A linear interval state estimation method for ac-dc distribution network based on state prediction

Abstract

The application discloses a state prediction-based linear interval state estimation method for AC-DC power distribution networks. The method uses historical states to predict the state interval at the current time, and corrects the interval based on a nonlinear optimization model to ensure the rationality of the predicted interval. Then, a nonlinear equation scaling method based on the mean value theorem is used to convert the nonlinear interval SE model into a linear optimization model, ensuring the completeness of the estimation interval. The algorithm proposed by the application can accurately obtain the interval information of the AC-DC power distribution network state in a weakly observable AC-DC power distribution network with a high proportion of new energy penetration, providing technical support for subsequent safety evaluation and optimal operation.

Description

TECHNICAL FIELD

[0001] The application relates to an interval state estimation (SE) method of an AC-DC power distribution network, in particular to an AC-DC power distribution network linear interval state estimation method based on state prediction. BACKGROUND

[0002] With the rise of clean replacement, multi-energy complementation and green power consumption, more and more new energy is connected to the distribution network in the form of distributed generation (DG), and the proportion of direct-current loads such as electric vehicles and information equipment is increasing. The traditional distribution network is gradually changing into an AC-DC active distribution network with multi-energy power supply. However, the increase of intermittent DG and flexible loads will further exacerbate the fluctuation of node voltage, which is easy to cause voltage out-of-limit and reduce power quality. Therefore, it is of great significance to predict the future voltage trend and real-time perceive the current operation state of the AC-DC distribution network for ensuring the safe and stable operation of the AC-DC distribution network system.

[0003] State estimation uses information such as measurement instruments to perceive the system operation state, and provides a data basis and technical support for subsequent advanced applications of the distribution management system such as optimal scheduling, safety assessment and fault self-healing. Due to the lack of real-time measurement of the distribution network, a large number of pseudo-measurements (such as DG output data and load power) based on historical data or prediction are needed to ensure the observability of the whole system. However, the error of the pseudo-measurements is difficult to guarantee, and the specific probability distribution is difficult to accurately obtain, which will lead to a significant decrease in the accuracy of point estimation methods such as weighted least square (WLS), and cannot meet the requirements. To solve this problem, the uncertainty variables need to be reasonably modeled in the state estimation of the distribution network, and the influence of their random fluctuations on the system state needs to be considered. The commonly used methods for handling uncertainty problems mainly include probability model, fuzzy number model and interval model. The former two models need to obtain the required probability density function or membership function in advance, while the interval model only needs the upper and lower bound information of the variable, and does not need a specific distribution, and has stronger applicability in practical application.

[0004] At present, the interval state estimation or power flow calculation method mainly includes the following categories: (I) interval constraint propagation method: ignoring the correlation of the same variable in different constraints, the conservativeness is higher. (II) method based on Krawczyk operator: low measurement coverage of distribution network and high configuration cost of PMU reduce the engineering practicability of the method in most distribution networks. (III) affine algorithm: the nonlinear operation of affine is relatively complex, the introduction of new noise elements will cause interval expansion, and the calculation result is relatively conservative. (IV) optimization method: the nonlinear optimization model of interval SE is a non-convex model, which cannot guarantee the completeness of the solution, and the linear optimization model is established by using Taylor expansion to ignore high-order terms, and the accuracy of linearization approximation depends on the middle value of the interval. The above researches are all for pure AC distribution network, for AC-DC hybrid distribution network, due to the wide access of distributed new energy, low measurement redundancy, and prominent three-phase imbalance, it is difficult to accurately obtain the system state under the influence of multiple uncertain factors by using the above methods. SUMMARY

[0005] The purpose of the application is to solve the above problems, the application provides a linear interval state estimation method for AC-DC distribution network based on state prediction, which can accurately obtain the interval information of AC-DC distribution network state in weakly observable AC-DC distribution network with high proportion of new energy penetration.

[0006] The technical scheme adopted by the application is a linear interval state estimation method for AC-DC distribution network based on state prediction, comprising the following steps:

[0007] (1) establishing a three-phase model of AC-DC distribution network according to the parameter information of AC-DC distribution network;

[0008] The parameter information includes: topological information of AC-DC distribution network, impedance of each branch, equivalent impedance of voltage source converter and control mode of voltage source converter. The control mode of voltage source converter is master-slave control mode, one converter station is taken as a master converter station to control the DC side node voltage and the AC grid side reactive power, and the remaining converter stations are taken as slave converter stations to control the AC grid side active power and a reactive variable (AC grid side voltage or AC grid side reactive power).

[0009] (2) expressing the measurement and state variable as an interval form, and establishing a nonlinear interval state estimation model of AC-DC distribution network according to the measurement equation and operation constraint;

[0010] The interval form is:

[0011]

[0012] In the formula, [x] is an interval number; x And are the upper and lower boundaries of x respectively.

[0013] The measurement equation is a calculation formula of the measurement with respect to the state variable, the operation constraint includes a relationship constraint between the state variables, a control constraint of the voltage source converter, a power balance constraint on the AC and DC sides of the voltage source converter, and a three-phase symmetry constraint of the AC outlet node of the voltage source converter. The nonlinear interval state estimation model of the AC / DC power distribution network is:

[0014]

[0015] In the formula, x i is a state variable, z i is a measurement, h(·) is a mapping relationship between the measurement vector and the state vector, and g([x])=0 is an operation constraint equation.

[0016] (3) According to the historical state, the interval form of the two-parameter exponential smoothing method is used to predict the state interval at the current time;

[0017] The interval form of the two-parameter exponential smoothing method is:

[0018]

[0019]

[0020] [b k ]=q([a k ]-[a k-1 ])+(1-q)[b k-1 ]

[0021] In the formula, k is the serial number of the time section; is a predicted interval; is a predicted interval of the previous time section; [x k ] is an estimated interval; [a k ] and [b k ] are intermediate variables; [a k-1 ] and [b k-1 ] are intermediate variables of the previous time section; p and q are smoothing parameters, and the values are [0, 1].

[0022] (4) The nonlinear interval state estimation model of the AC / DC power distribution network is converted into a linear interval state estimation model by using a nonlinear equation scaling method based on the mean value theorem, the predicted interval of step (3) is taken as the initial interval of the state variable, the measurement interval obtained by sampling the measurement system is taken as the initial interval of the measurement variable, and both are input into the linear interval state estimator to output a new state interval and a measurement interval;

[0023] The nonlinear equation scaling method based on the mean value theorem is:

[0024] Let the nonlinear equality equation be:

[0025] f(a) = 0

[0026] Then the original nonlinear equality equation is transformed into two linear constraints:

[0027]

[0028] where (J([a])) is a constant, and min and max are the minimum and maximum of the partial derivative of f(a) with respect to a, respectively. min / max

[0029] The linear interval state estimation model is:

[0030]

[0031] where h(·) is the mapping relationship between the measurement vector and the state vector; g(.) is the operating constraint function; H(x) and K(x) are the partial derivatives of h(x) and g(x), respectively; x i is the state variable; and z i is the measurement.

[0032] (5) If the state interval output by the linear interval state estimator is not empty, go to step (6). If the state interval output by the linear interval state estimator is empty, it means that there is an inaccurate prediction interval. At this time, the state variable conservative empirical interval is obtained according to the node voltage amplitude range [0.95, 1.05] p.u., the node voltage phase angle deviation range [-5°, +5°], and the line load flow range. The empirical interval is input into the nonlinear state estimator to obtain the state interval. The state interval and the prediction interval are compared. If the prediction interval of a state does not completely contain the interval of the state output by the nonlinear interval estimator, it means that the prediction interval of the state is inaccurate. After finding the state set with an inaccurate prediction interval, the midpoint of the interval of the state set output by the nonlinear interval estimator is taken as the center point, and the average width of the prediction interval of the state set at each previous time section is taken as the width, to regenerate a new prediction interval of the state set, and replace the original prediction interval of the state set to input into the linear interval state estimator, so as to output a new state interval and a measurement interval;

[0033] (6) The state interval and the measurement interval output by the linear interval state estimator are input again, so as to output a new state interval and a measurement interval;

[0034] (7) Repeat step (6) until the width of the state interval and the measurement interval no longer further decreases.

[0035] The criterion that the width of the state interval and the measurement interval no longer further decreases is: ​

[0036]

[0037] In the formula: l is the serial number of the iteration times; s is a preset convergence threshold.

[0038] Advantages: Compared with the prior art, the application has the following advantages: the application is aimed at the characteristics of the wide access of distributed new energy, low measurement redundancy, and prominent three-phase imbalance in AC / DC distribution network, and first constructs a linear interval SE model of AC / DC distribution network based on state prediction. The method predicts the state interval at the current time by using the historical state, and corrects the interval based on the nonlinear optimization model to ensure the rationality of the prediction interval; then, the nonlinear interval SE model is converted into a linear optimization model by using the nonlinear equation scaling method based on the mean value theorem, and the completeness of the estimated interval is ensured. The algorithm proposed in the application can accurately obtain the interval information of the state of the AC / DC distribution network in the weakly observable AC / DC distribution network with a high proportion of new energy penetration, and provides technical support for subsequent safety evaluation and optimal operation. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a converter model;

[0040] Figure 2 is a flow chart of the linear interval state estimation method of AC / DC distribution network based on state prediction according to the application;

[0041] Figure 3 is a test system diagram of AC / DC distribution network;

[0042] Figure 4 is a comparison diagram of the estimated interval of FAISE and Krawczyk algorithm in AC distribution network, including (a) the estimated interval distribution of the real part of the node voltage of AC distribution network (phase A), and (b) the estimated interval distribution of the imaginary part of the node voltage of AC distribution network (phase C);

[0043] Figure 5 is a comparison diagram of the estimated interval of FAISE and Krawczyk algorithm in DC distribution network;

[0044] Figure 6 is a diagram showing the change process of the average interval width of the real part of the AC node voltage under different branch current measurement configurations. DETAILED DESCRIPTION

[0045] The technical solutions of the application will be further described below in combination with the drawings and examples.

[0046] The linear interval state estimation method of AC / DC distribution network based on state prediction according to the application comprises the following steps:

[0047] (1) According to the parameter information of AC / DC distribution network, a three-phase model of AC / DC distribution network is established;

[0048] (2) The measurement and state variable are expressed in interval form, and a nonlinear interval state estimation model of AC / DC distribution network is established according to the measurement equation and operation constraints;

[0049] (3) According to the historical state, the two-parameter exponential smoothing method in interval form is used to predict the state interval at the current time;

[0050] (4) Using the nonlinear equation scaling method based on the mean value theorem, the nonlinear interval state estimation model of AC / DC distribution network is converted into a linear interval state estimation model, the predicted interval of step (3) is used as the initial interval of the state variable, and the measurement interval obtained by sampling the measurement system is used as the initial interval of the measurement variable. Both are input into the linear interval state estimator to output new state interval and measurement interval;

[0051] (5) If the state interval output by the linear interval state estimator is not empty, go to step (6), if the state interval output by the linear interval state estimator is empty set, it means that there is inaccurate prediction interval, at this time, according to the node voltage amplitude range [0.95, 1.05] p.u., the node voltage phase angle deviation range [-5°, +5°] and the line load flow range, the state variable conservative empirical interval is obtained, the empirical interval is input into the nonlinear state estimator to obtain the state interval, the state interval and the prediction interval are compared, if the prediction interval of a state does not completely contain the interval of the state output by the nonlinear interval estimator, it means that the prediction interval of the state is inaccurate, after finding the state set with inaccurate prediction interval, taking the midpoint of the interval of the state set output by the nonlinear interval estimator as the center point, and taking the average width of the prediction interval of the state set at each time section as the width, a new prediction interval of the state set is regenerated and replaces the original prediction interval to input into the linear interval state estimator to output new state interval and measurement interval;

[0052] (6) The state interval and measurement interval output by the linear interval state estimator are input again to output new state interval and measurement interval;

[0053] (7) Repeat step (6) until the width of the state interval and the measurement interval is no longer further reduced.

[0054] The following will be described in detail for several important parts:

[0055] 1. Modeling of AC / DC hybrid distribution network

[0056] 1) Converter equivalent model

[0057] DC distribution network and most of the DG need to be connected to AC distribution network through power electronic converters. Among them, voltage source converter (VSC) is the most widely used, and the power flow model of VSC is as shown in Figure 1 . Figure 1 In the formula: is the voltage phasor of VSC AC grid connection point; is the voltage phasor of VSC AC outlet node; subscript f, t is the node number; is the current phasor of VSC branch; are the equivalent resistance and reactance of VSC branch respectively; U d is the DC side voltage of VSC, subscript d is the DC node number; P vsc，d , P vsc，t are the active power of VSC DC side and AC side respectively, and the arrow direction in the figure is the positive direction; P vsc，loss is the active power loss of the converter.

[0058] The voltage and current in Figure 1 are expressed in rectangular coordinates The power balance relationship between VSC AC and DC sides is:

[0059] P vsc，d = P vsc，t + P vsc，loss

[0060]

[0061]

[0062] In the formula: η1, η2, η3 are the power loss coefficients of VSC; is the phase voltage amplitude of VSC branch .

[0063] 2) State variables

[0064] In the interval SE, the measured values and state variables are expressed by interval numbers, and the form of interval number is:

[0065]

[0066] In the formula: [x] is an interval number; and x are the upper and lower boundaries of x respectively.

[0067] The state variables of AC / DC distribution network selected are:

[0068] [x] = {[U re ], [U im], [I re ], [I im ], [I vsc ], [U dc ]} T

[0069] In the formula: [U re ] and [U im [I] represents the real and imaginary parts of the AC node voltage, respectively; re ] and [I im [I] represents the real and imaginary parts of the AC branch current, respectively; vsc [U] represents the amplitude range of the VSC branch current; dc [ ] represents the DC node voltage amplitude range.

[0070] The equation relating the AC node voltage state quantities and the real and imaginary parts of the branch current is as follows:

[0071]

[0072]

[0073] In the formula: subscripts i and j are the numbers of the communication nodes; branch road The resistance and reactance between phase φ and phase φ.

[0074] The relationship between the amplitude state quantity of the VSC branch current and the real and imaginary parts of the branch current is as follows:

[0075]

[0076] 3) Measurement equations for AC distribution networks

[0077] The measurement of AC distribution networks is voltage amplitude measurement. Branch current amplitude measurement and node injection power measurement Among them, voltage amplitude measurement is converted into the square of voltage amplitude. Branch current amplitude measurement converted to the square of branch current amplitude The converted measurement satisfies the error propagation law. Using state variables [U] re ]、[U im ]、[I re ]、[I im The symbol ] represents the measurement in an AC distribution network, which greatly simplifies the measurement equations and their partial derivatives. The specific form of the measurement equation is as follows:

[0078]

[0079]

[0080]

[0081]

[0082] where j∈i denotes the nodes connected to node i.

[0083] 4) Measurement equations of DC distribution network

[0084] The measurement of DC distribution network is the node voltage amplitude The branch current amplitude And the node injection power The specific form of the measurement equation is as follows:

[0085]

[0086]

[0087]

[0088] 5) Converter control variable equation and DG output measurement equation

[0089] VSC uses fully controlled devices, which can control active variables (DC side voltage, AC grid side active power) and reactive variables (AC grid side voltage, AC grid side reactive power) at the same time, so the control mode of a single VSC has multiple combinations. For the k VSCs connected to the DC distribution network, the master-slave control mode is considered, one converter station is taken as the master converter station to maintain the stability of the DC side node voltage, and the control mode of the remaining converter stations uses the combination of AC side grid active power and reactive variables. As a key facility coupling AC and DC distribution networks, the control information of the converter station needs to be transmitted to the dispatch center in time, and its control target value is close to the actual value, therefore, the control information of the VSC can be used as deterministic information to improve the observability of the system in the uncertainty analysis of the AC and DC distribution network.

[0090] Generally speaking, the structure of the converter itself is three-phase symmetric, and the impedance between phases has no coupling, so for the VSC equivalent model in Figure 1 There is In addition, when the VSC is connected to the AC distribution network, it can perform three-phase unbalanced compensation to make the port voltage three-phase symmetric:

[0091]

[0092] The state quantity in the above formula is changed to interval form and further expanded to obtain:

[0093]

[0094] According to the control mode of the VSC, there are the following constraint equations:

[0095]

[0096]

[0097]

[0098]

[0099] In the formula: is the set value of the DC side voltage of the VSC; is the set value of the total three-phase active and reactive power of the VSC flowing into the AC power distribution network through the AC grid connection point f; is the set value of the positive sequence voltage of the VSC to the grid connection point.

[0100] The grid connection mode of the DG has direct grid connection and grid connection through a converter. In the direct grid connection mode, the equivalent branch parameters are three-phase symmetrical, and the port voltage is three-phase symmetrical, which is similar to the grid connection through a converter. When the DG grid connection point does not install a measurement device, the output is generally obtained by a prediction method. Since it is difficult to accurately predict the instantaneous wind speed, solar radiation and other weather factors, the pseudo-measurement error obtained by prediction is much larger than the real-time measurement error. The DG output is the total three-phase power flowing into the power distribution network from the grid connection point, which is expressed in the form of an interval , and the measurement equation is:

[0101]

[0102]

[0103] 2. Three-phase interval SE model and linearization solving method

[0104] 1) Nonlinear interval SE model

[0105] In point estimation, the unified form of the measurement equation is:

[0106] z = h(x) + υ

[0107] In the formula: z is the measurement vector; h(·) is the functional relationship between the state vector and the measurement vector; and υ is the measurement error. Point estimation needs to assume the probability distribution of υ, and through a certain estimation criterion, a point in the measurement space is mapped to a point in the state space. However, in practice, this assumption may not hold.

[0108] Interval estimation is based on the theory that the error is unknown but bounded, which maps the measurement set to the state set, and the true value of the state is bounded in the set, so the estimation result has high reliability. The measurement equation in the interval form is:

[0109] [z] = h([x])

[0110] It can be seen that the measurement value is defined in [z], so the distribution of υ does not need to be considered separately.

[0111] The goal of interval estimation is to solve the upper and lower bounds of each state variable, so the following model can be established:

[0112]

[0113] In the formula: g([x]) = 0 is the operation constraint equation. The zero injection power is used as a virtual measurement, the measurement interval is 0, which can reduce the uncertainty of the state variable and improve the accuracy of state estimation.

[0114] Taking the measurement variable as the objective function, the upper and lower bounds of the measurement estimation value can be obtained:

[0115]

[0116] In order to ensure the reliability of the measurement interval, the pseudo measurement interval is generally set to be wide, and the above formula can shorten the pseudo measurement interval, and provide more accurate reference for analyzing the variables in the weak observation area of the system.

[0117] 2) Nonlinear equation scaling method based on mean value theorem

[0118] The original nonlinear optimization model comprehensively considers the upper and lower bound constraints of the measurement, the zero injection power constraint, the relationship constraint of the state variable and the control constraint of the converter, but since the model is non-convex, it cannot guarantee to obtain a global optimal solution. In order to improve the completeness of the result, the original nonlinear optimization model is converted into a linear convex optimization model.

[0119] Taking the measurement and state variable as independent variables, and using vector α to represent, then the interval of α is Wherein α = { x ; z}, Suppose the nonlinear equation is:

[0120] f(α) = 0

[0121] Take a point q0(q0∈[α]) randomly, and let the interval number [α]0= [ α , α0]∈[α], according to the mean value theorem, there exists ε∈[α]0, makes:

[0122] f(α0) = f( α )+J(ε)(α0- α )

[0123] where J(ε) is the partial derivative and J(ε) ∈ J([α]0). Thus, the above equation can be transformed as:

[0124]

[0125] Since J([α]0) ∈ J([α]), the above equation can be further scaled as:

[0126]

[0127] [α] is the known initial interval of state variables and the known measurement interval, thus in the two inequalities of the above equation, (J([α])) min / max is a constant.

[0128] Thus, the original nonlinear equality equation can be transformed into two linear constraints:

[0129]

[0130] 3) Linear interval SE model

[0131] The nonlinear equality scaling method based on the mean value theorem is used to scale the nonlinear equality in the original nonlinear optimization model and transform it into a linear optimization model:

[0132]

[0133] where h(·) is the mapping relationship between the measurement vector and the state vector; g(.) is the running constraint function; H(x) and K(x) are the partial derivatives of h(x) and g(x), respectively, x i ∈x is the state variable; z i ∈z is the measurement.

[0134] Since the nonlinear equality is scaled, the interval obtained by solving the linear interval SE model once has high conservatism, so it needs to be solved iteratively, and the specific steps are as follows:

[0135] (a) Set the initial interval of the state variable [x]0, and obtain the initial interval of the measurement [z]0 according to the measurement system;

[0136] (b) Set the iteration number l = 1;

[0137] (c) Solve the linear interval SE model to obtain the state variable interval [x] l , the measurement interval [z] l ;

[0138] (d) Compare {[x] l , [z] l} and {[x] l-1 , [z] l-1If the maximum difference in interval width is less than the convergence threshold ε, then stop the iteration; otherwise, proceed to step (e).

[0139] (e) Increment the iteration count by 1 and update (H(x)) min / max and (K(x)) min / max Proceed to step (c).

[0140] 3. Linear Interval SE Algorithm Based on State Prediction

[0141] With unchanged network structure and line parameters, the operating state of AC / DC distribution networks is affected by load power and distributed generation (DG) output power. On the one hand, in the long term, the changes in system state exhibit certain regularities. This invention modifies the two-parameter exponential smoothing method into an interval form to fit the trend of state changes. On the other hand, in shorter time periods, the system state fluctuates due to random fluctuations in load and DG power, which may lead to inaccurate prediction intervals (not including the true value). This invention designs a prediction interval correction method to identify and correct inaccurate prediction intervals, thereby helping to improve the reliability of interval SE estimation results.

[0142] The interval form of the two-parameter exponential smoothing method is:

[0143]

[0144]

[0145] [b k ] = q([a k ]-[a k-1 ])+(1-q)[b k-1 ]

[0146] In the formula: k is the sequence number of the time section; For the prediction interval; The prediction interval for the previous time segment; [x k ] represents the estimation interval; [a k ] and [b k ] is an intermediate variable; [a k-1 ] and [b k-1 ] represents the intermediate variable of the previous time segment; p and q are smoothing parameters with values ​​of [0, 1].

[0147] If the predicted interval is inaccurate, the estimated interval will inevitably not contain the true state value, and may result in an empty solution set for the interval SE. In this case, the present invention adopts the following correction scheme:

[0148] (a) Obtain the state variable conservative empirical interval according to the node voltage amplitude range [0.95, 1.05] p.u., the node voltage phase angle deviation range [-5°, +5°] and the line load flow range

[0149] (b) Take as the state search space, calculate the state interval [x k+1 ] opt by using the nonlinear interval SE model

[0150] (c) If a certain component [x k+1 ] opt of the state interval [x k+1，i ] opt is not completely contained in the predicted interval corresponding to the component , then is an inaccurate predicted interval, and all inaccurate predicted intervals are identified according to this principle

[0151] (d) Take the midpoint of [x k+1，np ] opt as the center point, take the average width of the predicted interval at the previous time section as the width, and regenerate the predicted interval instead of the original interval

[0152] It should be noted that under the premise that the measurement error interval contains the true value, although the solution of the nonlinear interval SE model is aggressive and not complete, the interval [x k+1 ] opt solved by the nonlinear interval SE model is a feasible solution that satisfies all constraints and contains the true value. Therefore, the predicted interval that cannot completely cover [x k+1 ] opt may be inaccurate, although step (c) may identify an accurate predicted interval as inaccurate, but the modified interval is accurate, and the reliability of the interval SE estimation result is not affected. The initial interval obtained from the state prediction is less conservative than the initial interval set according to subjective experience, which helps to reduce the number of iterations of the linear interval SE model and accelerate the convergence speed. The algorithm flow of the present application is shown in Figure 2 .

[0153] 4. Example analysis

[0154] 1) Example description

[0155] The test system of the present application is an AC-DC distribution network expanded from the IEEE33 node system, and the system structure is as shown in Figure 3The reference voltage of the AC distribution network is 12.66 kV, and the reference voltage of the DC distribution network is 10 kV, and the reference capacity is 10 MVA. The parameters and control mode of the VSC are shown in Table 1. The DGs are connected to the AC distribution network through the converters, wherein DG3 is a wind power system, and the remaining are photovoltaic power systems, and the grid-connected parameters are shown in Table 2. The DG in the DC distribution network is a photovoltaic power system, and the rated capacity is 400 kW. The measurement values are obtained by adding random noise on the basis of the true values of the power flow, and the maximum error of the real-time measurement (voltage amplitude, branch current amplitude, and part of the node injected power) is 5%; the maximum error of the pseudo-measurement of the load node power is 10%; and the maximum error of the pseudo-measurement of the DG output is 25%. The measurement configuration information is shown in Table 3, wherein the number of each measurement type is three-phase total.

[0156] Table 1 Parameters of VSC

[0157]

[0158] Table 2 Parameters of DG

[0159]

[0160] Table 3 Measurement configuration information

[0161]

[0162]

[0163] 2) Comparison of the algorithm of the application with point estimation based on WLS

[0164] According to the load curve and the DG output curve, 100 continuous time sections are tested, and at each time section, the point estimation based on WLS and the interval SE (forecast aided interval state estimation, FAISE) based on state prediction proposed in the application are used. The average estimation error and the maximum estimation error are used to measure the estimation accuracy of WLS:

[0165]

[0166]

[0167] In the formula, E avg and E max are the average estimation error and the maximum estimation error, respectively; N is the number of time sections; n is the number of state variables; the superscript est represents an estimated value; and the superscript true represents a true value.

[0168] For the interval SE, the true value coverage rate is used to measure the reliability, and the average interval width and the maximum interval width are used to measure the conservatism, and the calculation formula of each index is as follows:

[0169]

[0170]

[0171]

[0172] where C is the coverage of the true value, if c i，k = 1, otherwise c i，k = 0; W avg and W max are the average interval width and the maximum interval width, respectively.

[0173] The test results are shown in Table 4. It is obvious that FAISE has higher reliability and lower conservatism of the estimated interval. It can also be seen that the accuracy of the WLS estimation result is lower than that of FAISE, because the optimization objective of WLS is to make the measurement estimate close to the measurement value, which cannot guarantee that the point estimate is close to the true value of the state. In addition, WLS does not consider the upper and lower bound constraints of the measurement, which may cause the estimate of the measurement with lower weight to deviate from its true value and thus affect the result of state estimation.

[0174] Table 4 Estimation results of WLS and FAISE

[0175]

[0176] 3) Comparison of the algorithm of the present application with the Krawczyk-based linearization interval SE

[0177] The Krawczyk-based interval SE is to convert the measurement into voltage real part, imaginary part or current real part, imaginary part measurement to linearize the measurement equation. It should be noted that due to the loss of VSC and the three-phase imbalance of DG injected AC distribution network power, the control equation of VSC on the positive sequence voltage of the AC grid connection point, the power balance equation of VSC AC and DC sides considering loss, and the measurement equation of DG three-phase power and are difficult to be linearized by measurement conversion, while the linearization method in this paper does not require measurement conversion, and thus can be applied to the above equations. However, in order to objectively compare the two algorithms under the same conditions, the above constraint equations are removed in FAISE, so that the input measurements of the two interval estimators are the same. The estimated interval of the AC distribution network part state quantity and the DC distribution network state quantity is shown in Figure 4 and Figure 5 (a) in Figure 4 is the estimated interval distribution of the real part of the AC distribution network node voltage (A phase), and (b) is the estimated interval distribution of the imaginary part of the AC distribution network node voltage (C phase).

[0178] from Figure 4 andFigure 5 It can be seen that the interval range solved by FAISE is smaller than that solved by Krawczyk at any node. Through analysis, it can be known that since FAISE solves the intervals of both the measurement and the state at each iteration, and the reduction of the measurement interval helps to further reduce the state interval, therefore, FAISE can effectively alleviate the conservativeness of the uncertain state interval. It can be predicted that if the measurement that cannot be linearized by Krawczyk algorithm is added in FAISE, the conservativeness of the estimated interval will be further reduced, which shows that the linear interval SE model proposed in the application has certain superiority.

[0179] 4) Convergence performance and calculation efficiency

[0180] The real-time measurement of the distribution network is mainly the branch current, the number of real-time measurement of the amplitude of the branch current of the alternating distribution network is changed, and the convergence performance of the algorithm of the application is researched. It should be noted that when the upper and lower bounds of the state quantity and the measurement quantity of the AC-DC distribution network are solved by using the linear interval SE model proposed in the application, although the objective functions are different, the constraints are the same, therefore, all the linear optimization models in each iteration can be solved in parallel. Take ε = 10 -4 , Figure 6 The change of the average interval width of the real part of the AC node voltage in the iteration process under different real-time measurement configurations is shown. Figure 6 It can be seen that the less the number of branch current measurement is, the less the iteration number is, but the final estimated interval width is larger. When the number of current measurement is increased to 15 × 3, the reduction amplitude of the average width of the estimated interval is small, and the iteration number is gradually increased. It shows that it is not necessary to configure a large number of real-time measurements of branch currents, for the example, when the number of configuration is 15 × 3, a relatively narrow estimated interval can be obtained with a smaller iteration number.

[0181] Figure 6 The calculation time under each measurement configuration in the application is shown in Table 5. It can be seen from Table 5 that the calculation time of the algorithm of the application is less than 3s, which can meet the requirements of the state estimation of the distribution network.

[0182] Table 5 Iteration number and calculation time under different measurement configurations

[0183]

Claims

1. A state prediction based linear interval state estimation method for AC / DC distribution network, characterized in that, The method comprises the following steps: (1) establishing a three-phase model of the AC-DC distribution network according to parameter information of the AC-DC distribution network; (2) expressing the measurements and state variables in interval form, and establishing a nonlinear interval state estimation model of the AC-DC distribution network according to the measurement equations and operation constraints; (3) predicting the state interval at the current time according to the historical state by using an interval form of the two-parameter exponential smoothing method to obtain a predicted interval; (4) converting the nonlinear interval state estimation model of the AC-DC distribution network into a linear interval state estimation model by using a nonlinear equation scaling method based on the mean value theorem, taking the predicted interval as the initial interval of the state variable, and taking the measurement interval obtained by sampling the measurement system as the initial interval of the measurement variable, and inputting the linear interval state estimator; (5) if the state interval output by the linear interval state estimator is not empty, step (6) is performed, and if the state interval output by the linear interval state estimator is empty, an experience interval of the state variable is obtained according to the range of the node voltage amplitude, the range of the node voltage phase angle deviation and the range of the line load flow, the experience interval of the state variable is input into the nonlinear state estimator to obtain a first state interval, the first state interval and the predicted interval are compared, if the predicted interval of a state is not completely contained in the first state interval, a second state set is calculated, then a new predicted interval of the second state set is regenerated with the midpoint of the interval of the second state set output by the nonlinear interval estimator as the center point and the average width of the predicted interval of the second state set at each time section as the interval width, and the new predicted interval and the measurement interval are input into the linear interval state estimator, and the linear interval state estimator outputs a new state interval and a measurement interval; the second state set refers to a state set with an inaccurate predicted interval; (6) the state interval and the measurement interval output by the linear interval state estimator are input into the linear interval state estimator again, and the linear interval state estimator outputs an updated state interval and a measurement interval; (7) step (6) is repeated until the width of the state interval and the measurement interval no longer further decreases.

2. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The parameter information in step (1) comprises topological information of the AC-DC distribution network, branch impedances, equivalent impedances of the voltage source converters and control modes of the voltage source converters.

3. The state prediction based linear interval state estimation method for AC / DC hybrid distribution network according to claim 2, characterized in that: The control mode of the voltage source converter is a master-slave control mode, one converter station is taken as a master converter station to control the DC side node voltage and the reactive power at the AC grid-connected side, and the remaining converter stations are taken as slave converter stations to control the active power and the reactive power at the AC grid-connected side; the reactive power refers to the AC grid-connected side voltage or the AC grid-connected side reactive power.

4. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The interval form in step (2) is: where: [x] is an interval number; x and are the upper and lower bounds of x, respectively.

5. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The measurement equation in step (2) is a calculation formula of the measurement with respect to the state variable; the operation constraints comprise relationship constraints between the state variables, control constraints of the voltage source converters, power balance constraints of the AC-DC sides of the voltage source converters, and three-phase symmetry constraints of the AC outlet nodes of the voltage source converters; and the nonlinear interval state estimation model of the AC-DC distribution network is: min / max x i or min / max z i where: x i ∈x is a state variable; is a quantity measurement; h(·) is a mapping relationship of the quantity measurement and the state variable; g([x]) = 0 is a running constraint equation.

6. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The interval form of the two-parameter exponential smoothing method in step (3) is: [b k ] = q([a k ] - [a k-1 ]) + (1 - q)[b k-1 ] where k is the index of the time slice; is the prediction interval for the current time slice, is the prediction interval for the previous time slice;[x k ] is the estimation interval;[a k ] and [b k ] are intermediate variables,[a k-1 ] and [b k-1 ] are intermediate variables for the previous time slice; p and q are smoothing parameters, taking values in [0, 1].

7. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The nonlinear equation scaling method based on the mean value theorem in step (4) is: Let the original nonlinear equation be: f(α)＝0 The original nonlinear equation is converted into two linear constraints: In the formula, the vector a represents the independent variable, and the interval of a is (J([a])) min , (J([a])) max are the minimum and maximum values of the partial derivative of f(a) with respect to a, respectively.

8. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The linear interval state estimation model in step (4) is: min / max x i or min / max z i where h(·) is the mapping from the state vector to the measurement vector; g(·) is the running constraint function; H(x) and K(x) are the partial derivatives of h(x) and g(x) respectively, x i ∈x is the state variable; z i ∈z is the measurement variable, x and are the upper and lower bounds of x, respectively, z and are the upper and lower bounds of z, respectively.

9. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The node voltage amplitude range in step (5) is [0.95, 1.05] p.u., and the node voltage phase angle deviation range is [-5°, +5°].

10. The state prediction based linear interval state estimation method for AC / DC distribution network according to claim 1, characterized in that: The criterion that the width of the state interval and the measurement interval is no longer further reduced in step (7) is: In the formula, x is a state variable, z is a measurement, l is the serial number of the iteration times, and ε is a preset convergence threshold.

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