A power distribution system synchronous phasor information processing method in unbalanced and noisy environment

Abstract

The application provides a power distribution system synchronous phasor information processing method in an unbalanced and noisy environment, and belongs to the technical field of synchronous phasor measurement, and comprises the following steps: S1: establishing an alternating current signal dynamic state estimation model of a power distribution system; S2: in a three-phase power distribution system in an unbalanced and noisy interference environment, a recursive filtering method is used to calculate a phasor estimation value; S3: a mutually orthogonal voltage component signal is established by using a second-order generalized integrator phase-locked loop; S4: a linearization treatment is performed on a nonlinear system state equation, and a discrete state equation and an observation equation are designed; S5: estimation and correction combination recursion is adopted to perform time updating; and S6: state quantity estimation value filtering is performed, and the estimation value is corrected by using a variance matrix to perform measurement updating. The application can process power distribution system synchronous phasor information in an unbalanced and noisy interference environment, improve estimation accuracy, reduce estimation error, shorten convergence time, and provide accurate data for fault diagnosis.

Description

Technical Field

[0001] This invention relates to the field of synchronous phasor measurement technology, and in particular to a method for processing synchronous phasor information in a power distribution system under unbalanced and noisy environments. Background Technology

[0002] During the dynamic operation of a power distribution system, the synchronization phasor information of measurement nodes is easily affected by interference from non-fundamental frequency signals (integer harmonics), lead-induced noise, and noise interference caused by window function leakage effects, leading to three-phase imbalance in the power distribution system. Under conditions of low signal-to-noise ratio and harmonic distortion in an unbalanced power distribution system, accurate estimation of synchronization phasor information is difficult. Therefore, considering the characteristics of power distribution system operation conditions such as imbalance, low signal-to-noise ratio, and high harmonic content, this paper proposes a method for processing synchronization phasor information in unbalanced and noisy environments, utilizing modern control theory, power system dynamic equivalent modeling theory, and stability analysis theory. This method can improve the estimation performance of synchronization phasor information under low signal-to-noise ratio and high harmonic conditions, enhance the accuracy of synchronization phasor measurement in user-grid supply and demand interaction environments, and provide accurate data for power distribution system fault diagnosis, which has significant practical implications for the development of power systems.

[0003] A review of publicly available patent documents, publication number CN104423417A, discloses a synchronous phasor accurate timing system, comprising: a GPS timing module, a synchronization trigger circuit, a digital signal processor, a host PC, an AD sampling circuit, and a signal acquisition and conditioning unit. The output of the signal acquisition and conditioning unit is connected to the digital signal processor via the AD sampling circuit. The digital signal processor is connected to the host PC via a high-speed interface. The signal acquisition and conditioning unit acquires the sampled voltage or current signal and conditions and filters the signal to convert it into an analog voltage signal that is easy for the digital signal processor to process. The output of the GPS timing module is connected to the digital signal processor, and the input of the GPS timing module is connected to the synchronization trigger circuit. This invention only provides a synchronous phasor accurate timing system to ensure that the digital signal processor is not affected by fluctuations in temperature and other factors, and to achieve uniform data acquisition. However, it does not consider the impact of system imbalance and noise in the actual field environment. Publication (Announcement) No.: CN110568309B discloses a filter, a synchronous phasor measurement system, and a method. The filter described in this invention is an adaptive moving average filter with a fixed window length. The system includes a filter and a phase-locked loop (PLL) control loop, with the output of the PLL control loop cascaded with the input of the filter. The method includes acquiring the voltage signal output from the smart grid; inputting the voltage signal to the synchronous phasor measurement system; and acquiring the phasor measurement results and frequency measurement results output by the synchronous phasor measurement system. This invention utilizes a PLL-based synchronous phasor measurement algorithm, employing a fixed-length adaptive moving average filter to filter the ripple output of a type-1 PLL, and provides a timescale for the estimated parameters. The final measurement results show that the method based on the synchronous phasor measurement system can accurately estimate the grid frequency and phasors under grid distortion conditions. However, it does not consider the filter gain parameter update problem or the filter's noise immunity performance under dynamic smart grid conditions. Publication No. CN104020352A discloses a synchronous phasor measurement method applicable to Class M PMU units, comprising: combining a low-pass digital filter for phasor factors with the Discrete Fourier Transform (DFT) algorithm to calculate the initial measurement phasor after eliminating spectral leakage; fitting the dynamic phasor with a second-order Taylor series to obtain the measurement error caused by the DFT averaging effect, and compensating the initial phasor based on the error to obtain the accurate dynamic measurement phasor; setting a low-order digital filter for Class M phasor measurement units (PMUs) at the phasor uplink point, and using the accurate measurement phasor as input to obtain the final measurement phasor. By adopting the method disclosed in this invention, phasor measurement can be performed accurately and quickly when the input is a static signal or a dynamic signal; however, this invention can accurately measure low-frequency phasor signals but does not consider the influence of high-frequency harmonic distortion signals and nonlinear noise in the power grid. Summary of the Invention

[0004] The purpose of this invention is to provide a method for processing synchronous phasor information in a power distribution system under unbalanced and noisy environments, which can improve the estimation accuracy of phasor information during the dynamic operation of a power distribution system under unbalanced and noisy interference environments.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] This invention provides a method for processing synchronization phasor information in a power distribution system under unbalanced and noisy environments. The method comprises the following steps:

[0007] S1. Establish a dynamic state estimation model for AC signals in the power distribution system;

[0008] S2. Based on the dynamic state estimation model of AC signal of power distribution system, the filtered phasor estimate is calculated by recursive filtering method;

[0009] S3. Based on the filtered phasor estimates, a second-order generalized integrator phase-locked loop is used to establish mutually orthogonal voltage component signals.

[0010] S4. Based on the mutually orthogonal output signals, the state equation of the continuous nonlinear system is linearized to construct the linearized discrete state equation and observation equation of the extended Kalman filter of the power distribution system.

[0011] S5. Based on the linearized discrete state equation and observation equation of extended Kalman filtering, a recursive calculation method combining estimation and correction and the Riccati equation are adopted to estimate the time update process of error covariance.

[0012] S6. Based on the time update results of the extended Kalman filter, the estimated values ​​of the state variables are measured and updated using the Kalman gain coefficients to obtain optimized estimates.

[0013] S7. Feed the optimized estimate back to S2 for the next real-time estimation and correction.

[0014] Furthermore, the dynamic state estimation model for the AC signal of the power distribution system described in step S1 specifically includes:

[0015] The AC signal x(t) of the power distribution system is:

[0016] x(t)=Xcos(2πft+φ)

[0017] In the formula, f is the rated frequency of the power distribution system; X is the amplitude of the synchronous phasor; t is the sampling time; and φ is the angle between the first sampling point and the peak value of the input signal.

[0018] Furthermore, the recursive filtering method described in step S2 specifically includes:

[0019] When calculating the phasor of the new acquisition point, there are n-1 sampling points that are exactly the same as the old data window. The old phasor is recursively calculated to obtain the new phasor, which is the basis for recursive phasor update calculations. When the number of sampling points is n+r, the characteristic e of the fundamental frequency signal... -j(n+r) =e -jr The general formula for recursive filtering is:

[0020]

[0021] In the formula, x n+r X represents the synchronization phasor measurement signal of the power distribution system at time n+r, where r is the information update time. n+r Let X be the amplitude of the synchronous phasor measurement signal at time n+r. n Let be the amplitude of the synchronous phasor measurement signal at time n, where n is the time node.

[0022] Furthermore, in step S3, the second-order generalized integrator phase-locked loop outputs mutually orthogonal signals. A second-order infinite-gain bandpass filter is used, and a feedback loop is added to establish mutually orthogonal i / q voltage components X. i and X q ; Optimize the feedback gain coefficient k q k i Correction X i and X q Orthogonal fundamental i / q components X i (s) and X q The transfer function expression for (s) is as follows:

[0023]

[0024] In the formula, ω is the resonant angular frequency, ω=2πf.

[0025] Furthermore, step S4 involves linearizing the state equations of the continuous nonlinear system to construct the linearized discrete state equations and observation equations for the extended Kalman filter of the power distribution system. This process includes the following steps:

[0026] S4-1: Based on coordinate transformation theory, the synchronous phasor voltage signal is orthogonally decomposed. The actual measurement signal of the power distribution system and the local reference signal generated by the second-order generalized integrator phase-locked loop are phase rotated and integrated to obtain the input observation vector of the extended Kalman filter method.

[0027] The state equation expression for the continuous nonlinear system is as follows:

[0028]

[0029] In the formula, xn Let u be the system state vector. n To measure the input quantity, y n For system observations, w n-1 and v n Let f(x) be an uncorrelated Gaussian random noise vector with a mean of 0. n-1 ,u n-1 h(x) is the state transition matrix of a continuous system. n () represents the measurement matrix of a continuous system;

[0030] S4-2: When Δx n When the function f(x) is small enough, n-1 ,u n-1 )exist Expanding the Taylor series nearby, we obtain the following expressions for the linearized discrete state equation and observation equation:

[0031]

[0032] In the formula Φ n,n-1 H is the state transition matrix of a discrete system. n This is the measurement matrix for a discrete system.

[0033] Furthermore, the time update process for estimating the error covariance by employing a recursive calculation method combining estimation and correction and the Riccati equation, as described in step S5, specifically includes:

[0034] S5-1: Estimating the state vector x from the observation vector y(n-1) of the previous time step n Orthogonal projection on y(n-1) The calculation expression is as follows:

[0035]

[0036] In the formula, G n-1 =E(w n-1 w n-1 T ), The expectation of the noise components of the state vector;

[0037] The recursive calculation method combining estimation and correction calculates the optimal estimate of the current state based on the latest observation data at each time step. Its recursive update equation is expressed as follows:

[0038]

[0039] In the formula, K n P is the filter gain matrix. n-1 R is the minimum steady-state error covariance. n Let n be the noise phasor covariance;

[0040] S5-2: The Riccati equation is used to describe the estimation error covariance, and the prior error covariance matrix P of the constrained state estimation is given. n│n-1 The expression is as follows:

[0041]

[0042] In the formula, P n│n-1 It's about x t The minimum covariance matrix, with initial condition P(t0) = 0; when (Φ, E(w) n-1 w n-1 T When the condition is controllable and (Φ,H) is observable, the Riccati equation converges to a unique positive semidefinite matrix that is independent of the initial conditions.

[0043] Furthermore, the specific steps in step S6 for updating the estimated state variables using the Kalman gain coefficient to obtain the optimized estimate include:

[0044] S6-1: Situations where undesirable data appears in the measured values, including undesirable data.

[0045] The Kalman gain coefficient K is obtained analytically. n The system state is corrected and updated to obtain the estimated state variables at time n. The Kalman filter gain coefficient k is obtained from the Kalman gain matrix K. i and k q k i and k q The calculation formula is as follows:

[0046]

[0047] In the formula, q is the expected value of the process noise component w;

[0048] When the approximation condition is satisfied At that time, k i and k q for:

[0049]

[0050] In the formula, p f Covariance components, p f =p 12 / r,

[0051] Using P n│n-1 H n and R n Calculate the gain coefficient K n for:

[0052]

[0053] S6-2: Based on the principle of minimum variance of observation error and adherence to unbiased state, the prior estimate is corrected using the Kalman gain coefficient K. n and the prior error covariance matrix P n-1 The optimal estimated variance matrix P is calculated. n for:

[0054] P n =(IK n H n )P nn-1

[0055] S6-3: Utilizing the Kalman gain coefficient K n Given initial conditions and input vector x n The optimal estimate of the state variables is obtained through recursive calculation. for:

[0056]

[0057] After collecting new observation data, based on the estimate from the previous moment, and using the state transition equation of the signal process itself, under the recursive calculation framework of prediction-measurement-correction, the time update and measurement update feedback correction prediction information are iteratively executed, and the optimal estimate of the current state is obtained according to the recursive formula.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) In single-phase or unbalanced three-phase power distribution systems, the recursive filtering method reduces the computational burden on the processor, decreases the computational complexity of the method, and reduces the computational burden on the processor.

[0060] (2) By utilizing the orthogonal property of the second-order generalized integrator phase-locked loop, a second-order infinite gain bandpass filter is used and a feedback loop is added to establish orthogonal voltage components, thereby improving the accuracy of state estimation of unbalanced three-phase power distribution systems.

[0061] (3) Use Taylor series to solve the linearization problem of optimal state estimation of nonlinear equations, establish the state space variance of the noisy process, and accurately model the field state of the power distribution system.

[0062] (4) The time update equation calculates the current state and the estimated value of the error covariance matrix, and can predict and estimate the system state at the next time.

[0063] (5) The measurement update equation follows the principle of state unbiasedness and uses prior estimates and filter gain feedback to correct the posterior estimates for the next time step.

[0064] (6) In order to adapt to the changes in noise statistical characteristics, the expected error covariance iteration process is modeled as the Riccati equation and the Kalman gain coefficient is obtained by analytical solution, which improves the accuracy of state estimation.

[0065] (7) Under the recursive calculation framework of prediction-measurement-correction, the time update and measurement update feedback correction prediction information are executed iteratively, without the need to store a large amount of historical data, thus balancing calculation speed and accuracy. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a flowchart of a method for processing synchronous phasor information in a power distribution system under unbalanced and noisy conditions;

[0068] Figure 2 This is a structural diagram of the node topology of the IEEE 34-node power distribution system;

[0069] Figure 3 This is the output diagram of the voltage phasor waveform simulation experiment collected and measured at node 836;

[0070] Figure 4 This is the simulation output diagram of the recursive estimation calculation results of the fundamental signal of phase A voltage;

[0071] Figure 5 This is the simulation output diagram of the amplitude of the fundamental wave of the synchronous phasor voltage A-phase voltage recursively estimated.

[0072] Figure 6 This is the simulation output diagram of the recursive estimation amplitude of the fifth harmonic of the A-phase voltage of the synchronous phasor voltage;

[0073] Figure 7 This is the simulation output diagram of the voltage phasor information processing results under normal operating conditions;

[0074] Figure 8 This is the simulation output diagram of the voltage phasor information processing results under three-phase unbalanced state.

[0075] Figure 9 This is a simulation output diagram of the voltage phasor information processing results under a noise-free environment;

[0076] Figure 10This is a simulation output diagram of the voltage phasor information processing results under a signal-to-noise ratio of 10dB.

[0077] Figure 11 This is the simulation output diagram of the voltage estimation error based on the extended Kalman filter method;

[0078] Figure 12 This is the simulation output of the voltage estimation error based on the extended Kalman filter method in a noise-free environment;

[0079] Figure 13 The output diagram is a simulation experiment of the voltage estimation error based on the extended Kalman filter method under a signal-to-noise ratio of 15dB.

[0080] Figure 14 This is a comparison output diagram of simulation experiments of different information processing methods under three-phase unbalanced conditions;

[0081] Figure 15 This is the simulation output of the voltage estimation error value based on the improved Kalman filter method under a 20dB noise environment;

[0082] Figure 16 It is the voltage phasor information estimation error based on the improved Kalman filter method under different noise environments. Detailed Implementation

[0083] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0084] This invention provides a method for processing synchronization phasor information in a power distribution system under unbalanced and noisy environments. The original measurement parameters are obtained by the master station of the power distribution system using a PMU device to measure bus voltage and current information in real time. These measurement parameters include amplitude, frequency, and phase. The dispatch control center uses a cascaded filtering module to combine PMU measurement values ​​from different geographical locations in a unified time coordinate system to obtain the synchronization phasor information of the power distribution system. The above-mentioned filtering process using a cascaded filtering module improves the accuracy of the measurement information.

[0085] like Figure 1 As shown, Figure 1A flowchart of a method for processing synchronization phasor information in a power distribution system under unbalanced and noisy environments, provided by an embodiment of the present invention, is included in the following steps:

[0086] S1. Establish a dynamic state estimation model for AC signals in the power distribution system;

[0087] S2. Based on the dynamic state estimation model of AC signal of power distribution system, the filtered phasor estimate is calculated by recursive filtering method;

[0088] S3. Based on the filtered phasor estimates, a second-order generalized integrator phase-locked loop is used to establish mutually orthogonal voltage component signals.

[0089] S4. Based on the mutually orthogonal output signals, the state equation of the continuous nonlinear system is linearized to construct the linearized discrete state equation and observation equation of the extended Kalman filter of the power distribution system.

[0090] S5. Based on the linearized discrete state equation and observation equation of extended Kalman filtering, a recursive calculation method combining estimation and correction and the Riccati equation are adopted to estimate the time update process of error covariance.

[0091] S6. Based on the time update results of the extended Kalman filter, the estimated values ​​of the state variables are measured and updated using the Kalman gain coefficients to obtain optimized estimates.

[0092] S7. Feed the optimized estimate back to S2 for the next real-time estimation and correction.

[0093] Specifically, the dynamic state estimation model for the AC signal of the power distribution system mentioned in step S1 includes:

[0094] The AC signal x(t) of the power distribution system is:

[0095] x(t)=Xcos(2πft+φ)

[0096] In the formula, f is the rated frequency of the power distribution system; X is the amplitude of the synchronous phasor; t is the sampling time; and φ is the angle between the first sampling point and the peak value of the input signal.

[0097] Specifically, the recursive filtering method described in step S2 includes:

[0098] When calculating the phasor of the new acquisition point, there are n-1 sampling points that are exactly the same as the old data window. The old phasor is recursively calculated to obtain the new phasor, which is the basis for recursive phasor update calculations. When the number of sampling points is n+r, the characteristic e of the fundamental frequency signal... -j(n+r) =e -jr The general formula for recursive filtering is:

[0099]

[0100] In the formula, x n+r X represents the synchronization phasor measurement signal of the power distribution system at time n+r, where r is the information update time. n+r Let X be the amplitude of the synchronous phasor measurement signal at time n+r. n Let be the amplitude of the synchronous phasor measurement signal at time n, where n is the time node.

[0101] Specifically, in step S3, the second-order generalized integrator phase-locked loop outputs mutually orthogonal signals. A second-order infinite-gain bandpass filter is used, and a feedback loop is added to establish mutually orthogonal i / q voltage components X. i and X q The feedback gain coefficient k effectively reduces the initial offset. q k i Correction X i and X q Orthogonal fundamental i / q components X i (s) and X q The transfer function expression for (s) is as follows:

[0102]

[0103] In the formula, ω is the resonant angular frequency, ω=2πf.

[0104] Specifically, step S4 involves linearizing the state equations of the continuous nonlinear system to construct the linearized discrete state equations and observation equations for the extended Kalman filter of the power distribution system. This includes the following steps:

[0105] S4-1: Based on coordinate transformation theory, the synchronous phasor voltage signal is orthogonally decomposed. The actual measurement signal of the power distribution system and the local reference signal generated by the second-order generalized integrator phase-locked loop are phase rotated and integrated to obtain the input observation vector of the extended Kalman filter method.

[0106] The state equation expression for the continuous nonlinear system is as follows:

[0107]

[0108] In the formula, x n Let u be the system state vector. n To measure the input quantity, y n For system observations, w n-1 and v n Let f(x) be an uncorrelated Gaussian random noise vector with a mean of 0. n-1 ,u n-1 h(x) is the state transition matrix of a continuous system. n () represents the measurement matrix of a continuous system;

[0109] S4-2: When Δx n When the function f(x) is small enough, n-1 ,u n-1 )exist Expanding the Taylor series nearby, we obtain the following expressions for the linearized discrete state equation and observation equation:

[0110]

[0111] In the formula Φ n,n-1 H is the state transition matrix of a discrete system. n This is the measurement matrix for a discrete system.

[0112] Specifically, the time update process for estimating the error covariance by adopting a recursive calculation method combining estimation and correction and the Riccati equation in step S5 includes:

[0113] S5-1: Estimating the state vector x from the observation vector y(n-1) of the previous time step n Orthogonal projection on y(n-1) The calculation expression is as follows:

[0114]

[0115] In the formula, G n-1 =E(w n-1 w n-1 T ), The expectation of the noise components of the state vector;

[0116] The recursive calculation method combining estimation and correction calculates the optimal estimate of the current state based on the latest observation data at each time step. Its recursive update equation is expressed as follows:

[0117]

[0118] In the formula, K n P is the filter gain matrix. n-1 R is the minimum steady-state error covariance. n Let n be the noise phasor covariance;

[0119] S5-2: The Riccati equation is used to describe the estimation error covariance, and the prior error covariance matrix P of the constrained state estimation is given. n│n-1 The expression is as follows:

[0120]

[0121] In the formula, P n│n-1 It's about x tThe minimum covariance matrix, with initial condition P(t0) = 0; when (Φ, E(w) n-1 w n-1 T When the condition is controllable and (Φ,H) is observable, the Riccati equation converges to a unique positive semidefinite matrix that is independent of the initial conditions.

[0122] Specifically, the steps in step S6, which involve measuring and updating the estimated values ​​of the state variables using the Kalman gain coefficient to obtain optimized estimates, include:

[0123] S6-1: When poor data appears in the measured values, the Kalman gain coefficient K obtained through analytical methods is used. n The system state is corrected and updated to effectively suppress the influence of noise, and the estimated values ​​of the state variables at time n are obtained. The Kalman filter gain coefficient k is obtained from the Kalman gain matrix K. i and k q k i and k q The calculation formula is as follows:

[0124]

[0125] In the formula, q is the expected value of the process noise component w;

[0126] When the approximation condition is satisfied At that time, k i and k q for:

[0127]

[0128] In the formula, p f Covariance components, p f =p 12 / r,

[0129] Using P n│n-1 H n and R n Calculate the gain coefficient K n for:

[0130]

[0131] S6-2: Based on the principle of minimum variance of observation error and adherence to unbiased state, the prior estimate is corrected using the Kalman gain coefficient K. n and the prior error covariance matrix P n-1 The optimal estimated variance matrix P is calculated. n for:

[0132] P n=(IK n H n )P nn-1

[0133] S6-3: Utilizing the Kalman gain coefficient K n Given initial conditions and input vector x n The optimal estimate of the state variables is obtained through recursive calculation. for:

[0134]

[0135] After collecting new observation data, based on the estimate from the previous moment, and using the state transition equation of the signal process itself, under the recursive calculation framework of prediction-measurement-correction, the time update and measurement update feedback correction prediction information are iteratively executed, and the optimal estimate of the current state is obtained according to the recursive formula.

[0136] Example

[0137] like Figure 2 The diagram shows the topology of the IEEE 34-node distribution system. To analyze the effectiveness of the extended Kalman filter-based information processing method, the IEEE 34-node system was used as a test platform to process and analyze the synchronization voltage phasor information of the IEEE 34-node distribution system. The sampling frequency was 12.8 kHz, and the fundamental frequency was 50 Hz. In the IEEE 34-node distribution system, the voltage phasor information of node 836 was observed based on the extended Kalman filter method. The update process was used to observe the distribution system state model. Under high-order harmonic distortion, the state variables included the fundamental, third, fifth, and seventh harmonic components.

[0138] The main advantage of the Extended Kalman Filter (EKF) information processing method lies in its response under distortion conditions, as it can easily be extended using additional states to solve the state estimation problem for the fundamental and higher harmonic components. The EKF method can not only process information for the fundamental component but also be extended to observe the harmonic components of the voltage phasor signal, improving the estimation performance of the method. The computational cost for harmonic components includes adding two state variables for each harmonic and one state variable for each DC component.

[0139] To analyze the effectiveness of the synchronization phasor information processing method for power distribution systems under unbalanced and noise interference environments, information processing and analysis were performed on the synchronization voltage phasor information of an IEEE 34-node power distribution system. This system included one generator connected to the power distribution system in Arizona, USA; two distributed power sources, one photovoltaic and one wind power, with each distributed energy source initially operating at a stable point [i]; ten loads L1-L10, with a power consumption of 0.5MW+0.1Mvar; one transformer; and 33 AC lines. The sampling frequency was 12.8kHz, and the fundamental frequency was 50Hz.

[0140] Since the PMU device acquires power distribution system information from a global perspective, the measurement process and short-circuit fault process respectively introduce measurement noise interference and harmonic oscillations, forming a nonlinear power distribution system with strong transients, low signal-to-noise ratio, and high-order harmonic distortion. To address the accuracy problem of synchronous phasor measurement under low signal-to-noise ratio and high-order harmonic distortion conditions, a quasi-optimal estimation information processing method based on extended Kalman filtering is proposed to achieve accurate estimation of voltage phasor information under fault conditions.

[0141] When a power distribution system experiences a fault or disturbance, the electromagnetic quantities of various power components and the mechanical quantities such as the rotational speed of rotating motors will change. At this time, the power distribution system will undergo a complex electromechanical transient process, including phase fluctuations, noise interference, and a large number of high-order harmonics. In order to accurately estimate the synchronization phasor information under low signal-to-noise ratio and high-order harmonic distortion environments, a method is adopted to linearize the state equation and observation equation of the nonlinear discrete-time system. Synchronization phasor information processing is based on extended Kalman filtering within a prediction-measurement-correction recursive framework.

[0142] In the IEEE 34-bus distribution system, the voltage phasor information of node 836 is observed based on the improved Kalman filter method. The state of the distribution system is observed using time update and measurement update equations. Under the condition of high-order harmonic distortion, the state variables include the fundamental, third harmonic, fifth harmonic and seventh harmonic components.

[0143] Within the predict-measure-correct recursive framework, the state to be estimated is recursively derived using a feedback mechanism. First, the extended Kalman filter method is used to estimate the system state at a certain moment. Then, feedback is obtained by considering noisy measurement variables.

[0144] The Extended Kalman Filter (EKF) method comprises two parts: a time update equation and a measurement update equation. The time update equation primarily serves a predictive estimation function, specifically responsible for calculating the current state and the estimated value of the error covariance matrix, thus providing a predictive estimate for the next time state. The measurement update equation primarily serves a corrective function, specifically responsible for feedback, combining the prior estimate with the new measurement value to provide a corrected posterior estimate for the next time state.

[0145] like Figure 3 As shown, a simulation experiment was conducted to measure the voltage phasor signal U based on the extended Kalman filter method. a U b U c The waveform of the voltage phasor acquired and measured in node 836 is displayed.

[0146] like Figure 4 As shown, a simulation experiment was conducted to estimate the voltage i / q components U based on the extended Kalman filter method. i / Uq shows the recursive estimation results of the fundamental signal of phase A voltage based on the extended Kalman filter information processing method.

[0147] like Figure 5 As shown, harmonic analysis is performed on the synchronous phasor voltage waveform, and the amplitude U of the fundamental frequency of phase A voltage is recursively estimated. i .

[0148] like Figure 6 As shown, harmonic analysis is performed on the synchronous phasor voltage waveform, and the amplitude U of the fifth harmonic of phase A voltage is recursively estimated. i .

[0149] from Figure 3 , Figure 4 , Figure 5 and Figure 6 The simulation results show that the extended Kalman filter-based information processing method can still accurately extract the steady-state components of PMU measurements under complex operating conditions, capture the response of the power distribution system at different time scales, and accurately feed the steady-state components back to the diagnostic application.

[0150] To verify the effectiveness of the information processing method based on extended Kalman filtering under complex operating conditions of power distribution systems, the results of synchronous phasor information processing based on extended Kalman filtering in node 888 were analyzed.

[0151] like Figure 7 The figure shows the simulation output of the voltage phasor information processing results under normal operating conditions. In a normally operating power distribution system, the node voltage phasor diagram consists of phasors spaced 120° apart, with an amplitude equal to the phase voltage amplitude of 480V. The extended Kalman filter method is used to estimate the i / q components of the node voltage as U... ai =479.985V, U aq = 477.569V. The three-phase voltage components of the node voltage all move in circles on the i / q plane, with radii R and R, respectively. a =0.994, R b =0.994, R c=0.994, and moves counterclockwise over time.

[0152] like Figure 8 The figure shows the simulation output of voltage phasor information processing results under three-phase unbalanced conditions. To verify the effectiveness of the information processing method based on extended Kalman filtering in a power distribution system under three-phase unbalanced conditions, the voltage of phase A abruptly changes to 80% of its original value after 1 second, while the voltages of phases B and C remain unchanged. At this time, the node voltages are severely unbalanced. The measured voltage amplitudes of phases A and B are U... a =261.279V, U b =363.678V. The estimated values ​​based on the extended Kalman filter method are U a-ekf =259.932V and U b-ekf = 361.853V. At this time, the i / q components of the voltage phasor at node 888 observed using the extended Kalman filter method are U... ai =259.901V, U aq =59.964V; U bi =361.992V, U bq = 361.715V. The three-phase voltage components of the node voltage move along circles with different radii in the i / q plane, with radii R and R respectively. a =0.487, R b =0.995, R c =0.995, and moves counterclockwise over time.

[0153] like Figure 9 The figure shows the simulation output of voltage phasor information processing results under noise-free environment. It also shows the estimation results of the state estimation of the voltage phasor information at node 888 using the synchronous phasor information processing method based on extended Kalman filtering. The PMU device measures the voltage amplitudes of phase A and phase B as U... a = 367.652V. The estimated values ​​based on the extended Kalman filter method are U a-ekf = 367.942V. At this time, the i / q components of the voltage phasor at node 888 observed using the extended Kalman filter method are U ai =366.917V, U aq =368.964V. The three-phase voltage components of the node voltage move along circles with different radii in the i / q plane, with radii Ra = 0.999, and move counterclockwise with time. As the signal-to-noise ratio (SNR) decreases, the estimation error based on the extended Kalman filter increases, reaching its maximum at SNR = 10dB. Figure 10 As shown, the signal-to-noise ratio is 10dB. At this time, the estimated values ​​based on the extended Kalman filter method are U... a-ekf= 368.965V. At this time, the i / q components of the voltage phasor at node 888 observed using the extended Kalman filter method are U ai =367.263V, U aq =370.659V; estimation error e ai =0.001%, e aq =0.008%.

[0154] Simulation results show that updating the measurement noise covariance matrix using the extended Kalman filter method can filter out dynamic and unwanted data from the original PMU data. With the extended Kalman filter method corrected, updates are made based on the measurement results to filter out unwanted data and extract steady-state components, providing some compensation for the phase measurement error of the PMU, and the extracted fundamental component has high accuracy.

[0155] like Figure 11 As shown in the figure, the simulation output of the voltage estimation error based on the extended Kalman filter method is presented. Under different noise environments, based on the voltage phasor information at the 888 node output, the extended Kalman filter method is used to analyze and process the voltage phasor information of the voltage source, and the estimation error is shown in the figure. Figure 11 The figure shows the voltage phasor information estimation error based on the extended Kalman filter method under different noise environments. The center line of each box represents the median error, the top and bottom of the box represent the 75th and 2nd quantiles, respectively, and cross symbols indicate outliers. The average error em of the extended Kalman filter phasor estimation method is shown in the figure. The figure also shows the average error em of the extended Kalman filter phasor estimation method under different noise environments of 40dB, 30dB, 20dB, 15dB, and 10dB. EKF The relative errors were 0.010%, 0.032%, 0.123%, 0.182%, and 0.324%, respectively. The relative error of the extended Kalman filter phasor estimation method varied within the range of [0, 0.91%], which is relatively small.

[0156] To verify the accuracy of the synchronous phasor information processing method based on extended Kalman filtering, the voltage phasor signal was estimated using both the extended Kalman filtering method and the method based on the second-order general integrator (SOGI) under different noise environments, and their estimation accuracy was compared.

[0157] like Figure 12As shown, the simulation output of the voltage estimation error based on the extended Kalman filter method under noise-free environment is shown. A phase A short-circuit fault occurs in distribution branch 888-890 at 2s. The information processing method based on the extended Kalman filter method can quickly and accurately estimate the steady-state system after the fault. The estimated state curve matches the actual measured curve well, with an estimation error of 0.0283% and a convergence time of 0.017s. The estimation curve based on the SOGI method deviates significantly from the actual measured curve before and after the fault, with an estimation error of 0.0907% and a convergence time of 0.031s.

[0158] like Figure 13 The figure shown is the simulation output of the voltage estimation error based on the extended Kalman filter method under a signal-to-noise ratio of 15dB.

[0159] like Figure 14 As shown in the simulation comparison output diagram of different information processing methods, it can be seen that under different signal-to-noise ratio conditions, the synchronous phasor information processing method based on extended Kalman filter can quickly and accurately estimate the voltage phasor signal. The estimation curve obtained by the SOGI method is closer to the actual measured waveform signal than that obtained by the SOGI method. The simulation results show that the estimation effect of the information processing method based on extended Kalman filter is significantly better than that of the SOGI method.

[0160] like Figure 15 The simulation output of the voltage estimation error based on the improved Kalman filter method is shown in the figure. The state estimation results of the voltage phasor information of node 888 under 20dB noise environment are analyzed using the synchronization phasor information processing method based on the improved Kalman filter. The estimated voltage amplitude measured by the PMU device is 367.942V, with an estimation error range of 0.001-0.008%. Simulation results show that updating the measurement noise covariance matrix using the improved Kalman filter method can filter out dynamic bad data from the original PMU data. The time update equation calculates the current state and the estimated value of the error covariance matrix, and can predict the system state at the next time. The measurement update equation follows the unbiased state principle, using prior estimates and filter gain feedback to correct the posterior estimates at the next time. With the improved Kalman filter method corrected, updates are made based on the measurement results to filter out bad data and extract steady-state components, balancing computational speed and accuracy; the extracted fundamental component has high precision.

[0161] like Figure 16As shown, under different noise environments, the voltage phasor information estimation error based on the improved Kalman filter method exhibits higher state estimation accuracy in low-noise environments, with an average voltage amplitude estimation error ranging from 0.010% to 0.123%. However, the state estimation error increases in low-noise environments, with an average estimation error ranging from 0.182% to 0.324%, although the overall estimation accuracy remains high. This indicates that the proposed method models the expected error covariance iteration process as a Riccati equation and analytically solves for the Kalman gain coefficient, adapting to changes in noise statistical characteristics and improving state estimation accuracy.

[0162] Within the recursive calculation framework of prediction-measurement-correction, this method iteratively executes time updates and measurement updates to provide feedback correction and prediction information. It utilizes coordinate transformation theory to orthogonally decompose the input signal to achieve phase locking. Then, it uses a cascaded filtering module to eliminate the influence of harmonic components on the phase-locked result. This eliminates the need to store a large amount of historical data and balances computational speed and accuracy to achieve online signal processing of synchronous phasors under voltage imbalance and noise environments.

[0163] Based on simulation and comparative experimental results, it can be seen that the synchronization phasor information processing method based on extended Kalman filtering processes and removes bad data for synchronization phasor information in environments with low signal-to-noise ratio and high harmonic distortion. It uses coordinate transformation theory to orthogonally decompose the input signal to achieve phase locking, and then uses a cascaded filtering module to eliminate the influence of harmonic components on the phase-locking result. Its average estimation error is 0.0283% and the convergence time is 0.017s. It achieves fast and accurate estimation of the fundamental voltage signal under fault conditions, and solves the problem of accuracy of synchronization phasor measurement under user-grid supply and demand interaction conditions and voltage imbalance and harmonic conditions in the distribution system.

[0164] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A method for processing of synchronized phasor information of power distribution system in unbalanced and noisy environment, characterized in that, The synchronous phasor information processing method comprises the following steps: S1, establishing an alternating current signal dynamic state estimation model of a power distribution system; S2, based on the dynamic state estimation model of the alternating current signal of the power distribution system, using a recursive filtering method to obtain a filtered phasor estimation value; S3, based on the filtered phasor estimation value, using mutually orthogonal signals output by a second-order generalized integrator phase-locked loop; S4, based on the output mutually orthogonal signals, linearizing a state equation of a continuous nonlinear system, and constructing a linearized discrete state equation and an observation equation of an extended Kalman filter of the power distribution system; S5, based on the linearized discrete state equation and the observation equation of the extended Kalman filter, using an estimation and correction combined recursive calculation method and Riccati equation to estimate a time update process of an error covariance; S6, based on a time update result of the extended Kalman filter, using a Kalman gain coefficient to perform measurement update on an estimated value of a state quantity, and obtaining an optimized estimation value; S7, feeding back the optimized estimation value to S2 for real-time estimation and correction next time.

2. The method for processing of power system synchrophasor information in unbalanced and noisy environment according to claim 1, characterized in that, The specific form of the alternating current signal dynamic state estimation model of the power distribution system in step S1 is as follows: Power distribution system ac signal To: ； wherein is the nominal frequency of the power distribution system, X is the synchronous phasor magnitude, t is the sampling time, is the angle between the first sample point and the peak value of the input signal.

3. The method for processing of power system synchrophasor information in unbalanced and noisy environment according to claim 1, wherein, The recursive filtering method in step S2 specifically comprises: When calculating the new sampling point phasor, n-1 sampling points are the same as the old data window, and the new phasor is obtained by recursive operation on the old phasor, which is the recursive updating phasor calculation; when the sampling point is n+r, the characteristic e -j(n+r) =e -jr of the fundamental frequency signal is obtained, and the recursive filtering expression formula is: ； wherein is the synchronized phasor measurement signal of the power distribution system at time instant is the information update time instant, is the synchronized phasor measurement signal amplitude at time instant is the synchronized phasor measurement signal amplitude at time instant is the time node.

4. The method for processing of power system synchrophasor information in unbalanced and noisy environment according to claim 1, wherein, The second-order generalized integrator phase-locked loop outputs mutually orthogonal signals in step S3, a second-order infinite gain band-pass filter is used and a feedback loop is added to establish mutually orthogonal i / q voltage components X i and X q ; the feedback gain coefficient k q , k i is optimized to correct X i and X q , and the transfer function expressions of the orthogonal fundamental i / q components X i (s) and X q (s) are as follows: ； ； In the formula, is the resonant angular frequency, ω = 2πf.

5. The method for processing power system synchrophasor information in unbalanced and noisy environment according to claim 1, wherein, The linearization processing of the state equation of the continuous nonlinear system in step S4 and the construction of the linearized discrete state equation and the observation equation of the extended Kalman filter of the power distribution system specifically comprise the following steps: S4-1: based on the coordinate transformation theory, performing orthogonal decomposition on the synchronous phasor voltage signal, and obtaining an input observation vector of the extended Kalman filter method by performing phase rotation and integral zero processing on the actual measurement signal of the power distribution system and the local reference signal generated by the second-order generalized integrator phase-locked loop; The expression of the state equation of the continuous nonlinear system is as follows: ； wherein is the system state vector, u n is the measurement input quantity, is the system observation quantity, and is a Gaussian random noise vector with zero mean and uncorrelated, is the continuous system state transition matrix, h(x n is the continuous system measurement matrix; S4-2: When sufficiently small, the function In expanding the Taylor series around the neighborhood, the linearized discrete state equation and observation equation expressions are as follows: ； In the formula is a discrete system state transition matrix, is a discrete system measurement matrix.

6. The method for processing of power system synchrophasor information in unbalanced and noisy environment according to claim 1, wherein, The specific steps of using the estimation and correction combined recursive calculation method and Riccati equation to estimate the time update process of the error covariance in step S5 comprise: S5-1: Estimate the state vector x from the observation vector y(n-1) of the previous time instant n Orthogonal projection onto y(n-1) The calculation expression is as follows: ； where G n-1 = E(w n-1 w n-1 T ), is the expectation of the state vector noise component; The recursive calculation mode combined with the estimation and correction calculates the optimal estimation value of the current state according to the latest observation data at each time The recursive updating equation expression is as follows: ； wherein is a filter gain matrix, is a minimum steady-state error covariance, is a noise phasor covariance at time n. S5-2: The Riccati equation to describe the estimation error covariance, the prior error covariance matrix P of the constrained state estimation n│n-1 The expression is as follows: ； where P n│n-1 is the minimum covariance matrix with respect to x t , the initial condition ; when (Φ, E(w n-1 w n-1 T ) is controllable and (Φ, H) is observable, the Riccati equation converges to a unique positive semi-definite matrix independent of the initial condition.

7. The method for processing of power system synchrophasor information in unbalanced and noisy environment according to claim 1, wherein, The specific steps of using the Kalman gain coefficient to perform measurement update on the estimated value of the state quantity and obtaining the optimized estimation value in step S6 comprise: S6-1: When the bad data appears in the measured value, the Kalman gain coefficient K is obtained by n The system state is corrected and updated to obtain the state estimation value at time n The Kalman filter gain coefficient k is obtained from the Kalman gain matrix K i and k q , k i and k q The calculation formula is as follows: ； ； In the formula, q is a process noise component w expectation; When the approximation condition is satisfied k i and k q are: ； In the formula, covariance components, , ; Using P n│n-1 H n and R n Calculate the gain coefficient K n for: ； S6-2: According to the principle of minimum variance of observation error and state unbiased, the prior estimate is corrected by using Kalman gain coefficient K n and prior error covariance matrix P n-1 , the optimal estimation variance matrix P n is calculated as: ； S6-3: Utilize Kalman gain coefficient K n , given initial conditions and input vector x n , the optimal estimate of the state variable is computed recursively as : ； After new observation data is collected, according to the estimation at the previous moment, the state transition equation of the signal process itself is used to iteratively perform time update and measurement update feedback correction prediction information in the recursive calculation framework of prediction-measurement-correction, and the current optimal estimation value is obtained according to the recursive formula.

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