METHOD FOR GRID IMPEDANCE AND DYNAMICS ESTIMATION

Abstract

Estimating components of a grid impedance, Z, of a power grid being coupled to a power generating unit at a point of interconnection is disclosed. A voltage, Vmeas, across the point of interconnection; an active current, IP, and/or an active power, P, delivered by the power generating unit to the power grid; and a reactive current, IQ, and/or a reactive power, Q, delivered by the power generating unit are determined. A parameter estimation vector is estimated using a recursive adaptive filter algorithm, and on the basis of Vmeas, IP, P, IQ and/or Q. A model representation of the power grid is created on the basis of the parameter estimation vector, and a system DC gain vector for the power grid is calculated, using the model representation. Finally, Z, and/or a resistance, R, of Z, and/or a reactance, X, of Z, is derived from the system DC gain vector.

Claims

1. A method for estimating components of a grid impedance, Z, of a power grid coupled to a power generating unit at a point of interconnection, the method comprising: determining a voltage, V.sub.meas, across the point of interconnection; an active current, I.sub.P, and/or an active power, P, delivered by the power generating unit to the power grid; and a reactive current, I.sub.Q, and/or a reactive power, Q, delivered by the power generating unit to the power grid; estimating a parameter estimation vector using a recursive adaptive filter algorithm, and on the basis of the determined voltage, V.sub.meas, and the determined active current, I.sub.P, and/or active power, P; and the reactive current, I.sub.Q, and/or the reactive power, Q, the parameter estimation vector defining a set of estimated model parameters for a selected model of system response of the power grid; creating a model representation of the power grid on the basis of the parameter estimation vector, and by applying the set of parameters of the parameter estimation vector to the selected model; calculating a system DC gain vector for the power grid, using the model representation, the DC gain vector representing a correlation between voltage, V.sub.meas, on the one hand, and active current, I.sub.P, and/or active power, P; and reactive current, I.sub.Q, and/or reactive power, Q, on the other hand, at steady state of the power grid; and deriving the grid impedance, Z, and/or a resistance, R, of the grid impedance, Z, and/or a reactance, X, of the grid impedance, Z, from the system DC gain vector, where Z=R+jX.

2. The method of claim 1, wherein the determining a voltage, V.sub.meas, across the point of interconnection; an active current, I.sub.P, and/or an active power, P, delivered by the power generating unit to the power grid; and a reactive current, I.sub.Q, and/or a reactive power, Q, delivered by the power generating unit to the power grid comprises measuring the voltage, V.sub.meas, the active current, I.sub.P, the active power, P, the reactive current, I.sub.Q and/or the reactive power, Q.

3. The method of claim 1, wherein the recursive adaptive filter algorithm is a recursive least square algorithm.

4. The method of claim 1, wherein the recursive adaptive filter algorithm is a Kalman algorithm.

5. The method of claim 1, wherein the model representation of the power grid is a state space representation.

6. The method of claim 5, wherein the creating a model representation of the power grid comprises creating a state space representation of the form: $\begin{array}{c}\stackrel{.}{x}\left(t\right)=\mathrm{Ax}\left(t\right)\mathrm{Bu}\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+\mathrm{Du}\left(t\right),D=0\end{array}$ $\Downarrow$ $\begin{array}{c}{\stackrel{.}{x}}_1\left(t\right)\\ {\stackrel{.}{x}}_2\left(t\right)\end{array}=\left[\begin{array}{cc}a1& a2\\ a3& a4\end{array}\right]\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]+\left[\begin{array}{cc}b1& b2\\ b3& b4\end{array}\right]\left[\begin{array}{c}{I}_P\left(t\right)\\ I_Q\left(t\right)\end{array}\right]y\left(t\right)=\begin{array}{cc}[c1& c2]\end{array}\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\end{array}\right],y\left(t\right)=V_Z\left(t\right)+V_{\mathrm{dyn}}\left(t\right),$ where A, B, C and D are matrixes, and wherein the step of estimating a parameter estimation vector comprises estimating parameters for the matrixes A, B, C and D.

7. The method of claim 6, wherein the calculating a system DC gain vector comprises applying the formula:
K.sub.DC=D−CA.sup.−1B, where K.sub.DC is the system DC gain vector, and A, B, C and D are the matrixes of the state space representation.

8. The method of claim 1, further comprising the step of deriving a damping ratio, ζ, and/or an oscillation frequency, ω.sub.n, for voltage dynamics of the power grid on the basis of the model representation of the power grid.

9. The method of claim 8, wherein the voltage dynamics of the power grid comprises machine dynamics in the power grid.

10. The method of claim 1, wherein the deriving the grid impedance, Z, and/or the resistance, R, of the grid impedance, Z, and/or the reactance, X, of the grid impedance, Z, comprises deriving an X/R ratio on the basis of the resistance, R, and the reactance, X, of the grid impedance, Z.

11. The method of claim 1, wherein the power generating unit forms part of a renewable power plant, the method further comprising the step of controlling the power generating unit to provide a power feed into the power grid, based on the estimated grid impedance, Z, and/or the resistance, R, of the grid impedance, Z, and/or the reactance, X, of the grid impedance, Z.

12. The method of claim 11, wherein the controlling the power generating unit comprises controlling the active current, I.sub.P, and/or the active power, P, delivered by the power generating unit to the power grid; and the reactive current, I.sub.Q, and/or the reactive power, Q, delivered by the power generating unit to the power grid.

13. The method of claim 1, wherein the power generating unit is a wind turbine generator.

14. The method of claim 1, wherein the deriving the grid impedance, Z, and/or the resistance, R, of the grid impedance, Z, and/or the reactance, X, of the grid impedance, Z, comprises deriving an absolute value of the grid impedance, |Z|, using the formula:
|Z|=√{square root over (R.sup.2+X.sup.2)}.

15. The method of claim 1, wherein an angle, θ, of the grid impedance, Z, is derived on the basis of the resistance, R, and the reactance, X, of the grid impedance, Z, using the formula: $\theta ={\tan }^{-1}\left(\frac{X}{R}\right).$

16. A renewable power plant comprising a plurality of power generating units, coupled to a power grid at a point of interconnection, wherein at least one of the power generating units is adapted to provide a power feed into the power grid, based on a grid impedance, Z, a resistance, R, of a grid impedance, Z, and/or a reactance, X, of a grid impedance, Z, wherein the grid impedance, Z, the resistance, R, and/or the reactance, X, have been estimated in accordance with an operation of estimating components of the grid impedance, Z, of the power grid, comprising: determining a voltage, V.sub.meas, across the point of interconnection; an active current, I.sub.P, and/or an active power, P, delivered by the power generating unit to the power grid; and a reactive current, I.sub.Q, and/or a reactive power, Q, delivered by the power generating unit to the power grid; estimating a parameter estimation vector using a recursive adaptive filter algorithm, and on the basis of the determined voltage, V.sub.meas and the determined active current, I.sub.P, and/or active power, P; and the reactive current, I.sub.Q, and/or the reactive power, Q, the parameter estimation vector defining a set of estimated model parameters for a selected model of system response of the power grid: creating a model representation of the power grid on the basis of the parameter estimation vector, and by applying the set of parameters of the parameter estimation vector to the selected model: calculating a system DC gain vector for the power grid, using the model representation, the DC gain vector representing a correlation between voltage, V.sub.meas, on the one hand, and active current, I.sub.P, and/or active power, P; and reactive current, I.sub.Q, and/or reactive power, Q, on the other hand, at steady state of the power grid; and deriving the grid impedance, Z, and/or a resistance, R, of the grid impedance, Z, and/or a reactance, X, of the grid impedance, Z, from the system DC gain vector, where Z=R+jX.

17. A renewable power plant according to claim 16, wherein the power generating unit is a wind turbine generator.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The invention will now be described in further details with reference to the accompanying drawings, in which

[0086] FIG. 1 is a schematic diagram illustrating a power grid comprising a voltage source and a grid impedance, Z, which is estimated using a method according to an embodiment of the invention,

[0087] FIG. 2 is a block diagram illustrating a method according to an embodiment of the invention,

[0088] FIG. 3 is a flow chart illustrating a method according to an embodiment of the invention, and

[0089] FIG. 4 is a block diagram illustrating a state space model for use in a method according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

[0090] FIG. 1 is a schematic diagram illustrating a power grid 1 comprising a voltage source 2 and a grid impedance, Z. The voltage source 2 has a voltage as a sum of the voltages, V.sub.n and V.sub.dyn, wherein V.sub.n is a nominal voltage normally provided by a grid operator, and V.sub.dyn represents an oscillating voltage related to voltage dynamics 4 of the power grid 1.

[0091] The grid impedance, Z, is of the complex form Z═R+jX, wherein R is a real part of the grid impedance, Z, representing a resistive part of the grid impedance, Z. Similarly, X is an imaginary part of the grid impedance, Z, representing a reactive part of the grid impedance, Z. Thereby the grid impedance, Z, is represented by a resistance, R, and a reactance, X. There is a voltage, V.sub.Z, across the grid impedance, Z.

[0092] The voltage dynamics 3 of the power grid 1 are represented by an oscillation frequency, ω.sub.n, and a damping ratio, ζ. The damping ratio, describes the ability of a system to oppose the oscillatory nature of the system's transient response. Furthermore, the oscillation frequency, ω.sub.n, describes the frequency at which the voltage dynamics 3 oscillate. Thus, the voltage dynamics 3 of the power grid 1 may be used for gaining knowledge of the transient period of the voltage dynamics 3, how much the voltage dynamics 3 are damped, and when the voltage dynamics 3 reach steady state. Moreover, the oscillating voltage, V.sub.dyn, indicates an amplitude of the voltage dynamics. Thus, V.sub.dyn could, e.g., be estimated from the damping ratio, ζ, and oscillation frequency, ω.sub.n.

[0093] A voltage, V.sub.meas, is determined across a point of interconnection 4, e.g. by direct measurement. The point of interconnection 4 is the physical interface between the power grid 1 and a power generating unit (not shown) which delivers power to the power grid 1. Thereby the voltage, V.sub.meas, is a measure of the voltage between the power grid 1 and the rest of the power system, notably the power generating unit. The voltage, V.sub.meas, can further be represented as the sum of all voltages of the power grid 1, i.e. V.sub.meas=V.sub.dyn+V.sub.n+V.sub.z.

[0094] Furthermore, an active current, I.sub.P, and/or an active power, P, delivered by the power generating unit to the power grid 1 is/are determined, e.g. by direct measurement. Further, a reactive current, I.sub.Q, and/or a reactive power, Q, delivered by the power generating unit to the power grid 1 is/are also determined, e.g. by direct measurement. The active current, I.sub.P, as well as the active power, P, represents the active part of the power which the power generating unit provides to the power grid 1. Similarly, the reactive current, I.sub.Q, as well as the reactive power, Q, represents the reactive part of the power which the power generating unit provides to the power grid 1.

[0095] Thus, information regarding the voltage across the point of interconnection 4, in the form of V.sub.meas, the active power provided by the power generating unit, in the form of I.sub.P and/or P, and the reactive power provided by the power generating unit, in the form of I.sub.Q and/or Q, is now available.

[0096] The voltage, V.sub.meas, and the active current, I.sub.P, and/or the active power, P; and the reactive current, I.sub.Q, and/or the reactive power, Q, are then used for estimating the grid impedance, Z. This could, e.g., include estimating the grid impedance, Z, itself, and/or estimating the resistance, R, and/or the reactance, X. This could, e.g., be done in the following manner.

[0097] The oscillating voltage, V.sub.dyn, is derived on the basis of the voltage dynamics 3, and the nominal voltage, V.sub.n, is provided by the grid operator. Then the voltage, V.sub.Z, across the grid impedance, Z, is calculated from the measured voltage, V.sub.meas, as V.sub.Z=V.sub.meas−V.sub.n−V.sub.dyn. Finally, the grid impedance, Z, can be estimated by applying Ohm's Law and using V.sub.Z and the determined active current, I.sub.P, and/or active power, P; and the determined reactive current, I.sub.Q, and/or reactive power, Q.

[0098] FIG. 2 is a block diagram illustrating a method according to an embodiment of the invention. A number of input parameters, in the form of V.sub.meas, I.sub.P, P, I.sub.Q, and/or Q, which have previously been determined, e.g. in the manner described above with reference to FIG. 1, are fed to an estimator 5.

[0099] In the estimator 5, a parameter estimation vector is estimated, based on the input parameters, and using a recursive adaptive filter algorithm, such as a recursive least square algorithm and/or a Kalman algorithm. The parameter estimation vector defines a set of estimated model parameters for a selected model of system response of the power grid. Furthermore, the estimator 5 creates a model representation based on the selected model and the parameter estimation vector, by applying the set of parameters of the parameter estimation vector to the selected model. The model representation is a state space representation of the power grid, which is a mathematical model of the physical system as a set of input, output and state variables. Thus, the model representation depends on the parameter estimation vector, and thereby on changes in voltage and current and/or power parameters which formed the basis of the parameter estimation vector.

[0100] The estimator 5 outputs the model representation, which is used as an input to DC gain vector analyser 6 and an Eigen values analyser 7.

[0101] The DC gain vector analyser 6 calculates a DC gain vector for the power grid 1, using the model representation. Thus, changes in the model representation will be reflected in the calculated DC gain vector. Accordingly, changes in the determined voltage, current and/or power parameters are also reflected in the DC gain vector. The DC gain vector represents a correlation between voltage, on the one hand, and active and reactive power in the other hand, when the power grid is in a steady state.

[0102] The DC gain vector analyser 6 uses the DC gain to derive a grid impedance, Z, and/or a resistance, R, of the grid impedance, Z, and/or a reactance, X, of the grid impedance, Z, from the DC gain vector. For this reason, any changes in the calculated DC gain vector and in the determined voltage, current and/or power parameters will be reflected in the derived grid impedance, Z, and/or a resistance, R, of the grid impedance, Z, and/or a reactance, X, of the grid impedance, Z. Furthermore, this is an easy and fast manner of estimating the grid impedance, and accordingly the system may react fast to any changes in the grid impedance.

[0103] The derived grid impedance, Z, resistance, R, and/or a reactance, X, may further be used for deriving a short circuit ratio (SCR) of the power grid 1, a X/R ratio, an absolute value of the grid impedance, |Z|, and an angle, θ, of the grid impedance, Z.

[0104] The Eigen values analyser 7 derives a damping ratio, ζ, and an oscillation frequency, ω.sub.n, on the basis of the model representation. The damping ratio, ζ, and the oscillation frequency, ω.sub.n, represent the voltage dynamics 4 of the power grid 1, and could, e.g., be used for estimating an oscillating voltage, V.sub.dyn, of the power source 2 of the power grid 1, as described above with reference to FIG. 1.

[0105] Thus, based on the input parameters V.sub.meas, I.sub.P, P, I.sub.Q, and/or Q, an estimation is performed by the estimator 8. The estimator 8 estimates a parameter estimation vector and creates a model representation based on the parameter estimation vector. The model representation is used as an input to the DC gain vector analyser 6 and the Eigen values analyser 7.

[0106] FIG. 3 is a flow chart illustrating a method according to an embodiment of the invention. The method is initiated by a first step 8, in which a voltage, V.sub.meas, an active current, I.sub.P, and/or an active power, P; and a reactive current, I.sub.Q, and/or a reactive power, Q, are determined. V.sub.meas, I.sub.P, and/or P; and I.sub.Q, and/or Q may be determined in the manner described above with reference to FIG. 1.

[0107] In a second step 9, a parameter estimation vector is estimated using a recursive adaptive filter algorithm, such as a recursive least square algorithm or a Kalman algorithm, and on the basis of V.sub.meas, I.sub.P, and/or P; and I.sub.Q, and/or Q, e.g. in the manner described above with reference to FIG. 2.

[0108] In a third step 10, a model representation is created on the basis of the parameter estimation vector, e.g. in the manner described above with reference to FIG. 2.

[0109] In a fourth step 11, the model representation is used for calculating a system DC gain vector, e.g. in the manner described above with reference to FIG. 2.

[0110] In a fifth step 12, a grid impedance, Z, and/or a resistance, R, of the grid impedance, Z, and/or a reactance, X, of the grid impedance, Z, is derived, e.g. in the manner described with reference to FIGS. 1 and 2.

[0111] FIG. 4 is a block diagram illustrating a state space model for use in a method according to an embodiment of the invention, in the form of a multiple input, single output model. An input, u(k), representing active and reactive current of the system, is input to the state space model, and an output, y(k), representing voltage, V.sub.meas, is output by the state space model. A, B, C and D represent static and dynamic behaviour of the system, and may be in the form of suitable matrixes. A parameter estimation vector defines parameters to be applied to the matrixes in order to create a model representation of the actual power grid.

[0112] The model representation of FIG. 4 is of the form:

[00005]$\begin{array}{c}\stackrel{.}{x}\left(t\right)=\mathrm{Ax}\left(t\right)\mathrm{Bu}\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)+\mathrm{Du}\left(t\right),D=0\end{array}$$\Downarrow$$\begin{array}{c}{\stackrel{.}{x}}_1\left(t\right)\\ {\stackrel{.}{x}}_2\left(t\right)\end{array}=\left[\begin{array}{cc}a1& a2\\ a3& a4\end{array}\right]\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]+\left[\begin{array}{cc}b1& b2\\ b3& b4\end{array}\right]\left[\begin{array}{c}{I}_P\left(t\right)\\ I_Q\left(t\right)\end{array}\right]y\left(t\right)=\begin{array}{cc}[c1& c2]\end{array}\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\end{array}\right],y\left(t\right)=V_Z\left(t\right)+V_{\mathrm{dyn}}\left(t\right)$

[0113] The matrix A represents dynamics of the system, the matrixes B and C represent gain of the system, B being an input matrix and C being an output matrix, and the matrix D represents feedforward of the system, which may be set to zero and thereby not taken into account.