Intelligent power distribution network PMU-PSSE fusion fault accurate positioning method

Abstract

The invention relates to an intelligent power distribution network PMU-PSSE fusion fault accurate positioning method, and belongs to the field of fault positioning in a power distribution network, and the method comprises the following steps: defining fault positioning as an optimization problem, and carrying out the processing of a PSSE problem through employing a PMU before the fault; the PSSE information before the fault is utilized; searching a suspected fault path through the line phase voltage, and further determining a fault section in the path through the fault current; solving an optimization problem and positioning a fault; for different types of power distribution network faults, different calculation methods are specifically adopted to carry out fault positioning. According to the invention, the fault positioning problem in the distributed network is solved. According to the method, the voltage difference between the two ends of the line is calculated to serve as a new objective function, the voltage and the current at the branch point are estimated through the data of the PMU before and after the fault and the equation set of the pi-line model, and therefore the fault section and the fault position are recognized.

Description

Technical Field

[0001] The present invention belongs to the field of fault location in a power distribution network, and in particular relates to a method for determining a fault area and a fault location based on a phasor measurement unit (PMU) and engineering power system simulation software (PSSE). Background Art

[0002] Due to the extensiveness and complexity of distribution networks, fault location is one of the main challenges facing distribution networks. In order to provide power to users while reducing the frequency and magnitude of power outages, the precise location of the fault should be found with the greatest accuracy in the shortest time, thereby improving the reliability index and efficiency of the system. Therefore, it is necessary to use a method or device that can make decisions quickly and accurately.

[0003] In smart grids, the voltage and current of nodes are measured and calculated using phasor measurement units (PMUs) and control circuit laws, which can simultaneously measure the voltage and current of phasors in the grid. These devices are located on different buses and send their data to the control center at the same time, which is processed using the Global Positioning System (GPS) with an accuracy of less than one microsecond. The optimal configuration of the device is achieved using the control circuit equations in the network. In distribution lines, micro PMUs are used due to the short lines, which have higher accuracy and can store and analyze data on site.

[0004] There is still little research in the field of fault location based on optimization problems. Usually, most of the research based on matching algorithms is done by comparing measured information such as voltage and current in the network, and this matching method has many defects. Modeling the same real fault in the network in a laboratory environment and comparing these two non-homogeneous information items with each other to locate the fault is not ideal. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an optimization method based on the data of phasor measurement unit (PMU) and engineering power system simulation software (PSSE) to solve the fault location problem in the distribution network. The method calculates the voltage difference between the two ends of the line as a new objective function, and uses the data of PMU before and after the fault and the equation group of the π line model to estimate the voltage and current at the branch point, thereby identifying the fault section and location.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The present invention provides a method for determining a fault area and a fault location based on a phasor measurement unit (PMU) and a PSSE, comprising the following steps:

[0008] Step 1: Define fault location as an optimization problem and use PMU to handle PSSE problems before the fault occurs;

[0009] The weighted least squares method is used; the fault location of the distribution network is defined as an optimization problem, and a new objective function is designed. The control center uses the weighted least squares method to perform static analysis based on the data collected from the entire power grid and transmitted to the system control center to determine the current state of the busbar. The phase measurement function of the PMU is used to update the state estimation model based on the measured phase and amplitude of the voltage and current; the phase and amplitude changes of the voltage and current are tracked in real time through discrete Fourier transform and moving window methods;

[0010] Step 2: Utilize the PSSE information before the fault;

[0011] Use the PSSE information before the fault to estimate the voltage and current of the network node after the fault occurs; identify the fault area by the changing current direction and voltage drop; combine the voltage drop calculated in advance by PSSE and the data measured by PMU, and use the formula to calculate the terminal current and voltage of the fault line;

[0012] Step 3: Find the suspected fault path through the line phase voltage, and further determine the fault section through the fault current in the path;

[0013] According to the characteristic voltage amplitude obtained at each measuring point, the location of the maximum or minimum characteristic voltage of the measuring point is determined; the fault point is preliminarily determined to be between the substation and the measuring point where the characteristic voltage is optimal; this path is named as the suspected fault path, where the fault may occur in any area; the characteristic voltage of the suspected fault path is known, and the fault section needs to be further determined;

[0014] Step 4: Optimization problem solving and fault location;

[0015] Define the π model state of the power grid line, describe the behavior of the line in normal and fault conditions through the relationship between voltage and current, solve the optimization problem through variational method, and use genetic algorithm to optimize the objective function of the fault location;

[0016] Step 5: For different types of distribution network faults, different calculation methods are used to locate the fault.

[0017] Furthermore, in the step 1, the state of the power system is defined as a set of magnitudes and angles of voltages and currents, and the best estimate of the state variables is found so that the best fit of the measured data is obtained in the power flow model of the power system;

[0018] According to the mathematical relationship between the measured value and the system state value, the PSSE mathematical model is written as the following equation:

[0019] Z=h(x)+e

[0020] Where Z is the vector of measured variables, x is the vector of state variables, i.e. the vector of bus voltage amplitude and phase and bus current amplitude and phase, h is the vector of nonlinear functions connecting state variables and measured variables, and e is the vector of measurement errors;

[0021] Assume that the error {e1,e2,…,e N} is an independent random error with a Gaussian distribution with mean zero; the measurement error e i Variance It is an indicator of the degree of certainty of a particular measurement. A larger variance value indicates that the corresponding measurement is not very accurate. Finally, the covariance matrix (R) of the measurement error is expressed as:

[0022]

[0023] Since the error of e is a random variable, the measured value of Z will also be random; where Z is a normal distribution with mean h(x) and covariance r; the probability density function Z is expressed as:

[0024]

[0025] For static estimation problems, the x state vector is estimated by observing or measuring a set of network variables called Z; the value of x is estimated by maximizing the probability density function; the estimated value of x is called the "maximum likelihood estimate". Given the exponential nature of the above formula, maximizing f(Z) is equivalent to minimizing the quadratic expression of its power term, and the minimization formula is:

[0026]

[0027] To make the estimation more accurate, the square of the weighted error and the accurate measurement value should be minimized;

[0028] The phasor representation of a sinusoidal quantity is:

[0029]

[0030] In this case, X(t) represents the signal sampled at time t = τ, X(t) = X k , where t is the sampling interval; using discrete Fourier transform (DFT), the phase X(t) is defined as:

[0031]

[0032]

[0033] Where N is the number of samples within a certain base frequency period, and θ is the sampling angle corresponding to τ:

[0034]

[0035] For most measurement and relay equipment applications, the typical sampling rate is 12 times the power system frequency. The above discrete Fourier transform equation is non-recursive. In practical applications, the calculation of the time-varying phase uses the following equation as an iterative equation. Assume that X r is the phasor obtained from the sample set x{k=r,r+1,…,N+r-1}. In this case, when a new sample is obtained, the new sample set is displayed as x{k=r+1,…,N+r}. At this time, the updated phasor is obtained by the following formula:

[0036]

[0037] In the case where two samples are required at each stage, the recursive calculation method with a moving sampling window is faster than the non-recursive calculation method; if X(t) has transient changes, the moving window will track the changes in amplitude and phase with a delay that depends on the sampling time rate, extract the relationship between these phasors and the system state variables, and obtain the relationship between the measured data of the PMU in the line and the transformer with state variables through the branch current equation of the line π model; the current I ij The relationship is calculated as:

[0038] I ij =C ij +jD ij =[(R ij +jL ij )+(g si +jb si )]V i ∠θ i -(R ij +jL ij )V j ∠θ j

[0039] C ij =V i [(R ij +g si )cosθ i -(L ij +b si )sinθ i ]-V j [R ij cosθ j -L ij sinθ j ]

[0040] D ij =V i [(L ij +b si )cosθ i+(R ij +g si )sinθ i ]-V j [L ij cosθ j +R ij sinθ j ]

[0041] Since the data measured by the PMU participates in the Jacobian matrix of state estimation, the linear relationship between the branch current equation and the corresponding bus and terminal voltage amplitude and voltage angle is considered, and the contribution of the PMU to the target vector and the Jacobian state estimation matrix is ​​expressed as:

[0042]

[0043] Furthermore, in step 2, the voltage drop calculation performed by the PSSE before the fault occurs is used to estimate the terminal current of each fault line; the voltage value measured by the PMU is put into the PSSE problem, and the line voltage drop is considered to estimate the voltage value V under the pre-fault condition. 1-PSSE ,V 2-PSSE , and current I 1-PSSE ;

[0044]

[0045] After a fault occurs, the PMU can only measure V 1-PSSE ,V 2-PSSE , so at this time, the known voltage drop (ΔV 1-2 ). The size of V 2-failt :

[0046] V 2-fault =V 1-fault -ΔV 1-2

[0047] Then, I can be obtained through the line transmission matrix 2-fault :

[0048]

[0049] In this way, the voltage and current changes at the beginning and end of the fault line can be calculated when the fault occurs; in addition, according to I 1-fault and I 2-fault Calculate the fault point voltage (V f ):

[0050] V f =V 1-fault -xZ L I 1-fault

[0051] Vf =V 2-fault -(Lx)Z L· I 2-fault

[0052] Furthermore, in step 3, the fault may occur in any area of ​​the suspected fault path. The characteristic voltage on the low-voltage side of the suspected fault path is known, and the fault section needs to be further determined. The fault determination index C of the fault section is defined as:

[0053]

[0054] In the formula, ΔU is the characteristic voltage phasor difference at both ends of the line segment, and Zsegment is the line impedance of the line segment. At this time, it is necessary to calculate the fault judgment index of each segment. The fault segment can be found through the difference of index C;

[0055] Thus the location of the fault x is estimated:

[0056]

[0057] For different types of faults, different objective functions are applied to locate the fault. Using the information of PSSE and PMU, the fault location of the distribution network is defined as an optimization problem. Then the fault location is estimated by solving the problem. First, the characteristics of the traveling wave model are used to connect the voltage and current at the beginning and end of the line. Under normal fault-free conditions, the relationship between the voltage and current at the beginning of the line is:

[0058]

[0059] In the formula is a constant or diffusion coefficient, is the characteristic impedance in Ω, Z and γ are the series impedance and shunt admittance respectively. After a little algebraic operation, the above steady-state equation can be written as follows:

[0060] V R +Z c I R =(V S +Z c I S ) -γL

[0061] Furthermore, in step 4, it is now assumed that a fault occurs at point F at a distance x, and the fault voltage at the start and end of the line is calculated by the KVL law. The identification of the network line with the maximum voltage or current amplitude difference is defined as the optimization problem of finding the fault distribution section. Therefore, the objective function of the fault location problem is defined as:

[0062]

[0063] Where, L = number of network lines = 1,…,N, i = number of network buses = 1,…,M, j = number of network buses = 1,…,M, I≠j; In the objective function of the above formula, the change of the current at both ends of the line is used to replace the change of the voltage at both sides of the line. The proposed objective function is used for all types of faults, including short circuit faults and series faults. For different types of faults, the method of calculating the distance from the starting point of the fault line to the end point of the fault line is used. According to the π model of the network line, the position of the fault x is:

[0064]

[0065] Since fault location is defined as an optimization problem, the objective function of fault location is given by the following equation, where for variable x, the difference in fault voltage calculated from the perspective of both sides of the line is considered, where x is the fault location, F is the fault point, and i, j are the nodes at the start and end of the fault line; since the voltage at the fault location must be equal from the perspective of both sides of the line, the solution to the problem is close to zero;

[0066]

[0067] The above equation defines the objective function of the problem as accurately locating the fault between the two fault buses ij. The basis of the work is to move the length of the fault location between the two buses i and j respectively, and calculate the fault voltage from the perspective of the two buses i and j, that is, V F→i ,V F→j , and repeat this process until the objective function of the problem reaches a minimum at x.

[0068] Further, in the step 5, there are two types of distribution network faults: short circuit faults and series faults. The calculation of the voltage and current at the fault point depends on the type of fault in the network and will vary according to the characteristics of each fault. In a short circuit fault, the fault current increases and then the voltage decreases, while in a series fault, the opposite occurs, that is, the voltage increases and the current decreases.

[0069] For a single-phase short-circuit fault, the positive, negative, and zero sequence components of the fault current and voltage are used. In this case, the sequence-based fault voltage (VF) is calculated by the following formula:

[0070] V F0→i =cosh(γ0x)V i0 -Z c0 sin h(γ0x)I i0

[0071] V F+→i =cosh(γ + x)V i+ -Z c+ sin h(γ + x)Ii+

[0072] V F-→i =cosh(γ-x)V i- -Z c- sin h(γ-x)I i-

[0073]

[0074] For two-phase and three-phase faults, the zero sequence can be omitted and the fault voltage (VF) can be calculated based on the positive and negative sequence:

[0075]

[0076] For series faults, the analysis is performed through symmetrical components. In this type of fault, the fault phase current decreases at the beginning of the line and becomes zero at the end of the line. Similarly, in this type of fault, the voltage of the unfaulted phase is zero and the voltage of the faulted phase increases. For a single conductor open circuit fault, the following is established:

[0077]

[0078] For two open-circuit faults:

[0079]

[0080] Advantages and effects of the present invention: For the present invention, the goal of the initial stage is to estimate the voltage and current of the network nodes and then estimate the voltage drop on the network line. This stage occurs before the fault occurs. In the second stage, after the fault occurs, the goal is to use the value of the PMU and use the information of the first stage to identify the faulty part. The goal of the third stage is to locate the fault after the fault line is determined in the second stage. These three actions are classified as optimization problems. The present invention uses a genetic algorithm (GA) to solve this problem and improves the calculation accuracy.

[0081] That is, the present invention calculates the voltage difference between the two ends of the line as a new objective function, and uses the data of the PMU before and after the fault and the equation group of the π-line model to estimate the voltage and current at the branch point, thereby identifying the fault section and location. It has the advantages of being simple, easy to operate, efficient and accurate, and is applicable to different types of short circuits and series faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 A schematic diagram of a PMU connection bus in the present invention;

[0083] Figure 2 This is a schematic diagram of the π-line model used as an input to a power grid branch in the present invention;

[0084] Figure 3 A schematic diagram of the positioning method used in the present invention;

[0085] Figure 4 A schematic diagram of a suspected fault path in the present invention;

[0086] Figure 5a It is a schematic diagram of the circuit state in the present invention;

[0087] Figure 5b This is a schematic diagram of the π-line model in a fault-free state of the present invention;

[0088] Figure 6 This is a schematic diagram of the fault types to which the present invention is applicable;

[0089] Figure 7 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0090] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0091] Example

[0092] The present invention provides a method for determining a fault area and a fault location based on a phasor measurement unit (PMU) and a PSSE, comprising the following steps:

[0093] Step 1: Define fault location as an optimization problem and use PMU to handle PSSE problems before the fault occurs;

[0094] The weighted least squares method is used; the fault location of the distribution network is defined as an optimization problem, and a new objective function is designed. The control center uses the weighted least squares method to perform static analysis based on the data collected from the entire power grid and transmitted to the system control center to determine the current state of the busbar. The phase measurement function of the PMU is used to update the state estimation model based on the measured phase and amplitude of the voltage and current. The phase and amplitude changes of the voltage and current are tracked in real time through discrete Fourier transform and moving window methods.

[0095] The fault location of the distribution network is defined as an optimization problem, and a new objective function is designed. For the control center, based on the data collected from the entire power grid and transmitted to the system control center, a static analysis is performed through the weighted least squares method to determine the current state of the busbar and find the best estimate of the state variable. The maximum likelihood estimation is used to optimize the estimate of the state variable through the covariance matrix of the measurement error. The state of the power system is defined as a set of voltage and current magnitudes and angles. The best estimate of the state variable is found so that the best fit of the measured data is obtained in the power flow model of the power system.

[0096] According to the mathematical relationship between the measured value and the system state value, the PSSE mathematical model is written as the following equation:

[0097] Z=h(x)+e

[0098] Where Z is the vector of measured variables, x is the vector of state variables (amplitude and phase of bus voltage and current), h is the vector of nonlinear functions connecting state variables and measured variables, and e is the vector of measurement errors.

[0099] Assume that the error {e1,e2,…,e N} is an independent random error with a Gaussian distribution with mean zero. The measurement error e i Variance is an indicator of the degree of certainty of a particular measurement. Large variance values ​​indicate that the corresponding measurement is not very accurate. Finally, the covariance matrix (R) of the measurement error can be expressed as:

[0100]

[0101] Since the error of e is a random variable, the measured value of Z will also be random. Where Z is a normal distribution with mean h(x) and covariance r. The probability density function Z can be expressed as:

[0102]

[0103] For static estimation problems, the x state vector can be estimated by observing or measuring a set of network variables called Z. It makes sense to estimate the value of x by maximizing the probability density function. The estimated value of x is called the "maximum likelihood estimate". Given the exponential nature of the above equation, maximizing f(Z) is equivalent to minimizing the quadratic expression of its power terms. The minimization formula is:

[0104]

[0105] The state estimation model is updated based on the measured phase and amplitude of the voltage and current using the phase measurement function of the PMU. The phase and amplitude changes of the voltage and current are tracked in real time through the discrete Fourier transform (DFT) and moving window method.

[0106] The phasor representation of a sinusoidal quantity (such as X) can be expressed as:

[0107]

[0108] In this case, X(t) represents the signal sampled at time t = τ, X(t) = X k , where t is the sampling interval. Using the discrete Fourier transform (DFT), the phase X(t) is defined as:

[0109]

[0110] Where N is the number of samples within a certain base frequency period, and θ is the sampling angle corresponding to τ:

[0111]

[0112] The above discrete Fourier transform equation is non-recursive. In practical applications, the calculation of the time-varying phase uses the following equation as an iterative equation. Assume that X r is the phasor obtained from the sample set x{k=r,r+1,…,N+r-1}. In this case, when a new sample is obtained, the new sample set is displayed as x{k=r+1,…,N+r}. At this time, the updated phasor can be obtained by the following formula:

[0113]

[0114] In the case where two samples are required at each stage, the recursive calculation method with a moving sampling window is faster than the non-recursive calculation method. If X(t) has transient changes, the moving window will track the changes in amplitude and phase with a delay that depends on the sampling time rate.

[0115] like Figure 1 As shown, the PMU can measure the magnitude and angle of the bus voltage, as well as the current of the lines and transformers connected to the bus. In order to use the PMU for state estimation, the PMU bus voltage phasor and the current of the connected line must be considered in the measurement vector z, and the nonlinear function of these phasors and the system state variables must be considered in the vector h. To do this, the relationship between these phasors and the system state variables must be extracted. Through the branch current equation of the line π model, the relationship between the measured data of the PMU in the line and the transformer with state variables can be obtained.

[0116] according to Figure 2 , current I ij The relationship can be calculated as:

[0117] I ij =C ij +jD ij =[(Rij +jL ij )+(g si +jb si )]V i ∠θ i -(R ij +jL ij )V j ∠θ j

[0118] C ij =V i [(R ij +g si )cosθ i -(L ij +b si )sinθ i ]-V j [R ij cosθ j -L ij sinθ j ]

[0119] D ij =V i [(L ij +b si )cosθ i +(R ij +g si )sinθ i ]-V j [L ij cosθ j +R ij sinθ j ]

[0120] Since the data measured by the PMU participates in the Jacobian matrix of state estimation, the linear relationship between the branch current equation and the corresponding bus and terminal voltage amplitude and voltage angle can be considered, and the contribution of the PMU to the target vector and the Jacobian state estimation matrix can be expressed as:

[0121]

[0122] Step 2: Using the PSSE information before the fault: Using the PSSE information before the fault to estimate the voltage and current of the network node after the fault occurs;

[0123] The fault area is identified by the changing current direction and voltage drop. The terminal current and voltage of the fault line are calculated using the formula by combining the voltage drop calculated in advance by PSSE and the data measured by PMU.

[0124] The voltage drop calculation performed by the PSSE before the fault occurs can be used to estimate the terminal current of each fault line. The voltage value measured by the PMU is put into the PSSE problem, and the line voltage drop is considered to estimate the voltage value V under the pre-fault condition. 1-PSSE ,V 2-PSSE , and current I 1-PSSE .

[0125]

[0126] After a fault occurs, the PMU can only measure V 1-PSSE ,V 2-PSSE , so at this time, the known voltage drop (ΔV 1-2 ). The size of V -fault :

[0127] V -fault =V 1-fault -ΔV 1-2

[0128] Then, I can be obtained through the line transmission matrix -fault :

[0129]

[0130] In this way, the voltage and current changes at the beginning and end of the fault line can be calculated when the fault occurs. 1-fault and I 2-fault Calculate the fault point voltage (V f ):

[0131] V f =V 1-fault -xZ L I 1-fault

[0132] V f =V 2-fault -(Lx)Z L· I 2-fault

[0133] Step 3: Find the suspected fault path through the line phase voltage, and further determine the fault section through the fault current in the path;

[0134] According to the characteristic voltage amplitude obtained at each measuring point, the location of the maximum or minimum characteristic voltage of the measuring point is determined. It can be preliminarily determined that the fault point is between the substation and the measuring point where the characteristic voltage is optimal. This path is named as the suspected fault path, in which the fault may occur in any area. Figure 3In the simple distribution network topology shown in the figure, the voltage measurement points are configured at the low-voltage side of the substation and the end of each long branch (nodes 5, 7, 9, 11, and 14). When a single-phase grounding fault occurs at F, Figure 3 As shown, the characteristic voltage amplitudes of the low-voltage side measurement points of nodes 5, 7, 9, 11, and 14 are compared. The low-voltage side characteristic voltage (negative sequence voltage) amplitude of node 11 is the largest, and the path between node 1 and node 11 is identified as a suspected fault path. Subsequently, the path is divided into several sections according to the branches with measurement points on the path. The voltage and current at both ends of the line are obtained at nodes 2 and 3. Therefore, the suspected fault path can be divided into three sub-parts and marked in order, as shown in FIG. Figure 3 As shown in the dashed box.

[0135] Figure 3 A simplified schematic diagram is shown in Figure 4 As shown. Given the suspected fault path (node ​​1 to node 11) and the low-voltage side characteristic voltages of nodes 5, 9, and 11, it is necessary to further determine the fault segment. The fault determination index C of the fault segment is defined as:

[0136]

[0137] In the formula, ΔU is the characteristic voltage phasor difference at both ends of the line segment, and Zsegment is the line impedance of the line segment. At this time, it is necessary to calculate the fault judgment index of the three segments. Segments 1 and 2 are both located upstream of the fault point, while segment 3 contains both the upstream and downstream of the fault point. Therefore, the index C of segments 1 and 2 should be approximately equal to and much larger than that of segment 3. Through the difference in index C, it can be found that there is a fault inside segment 3.

[0138] Thus the location of the fault x is estimated:

[0139]

[0140] For different types of faults (short circuit faults and series faults), different objective functions are applied to fault location.

[0141] The present invention uses the information of PSSE and PMU to try to define the fault location of the distribution network as an optimization problem. Then the fault location is estimated by solving the problem. First, the voltage and current at the beginning and end of the line are connected using the characteristics of the traveling wave model. Figure 5a , 5b The state of the grid lines using the π model is shown. Under normal circumstances (no faults), the relationship between the voltage and current at the beginning of the line is:

[0142]

[0143] In the formula is a constant or diffusion coefficient, is the characteristic impedance in Ω, z and γ are the series impedance and shunt admittance respectively. With a little algebraic operation, the above steady-state equation can be written as follows:

[0144] V R +Z c I R =(V S +Z c I S ) -γL

[0145] Step 4: Optimization problem solving and fault location;

[0146] Define the π model state of the power grid line, and describe the behavior of the line under normal and fault conditions through the relationship between voltage and current. Solve the optimization problem through variational method, and use genetic algorithm to optimize the objective function of the fault location.

[0147] Now assume that a fault occurs at point F at a distance x, and the fault voltage at the start and end of the line is calculated by the KVL law. Define the identification of the network line with the largest voltage or current amplitude difference as an optimization problem for finding the fault distribution section. Therefore, the objective function of the fault location problem can be defined as:

[0148]

[0149] Where, L = number of network lines = 1,…,N, i = number of network buses = 1,…,M, j = number of network buses = 1,…,M, I≠j. In the objective function of the above formula, the change in voltage on both sides of the line can be replaced by the change in current at both ends of the line. Since the absolute value of the voltage or current at both ends of the line is used, the changes in both cases are incremental. As we all know, the voltage decreases in a short circuit fault and increases in a series fault. But since the absolute value of the voltage is used, these changes will be incremental, so the proposed objective function can be used for all types of faults, including short circuits and series faults. A method for calculating the distance from the start point of the fault line to the end point of the fault line for different types of faults. Now, according to the π model of the network line, the location of the fault x is:

[0150]

[0151] Since the attempt in the present invention is to define fault location as an optimization problem, the objective function of fault location is given by the following formula, where for variable x, the difference of the fault voltage calculated from the perspective of both sides of the line is considered, where x is the fault location, F is the fault point, and i, j are the nodes at the start and end of the fault line. Since the voltage at the fault location must be equal from the perspective of both sides of the line, the solution of the problem is close to zero.

[0152]

[0153] The above equation defines the objective function of the problem as accurately locating the fault between two fault buses ij. The basis of the work is to move the length of the fault location between the two buses i and j respectively, and calculate the fault voltage from the perspective of the two buses i and j, that is, V F→i ,V F→j , and repeat this process until the objective function of the problem reaches a minimum at x.

[0154] Step 5: According to different types of distribution network faults, different calculation methods are used to locate the fault;

[0155] There are two types of distribution network faults: short circuit faults and series faults. The calculation of voltage and current at the fault point depends on the type of fault in the network and will vary according to the characteristics of each fault. In a short circuit fault, the fault current increases and then the voltage decreases, while in a series fault, the opposite occurs, that is, the voltage increases and the current decreases. Figure 6 Different types of faults are shown that the present invention will detect.

[0156] For a single-phase short-circuit fault, the positive, negative, and zero sequence components of the fault current and voltage are required. At this time, the sequence-based fault voltage (VF) can be calculated as follows:

[0157] V f0→i =cosh(γ0x)V i0 -Z c0 sin h(γ0x)I i0

[0158] V F+→i =cosh(γ + x)V i+ -Z c+ sin h(γ + x)I i+

[0159] V F-→i =cosh(γ-x)V i- -Z c- sin h(γ-x)I i-

[0160]

[0161] For two-phase and three-phase faults, the zero sequence can be omitted and the fault voltage (VF) can be calculated based on the positive and negative sequences. Therefore, we have:

[0162]

[0163] For series faults, it can be analyzed by symmetrical components. In this type of fault, the fault phase current decreases at the beginning of the line and becomes zero at the end of the line. Similarly, in this type of fault, the voltage of the unfaulted phase is zero and the voltage of the faulted phase increases. For a single conductor open circuit fault, establish:

[0164]

[0165] For two open-circuit faults:

[0166]

[0167] Taking the fault of the IEEE 123 node distribution feeder as an example, the present invention is used to locate the fault, and the performance sensitivity analysis of the fault parameters in actual operation is shown in Table 1:

[0168] Table 1 Performance sensitivity analysis of the present invention to fault parameters

[0169]

[0170] The performance sensitivity analysis results of the algorithm proposed in the present invention to PMU measurement errors are shown in Table 2:

[0171] Table 2 Performance sensitivity analysis of the present invention to PMU measurement error

[0172]

[0173] The above are only specific embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for accurately locating faults in a PMU-PSSE fusion system of a smart distribution network, characterized in that The steps include: Step 1: Define fault location as an optimization problem and use PMU to handle PSSE problems before the fault occurs; The weighted least squares method is used; the fault location of the distribution network is defined as an optimization problem, and a new objective function is designed. The control center uses the weighted least squares method to perform static analysis based on the data collected from the entire power grid and transmitted to the system control center to determine the current state of the busbar. The phase measurement function of the PMU is used to update the state estimation model based on the measured phase and amplitude of the voltage and current; the phase and amplitude changes of the voltage and current are tracked in real time through discrete Fourier transform and moving window methods; Step 2: Utilize the PSSE information before the fault; Use the PSSE information before the fault to estimate the voltage and current of the network node after the fault occurs; identify the fault area by the changing current direction and voltage drop; combine the voltage drop calculated in advance by PSSE and the data measured by PMU, and use the formula to calculate the terminal current and voltage of the fault line; Step 3: Find the suspected fault path through the line phase voltage, and further determine the fault section through the fault current in the path; According to the characteristic voltage amplitude obtained at each measuring point, the location of the maximum or minimum characteristic voltage of the measuring point is determined; the fault point is preliminarily determined to be between the substation and the measuring point where the characteristic voltage is optimal; this path is named as the suspected fault path, where the fault may occur in any area; the characteristic voltage of the suspected fault path is known, and the fault section needs to be further determined; Step 4: Optimization problem solving and fault location; Define the π model state of the power grid line, describe the behavior of the line in normal and fault conditions through the relationship between voltage and current, solve the optimization problem through variational method, and use genetic algorithm to optimize the objective function of the fault location; Step 5: For different types of distribution network faults, different calculation methods are used to locate the fault.

2. According to claim 1, a smart distribution network PMU-PSSE fusion fault accurate positioning method is characterized in that: In the step 1, the state of the power system is defined as a set of magnitudes and angles of voltage and current, and the best estimate of the state variables is found so that the best fit of the measured data is obtained in the power flow model of the power system; According to the mathematical relationship between the measured value and the system state value, the PSSE mathematical model is written as the following equation: Z=h(x)+e Where Z is the vector of measured variables, x is the vector of state variables, i.e. the vector of bus voltage amplitude and phase and bus current amplitude and phase, h is the vector of nonlinear functions connecting state variables and measured variables, and e is the vector of measurement errors; Assume that the errors {e1,e2,…,e N } is an independent random error with a Gaussian distribution with mean zero; the measurement error e i Variance It is an indicator of the degree of certainty of a particular measurement. A larger variance value indicates that the corresponding measurement is not very accurate. Finally, the covariance matrix (R) of the measurement error is expressed as: Since the error of e is a random variable, the measured value of Z will also be random; where Z is a normal distribution with mean h(x) and covariance r; the probability density function Z is expressed as: For static estimation problems, the x state vector is estimated by observing or measuring a set of network variables called Z; the value of x is estimated by maximizing the probability density function; the estimated value of x is called the "maximum likelihood estimate". Given the exponential nature of the above formula, maximizing f(Z) is equivalent to minimizing the quadratic expression of its power term, and the minimization formula is: To make the estimation more accurate, the square of the weighted error and the accurate measurement value should be minimized; The phasor representation of a sinusoidal quantity is: In this case, X(t) represents the signal sampled at time t = τ, X(t) = X k , where t is the sampling interval; using discrete Fourier transform (DFT), the phase X(t) is defined as: Where N is the number of samples within a certain base frequency period, and θ is the sampling angle corresponding to τ: For most measurement and relay equipment applications, the typical sampling rate is 12 times the power system frequency. The above discrete Fourier transform equation is non-recursive. In practical applications, the calculation of the time-varying phase uses the following equation as an iterative equation. Assume that X r is the phasor obtained from the sample set x{k=r,r+1,…,N+r-1}. In this case, when a new sample is obtained, the new sample set is displayed as x{k=r+1,…,N+r}. At this time, the updated phasor is obtained by the following formula: In the case where two samples are required at each stage, the recursive calculation method with a moving sampling window is faster than the non-recursive calculation method; if X(t) has transient changes, the moving window will track the changes in amplitude and phase with a delay that depends on the sampling time rate, extracting the relationship between these phasors and the system state variables, and obtaining the relationship between the measured data of the PMU in the line and the transformer with state variables through the branch current equation of the line π model; Current I ij The relationship is calculated as: I ij =C ij +jD ij =[(R ij +jL ij )+(g si +jb si )]V i ∠θ i -(R ij +jL ij )V j ∠θ j C ij =V i [(R ij +g si )cosθ i -(L ij +b si )sinθ i ]-V j [R ij cosθ j -L ij sinθ j ] D ij =V i [(L ij +b si )cosθ i +(R ij +g si )sinθ i ]-V j [L ij cosθ j +R ij sinθ j ] Since the data measured by the PMU participates in the Jacobian matrix of state estimation, the linear relationship between the branch current equation and the corresponding bus and terminal voltage amplitude and voltage angle is considered, and the contribution of the PMU to the target vector and the Jacobian state estimation matrix is ​​expressed as:

3. According to claim 1, a smart distribution network PMU-PSSE fusion fault accurate positioning method is characterized in that: In the step 2, the voltage drop calculation performed by the PSSE before the fault occurs is used to estimate the terminal current of each fault line; Put the voltage value measured by the PMU into the PSSE problem and consider the line voltage drop to estimate the voltage value V under the pre-fault condition. 1-PSSE ,V 2-PSSE , and current I 1-PSSE ; After a fault occurs, the PMU can only measure V 1-PSSE ,V 2-PSSE , so at this time, the known voltage drop (ΔV 1-2 ). The size of V 2-fault : V -fault =V 1-fault -ΔV 1-2 Then, I can be obtained through the line transmission matrix -fault : In this way, the voltage and current changes at the beginning and end of the fault line can be calculated when the fault occurs; in addition, according to I 1-fault and I 2-fault Calculate the fault point voltage (V f ): V f =V 1-fault -xZ L ·I 1-fault V f =V 2-fault -(L-x)Z L ·I 2-fault 。 4. According to claim 1, a smart distribution network PMU-PSSE fusion fault accurate positioning method is characterized in that: In step 3, the fault may occur in any area of ​​the suspected fault path. The characteristic voltage on the low-voltage side of the suspected fault path is known, and the fault section needs to be further determined. The fault determination index C of the fault section is defined as: In the formula, ΔU is the characteristic voltage phasor difference at both ends of the line segment, and Zsegment is the line impedance of the line segment. At this time, it is necessary to calculate the fault judgment index of each segment. The fault segment can be found through the difference of index C; Thus the position of the fault x is estimated: For different types of faults, different objective functions are applied to fault location. Using the information of PSSE and PMU, the distribution network fault location is defined as an optimization problem. Then the fault location is estimated by solving the problem; first, the characteristics of the traveling wave model are used to connect the voltage and current at the beginning and end of the line. Under normal circumstances without faults, the relationship between the voltage and current at the beginning of the line is: In the formula is a constant or diffusion coefficient, is the characteristic impedance in Ω, Z and γ are the series impedance and shunt admittance respectively. After a little algebraic operation, the above steady-state equation can be written as follows: V R +Z c I R =(V S +Z c I S )e -γL 。 5. The method for accurately locating PMU-PSSE fusion faults in a smart distribution network according to claim 1, characterized in that: In the above step 4, it is now assumed that a fault occurs at point F at a distance x. The fault voltages at the start and end of the line are calculated by the KVL law. The identification of the network line with the maximum voltage or current amplitude difference is defined as the optimization problem of finding the fault distribution section. Therefore, the objective function of the fault location problem is defined as: Where, L = number of network lines = 1,…,N, i = number of network buses = 1,…,M, j = number of network buses = 1,…,M, I≠j; In the objective function of the above formula, the change of the current at both ends of the line is used to replace the change of the voltage at both sides of the line. The proposed objective function is used for all types of faults, including short circuit faults and series faults. For different types of faults, the method of calculating the distance from the starting point of the fault line to the end point of the fault line is used. According to the π model of the network line, the position of the fault x is: Since fault location is defined as an optimization problem, the objective function of fault location is given by the following equation, where for variable x, the difference in fault voltage calculated from the perspective of both sides of the line is considered, where x is the fault location, F is the fault point, and i, j are the nodes at the start and end of the fault line; since the voltage at the fault location must be equal from the perspective of both sides of the line, the solution to the problem is close to zero; The above equation defines the objective function of the problem as accurately locating the fault between the two fault buses ij. The basis of the work is to move the length of the fault location between the two buses i and j respectively, and calculate the fault voltage from the perspective of the two buses i and j, that is, V F→i ,V F→j , and repeat this process until the objective function of the problem reaches a minimum at x.

6. The method for accurately locating PMU-PSSE fusion faults in a smart distribution network according to claim 1, characterized in that: In the step 5, there are two types of distribution network faults: short circuit faults and series faults. The calculation of the voltage and current at the fault point depends on the type of fault in the network and will vary according to the characteristics of each fault. In a short circuit fault, the fault current increases and then the voltage decreases, while in a series fault, the opposite occurs, that is, the voltage increases and the current decreases. For a single-phase short-circuit fault, the positive, negative, and zero sequence components of the fault current and voltage are used. In this case, the sequence-based fault voltage (VF) is calculated by the following formula: V F0→i =cosh(γ0x)V i0 -Z c0 sin h(γ0x)I i0 V F+→i =cosh(γ + x)V i+ -Z c+ sin h(γ + x)I i+ V F→i =cosh(γ-x)V i- -Z c -sin h(γ-x)I i- For two-phase and three-phase faults, the zero sequence can be omitted and the fault voltage (VF) can be calculated based on the positive and negative sequence: For series faults, the analysis is performed through symmetrical components. In this type of fault, the fault phase current decreases at the beginning of the line and becomes zero at the end of the line. Similarly, in this type of fault, the voltage of the unfaulted phase is zero and the voltage of the faulted phase increases. For a single conductor open circuit fault, the following is established: For two open-circuit faults:

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