System parameter estimation method and estimation device

Abstract

To suppress the estimation error of apparent system parameters.SOLUTION: A method for estimating apparent system parameters when viewing a power system from an inverter connected to the power system at an interconnection point includes fitting V2 or V in the form of α×P+β×Q+γ using the least squares method with weight w, where P is active power, Q is reactive power, w is a weight that decreases as the apparent power increases, V is the voltage at the interconnection point, and α, β, and γ are coefficients, to estimate the system parameters.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a system parameter estimation method and an estimation device. [Background technology]

[0002] Conventionally, there has been known a method of estimating the impedance of an existing power system by varying the active power and reactive power output to a point of interconnection with the existing power system that supplies power to a load (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 4371062 Summary of the Invention [Problem to be solved by the invention]

[0004] However, in the conventional technology, the power system impedance is estimated by assuming that the voltage at the interconnection point changes in proportion to the active power and the reactive power, which may result in a large estimation error.

[0005] The present disclosure provides a system parameter estimation method and estimation device that can reduce estimation errors in apparent system parameters. [Means for solving the problem]

[0006] The present disclosure provides: A method for estimating apparent system parameters when viewing a power system from an inverter connected to the power system at a connection point, comprising: When P is the active power, Q is the reactive power, w is the weight that decreases as the apparent power increases, V is the voltage at the interconnection point, and α, β, and γ are coefficients, V 2Alternatively, the present invention provides a system parameter estimation method for estimating the system parameters by fitting V in the form of α×P+β×Q+γ using the least squares method with weight w.

[0007] The present disclosure also provides: An estimation device that estimates apparent system parameters when viewing a power system from an inverter that is connected to the power system at a connection point, comprising: When P is the active power, Q is the reactive power, w is the weight that decreases as the apparent power increases, V is the voltage at the interconnection point, and α, β, and γ are coefficients, V 2 Alternatively, an estimation device is provided that has a calculation circuit that estimates the system parameters by fitting V in the form of α×P+β×Q+γ using the least squares method with weight w. [Effects of the Invention]

[0008] According to the present disclosure, it is possible to suppress estimation errors in apparent system parameters. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 2 is a diagram showing a state in which a grid-connection inverter is connected to a power grid. [Figure 2] FIG. 10 is an equivalent diagram for explaining a method for estimating system parameters. [Figure 3] FIG. 10 is a characteristic diagram of an example of weight w. [Figure 4] FIG. 10 is a diagram showing an example of a plurality of data (P, Q) used during a simulation. DETAILED DESCRIPTION OF THE INVENTION

[0010] The following describes the embodiments.

[0011] 1 is a diagram showing a state in which a grid-connection inverter 5 is connected to a power system 1. When a grid-connection inverter 5 is connected to a power system 1, the actual power system 1 includes a large number of generators or loads.

[0012] The estimation device 7 according to this embodiment estimates apparent system parameters, which are how the power system 1 looks when viewed from the inverter 5 in a state where the inverter 5 is interconnected to the power system 1 at the interconnection point 3. Specific examples of apparent system parameters include the system impedance Z (=R+jX) of the power system 1, the voltage of the power system 1 (system voltage V g ) When the system impedance Z is expressed as a complex number such as R+jX, the real part is called the electrical resistance R of the power system 1, and the imaginary part is called the reactance of the power system 1. The estimation device 7 is a device that can estimate these apparent system parameters using a simple method and suppress the estimation error.

[0013] The estimation device 7 has a calculation circuit that estimates apparent system parameters when the power system 1 is viewed from the inverter 5 connected to the power system 1 at the connection point 3. The functions of the calculation circuit are realized by a processor such as a CPU (Central Processing Unit) operating according to a program stored in a memory. The functions of the estimation device 7 may also be realized by an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integrated Circuit).

[0014] Fig. 2 is an equivalent diagram for explaining a method for estimating system parameters. P is the active power output from the inverter 5 to the interconnection point 3, Q is the reactive power output from the inverter 5 to the interconnection point 3, V is the voltage at the interconnection point 3 (interconnection point voltage), and δ is the system voltage V g is the phase difference of the interconnection point voltage V relative to

[0015] In this case, the complex power is expressed as the product of the voltage expressed in phasor and the complex conjugate of the current expressed in phasor, so

[0016]

number

[0017] If we separate Equation 1 into real and imaginary parts, we get

[0018]

number

[0019] Since the phase difference δ when looking at the power grid 1 from the inverter 5 is unknown, sin 2 δ+cos 2 Eliminating the phase difference δ using the equation δ=1, we get

[0020]

number

[0021] Rearranging equation 4, we get

[0022]

number

[0023] R, X and V that always satisfy this equation 5 g However, as is clear from Equation 5, R, X and V g If is an unknown fixed value, the interconnection point voltage V changes nonlinearly with respect to P and Q. Therefore, it is difficult to find R, X, and Vg that satisfy Equation 5 with high accuracy.

[0024] However, (P 2 +Q 2 ) is small, approximately,

[0025]

number

[0026] R, X, and V g If this approximation can be used to estimate V 2 By fitting the equation as a linear equation of P and Q (α×P×β×Q+γ), the system parameters (i.e., R, X, and V g ) can be estimated. α, β, γ are coefficients (α=2R, β=2X, γ=V g 2 ).

[0027] However, Equation 6 (P 2 +Q 2 ) is small, so fitting Equation 6 using the ordinary least squares method gives R, X, and V g There is a risk that the estimation error will be large.

[0028] Therefore, the estimation device 7 according to this embodiment uses (P 2 +Q 2 ) is larger, the weight w becomes smaller (approaching zero). By fitting Equation 6 using the "weighted least squares" method, the system parameters (i.e., R, X, and V g ) is estimated. The weight w is calculated by fitting using the least squares method. 2 +Q 2 When ) is large, it has the effect of neglecting the third term on the left side of Equation 5. The weight w is 2 +Q 2 ) is a value that decreases as the apparent power output from the inverter 5 increases, so it can be said that the weight decreases as the apparent power output from the inverter 5 increases. The estimation device 7 fits Equation 6 using the least squares method with weight w, thereby estimating the system parameters with simple calculations and suppressing the estimation error.

[0029] When fitting is performed in the form of Equation 6, it is required to prepare three or more different data points (P, Q, V). However, even if there are three or more points, if (P, Q) are in a linear relationship (the power factor is fixed), three or more independent equations cannot be obtained, and fitting is not possible. For this reason, three or more different data points that do not result in a constant power factor are used for fitting. In other words, this condition is met when the rank of the matrix in which the vectors (P, Q, 1) are arranged is three.

[0030] Next, a specific example of fitting will be described.

[0031] The data of the i-th point (active power P, reactive power Q, interconnection point voltage V) used in the estimation by the above fitting is (P i ,Q i ,V i ) and y i =V 2 Furthermore, (P i ,Q i ) is determined based on the magnitude of the weights w for the weighted least squares operation. i Let's say.

[0032] Error (y i -(α×P i +β×Q i +γ)) weight w i The sum of squares E is

[0033]

number

[0034] To find α, β, and γ that minimize E,

[0035]

number

[0036] Equation 8 can be expressed as a determinant:

[0037]

number

[0038] The estimation device 7 calculates three or more different data points (P i ,Q i ,V i ) to calculate Equation 9, and estimate α, β, and γ. R=α / 2,X=β / 2,V g Therefore, the estimation device 7 uses the estimated α, β, or γ to calculate the system parameters (R, X, or V g ) can be easily estimated.

[0039] The estimation device 7 may, for example, estimate α, β, or γ (or R, X, or V g ) and adjusts the control conditions or output of the inverter 5. The estimation device 7 uses the estimated α, β, or γ (or R, X, or V g ) may be used to derive the power factor of the inverter 5.

[0040] An example of an equation that defines the weight w is Equation 10.

[0041]

number

[0042] FIG. 3 is a characteristic diagram of an example of the weight w, showing the change in the weight w expressed by Equation 10. Note that the equation defining the weight w is not limited to Equation 10, and can be expressed as (P2 +Q 2 ) or the weight w may be reduced as the apparent power increases.

[0043] Next, an example of the results of simulating the above estimation method will be shown.

[0044] In this simulation, V and V are defined by P, Q, R, X and PU values ​​normalized by the device capacitance. g R=0.20, X=0.30, V g = 1.050" and the interconnection point voltage V when P and Q are varied is given by the solution of equation 5 above.

[0045] As shown in FIG. 4, when a plurality of data (P, Q, V) are used when (P, Q) is varied and the weight w is expressed by the above equation 10 (λ=100), the estimation device 7 solves the equation expressed by the above equation 9, thereby α=0.387, β=0.605, γ=1.103 The estimation device 7 calculates these derived α, β, and γ as R=α / 2, X=β / 2, and V g = √γ, R = 0.193, X = 0.303, V g In this way, the estimation device 7 estimates that the above set values ​​"R=0.20, X=0.30, V g =1.050" can be estimated almost accurately.

[0046] As a comparison example, when calculating with w=1 (no weighting), α=0.357, β=0.626, γ=1.105 R=0.178,X=0.313,V g =1.051 The result is as follows: The estimation error is suppressed when there is weight w compared to when there is no weight w.

[0047] In the above embodiment, the linear equation "V 2The system parameters are estimated by fitting the equation "=α×P×β×Q+γ" using the least squares method with weights w (α=2R, β=2X, γ=V g 2 ). However, "V 2 As a variant, instead of "V = α × P × β × Q + γ", the system parameters may be estimated by fitting using the least squares method with weight w in the form of "V = α × P × β × Q + γ" (α = R, β = X, γ = V g ).

[0048] In this modified example, the α, β, and γ that minimize E in the above equation 7 are found in the same manner as in the above embodiment. 2 +Q 2 ) is larger, the smaller the value may be, as in the above embodiment.

[0049] Although the embodiments have been described above, they are presented as examples and the present invention is not limited to the above embodiments. The above embodiments can be implemented in various other forms, and various combinations, omissions, substitutions, modifications, etc. can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as set forth in the claims. [Explanation of symbols]

[0050] 1 Power system 3 interconnection points 5 inverters 7 Estimation device

Claims

1. A method for estimating apparent system parameters when viewing a power system from an inverter connected to the power system at a connection point, comprising: When P is the active power, Q is the reactive power, w is the weight that decreases as the apparent power increases, V is the voltage at the interconnection point, and α, β, and γ are coefficients, V ２ Alternatively, the system parameter estimation method estimates the system parameters by fitting V in the form of α×P+β×Q+γ using the least squares method with weight w.

2. The data (P ｉ , Q ｉ , V ｉ 2. The system parameter estimation method according to claim 1, wherein the conditions are that the number of different points is three or more and the power factor is not constant.

3. The system parameters include the electrical resistance R of the power system, the reactance X of the power system, or the voltage V of the power system. ｇ and Based on the α, β, and γ obtained by the above estimation, R, X, or V ｇ The system parameter estimation method according to claim 2, further comprising estimating

4. V ２ is in the form of α×P+β×Q+γ, R=α / 2, X=β / 2, V ｇ 4. The system parameter estimation method according to claim 3, wherein:

5. Let V be of the form α×P+β×Q+γ, R = α, X = β, V ｇ The system parameter estimation method according to claim 3, wherein γ is set to γ.

6. 6. The system parameter estimation method according to claim 1, wherein the weight w is expressed by the following equation, where λ is a number greater than 1: [Equation 1]

7. An estimation device that estimates apparent system parameters when viewing a power system from an inverter that is connected to the power system at a connection point, comprising: When P is the active power, Q is the reactive power, w is the weight that decreases as the apparent power increases, V is the voltage at the interconnection point, and α, β, and γ are coefficients, V ２ or V in the form of α×P+β×Q+γ using a least squares method with weight w, thereby estimating the system parameters.

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