Reactive Power Output Estimation Method of Synchronous Condenser Based on Kalman Filter

Abstract

The present invention discloses a method for estimating the reactive power output of a synchronous condenser based on Kalman filtering (KF), which includes the following steps: establishing a Kalman filtering system; obtaining the PMU measurement parameters of the synchronous condenser; inputting the PMU measurement parameters of the synchronous condenser into the Kalman filtering system to obtain filtered output parameters; and calculating the reactive power output value of the synchronous condenser according to the filtered output parameters. The present invention effectively filters out the noise interference in PMU measurement, reduces the storage amount of data required for estimation, and improves the estimation accuracy of the reactive power output of the synchronous condenser.

Description

Technical Field

[0001] The present invention belongs to the field of high - voltage direct - current (HVDC) transmission system engineering, and particularly relates to a method for estimating the reactive power output of a synchronous condenser based on Kalman filtering. Background Technique

[0002] In China, to a certain extent, energy and load are distributed in a reverse manner. The use of long - distance HVDC transmission can achieve the optimal allocation of energy on a large scale. With the continuous increase of transmission power, the characteristics of "strong HVDC and weak AC" in the power grid are further highlighted, and the impact of the DC grid on the AC grid is increasing. Insufficient reactive power reserves in the grid can lead to voltage instability. Synchronous condensers are widely used in HVDC transmission systems because they have the advantages of small influence of the regulation ability on the system and high field - forcing ability. They provide short - circuit capacity for the system during system faults. As a dynamic reactive power compensation device, it is an effective solution to solve the reactive power compensation problem in HVDC transmission systems. The reactive power output of a synchronous condenser is an important parameter during operation. The synchronous condenser often operates under the condition of drastic changes in reactive power output, and its reactive power output ability is directly related to the transient stability of the transmission system. Therefore, accurate estimation is of great significance.

[0003] At present, from relevant domestic and foreign literature, it can be known that the reactive power output of a synchronous condenser can be obtained through means such as analytical calculation, direct reading by a PMU, neural network, and pure finite - element analysis. However, analytical calculation cannot guarantee the calculation accuracy at the moment when the synchronous condenser quickly provides reactive power support. The PMU measurement data contains large noise. The neural network requires a large amount of training data, and it is difficult to obtain the reactive power transient data of the synchronous condenser. The method based on finite - element analysis can accurately calculate the transient reactive power, but the calculation time is long and it cannot adapt to the reactive power output calculation under complex transient conditions. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide a method for estimating the reactive power output of a synchronous condenser based on Kalman filtering, which can effectively filter out the noise interference of PMU measurement, reduce the storage amount of data required for estimation, and improve the estimation accuracy of the reactive power output of the synchronous condenser.

[0005] To solve the above - mentioned technical problems, the present invention provides a method for estimating the reactive power output of a synchronous condenser based on Kalman filtering, including the following steps:

[0006] Establish a Kalman filtering system; obtain the PMU measurement parameters of the synchronous condenser; input the PMU measurement parameters of the synchronous condenser into the Kalman filtering system to obtain the filtered output parameters; calculate the reactive power output value of the synchronous condenser according to the filtered output parameters.

[0007] Optionally, the synchronous condenser PMU measurement parameters include direct-axis voltage, quadrature-axis voltage, direct-axis current, and quadrature-axis current, and the filtered output parameters include direct-axis voltage, quadrature-axis voltage, direct-axis current, and quadrature-axis current.

[0008] Optionally, the establishment of the Kalman filter system includes: constructing a practical state-space model of the synchronous condenser; discretizing the practical state-space model; and constructing a Kalman filter system according to the discretized practical state-space model.

[0009] Optionally, the construction of the practical state-space model includes the following steps: constructing a synchronous condenser mathematical model of the subtransient electromotive force; selecting a state vector, and establishing a practical state-space model of the synchronous condenser according to the synchronous condenser mathematical model of the subtransient electromotive force.

[0010] Optionally, the synchronous condenser mathematical model of the subtransient electromotive force is as follows:

[0011]

[0012] where e″ d and e′ d are the direct-axis subtransient and transient induced electromotive forces respectively; e″ q and e′ q are the quadrature-axis subtransient and transient induced electromotive forces respectively; are the first-order derivatives of e″ q , e′ q , e″ d , and e′ d respectively; T″ do and T′ do are the direct-axis subtransient and transient open-circuit time constants respectively; T″ qo and T′ qo are the quadrature-axis subtransient and transient open-circuit time constants respectively; x″ d and x′ d are the direct-axis subtransient and transient reactances respectively; x″ q and x′ q are the quadrature-axis subtransient and transient reactances respectively; x d and x q are the direct-axis and quadrature-axis synchronous reactances respectively; u d and u q are the direct-axis and quadrature-axis voltages respectively; i d and i q are the direct-axis and quadrature-axis currents respectively; r a is the stator resistance.

[0013] Optionally, the calculation formula for the reactive power output value of the synchronous condenser is:

[0014]

[0015] Among them, is the estimated value of the synchronous condenser's reactive power output, are the direct-axis and quadrature-axis voltages output by the filtering system respectively; are the direct-axis and quadrature-axis currents output by the filtering system respectively.

[0016] Optionally, the working process of the Kalman filtering system includes the following steps:

[0017] Set the initial value of the Kalman filter, update the state estimate, update the error covariance, obtain the filtering gain matrix according to the actual measurement value of the PMU, update the state estimate according to the measurement value, update the error covariance according to the measurement value, and output the filtering parameters.

[0018] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The Kalman filtering (KF) estimation method for the dynamic reactive power output of the synchronous condenser proposed by the present invention combines the PMU measurement parameters of the condenser, effectively filtering out the noise interference in the PMU measurement; and a practical state model is constructed through the transient and subtransient electromotive forces of the condenser; the synchronous condenser often operates in the situation of rapid reactive power change, and considering the subtransient electromotive force for modeling can improve its modeling accuracy; the method of the present invention obtains the filtering value through the iterative update of the Kalman filter (KF), and calculates the estimated value of the reactive power output from the filtering value. The filtering and prediction interact with each other throughout the process. Only the filtering value of the previous moment and the prediction value of the current moment need to be stored, and a large amount of observation data does not need to be stored. The measurement noise is well suppressed, and it can meet the working conditions of the synchronous condenser with drastic reactive power changes. Description of the Drawings

[0019] Figure 1 is the operation flowchart of the method for estimating the reactive power output of the synchronous condenser based on Kalman filtering according to the embodiment of the present invention;

[0020] Figure 2 is the schematic diagram of the simulation model of the high-voltage direct-current transmission system including the estimation of the dynamic reactive power output of the synchronous condenser according to the embodiment of the present invention;

[0021] Figure 3 is the schematic diagram of the algorithm structure for estimating the reactive power output of the synchronous condenser according to the embodiment of the present invention;

[0022] Figure 4 is the curve of the receiving-end voltage change of the high-voltage direct-current transmission simulation system according to the embodiment of the present invention;

[0023] Figure 5 is the comparison diagram of the theoretical calculation value of the reactive power of the condenser, the reactive power calculation value with added white noise, and the estimated value of the KF filtering system according to the embodiment of the present invention;

[0024] Figure 6Comparison chart of reactive power output error and KF filtering system estimation error when adding white noise according to an embodiment of the present invention. Detailed implementation manners

[0025] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0026] Embodiment 1

[0027] In one embodiment, a method for estimating the reactive power output of a synchronous condenser based on Kalman filtering is implemented, including the following steps:

[0028] Install a PMU measurement unit on the synchronous condenser to obtain the PMU measurement parameters of the synchronous condenser. The PMU measurement parameters include direct-axis voltage, quadrature-axis voltage, direct-axis current, and quadrature-axis current.

[0029] Establish a full-order practical state space model of the synchronous condenser with the transient and subtransient electromotive forces of the condenser as state variables. The mathematical model of the synchronous condenser with transient electromotive force is as follows:

[0030]

[0031] Where, e″ d , e′ d are the direct-axis subtransient and transient induced electromotive forces respectively; e″ q , e′ q are the quadrature-axis subtransient and transient induced electromotive forces respectively; are the first derivatives of e″ q , e′ q , e″ d , e′ d respectively; T″ do , T′ do are the direct-axis subtransient and transient open-circuit time constants respectively; T″ qo , T′ qo are the quadrature-axis subtransient and transient open-circuit time constants respectively; x″ d , x′ d are the direct-axis subtransient and transient reactances respectively; x″ q , x′ q are the quadrature-axis subtransient and transient reactances respectively; x d , x q are the direct-axis and quadrature-axis synchronous reactances respectively; u d , u q are the direct-axis and quadrature-axis voltages respectively; i d , i q are the direct-axis and quadrature-axis currents respectively; r a is the stator resistance.

[0032] Select the state vector x and let

[0033] x = [x1 x2 x3 x4] T = [e″ q e′ q e″ d e′ d T (2)

[0034] Select the input vector u and let u = [i d E f i q T , select the output vector y and let Establish the practical state - space model of the synchronous condenser, that is

[0035]

[0036] Among them,

[0037]

[0038]

[0039]

[0040] Discretize the practical state - space model shown in formula (3) to obtain the discrete state - space model of the synchronous condenser as:

[0041] x k+1 = G k x k + H k U k + w k (4)

[0042] y k = C k x k + D k U k + v k (5)

[0043] In the formula, x k+1 is the system state vector at the next moment, x k is the system state vector at this moment, G k is the system matrix of the discrete system, H k is the input matrix of the discrete system, U k is the input vector of the discrete system, y k is the output vector of the discrete system, C k is the output matrix of the discrete system, D k ​​is the direct transfer matrix of the discrete system, w k is the system white noise, v k is the measurement white noise.

[0044] The dynamic reactive power output of the synchronous condenser is estimated using a Kalman filter system. The filter framework is as Figure 2 shown and specifically includes:

[0045] Set the initial values of the Kalman filter: P0 = var(x0);

[0046] State estimation update:

[0047] Error covariance update:

[0048] Filter gain matrix:

[0049] State estimation is updated according to the measurement value:

[0050] Error covariance is updated according to the measurement value:

[0051] where y k is composed of the direct-axis voltage, quadrature-axis voltage, direct-axis current, and quadrature-axis current after equivalent transformation of the values at the machine terminal of the synchronous condenser measured by the PMU measurement unit. is the initial value of the KF filter, P0 is the initial value of the filter covariance, E(x0) is the expectation, var(x0) is the variance. is the system state estimation value at this moment, is the state filter value at the previous moment, u k-1 is the system input vector. is the updated value of the error covariance at this moment, is the updated value of the error covariance at the previous moment according to the actual measurement, and R is the measurement noise variance matrix. L k is the filter gain matrix, and Q is the process noise variance matrix. is the system state filter value at this moment, is the updated value of the error covariance at this moment according to the actual measurement, and E is the 4th-order identity matrix.

[0052] The measurement noise variance matrix R and the process noise variance matrix Q have a greater impact on the filtering performance and are selected through continuous parameter debugging.

[0053] The value of the reactive power output can be calculated through the following formula from the output of the filter:

[0054]

[0055] Among them, is the estimated value of the reactive power output of the synchronous condenser, are the direct-axis and quadrature-axis voltages output by the filtering system respectively; are the direct-axis and quadrature-axis currents output by the filtering system respectively.

[0056] Embodiment 2

[0057] Another embodiment of the present invention is a high-voltage direct-current power transmission system including a synchronous condenser. Among them, the dynamic reactive power output estimation of the synchronous condenser adopts the method described in Embodiment 1.

[0058] A simulation model of the dynamic reactive power KF estimation of the synchronous condenser of the present invention as shown in Figure 2 is established in the MATLAB / Simulink environment. The entire simulation case includes a high-voltage direct-current power transmission system, a 300 Mvar synchronous condenser, a transformer, and an adjustable voltage source. The synchronous condenser adopts a static self-excited excitation method. The main parameters of the synchronous condenser model are as follows:

[0059] Table 1 Simulation case parameter table

[0060]

[0061] In this simulation case, the excitation voltage, the direct-axis current of the synchronous condenser, and the quadrature-axis current of the synchronous condenser are the system input quantities. A practical state-space model of the synchronous condenser is established with the direct-axis voltage of the synchronous condenser and the quadrature-axis voltage of the synchronous condenser as the output quantities, and the reactive power output is calculated with the terminal voltage of the synchronous condenser as the measurement input of the Kalman filter system.

[0062] Based on the measured values of the simulation system, white noise is superimposed to simulate the actual measured values, and the theoretical calculated values, the calculated values with added white noise, and the estimated values of the KF filtering system are compared.

[0063] The filtering results and analysis of the Kalman filtering method for the dynamic reactive power output of the synchronous condenser in the high-voltage direct-current power transmission system are as follows:

[0064] Based on Figure 2 in the simulation model and Figure 3 in the KF filtering estimation system, Figure 4 is the voltage change curve when the voltage at the receiving end of the high-voltage direct-current power transmission simulation system drops by 50% at 1.2 s; Figure 5 is the comparison diagram of the theoretical calculated value of the reactive power of the synchronous condenser, the calculated value of the reactive power with added white noise, and the estimated value of the KF filtering system; the simulation results show that the KF filtering system can effectively suppress the measurement noise; when the system drops and the synchronous condenser instantaneously provides reactive power support, the dynamic reactive power estimation method based on KF can maintain a high accuracy; Figure 6It is a comparison chart of the reactive power output error and the estimated value error of the KF filtering system when adding white noise. The simulation results show that the estimated value error is less than the reactive power output calculation error when adding noise.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or equivalently replaced, and any modification or equivalent replacement without departing from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A method for estimating the reactive power output of a synchronous condenser based on Kalman filtering, characterized in that, Including the following steps: Constructing a synchronous condenser mathematical model of the subtransient electromotive force: (1) wherein, are the direct-axis subtransient and transient induced electromotive forces respectively; are the quadrature-axis subtransient and transient induced electromotive forces respectively; are respectively the first derivatives of; are the direct-axis subtransient and transient open-circuit time constants respectively; are the quadrature-axis subtransient and transient open-circuit time constants respectively; are the direct-axis subtransient and transient reactances respectively; are the quadrature-axis subtransient and transient reactances respectively; are the direct-axis and quadrature-axis synchronous reactances respectively; are the direct-axis and quadrature-axis voltages respectively; are the direct-axis and quadrature-axis currents respectively; is the stator resistance; Selecting a state vector x and letting (2) Select the input vector u and let , select the output vector y and let , and establish the practical state-space model of the synchronous condenser, that is (3) Among them, , ， ； Discretizing the practical state space model shown in Equation (3) to obtain the discrete state space model of the synchronous condenser as: (4) (5) wherein, is the system state vector at the next moment, is the system state vector at this moment, is the system matrix of the discrete system, is the input matrix of the discrete system, is the input vector of the discrete system, is the output vector of the discrete system, is the output matrix of the discrete system, is the direct transfer matrix of the discrete system, is the system white noise, is the measurement white noise; Discretizing the practical state space model; Constructing a Kalman filter system according to the discretized practical state space model; Obtaining the PMU measurement parameters of the synchronous condenser; Inputting the PMU measurement parameters of the synchronous condenser into the Kalman filter system to obtain the filtered output parameters; Calculating the reactive power output value of the synchronous condenser according to the filtered output parameters.

2. The method for estimating the reactive power output of a synchronous condenser based on Kalman filtering according to claim 1, wherein The PMU measurement parameters of the synchronous condenser include the direct-axis voltage, quadrature-axis voltage, direct-axis current, and quadrature-axis current, and the filtered output parameters include the direct-axis voltage, quadrature-axis voltage, direct-axis current, and quadrature-axis current.

3. The method for estimating the reactive power output of a synchronous condenser based on Kalman filtering according to claim 2, wherein The calculation formula for the reactive power output value of the synchronous condenser is: （6） wherein, is the estimated reactive power output of the synchronous condenser, are the direct-axis and quadrature-axis voltages output by the filtering system respectively; are the direct-axis and quadrature-axis currents output by the filtering system respectively.

4. The method for estimating the reactive power output of a synchronous condenser based on Kalman filtering according to any one of claims 1-3, characterized in that The working process of the Kalman filter system includes the following steps: Setting the initial value of the Kalman filter, updating the state estimate, updating the error covariance, obtaining the filter gain matrix according to the actual PMU measurement value, updating the state estimate according to the measurement value, updating the error covariance according to the measurement value, and outputting the filtered parameters.

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