Methods for network impedance and dynamics estimation

Abstract

A method for estimating the grid impedance Z component of a power grid (1) coupled to a power generation unit at an interconnection point (4) is disclosed. The voltage V across the interconnection point (4) meas ; the active current I delivered by the power generation unit to the power grid (1) P and / or the active power P; and the reactive current I delivered by the power generation unit to the power grid (1) Q and / or the reactive power Q are determined. A recursive adaptive filter algorithm is used, and based on V meas , I P , P, I Q and / or Q, a parameter estimation vector is estimated. Based on the parameter estimation vector, a model representation of the power grid (1) is created, and using the model representation, a system DC gain vector for the power grid (1) is calculated. Finally, the grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z are derived from the system DC gain vector.

Description

Technical Field

[0001] The invention relates to a method for estimating a component of a grid impedance. Furthermore, the invention relates to an arrangement for controlling the feeding of power into a grid based on the estimated component of the grid impedance. Background Art

[0002] The electrical grid relies on power feeds from power generating units. The amount of power feed required to the grid is determined by the grid impedance, which therefore determines the amount of active and reactive power fed into the grid. Methods for estimating grid impedance are known in the art, for example, the grid impedance can be estimated by a Thévenin equivalent model of the grid. However, Thévenin's theorem is only applicable to linear grids. Furthermore, the grid impedance of a grid often changes over time due to grid variations and may therefore have to be recalculated.

[0003] US 2015 / 0025860 discloses a method for estimating grid characteristics of a grid coupled to a generator at a common coupling point. The grid characteristics are estimated by a grid model using voltage, current and the phase angle between the voltage and current at the common coupling point as input parameters. The input parameters are used in equations solved at at least three different operating points.

[0004] EP 2 688 172 discloses a method for controlling the operation of an electric power system. The method measures the change in the measured local voltage when reactive power is injected into the electric power system to increase the system voltage, or absorbed from the electric power system to reduce the system voltage. Thus, the change in the local voltage due to the change in reactive power generation or absorption is an indication of the system impedance and therefore also allows the short circuit ratio (SCR) to be calculated.

[0005] EP 1 841 037 A2 discloses a method for determining a parameter value associated with an electrical network. The electrical network has an interconnection point, where the electrical network is electrically coupled to a power source. The method comprises measuring real power and reactive power at the interconnection point of the electrical network to obtain a plurality of real power values ​​and a plurality of reactive power values. The method further comprises measuring a voltage at the interconnection point to obtain a plurality of voltage values. Using the plurality of real power values, the plurality of reactive power values, and the plurality of voltage values ​​and a mathematical estimation technique, at least one parameter value associated with the electrical network is estimated. Summary of the invention

[0006] It is an object of embodiments of the present invention to provide a method for estimating a grid impedance of a power grid in a simple and fast manner.

[0007] It is a further object of embodiments of the present invention to provide a renewable power plant capable of providing a power feed to a grid more accurately than similar prior art renewable power plants.

[0008] It is another object of embodiments of the present invention to provide a renewable power plant capable of adjusting the power feed to a grid according to changes in the grid impedance.

[0009] According to a first aspect, the invention provides a method for estimating a grid impedance Z component of a grid coupled to a power generation unit at an interconnection point, the method comprising the following steps:

[0010] - Determine the voltage V across the interconnection point meas ; Active current I delivered to the grid by the power generation unit P and / or active power P; and reactive current I delivered to the grid by the power generation unit Q and / or reactive power Q,

[0011] - Using a recursive adaptive filter algorithm, and based on the determined voltage V meas and determine the active current I P and / or active power P; and reactive current I Q and / or reactive power Q, an estimated parameter estimation vector, the parameter estimation vector defining a set of estimated model parameters for a selected model of the system response of the power grid,

[0012] - creating a model representation of the power grid based on the parameter estimation vector and by applying the parameter set of the parameter estimation vector to the selected model,

[0013] - Using the model representation, a system DC gain vector is calculated for the power grid, which represents the voltage V at the steady state of the power grid. meas On the other hand, the active current I P and / or active power P, reactive current I Q and / or the correlation between reactive power Q, and

[0014] - 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 from the system DC gain vector, wherein Z=R+jX.

[0015] Thus, according to a first aspect, the present invention provides a method for estimating a grid impedance Z component of a power grid.In the present context, the term "grid" should be interpreted as an interconnected power grid for delivering power from producers to consumers.

[0016] The power grid can have different topologies. Examples of such topologies are, for example, radial power grids and mesh power grids.

[0017] The electrical network may also have electrical components coupled thereto, i.e., the electrical components may be coupled to the interconnected electrical network. The electrical components may, for example, be resistive, capacitive, and / or inductive. Examples of such electrical components include, but are not limited to, switchgear, transformers, or capacitor banks.

[0018] The grid has a grid impedance Z. The grid impedance Z has a complex form Z=R+jX, where R is the real part of the complex grid impedance Z, representing the resistive part of the complex grid impedance Z. Similarly, X is the imaginary part of the complex grid impedance Z, representing the reactive part of the complex grid impedance Z. The imaginary part X may be zero, in which case the grid impedance Z is purely resistive. Similarly, the real part R may be zero, in which case the grid impedance Z is purely reactive. Alternatively, the real part R and the imaginary part X may be non-zero, in which case the grid impedance Z includes a resistive part and a reactive part.

[0019] The electrical grid is coupled to the power generating unit at an interconnection point. The interconnection point may be viewed as the physical interface between the electrical grid and the power generating unit, ie the point at which the power generating unit is coupled to the interconnected electrical grid.

[0020] In this document, the term "power generation unit" should be interpreted as a unit that is capable of generating power and supplying all or part of the generated power to the grid. The power generation unit may be a conventional unit, such as a power plant, an internal combustion engine, etc., or it may be a renewable power generation unit, such as a wind turbine, a photovoltaic cell, etc.

[0021] In the method according to the first aspect of the invention, the voltage V across the interconnection point meas ; Active current I delivered to the grid by the power generation unit P and / or active power P; and reactive current I delivered to the grid by the power generation unit Q And / or the reactive power Q is initially determined.

[0022] Therefore, initially determine the voltage V across the interconnection point meas Voltage V meas is the voltage across the point between the grid and the power generation unit, i.e. across the point where the power generation unit is coupled to the grid. Accordingly, the voltage V meas It is the voltage before the power generation unit and towards the grid.

[0023] In addition, determine the active current I P and / or active power P. Therefore, only the active current I P Alternatively, only the active power P may be determined. As another alternative, the active current I may be determined P And active power P. Active current I P Represents the active current I delivered to the grid by the power generation unit P Similarly, the active power P represents the amount of active power delivered to the grid by the power generation unit. Therefore, the active current I P And the active power P represents the active part of the power provided by the power generating unit to the grid.

[0024] In addition, determine the reactive current I Q and / or reactive power Q. Therefore, only the reactive current I Q Alternatively, only the reactive power Q may be determined. As another alternative, the reactive current I may be determined Q And reactive power Q. Reactive current I Q Represents the reactive current I delivered to the grid by the power generation unit Q Similarly, reactive power Q represents the amount of reactive power delivered to the grid by the power generation unit. Therefore, the reactive current I Q And the reactive power Q represents the reactive part of the power provided by the power generating unit to the grid.

[0025] Therefore, by determining the voltage V meas , Active current I P and / or active power P, and reactive current I Q and / or reactive power Q, having obtained information about the voltage across the interconnection point, about the active part of the power delivered to the grid by the power generation unit, and about the reactive part of the power delivered to the grid by the power generation unit.

[0026] Voltage V meas ,I P and / or P, and I Q The determination of Q and / or Q can be performed, for example, by direct measurement. The direct measurement can be performed, for example, with the aid of a power meter. As an alternative, the voltage V meas , Active current I P and / or active power P, and reactive current I Q And / or the reactive power Q can be derived from other parameters, which can be measured. For example, knowing the voltage V meas And reactive power Q, the reactive current I can be derived Q .

[0027] Next, a recursive adaptive filter algorithm is used and based on the determined voltage V meas , and the determined active current I P and / or active power P, and determined reactive current I Q and / or reactive power Q, estimating a parameter estimation vector. Because the parameter estimation vector is estimated based on previously determined voltage and current and / or power parameters, the resulting parameter estimation vector depends on these parameters, and therefore, changes in the voltage and current and / or power parameters will be reflected in the estimated parameter estimation vector.

[0028] The parameter estimate vector defines a set of estimated model parameters for the selected model of the system response of the power grid. Thus, a model is selected that reflects how the power grid is expected to react in response to changes in voltage, active power and / or reactive power. Thus, the selected model takes into account general considerations about the power grid and the power generation units, and the selected model can be regarded as a "type" of model. However, the exact system response of the actual power grid is determined by the set of model parameters that need to be applied to the selected model. According to the present invention, these model parameters are estimated in the form of a parameter estimate vector.

[0029] In this context, the term "recursive adaptive filter algorithm" should be interpreted as a filter having a spatial state model controlled by variable parameters, and adjusting those parameters according to an optimization algorithm. This will be described in more detail below.

[0030] Next, a model representation of the electrical network is created based on the parameter estimation vector and by applying the parameter set of the parameter estimation vector to the selected model. Because the model representation of the electrical network is created based on the parameter estimation vector, the resulting model representation depends on the parameter estimation vector and thus on the changes in the voltage and current and / or power parameters that form the basis of the parameter estimation vector. More specifically, the parameter set identified when estimating the estimation vector is applied to the selected model. Thus, based on the selected model and including the applied parameter set, the resulting model representation reflects the actual behavior of the actual system under actual prevailing conditions.

[0031] The model representation of the power grid can be a state space representation, and can be the following mathematical form

[0032]

[0033] The state space representation will be described in more detail below.

[0034] Next, a system DC gain vector is calculated for the power grid using the model representation. Since the system DC gain vector for the power grid is calculated using the model representation, the calculated system DC gain vector depends on the model representation. Therefore, changes in the model representation will be reflected in the calculated system DC gain vector. Accordingly, changes in the determined voltage, current and / or power parameters are also reflected in the DC gain vector.

[0035] The DC gain vector represents that in the steady state of the power grid, on the one hand, the voltage V meas On the other hand, the active current I P and / or active power P, reactive current I Q and / or the reactive power Q. This is due to the fact that the parameters of the estimation vector (which are applied to the selected model in order to create the model representation) are based on the voltage V meas, information about active power and information about reactive power. Each vector element of the DC gain vector can be for each input I p and I q The gain scalar value, in steady state, forms the output V meas .

[0036] In this document, the term "stable state of the grid" should be interpreted as a state of the grid in which dynamic effects (such as those caused by system changes) have been weakened, i.e., a state with substantially no dynamics. Accordingly, the calculated DC gain vector reflects the voltage V when the dynamic effects are not taken into account. meas How to react to changes in active power and / or reactive power. However, according to the invention, the DC gain is calculated despite the fact that dynamic effects are actually present.

[0037] The system DC gain vector can be calculated using the above state-space representation and can have the following form

[0038] K DC =D-CA -1 B

[0039] Finally, the grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z are derived from the system DC gain vector, where Z=R+jX. Since the DC gain vector represents the correlation between voltage, active power and reactive power at the grid steady state, it is a suitable measure of the grid impedance Z, since the grid impedance Z is also related to the steady state of the grid.

[0040] The derivation may be performed by calculating and / or solving for the system DC gain vector. Because the grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z are derived from the system DC gain vector, the derived grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z depend on the calculated system DC gain vector. Therefore, any changes in the calculated system DC gain vector and the determined voltage, current and / or power parameters will be reflected in the derived grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z.

[0041] The system DC gain vector can be of the form above, and can therefore be derived as follows

[0042]

[0043] As mentioned above, in this case, each vector element of the DC gain vector is a vector for each input I p and I q The gain scalar value, in steady state, forms the output V meas .

[0044] One advantage is that the estimation of the parameter estimation vector requires few input variables, namely the determined voltage V meas and determine the active current I P and / or active power P; and the determined reactive current I Q And / or reactive power Q. This allows the estimation method to be simple because the number of changes to be handled is low. In addition, the recursive adaptive filter algorithm provides an accurate and reliable estimate of the parameter estimate vector, and thereby an accurate and reliable estimate of the parameters required for providing an accurate model representation of the power grid. The model representation of the power grid applies the parameters from the estimated parameter estimate vector to the selected model, and the model representation created thereby will also be accurate. The system DC gain vector calculated using the model representation is a simple way to represent the power grid impedance Z. Thus, the power grid impedance Z, and / or the resistance R of the power grid impedance Z, and / or the reactance X of the power grid impedance Z are derived in a quick and easy manner.

[0045] Furthermore, the method of the invention allows the grid impedance to be derived while taking into account the dynamics, in the sense that the dynamic behavior of the grid local to the power generating unit is taken into account. Such local dynamic behavior may for example be caused by other automatic voltage regulation AVR units. As renewable energy plants increasingly replace conventional power plants, more local AVR units will be added, resulting in the grid having more and more dynamic behavior on the voltage when injecting active and reactive power. A complete knowledge of the grid is available, including static as well as dynamic behavior. Thereby a more accurate voltage control can be obtained.

[0046] Determine the voltage V across the interconnection point meas ; Active current I delivered to the grid by the power generation unit P and / or active power P; reactive current I delivered to the grid by the power generation unit Q and / or reactive power Q may include measuring the voltage V meas , Active current I P , active power P, reactive current I Q and / or reactive power Q. According to this embodiment, the voltage V meas ,I P and / or P and I Q The determination of Q and / or Q is performed by direct measurement. These measurements can be measured directly in the power grid, which is a fast and reliable way to determine the parameters. The measurements can be performed, for example, with the aid of power meters, current transformers, phasor measurement units and wattmeters.

[0047] Alternatively, the voltage V meas ,I P and / or P and I QThe measurement of and / or Q can be performed by indirect measurement, where V meas ,I P and / or P and I Q and / or Q are not directly measured, but other relevant parameters can be measured, as well as V meas ,I P and / or P and I Q and / or Q may be derived therefrom.

[0048] The recursive adaptive filter algorithm can be a recursive least squares algorithm. According to this embodiment, the recursive least squares algorithm recursively finds the coefficients that minimize the weighted linear least squares (weighted linear regression) cost function associated with one or more input signals. Similarly, the algorithm can provide one or more output signals. The recursive least squares algorithm provides a fast and efficient data processing method.

[0049] Alternatively or additionally, the recursive adaptive filter algorithm can be a Kalman algorithm. According to this embodiment, the Kalman algorithm uses a series of measurements observed over time and generates estimates of unknown variables by estimating the joint probability distribution of the variables for each time frame. The Kalman algorithm provides a computationally efficient and fast method for data processing.

[0050] Alternatively or additionally, another recursive adaptive filter algorithm, such as a least mean square algorithm or similar may be used.The least mean square algorithm provides an estimation algorithm with low complexity and simple implementation.

[0051] The model representation of the power grid can be a state space representation. According to this embodiment, the state space representation of the power grid is a mathematical model of the physical system as a set of input, output and state variables. The state space representation can be adapted to a multi-input multi-output system.

[0052] For example, the step of creating a model representation of the electrical grid may include creating a state-space representation of the form:

[0053]

[0054] Wherein, A, B, C and D are matrices, and the step of estimating the parameter estimation vector may include estimating the parameters of the matrices A, B, C and D.

[0055] According to this embodiment, u(t) represents the input to the state-space model at time t, in the form of active current I at time t, P (t) and reactive current I Q (t). y(t) represents the output of the state-space model at time t, in the form of the measured voltage V meas (t). Voltage V meas (t) includes the static part VZ (t) and the dynamic part V dyn (t).

[0056] Matrix A represents the dynamic behavior of the system. Matrix B and matrix C represent the gain response of the system, B is the input matrix, and C is the output matrix. Matrix D represents the feedforward of the system. According to this embodiment, D=0, i.e. the feedforward of the system is not considered. In this case, the estimation vector is a list of values ​​of the parameters constituting matrices A, B, C and D, and thus provides all the necessary information required to describe the system by means of a model representation.

[0057] The step of calculating the system DC gain vector may include applying the following formula:

[0058] K DC =D-CA -1 B,

[0059] Among them, K DC is the system DC gain vector, and A, B, C, and D are matrices of the state-space representation.

[0060] According to this embodiment, once the parameters of the respective matrices have been obtained in the form of parameter estimation vectors, the DC gain vector is calculated by means of performing simple matrix operations on the resulting matrices. This is an easy calculation, and thus the DC gain vector can be obtained quickly and easily.

[0061] The method may further comprise the step of deriving a damping ratio ζ and / or an oscillation frequency ωn of the voltage dynamics of the grid based on the model representation of the grid.According to this embodiment, the model representation of the grid may also be used to derive a damping ratio ζ and / or an oscillation frequency ωn of the voltage dynamics of the grid.

[0062] The damping ratio ζ describes the ability of the system to counteract the oscillatory nature of the system's transient response. Large values ​​of the damping ratio ζ produce transient responses with less oscillatory nature. Similarly, lower values ​​of the damping ratio ζ produce transient responses with more oscillatory nature. A system with a damping ratio ζ can be undamped (ζ=0), underdamped (ζ<1), critically damped (ζ=1), or overdamped (ζ>1).

[0063] The oscillation frequency ωn of the voltage dynamics describes the frequency of the voltage dynamics oscillations. The damping ratio ζ and / or the oscillation frequency ωn are derived based on a model representation of the power grid. An eigenvalue analysis of the model representation of the power grid can be used to derive the damping ratio ζ and / or the oscillation frequency ωn. Eigenvalues ​​are a set of scalar quantities associated with a system of linear equations, i.e., a matrix equation, often referred to as eigenvalues ​​or characteristic roots.

[0064] Thus, according to this embodiment, information about the dynamics of the grid is obtained. Information about the dynamics of the grid can be used to obtain knowledge about the transient period of the voltage dynamics, the degree to which the voltage dynamics are damped, and when the voltage dynamics reaches a steady state. In addition, the oscillating voltage V indicating the amplitude of the voltage dynamics dyn It can be estimated from the derived damping ratio ζ and oscillation frequency ωn.

[0065] The information obtained can also be used to control the voltage V determined across the interconnection point meas The grid may have a nominal voltage V n , oscillation voltage V dyn and the voltage V across the grid impedance z .

[0066] The voltage V determined across the interconnection point meas It can be expressed as the sum of the voltages of the grid, so that V meas =V dyn +V n +V z By obtaining information about the dynamics (damping ratio ζ and oscillation frequency ωn), the oscillation voltage V can be derived dyn . Nominal voltage V n Normally provided by the grid operator. Accordingly, by determining V meas And export V dyn , the voltage V across the grid impedance can be derived z Then, using Ohm's law, and based on the derived voltage V z and determine the current I P and I Q , the grid impedance Z can be easily derived.

[0067] Furthermore, the information obtained can be used to provide an adaptive voltage control of the power generation unit, which takes into account the grid impedance Z, the resistance R, the reactance X, the oscillation frequency ω n Thus, the voltage and active current I provided to the grid by the power generation unit are P and / or reactive current I Q can be controlled to handle such changes, such as dynamic changes in the damping system.

[0068] The voltage dynamics of the grid may include machine dynamics in the grid. According to this embodiment, the machine dynamics may be components originating from electromechanical generators in the grid. Alternatively or additionally, the voltage dynamics may include dynamics caused by other voltage regulation mechanisms in the grid. This may, for example, include an automatic voltage regulation (AVR) unit located at another power plant nearby.

[0069] The step of 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 may include deriving a ratio X / R based on the resistance R and the reactance X of the grid impedance Z. According to this embodiment, the ratio X / R is a ratio of an imaginary part X of the complex grid impedance Z, representing the reactive part of the complex grid impedance Z, and a real part R of the complex grid impedance Z, representing the resistive part of the complex grid impedance Z. Therefore, the grid impedance Z itself may not necessarily be derived according to this embodiment.

[0070] The X / R ratio may have an impact on the level of short circuit current that requires a circuit breaker to interrupt. A circuit breaker is an automatic device used to stop the flow of current in a circuit as a safety measure. The X / R ratio may also be used as a design factor for transformers in a power grid.

[0071] The power generation unit may form part of a renewable power plant, and the method may further comprise the step of controlling the power generation unit to provide a power feed into the grid based on an estimated grid impedance Z, and / or a resistance R of the grid impedance Z, and / or a reactance X of the grid impedance Z. According to this embodiment, the power generation unit forms part of a renewable power plant comprising one or more renewable power generation units, such as wind turbines, photovoltaic cells, etc., and the power generation unit may thus be such a renewable power generation unit.

[0072] Furthermore, according to this embodiment, the method further comprises the step of controlling the power generation unit to provide power feed into the grid based on the estimated grid impedance Z, resistance R and / or reactance X. Thus, the power generation unit is controlled in such a way that the power actually fed into the grid by the power generation unit is consistent with the grid impedance Z, and thereby the power delivered to the grid by the power generation unit can be easily adapted to follow any changes in the grid impedance.

[0073] The step of controlling the power generation unit to provide a power feed into the grid may be performed by controlling the slope of the active power feed and / or reactive power feed relative to 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. The step of controlling the slope of the active power feed and / or reactive power feed from the power generation unit may be performed, for example, by having a gain on the active power generation and reactive power generation of the power generation unit depending 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.

[0074] Alternatively, a look-up table may be used to control the active power feed and / or reactive power feed depending 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.

[0075] The step of controlling the power generation unit may include controlling the active current I delivered by the power generation unit to the grid P and / or active power P; and reactive current I delivered to the grid by the power generation unit Q and / or reactive power Q. According to this embodiment, based on the estimated grid impedance Z, resistance R and / or reactance X, the power provided by the power generating unit to the grid is controlled.

[0076] The power generation unit is thus controlled in such a way that the active current I P and / or active power P; and reactive current I Q The reactive power Q and / or the grid impedance Z, resistance R and / or reactance X are consistent. Thus, the active current I delivered to the grid by the power generation unit is P and / or active power P; and reactive current I Q And / or reactive power Q can be easily adapted to follow any changes in grid impedance Z, resistance R and / or reactance X.

[0077] Controls the active current I delivered by the power generation unit to the grid P and / or active power P; and reactive current I delivered to the grid by the power generation unit Q The step of determining the active power generation and reactive power Q of the power generation unit depending 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 may be performed by gaining the active power generation and reactive power generation of the power generation unit.

[0078] Alternatively or additionally, the gains to the active power generation and reactive power generation of the power generation unit may depend on other system parameters, such as a voltage V determined across the interconnection point. meas and / or grid frequency.

[0079] The power generating unit may be a wind turbine generator. According to this embodiment, the power generating unit is a renewable power generating unit in the form of a wind turbine. The wind turbine may be a stand-alone wind turbine, or it may form part of a wind farm comprising two or more wind turbines. Alternatively, the power generating unit may be in the form of another renewable power generating unit, such as one or more photovoltaic cells, a hydroelectric generator, etc.

[0080] The step of 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 may comprise deriving the absolute value of the grid impedance |Z|, using the formula:

[0081]

[0082] According to this embodiment, the absolute value of the grid impedance Z is derived as the square root of the square of the resistance R of the grid impedance Z plus the square of the reactance X of the grid impedance Z.

[0083] The method may further include determining a short circuit ratio is the reciprocal of the absolute value of the grid impedance |Z|. According to this embodiment, the short circuit ratio is derived. The short circuit ratio is a measure of the stability of the electromechanical generator. The short circuit ratio is the ratio of the excitation current required to produce the rated armature voltage at open circuit to the excitation current required to produce the rated armature current under three-phase short circuit conditions. The SCR is an easy and reliable way to represent the operating characteristics of an electromechanical generator. Therefore, the derived SCR can be used to determine whether the grid is stable, and this in turn can be used to determine whether to apply appropriate measures in this regard.

[0084] Based on the resistance R and reactance X of the grid impedance Z, the angle θ of the grid impedance Z can be derived using the following formula:

[0085]

[0086] According to this embodiment, the angle θ is derived as the inverse tangent of the ratio X / R. The angle θ of the grid impedance Z can be used to represent the grid impedance Z in another mathematical form that does not specify the resistance R and the reactance X. Assuming that the absolute value of the grid impedance |Z| and the angle θ of the grid impedance Z are known, the grid impedance can be represented by the following mathematical form:

[0087] Z=|Z|∠θ=|Z|(cosθ+j sinθ)=|Z|e jθ .

[0088] According to a second aspect, the invention provides a renewable power plant comprising a plurality of power generating units, which are coupled to a grid at an interconnection point, wherein at least one of the power generating units is adapted to: provide power feed into the grid based on a grid impedance Z, a resistance R of the grid impedance Z and / or a reactance X of the grid impedance Z, wherein the grid impedance Z, the resistance R and / or the reactance X have been estimated according to the method according to the first aspect of the invention.

[0089] Thus, according to a second aspect, the invention provides a renewable power plant comprising a plurality of power generating units, the plurality of power generating units being coupled to a grid at an interconnection point. Based on a grid impedance Z, a resistance R of the grid impedance Z and / or a reactance X of the grid impedance Z, at least one of the power generating units is adapted to provide a power feed into the grid. The grid impedance Z, the resistance R of the grid impedance Z and / or the reactance X of the grid impedance Z have been estimated according to the method according to the first aspect of the invention. Accordingly, the explanations above with reference to the first aspect of the invention apply equally here.

[0090] Thus, the renewable power plant according to the second aspect of the invention is configured to provide a power feed into the grid which, for the reasons described above with reference to the first aspect of the invention, is consistent with the grid impedance Z, the resistance R of the grid impedance Z and / or the reactance X of the grid impedance Z. Thus, the power delivered to the grid by the renewable power plant may be easily adapted to follow any changes in the grid impedance.

[0091] An advantage is that at least one power generating unit of the renewable power plant is adapted to provide a power feed based on an estimated grid impedance Z, a resistance R of the grid impedance Z and / or a reactance X of the grid impedance Z, wherein the estimation is according to the method according to the first aspect of the invention, since thereby the power feed can be controlled in a manner that closely follows any changes in the grid impedance Z. Such consistency between the power feeds of the plurality of power generating units and the estimated grid impedance Z, resistance R and / or reactance X enables the renewable power plant to provide an accurate power feed in a reliable manner.

[0092] Furthermore, the consistency between the power feeds of the plurality of power generation units and the estimated grid impedance Z, resistance R and / or reactance X also enables the renewable power plant to adapt the power feed to the grid in a fast and accurate manner according to changes in the grid impedance, since the grid impedance Z, resistance R and / or reactance X are determined in a fast and reliable manner, as described above, and therefore the power generation units are able to react quickly to any changes in the grid impedance Z.

[0093] The power generation unit may be a wind turbine generator. According to this embodiment, the power generation unit is a renewable power generation unit in the form of a wind turbine. Alternatively, the power generation unit may be in the form of another renewable power generation unit, such as one or more photovoltaic cells, a hydroelectric generator, etc.

[0094] The renewable power plant may include a plurality of wind turbines.Alternatively or additionally, the renewable power plant may include one or more alternative kinds of renewable power generators, such as photovoltaic cells, hydroelectric generators, battery storage, and the like. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] The present invention will now be described in more detail with reference to the accompanying drawings, in which

[0096] Figure 1 is a schematic diagram illustrating a power grid including a voltage source and a power grid impedance Z estimated using a method according to an embodiment of the present invention,

[0097] Figure 2 is a block diagram illustrating a method according to an embodiment of the present invention,

[0098] Figure 3is a flow chart illustrating a method according to an embodiment of the present invention, and

[0099] Figure 4 is a block diagram illustrating a state-space model used in a method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0100] Figure 1 is a schematic diagram illustrating a power grid 1 including a voltage source 2 and a grid impedance Z. The voltage source 2 has a voltage V n and V dyn The sum of the voltages, where V n is the nominal voltage normally provided by the grid operator, V dyn represents an oscillating voltage associated with the voltage dynamics 4 of the grid 1 .

[0101] The grid impedance Z has a complex form Z=R+jX, where R is the real part of the grid impedance Z, representing the resistive part of the grid impedance Z. Similarly, X is the imaginary part of the grid impedance Z, representing the reactive part of the grid impedance Z. Thus, the grid impedance Z is represented by the resistance R and the reactance X. There is a voltage V across the grid impedance Z z .

[0102] The voltage dynamics 3 of the grid 1 is determined by the oscillation frequency ω n and the damping ratio ζ. The damping ratio ζ describes the system's ability to counteract the oscillatory nature of the system's transient response. In addition, the oscillation frequency ω n describes the frequency of the oscillation of the voltage dynamics 3. Therefore, the voltage dynamics 3 of the grid 1 can be used to obtain knowledge of the transient period of the voltage dynamics 3, the degree to which the voltage dynamics 3 are damped, and when the voltage dynamics 3 reach a steady state. In addition, the oscillating voltage V dyn Indicates the magnitude of voltage dynamics. Therefore, V dyn For example, it can be obtained from the damping ratio ζ and the oscillation frequency ω n To estimate.

[0103] The voltage V across the interconnection point 4 meas For example, it is determined by direct measurement. The interconnection point 4 is the physical interface between the grid 1 and the power generation unit (not shown) that delivers power to the grid 1. Thus, the voltage V meas It is a measure of the voltage between the grid 1 and the rest of the power system, in particular the power generation units. meas It can also be expressed as the sum of all voltages of the grid 1, that is, V meas =V dyn +V n +V z .

[0104] In addition, the active current I delivered by the power generation unit to the grid 1 is Pand / or the active power P is determined, for example, by direct measurement. In addition, the reactive current I delivered by the power generation unit to the grid 1 Q The active current I and / or the reactive power Q are also determined, for example, by direct measurement. P And the active power P represents the active part of the power provided by the power generation unit to the grid 1. Similarly, the reactive current I Q And reactive power Q represents the reactive part of the power provided by the power generation unit to the grid 1 .

[0105] Therefore, with respect to the voltage across the interconnection point 4 (in the form of V meas ), the active power provided by the power generation unit (in the form of I P and / or P), and the reactive power provided by the power generation unit (in the form of I Q and / or Q) information is now available.

[0106] Voltage V meas And the active current I P and / or active power P; and reactive current I Q The and / or reactive power Q are then used to estimate the grid impedance Z. This may for example comprise estimating the grid impedance Z itself, and / or estimating the resistance R, and / or the reactance X. This may for example be done in the following way.

[0107] Oscillation voltage V dyn Based on the voltage dynamics 3 derived, and the nominal voltage V n Provided by the grid operator. Then, the voltage V across the grid impedance Z z From the measured voltage V meas Calculate, that is, V z =V meas -V n -V dyn Finally, the grid impedance Z can be estimated by applying Ohm’s law and using V z and determine the active current I P and / or active power P; and the determined reactive current I Q and / or reactive power Q.

[0108] Figure 2 is a block diagram illustrating a method according to an embodiment of the present invention. A number of input parameters (in the form of V meas ,I P ,P,I Q and / or Q, previously determined) such as with reference to above Figure 1 The described manner is fed to the estimator 5.

[0109] 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 squares algorithm and / or a Kalman algorithm. The parameter estimation vector defines a set of estimated model parameters for the selected model of the system response of the power grid. Furthermore, based on the selected model and the parameter estimation vector, the estimator 5 creates a model representation 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, as a set of input, output and state variables, is a mathematical model of the physical system. Therefore, the model representation depends on the parameter estimation vector and thereby on the changes in the voltage and current and / or power parameters that form the basis of the parameter estimation vector.

[0110] The estimator 5 outputs a model representation which is used as input to a DC gain vector analyser 6 and an eigenvalue analyser 7 .

[0111] The DC gain vector analyzer 6 uses the model representation to calculate the DC gain vector of the power grid 1. Therefore, changes in the model representation will be reflected in the calculated DC gain vector. Correspondingly, changes in the determined voltage, current and / or power parameters are also reflected in the DC gain vector. The DC gain vector represents the correlation between the voltage on the one hand and the active power and reactive power on the other hand when the power grid is in a stable state.

[0112] The DC gain vector analyzer 6 uses the DC gain to derive the grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z from the DC gain vector. For this reason, any changes in the calculated DC gain vector and the determined voltage, current and / or power parameters will be reflected in the derived grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z. Furthermore, this is an easy and fast way to estimate the grid impedance, and accordingly, the system can react quickly to any changes in the grid impedance.

[0113] The derived grid impedance Z, resistance R and / or reactance X may also be used to derive the short circuit ratio (SCR) of the grid 1 , the X / R ratio, the absolute value of the grid impedance |Z| and the angle θ of the grid impedance Z.

[0114] Based on the model representation, the eigenvalue analyzer 7 derives the damping ratio ζ and the oscillation frequency ω n Damping ratio ζ and oscillation frequency ω n represents the voltage dynamics 4 of the grid 1 and can be used, for example, to estimate the oscillating voltage V of the source 2 of the grid 1 dyn , as mentioned above Figure 1 described.

[0115] Therefore, based on the input parameter V meas ,I P ,P,I Qand / or Q, the estimation is performed by an estimator 8. The estimator 8 estimates a parameter estimation vector and based on the parameter estimation vector, creates a model representation. The model representation is used as an input to a DC gain vector analyzer 6 and an eigenvalue analyzer 7.

[0116] Figure 3 is a flow chart illustrating a method according to an embodiment of the present invention. The method starts with a first step 8, in which a voltage V meas , Active current I P and / or active power P; and reactive current I Q and / or reactive power Q is determined. V meas ,I P and / or P and I Q And / or Q can refer to the above Figure 1 Determined in the manner described.

[0117] In a second step 9, a recursive adaptive filter algorithm, such as a recursive least squares algorithm or a Kalman algorithm, is used and based on V meas ,I P and / or P, and I Q and / or Q, such as those referenced above Figure 2 The parameter estimation vector is estimated in the manner described.

[0118] In a third step 10, based on the parameter estimation vector, for example as mentioned above with reference Figure 2 In the manner described, create a model representation,

[0119] In a fourth step 11, the model representation is used to calculate the system DC gain vector, for example as described above with reference to Figure 2 The method described.

[0120] In the fifth step 12, for example, with reference to Figure 1 and Figure 2 The grid impedance Z, and / or the resistance R of the grid impedance Z, and / or the reactance X of the grid impedance Z are derived in the manner described.

[0121] Figure 4 is a block diagram illustrating a state-space model used in a method according to an embodiment of the present invention, in the form of a multiple-input, single-output model. Inputs u(k) representing the active and reactive currents of the system are input to the state-space model, as well as inputs representing the voltage V meas The output y(k) is output by the state space model. A, B, C and D represent the static and dynamic behavior of the system and can be in the form of suitable matrices. The parameter estimation vector defines the parameters to be applied to the matrix to create a model representation of the actual power grid.

[0122] Figure 4 The model representation is in the following form:

[0123]

[0124] Matrix A represents the dynamics of the system, matrix B and matrix C represent the gains of the system, B is the input matrix, and C is the output matrix, and matrix D represents the feedforward of the system, which can be set to zero and thus not taken into account.

Claims

1. A method for estimating a grid impedance Z component of a grid (1) coupled to a power generation unit at an interconnection point (4), the method comprising the following steps: - Determine the voltage V across the interconnection point (4) meas ; Active current I delivered by the power generation unit to the grid (1) P and / or active power P; and the reactive current I delivered by the power generation unit to the grid (1) Q and / or reactive power Q, - Using a recursive adaptive filter algorithm, and based on the determined voltage V meas and determine the active current I P and / or active power P; And the reactive current I Q and / or reactive power Q, an estimated parameter estimation vector, the parameter estimation vector defining an estimated model parameter set for a selected model of the system response of the power grid (1), - creating a model representation of the power grid (1) in the form of a state space representation of the power grid (1) based on the parameter estimation vector and by applying the parameter set of the parameter estimation vector to the selected model, - Using the model representation, a system DC gain vector is calculated for the power grid (1), wherein the DC gain vector represents that at the steady state of the power grid (1), on the one hand, the voltage V meas On the other hand, the active current I P and / or active power P, reactive current I Q and / or the correlation between reactive power Q, and - 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 from the system DC gain vector, wherein Z=R+jX; Wherein, the method further comprises: - Based on the model representation of the power grid, the damping ratio ζ and the oscillation frequency ω for the voltage dynamics (3) of the power grid (1) are derived n ,as well as - From the derived damping ratio ζ and oscillation frequency ω n To estimate the oscillating voltage V indicating the amplitude of the voltage dynamics dyn .

2. The method according to claim 1, wherein: Determine the voltage V across the interconnection point (4) meas ; Active current I delivered by the power generation unit to the grid (1) P and / or active power P; reactive current I delivered by the power generation unit to the grid (1) Q and / or reactive power Q comprises: measuring the voltage V meas , Active current I P , active power P, reactive current I Q , and / or reactive power Q.

3. The method according to claim 1 or 2, wherein: The recursive adaptive filter algorithm is a recursive least squares algorithm.

4. A method according to any one of the preceding claims, wherein: The recursive adaptive filter algorithm is the Kalman algorithm.

5. The method according to claim 1, wherein: The step of creating a model representation of the power grid (1) comprises creating a state space representation of the form: Wherein, A, B, C and D are matrices, and wherein the step of estimating the parameter estimation vector comprises: estimating parameters for matrices A, B, C and D.

6. The method according to claim 5, wherein: The steps to calculate the system DC gain vector include applying the following formula: K DC =D-CA -1 B, Among them, K DC is the system DC gain vector, and A, B, C, and D are matrices of the state-space representation.

7. The method according to claim 1, wherein: The voltage dynamics (3) of the power grid (1) include the dynamics of the machines in the power grid (1).

8. A method according to any one of the preceding claims, wherein: The step of 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: based on the resistance R and reactance X of the grid impedance Z, deriving an X / R ratio.

9. A method according to any one of the preceding claims, wherein: The power generation unit forms part of a renewable power plant, the method further comprising the step of controlling the power generation unit to provide power feed into the grid based on an estimated grid impedance Z, and / or a resistance R of the grid impedance Z, and / or a reactance X of the grid impedance Z (1).

10. The method according to claim 9, wherein: The step of controlling the power generation unit comprises: controlling the active current I delivered by the power generation unit to the power grid (1) P and / or active power P; and reactive current I delivered by the power generation unit to the grid (1) Q and / or reactive power Q.

11. A method according to any one of the preceding claims, wherein: The power generating unit is a wind turbine generator.

12. A method according to any one of the preceding claims, wherein: The step of 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 the absolute value of the grid impedance |Z| using the following formula:

13. A method according to any one of the preceding claims, wherein: The angle θ of the grid impedance Z is derived based on the resistance R and reactance X of the grid impedance Z using the following formula:

14. Renewable power plants, including: A plurality of power generation units coupled to a power grid (1) at an interconnection point (4), wherein at least one of the power generation units is adapted to provide a power feed into the power grid (1) based on a grid impedance Z, a resistance R of the grid impedance Z, and / or a reactance X of the grid impedance Z, wherein the grid impedance Z, the resistance R, and / or the reactance X have been estimated according to the method of any of the preceding claims.

15. The renewable power plant of claim 14, wherein: The power generating unit is a wind turbine generator.

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