obtain a regularized solution to enhance numerical stability:

[0111]

[0112] The specific steps in step three are as follows:

[0113] 1) Enumerate deployment combinations and select the optimal scheme

[0114] For a given number of PMUs N enumerate different deployment combination sets in the candidate bus , calculate the minimum evaluation index of each combination , and determine the optimal deployment scheme under the given number of PMUs based on the minimum criterion:

[0115]

[0116] Taking four PMUs as an example, there are combinations, for each combination, the optimal linear coefficient is solved and substituted into the evaluation index to calculate the fitness, and finally the optimal combination “1, 2, 15, 29” is obtained, which is marked in magenta in Figure 1 .

[0117] 2) Determine the minimum number of PMUs according to the accuracy threshold

[0118] In this embodiment, the is taken as a monitoring error index to determine the minimum number of PMUs that meet the target accuracy threshold: ε

[0119]

[0120] Under different PMU numbers and different deployment combinations ​The distribution is shown in Figure 2 The distribution shows that there is an optimal deployment combination for each PMU number, and each optimal combination is connected by a line, which can provide guidance for PMU number selection; for example, when the monitoring error is required to be less than 10%, at least 4 PMUs are needed.

[0121] The specific steps in step four are:

[0122] 1) Load disturbance scenario verification

[0123] When the bus 23 has a 700 MW load increase, the inertial center frequency monitoring results of the optimal deployment combination and other deployment combinations are compared, as shown in Figure 3 To simulate the actual measurement error, a Gaussian noise with a mean of 0 and a standard deviation of 10% of the maximum state change is superimposed on the bus frequency. The simulation results show that the linear combination coefficients corresponding to different deployment combinations have significant differences in monitoring performance, which illustrates the necessity of PMU optimal deployment; at the same time, the superiority of the method of the present application is also verified compared with the existing method.

[0124] 2) Generator rejection scenario verification and coefficient update

[0125] When the generator is rejected at bus 34 and bus 39 respectively, the monitoring inertial center frequency obtained by the optimal deployment combination is compared with the actual value, as shown in Figure 4 The results show that the monitoring effect is still good in the case of bus 34 rejection; in the case of bus 39 rejection, due to the large inertia of the rejected generator, if the original linear combination coefficient is still used, the monitoring performance will be relatively poor, at this time, the monitoring accuracy can be significantly improved by updating the linear combination coefficient (the blue curve in Figure 4 ).

[0126] 3) Robustness verification under parameter uncertainty and coefficient averaging

[0127] Under the system parameter uncertainty scenario, it is assumed that the generator inertia constant and the line impedance both have a 5% Gaussian uncertainty, 100 operating conditions are generated, and the of different linear combination coefficients under different conditions are compared, as shown in Figure 5 Among them correspond to the optimal coefficients obtained under two groups of random conditions respectively, is the average coefficient obtained by solving again and then averaging according to the multi-condition. The results show that the average coefficient can obtain better monitoring accuracy and robustness.

[0128] 4) Inertia change scenario verification in disturbance process

[0129] When the system inertia parameter changes during the disturbance process, the influence of different coefficient strategies on the full dynamic monitoring is further verified. Specifically, it is assumed that the inertia constant of the generator at bus 39 increases 1 second after the disturbance; the monitoring effects of the coefficients corresponding to the pre-disturbance working condition , the coefficients corresponding to the post-disturbance working condition , and the average coefficient are compared, as shown in Figure 6 . The results show that the use of the average coefficient can more accurately track the entire dynamic process (indicated by the green curve in Figure 6 ), thereby verifying the applicability of the present application in the parameter change scenario during the disturbance.

[0130] The above is the implementation and verification process of the method of the present application in the IEEE-39 bus system. As can be seen from the results of Figure 1 – Figure 6 : the evaluation index and closed-form / regularization coefficient solving proposed by the present application can systematically screen the PMU deployment location and determine the required number of PMUs, and can accurately monitor the inertia center frequency full dynamic process in scenarios such as load disturbance, generator removal, and parameter uncertainty and disturbance, and has good robustness.

[0131] To verify the applicability and scalability of the PMU optimal deployment inertia center frequency monitoring method described in this embodiment in large-scale power systems, based on the completion of the IEEE-39 bus system verification, this embodiment further selects the IEEE-118 bus system as the test system to analyze and verify the monitoring effect of the method of the present application under the condition that the system size is significantly increased, and the results are shown in Figure 7 .

[0132] The IEEE-118 bus system contains more synchronous generators and load nodes, and the network structure is more complex, and the system frequency dynamic characteristics are more sensitive to the disturbance location and inertia distribution. In this system, each bus is used as a candidate deployment location for PMU, and the same inertia center frequency definition method, bus frequency linear combination model and monitoring accuracy evaluation index as the IEEE-39 bus system are used to enumerate and compare different PMU quantities and their deployment combinations.

[0133] Under typical disturbance scenarios, the bus frequency signals collected by the optimal PMU deployment scheme are used to estimate the inertia center frequency in real time, and the estimation results are compared with the true inertia center frequency calculated directly from the synchronous generator frequency. As can be seen from Figure 7 , in the IEEE-118 bus system, the method of the present application can better track the dynamic change process of the inertia center frequency, and the monitoring results are in good consistency with the true inertia center frequency.

[0134] Further analysis shows that as the system scale increases, the number of PMUs required to achieve the same monitoring accuracy increases accordingly, but by reasonably selecting the PMU deployment location, effective monitoring of the inertial center frequency can still be achieved under the condition of limited PMU number. This shows that the method described in this embodiment not only applies to medium-sized power systems, but also has good applicability and stability in large-scale complex power systems.

[0135] In summary, the present application proposes a power system inertial center frequency monitoring method based on PMU optimized deployment. In view of the problem that the inertial center frequency is difficult to obtain with high accuracy in the existing power system operation, a limited number of phasor measurement units are reasonably configured at the system bus to effectively characterize the overall frequency dynamic characteristics of the system. This method avoids direct measurement of the frequency at the end of all synchronous generators, reducing the complexity of measurement device deployment and data communication.

[0136] Under the condition of limited PMU number, the present application analyzes the internal correlation between bus frequency and synchronous generator frequency, constructs a linear combination model of bus frequency, and introduces an evaluation mechanism based on inertia parameter fitting error to quantify and compare the monitoring performance of different PMU deployment schemes, thereby determining the corresponding optimal deployment scheme and the minimum PMU number required.

[0137] Simulation and analysis results show that the method of the present application can maintain good monitoring accuracy and numerical stability under various operating conditions and disturbance scenarios, taking into account monitoring performance and engineering implementability, and has promotional and application value. Embodiment

[0138] The present embodiment proposes a PMU optimized deployment monitoring device for monitoring the inertial center frequency of a power system under limited measurement. Based on bus frequency measurement and linear combination reconstruction principles, the device realizes high-precision dynamic monitoring of the inertial center frequency of the power system under the condition of limited PMU number.

[0139] The PMU optimized deployment monitoring device comprises:

[0140] An inertial center frequency modeling module for establishing a mathematical expression model of the inertial center frequency according to the inertia parameters and rotational frequency of each synchronous generator in the system, and generating a corresponding normalized inertia time constant vector;

[0141] A bus frequency mapping modeling module for establishing a linear mapping relationship between bus frequency and synchronous generator frequency based on the power system network topology and line parameters, forming a bus frequency influence coefficient matrix;

[0142] a bus frequency linear combination construction module configured to collect bus frequency signals at selected PMU-deployed buses and construct a linear combination expression of the bus frequencies to realize reconstruction of the center-of-inertia frequency with a limited number of bus frequencies;

[0143] a linear combination coefficient solving module configured to solve optimal coefficients of the linear combination of the bus frequencies based on a bus frequency mapping relationship and a center-of-inertia frequency model under a steady-state consistency constraint;

[0144] a monitoring accuracy evaluation module configured to construct a monitoring accuracy evaluation index based on a normalized center-of-inertia time constant fitting error and quantitatively evaluate the center-of-inertia frequency monitoring performance under different PMU deployment schemes;

[0145] a PMU deployment optimization module configured to enumerate and comparatively analyze candidate bus deployment combinations under a given PMU number condition and select an optimal PMU deployment scheme according to the monitoring accuracy evaluation index;

[0146] a minimum PMU number determination module configured to determine a minimum PMU number required for center-of-inertia frequency monitoring under a premise of meeting a preset monitoring accuracy threshold;

[0147] a center-of-inertia frequency dynamic monitoring module configured to estimate and output the center-of-inertia frequency in real time based on the optimal PMU deployment scheme and corresponding linear combination coefficients under operating scenarios such as load disturbance, generator tripping and system parameter variation.

[0148] Further, the device further comprises:

[0149] a disturbance scenario analysis module configured to analyze dynamic variation characteristics of the center-of-inertia frequency under different types of system disturbance conditions to verify accuracy and consistency of the monitoring results;

[0150] a robustness analysis module configured to analyze and evaluate monitoring accuracy and numerical stability of the PMU optimal deployment monitoring device under conditions of uncertainty of the synchronous generator inertia parameters or network parameters.

[0151] The specific implementation manners of the functional modules in the PMU optimal deployment monitoring device are described in the specific implementation process of the PMU optimal deployment method for monitoring the center-of-inertia frequency of the power system in Embodiment One, which will not be described here again.

[0152] Those skilled in the art should understand that the embodiments of the present application can be embodied in a computer program product, a method or a system. Therefore, the present application can be embodied in a form of a complete hardware embodiment, a complete software embodiment or a combination of software and hardware.

Claims

1. A PMU optimization deployment method for monitoring the center frequency of the inertia of a power system under limited metering, characterized in that, The method comprises the following steps: Step 1, constructing a linear relationship model between the inertia center frequency of a synchronous generator and the bus frequency; Step 2, based on the linear relationship model, constructing a monitoring accuracy evaluation index and solving corresponding linear combination coefficients for a given combination of PMU number and candidate deployment location; Step 2 specifically comprises the following steps: Step 2.1, for a given number of PMUs combination with a certain bus , based on and k to get an estimated vector of normalized inertia time constants ; Step 2.2, defining the first i Absolute percentage error in the normalized inertia time constant of the synchronous generator: ； Step 2.3, Constructing the relative error vector and define the monitoring accuracy evaluation index based on the two-norm: ； wherein, is a normalized bus frequency mapping matrix, wherein is a diagonal matrix composed of normalized inertia time constants of each synchronous generator, which is used to describe the mapping relationship of bus frequency linear combination to the frequency of each synchronous generator in the sense of normalized inertia weight; and matrix then depicts the information completeness and numerical distinguishability of bus combination in the overall system inertia parameter fitting; is a full 1 vector with dimension, and ‖·‖2 represents the two-norm of a vector; Step 2.4, constraint conditions Next, the linear combination coefficients that minimize the evaluation index are solved, and an optimization model is constructed: ； Step 3, comparing and screening between different PMU deployment location combinations to determine the optimal deployment scheme under a given PMU number; Step 3 specifically comprises the following steps: Step 3.1, Enumerate all bus combinations in the set of candidate buses for a given PMU number N, get the combination set , the total number of combinations is , where represents the number of different combinations of N buses selected from the system candidate buses under the condition that the given PMU number is N; represents the combination number symbol, and its mathematical meaning is the number of combinations that can be formed by selecting N elements from elements; Step 3.2, on the set each bus combination , calculate its minimum evaluation index ; Step 3.3, selecting the bus combination that minimizes the evaluation index as the optimal deployment scheme through the following optimization criteria: ； Step 4, determining the minimum PMU number that meets the requirement based on the monitoring accuracy threshold, and giving a recommended deployment scheme accordingly; Step 4 specifically comprises the following steps: Step 4.1, set the monitoring accuracy threshold value as and calculate the optimal evaluation index under different PMU quantities . ; Step 4.2, determine the minimum PMU number that satisfies the evaluation index square root as the monitoring error index wherein: ； Step 5, using the bus frequency collected by the optimal deployment scheme to estimate and dynamically monitor the inertia center frequency in real time.

2. The PMU optimal deployment method for monitoring the center frequency of power system inertia under limited measurements according to claim 1, characterized in that, Step 1 specifically comprises the following steps: Step 1.

1. Obtain the number of synchronous generators in the system , the frequency of each synchronous generator , the inertia constant , and calculate the normalized inertia time constant where: ； Step 1.

2. Constructing the inertial center frequency from the normalized inertial time constant Definition: ； Step 1.

3. Establish bus frequency of arbitrary bus j based on frequency divider theory Linear mapping relationship between bus frequency and synchronous generator frequency: ； wherein, represents the influence coefficient of synchronous generator i on bus j frequency, which is calculated based on the augmented admittance matrix reflecting the system network topology and line parameters; Step 1.4, when the selected When the bus frequency of a PMU-equipped bus is used to estimate the center frequency of inertia, a linear combination of bus frequencies is constructed: ； wherein is a linear combination coefficient corresponding to the bus frequency; Step 1.

5. Comparing the frequency of each synchronous generator The coefficient consistency of the above equations gives the matrix relationship: ； wherein, is the matrix composed of the selected bus combinations corresponding to , is the vector of normalized inertia time constants of each synchronous generator in the system, wherein denotes the normalized inertia time constant of the i-th synchronous generator, used to characterize the relative weight of this generator in the overall inertia of the system; is the vector of bus frequency linear coefficients; when the relationship is satisfied, the center of inertia frequency is represented in real time by the bus frequency as: 。 3. The PMU optimal deployment method for monitoring the center frequency of power system inertia under limited measurements according to claim 1, characterized in that, In step 2.3, when the matrix The closed-form solution for the linear combination coefficients is ； wherein , and .

4. The PMU optimal deployment method for monitoring the center frequency of power system inertia under limited measurements according to claim 1, characterized in that, When the matrix When the matrix is not invertible or the condition number exceeds a threshold, a regularization coefficient To enhance numerical stability, linear combination coefficients is solved as follows: ； where I is an identity matrix, By replacing the matrix A with and the corresponding way to calculate the.

5. The PMU optimal deployment method for monitoring the center frequency of power system inertia under limited measurements according to claim 1, characterized in that, Step 5 specifically comprises the following steps: Step 5.

1. Collecting bus frequency at the optimal deployment bus ; Step 5.2, adopt the linear combination coefficients corresponding to the optimal deployment scheme Weighted sum of bus frequencies to obtain an inertia center frequency estimate Step 5.3, outputting the inertia center frequency estimate as the dynamic monitoring result of the system inertia center frequency.

6. The PMU optimal deployment method for monitoring the center frequency of power system inertia under limited measurements according to claim 1, characterized in that, When there is uncertainty in the line impedance and generator inertia time constant of the monitored power system or the line impedance and generator inertia time constant change during disturbance, the linear combination coefficients are calculated for multiple sampling operating conditions respectively, and the obtained linear combination coefficients are averaged, and the averaged linear combination coefficients are used for inertia center frequency monitoring.

7. A PMU optimized deployment system for monitoring the center frequency of the inertia of a power system under limited metering, for implementing the method of claim 1, characterized by, The method comprises the following steps: A modeling unit is configured to construct a linear relationship model between the inertia center frequency of a synchronous generator and the bus frequency; A calculation unit is configured to construct a monitoring accuracy evaluation index and solve corresponding linear combination coefficients for a given combination of PMU number and candidate deployment location; a screening unit is configured to compare and screen between different PMU deployment location combinations to determine the optimal deployment scheme under a given PMU number; a determination unit is configured to determine the minimum PMU number that meets the requirement and give a recommended deployment scheme accordingly; and a monitoring unit is configured to use the bus frequency collected by the optimal deployment scheme to estimate and dynamically monitor the inertia center frequency in real time.

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