JP2010193535A - Apparatus for stabilizing non-linear system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus for stabilizing a non-linear system, capable of estimating an internal phase angle of a generator from information available in a sub-station, and suppressing fluctuation in power by output of an optimal control gain, even if the variation of generator effective power enters a non-linear region due to an increase in the variation in generator phase angle. <P>SOLUTION: The apparatus uses an estimated generator effective power output value, an estimated generater internal voltage value, an estimated generater frequency value, an estimated generator internal phase angle value, an estimated system voltage value and a system impedance as auxiliary input into a reactive power compensator so that variation in a phase angle after a fault can be maintained within a predetermined value, and operates a control amount of stabilization control on the basis of a strict linearizing method based on differential geometry. By doing this, even if the generator output enters a region indicating non-linear characteristics, a fluctuation suppressing effect is not reduced, and a generator phase angle and the fluctuation of sub-station voltage after a system fault can be promptly stabilized. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a non-linear system stabilization device, and particularly to transient stability problems and voltage fluctuation problems caused by the occurrence of power system failures, etc., in order to maintain system stability and maintain the voltage fluctuation amount within a set value. The present invention relates to a non-linear system stabilization device that performs reactive power compensation.

  Recently, due to the difficulty in locating power sources, the tendency to install power sources in remote locations has become prominent, and along with this, the power system is also trending toward large-capacity power transmission over long-distance transmission lines. In order to improve the stability against such a trend, there is an example in which a reactive power compensator to which a power fluctuation suppression function is added is installed. In addition, a large amount of distributed power sources are introduced in an environment where power regulations are relaxed, and an unpredictable power flow state may occur in existing power transmission facilities, which may be effectively used up to the heat capacity limit. For this reason, a device such as a reactive power compensator is planned to enhance the power transmission capability, but this device is likely to be used even in a non-linear operating region.

  In a conventional power system, linear approximation is controlled at a certain operating point with respect to its own nonlinearity. On the other hand, in the field of control theory, nonlinear control theory called “strict linearization method” based on differential geometry theory has been constructed. Based on such a situation, a configuration method of a nonlinear control system in consideration of the nonlinearity of the object has been developed.

  The “strict linearization method” is a method in which a target is equivalently converted into a linear system by applying a nonlinear mapping of state quantities and nonlinear feedback to the target model, unlike the conventional approximation method. However, if a method of directly constructing a control system while expressing a power system model with a nonlinear differential equation is used, there is a problem that the model needs to be expressed with a large number of state variables. For this reason, in non-linear control, it is necessary to measure remote state quantities such as transmission line operation information and generator internal parameter information constituting the power system and use them as control inputs.

  Since the power system is a typical nonlinear system, it is considered reasonable to design an auxiliary controller for the reactive power compensator using nonlinear control theory. [Non-patent Document 1] and [Non-Patent Document 2] have published the effects of application of an auxiliary control device for nonlinear power control and power system stabilization applied to a reactive power compensator.

  In recent years, synchronous measurement technology is being introduced also in the field of electric power systems, and high-precision phase angle information and the like at remote multipoints can be easily used. Therefore, in [Non-patent Document 1] and [Non-Patent Document 2], information on remote points can be obtained, and the possibility of improving system stability by nonlinear control of the self-excited reactive power compensator (STATCOM) is quantitatively evaluated. Evaluating.

Hiroshi Konishi, Masuo Goto, Akihiko Yokoyama, Qiang Lu: "Nonlinear system stabilization control by STATCOM, 2002 IEEJ National Conference 6-206, (2002) Hiroshi Konishi, Masuo Goto, Akihiko Yokoyama, Qiang Lu: "Simulator test of nonlinear system stabilization control by STATCOM", IEEJ B Section Conference 117, (2002)

  If a method of directly constructing a control system while expressing a power system model with a nonlinear differential equation is employed, there is a problem that the model needs to be expressed with a large number of state variables. For this reason, in the conventional techniques described in [Non-Patent Document 1] and [Non-Patent Document 2], in the non-linear control, the state quantity of the remote place such as the generator internal voltage, phase angle and frequency constituting the power system is measured However, it is necessary to use the control input.

  On the other hand, the reactive power compensator is generally installed at a midpoint substation of a power supply system, and system information such as a power plant needs to be obtained via a communication line. In addition to the cost problem, installing communication lines has a problem of ensuring the reliability of communication lines.

  In addition, the optimum value of the control gain for system stabilization changes due to the change in the system configuration of the power system, the opening of the transmission line due to failure removal, and the change in the generator output. It is required that the optimum stabilization control system gain can be automatically and quickly reset even in response to such changes in operating conditions.

  An object of the present invention is to provide a nonlinear system stabilization device that can minimize the installation capacity of a reactive power compensator and can quickly and accurately converge power fluctuations through stabilization control.

  Another object of the present invention is that the generator internal phase angle can be estimated from information available at the substation, and even if the generator phase angle fluctuation increases and the fluctuation of the generator active power enters the nonlinear region, the optimum control gain is obtained. Is to provide a nonlinear system stabilizing device that can suppress power fluctuation.

  The nonlinear system stabilization device of the present invention estimates the internal voltage, phase angle, frequency, etc. of the target generator using information available at the substation where the reactive power compensator is installed, and uses it as an input signal for nonlinear control. use.

  In addition, for changes in the system configuration of the power system, changes in the output of the transmission line and generator output due to fault removal, the generator active power estimate, the generator internal voltage estimate, the generator internal phase angle estimate, Since the machine frequency estimated value and the transmission line reactance estimated value are input, the optimum control gain corresponding to the system change can be secured.

  The present invention relates to a reactive power compensator for supplying reactive power to an electric power system, wherein the control device separately generates a generator active power output estimated value, a generator internal voltage estimated value, a generator internal phase angle separately from maintaining the voltage of the power system. Calculate the control amount based on the estimated value, generator frequency estimated value, system voltage estimated value, and system reactance estimated value, and adjust the control gain of the reactive power output circuit for compensation in order to suppress power fluctuations by the calculated controlled variable Department.

  In addition, the nonlinear power system is rigorously linearized by input transformation based on differential geometry, dynamic linearization feedback, and coordinate transformation, and the gain of the linear controller is optimized to compensate for the reactive power for compensation. A control gain adjustment unit of the output circuit is provided.

  Instead of using the generator internal phase angle, the generator internal phase angle is estimated based on the substation bus voltage fluctuation, the generator internal voltage estimate, the grid voltage estimate, and the grid reactance estimate. Is calculated.

  Further, instead of using the generator internal voltage, the generator internal voltage is estimated based on the substation bus voltage, the system reactance estimated value, and the generator current estimated value, and the optimum control amount is calculated.

  In addition, instead of using the generator frequency, based on the substation bus frequency, the generator internal voltage estimate, the grid voltage estimate, the grid reactance estimate, the generator internal phase angle initial value, and the bus phase angle initial value, The optimum control amount is calculated by estimating the frequency.

  According to the present invention, the control amount is calculated in consideration of the influence of the nonlinear characteristics of the system, so that the control amount conforms to the actual system, and the facility capacity of the reactive power compensator can be minimized and stabilized. The power fluctuation can be converged quickly and accurately by the control. In addition, even if the optimum value of the control gain for system stabilization changes due to changes in the system configuration of the power system, opening of the transmission line due to failure removal, or changes in the generator output, etc. Can be easily reset automatically.

It is a block diagram of the nonlinear system stabilization apparatus which is embodiment of this invention. It is an electrical equivalent circuit diagram for demonstrating the basic principle of this Embodiment. It is a block diagram explaining the idea of exact linearization by differential geometry. It is an electrical equivalent circuit diagram for demonstrating the relationship between the voltage and phase angle in a transient state. It is a vector diagram for demonstrating the voltage phase angle characteristic in a transient state. It is a graph showing a temporal change of the generator phase angle δ and the substation bus voltage V ₂ at the time of power oscillation occurs. It is an electrical equivalent circuit diagram for demonstrating the relationship between a generator internal voltage, an internal phase angle, a substation voltage, an electric current, and a phase angle. It is a vector diagram for demonstrating the relationship between a generator internal voltage, a substation voltage, and an electric current. It is a block diagram of the nonlinear control apparatus which is Example 1 of this invention. It is a block diagram of the nonlinear control apparatus which is Example 2 of this invention.

  Embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows the overall configuration of a power supply system 16 to which the reactive power compensator 1 of the present embodiment is applied.

  As shown in FIG. 1, the generator 6 is connected to the power transmission line 14 via a generator bus 8, a generator transformer 9, and a power plant bus 33. The transmission line 14 generally has a loop configuration, a mesh configuration, or a radial configuration. FIG. 1 shows an example of a radial system. The generator 6 is provided with an automatic voltage control device 7 for controlling the generator 6 by feeding back the voltage of the generator bus 8 in order to control the voltage of the generator bus 8 to be constant.

  The power transmission line 14 is connected to the substation bus 10, and the substation bus 10 is connected to the system side power transmission line 15 and connected to the main system 12 via the system side substation bus 11.

A load 5 is connected to the substation bus 10 via a load transformer 13, and the reactive power compensator 1 is connected via an auxiliary transformer 4. The reactive power compensator 1 includes a reactive power output circuit that supplies reactive power to the power system and adjusts the voltage of the power system. The reactive power compensator 1 is connected to a voltage control block 3 and a non-linear control device 2. The voltage control block 3 _{receives the} substation bus voltage 22 as an input and minimizes the deviation from the target value V _2ref , thereby substation bus. Control is performed so that the voltage 22 becomes a target value, and the non-linear control device 2 performs power fluctuation suppression control by adding a control output 40 to the control output 39 of the voltage control block 3. The reactive power compensator 1, the voltage control block 3, and the nonlinear controller 2 constitute a nonlinear system stabilizing device.

  In general, the power supply system 16 includes such a generator 6, a generator bus 8, a generator transformer 9, a substation bus 10, a load transformer 13, a load 5, a generator side transmission line 14, and a system side transmission. An electric wire 15 is used. The reactive power compensator 1 uses the power supply system 16 as a target system for voltage control and power fluctuation suppression control.

(1) Exact linearization by differential geometric approach First, exact linearization based on differential geometry will be described. FIG. 2 shows an equivalent circuit corresponding to a power system to which the reactive power compensator 1 is applied. The reactive power compensator 1 is assumed to be connected to the midpoint of the power transmission system of the one-machine infinite bus system. In this system, the internal state of the generator 6 is expressed by a rotor equation of motion shown in Equation 1.

Where δ is the generator internal phase difference angle (rad), ω is the generator angular velocity (rad / s), 2H is the inertia constant (MWs / MVA), D is the intrinsic damping (pu), and P _m is the machine torque (p.u.), the P _e is an electrical torque (p.u.).

  If the time region where the electromagnetic transient between the transmission line and the reactive power compensator 1 occurs is ignored, the active power of the generator 6 can be expressed by Equation 2 from FIG.

Wherein, X ₁ is represents a reactance to the installation point of the generator internal reactive power compensator from voltage 1, the generator is the sum of the reactance of transformers and power lines. X ₂ represents the reactance from the substation bus voltage to the system side substation bus 11. E _q ′ is the generator internal voltage, V _S is the system voltage, and B _C is the equivalent susceptance of the reactive power compensator 1 as seen from the installation point.

Further, assuming that the generator internal voltage E _q ′ and the mechanical torque P _m are constant, the one-machine infinite bus system described above can be described by the nonlinear equation of state shown in Equation 3.

Here, δ (t) and ω (t) are state variables, and B _c is a control intermediate input. When the control input is selected as shown in Equation 4, Equation 3 can be written as Equation 5 as an affine nonlinear form. Here, X and f (X) can be expressed by Equation 6.

  Next, exact linearization will be described. FIG. 3 is a block diagram showing a control system using strict linearization by linearization feedback and coordinate transformation. Let us consider linearizing the nonlinear system expressed by Equation 5 by coordinate transformation and feedback. That is, consider a new output Z and a new input V shown in equations 7 and 8.

  If the number of state equations 5 satisfies the Frobenius theorem, the function h (x) is always present. Coordinate transformation and feedback for linearizing the system using h (x) are expressed by Equations 9 and 10.

  The definition of the Lie derivative of h (x) with respect to f (x) in the above equation is expressed by Equation 11.

  Here, 1 / β (x) is an input conversion gain, and α (x) / β (x) is a gain of dynamic linearization feedback. Here, α (x) and β (x) can be expressed by Equations 12 and 13.

  Next, a linear controller design method will be described. The linearized system is expressed by Equations 14 and 15.

  The optimal control law for this linearized system is expressed by Equation 16, and the evaluation index J expressed by Equation 17 is selected for the multi-input multi-output system expressed by Equation 12 in order to design an optimal control controller. .

  The feedback control input variable V that minimizes the evaluation index J can be calculated by Equation 18.

  Here, P is a non-negative solution of the Riccati equation shown in Equation 19.

  When the weight matrices Q and R are selected as in Expression 20, the control input variable V is expressed by Expression 21.

  From Equation 10 and Equation 21, the nonlinear control input u of the nonlinear system expressed by Equation 5 is given by Equation 22.

By substituting Equation 22 into Equation 4, the reactive power command B _c for the reactive power compensator represented by Equation 23 is obtained.

  If Expression 1 is used, Expression 23 can be expressed as Expression 24.

Equation 24 gives a reactive power command B _c by nonlinear control for the reactive power compensator 1.

(2) Method for Estimating Generator Internal Phase Angle A method for estimating the generator internal phase angle required as an input signal for nonlinear control from information in the substation in which the reactive power compensator 1 is installed will be described.

The voltage V ₂ of the substation bus 10 can be expressed by Equation 25 using the reactance X ₁ from the power plant to the substation and the reactance X ₂ from the substation to the grid.

From Equation 25, the magnitude of the bus voltage V ₂ can be expressed by Equation 26.

From Equation 26, the phase difference angle estimation value δ _s inside the generator is given by Equation 27. From Equation 27, the generator phase angle fluctuation can be estimated from the voltage fluctuation of the substation bus 10.

4 shows the power supply system when the voltage of the substation where the reactive power compensator 1 is installed and the generator internal voltage fluctuate. FIG. 5 shows the relationship between the system voltage, the substation voltage and the generator internal voltage. FIG. FIG. 6 illustrates temporal changes in the generator internal phase angle δ when the voltage V ₂ of the substation bus 10 fluctuates in a sine wave shape.

(3) Method for Estimating Generator Internal Voltage A method for estimating the generator internal voltage required as an input signal for nonlinear control from information in the substation where the reactive power compensator 1 is installed will be described.

As shown in FIG. 7, first, the voltage V ₂ of the substation bus 10 of the substation where the reactive power compensator 1 is installed and the current I ₁ flowing from the generator 6 into the substation bus are measured. Then determining the reactance X ₁ from the generator internal voltage to the substation bus from the operation information of the transmission line obtained by the substation.

The internal voltage E _q ′ of the generator 6 is calculated using Equation 28 from the voltage V ₂ of the substation bus 10, the transmission line current I ₁ and the reactance X ₁ . A vector diagram representing these relationships is shown in FIG.

(4) Generator frequency estimation method A method of estimating a generator frequency required as an input signal for nonlinear control from information in a substation in which the reactive power compensator 1 is installed will be described.

As shown in FIG. 7, when the active power flow flowing from the generator to the substation where the reactive power compensator 1 is installed via the transmission line is P ₁ , it can be expressed by Equation 27.

Where E _q ′ is the generator internal voltage, V ₂ is the substation voltage, θ _G is the generator phase angle, θ ₂ is the substation position angle, X ₁ is the reactance from the generator to the substation, and X ₂ is The reactance from the substation to the grid.

When the phase angle theta _G and theta ₂ changes by [Delta] [theta] _G and [Delta] [theta] ₂ by power fluctuation, and [Delta] P ₁ the change in P _1, the initial value of the phase angle theta _G and theta ₂ to the respective theta _G0 theta ₂₀ to the , Equation 30 is obtained, and Equation 31 is obtained by differentiating both sides of Equation 30.

When the active power flow that flows from the substation where the reactive power compensator 1 is installed to the grid via the transmission line is P ₂ , and the phase angles θ ₂ and θ _S change by Δθ ₂ and Δθ _S , the change of P ₂ When the minute is ΔP ₂ and the initial values of the phase angles θ ₂ and θ _S are θ ₂₀ and θ _S0 , respectively, Equation 32 is obtained.

If the load of the reactive power compensator 1 was placed substation is small, the number 31 and number 32 are equal, since when the capacity of the system side is larger Delta] f _s is substantially zero, the estimation of the generator frequency If the value is f _GS , it can be expressed by Equation 33.

  An example of obtaining a control amount for suppressing power fluctuation will be described in Example 1 and Example 2.

  FIG. 9 is a configuration diagram of the nonlinear control device 2 according to the first embodiment of the present invention. The present embodiment shows a case where the reactive power compensator 1 is installed in an intermediate substation of the power supply system.

  As shown in FIG. 9, the non-linear controller 2 is configured by, for example, a general purpose or dedicated digital controller, and includes a generator internal phase angle estimation unit 17, a generator internal voltage estimation unit 18, a generator frequency estimation unit 19, A differential calculation unit 20 and a control amount calculation unit 21 are included.

  In the generator internal phase angle estimator 17, the substation bus voltage 22, the system voltage estimate 23, the reactance 24 from the generator 6 to the substation bus 10, the reactance 25 from the substation to the grid, and the generator internal voltage estimate 26, the generator internal phase angle estimation value is calculated based on Equation 27.

  Here, the system voltage estimated value 23 is controlled so as not to change greatly and to keep the voltage constant because the system capacity is large, and therefore it can be assumed that it does not change from the initial value, and the initial value is used. The reactance 24 from the generator 6 to the substation bus 10 is calculated from a design value or an actual measurement value because the reactance of the generator, the transformer, and the transmission line is constant. Since the operating condition (number of lines) of the transmission line connected to the substation can be detected, it can be reflected in the assumed reactance. The reactance 25 from the substation to the grid can be obtained in the same manner as the reactance from the generator to the substation bus.

  The generator internal voltage estimated value 26 can be obtained by Equation 28 as described in (3) Generator internal voltage estimation method, and uses the output of the generator internal voltage estimation unit 18 shown in FIG. . That is, the generator internal voltage estimation unit 18 uses the substation bus voltage 22, the inflow current 27 from the generator 6 to the substation bus 10, and the reactance 24 from the generator 6 to the substation bus 10, to Based on this, the generator internal voltage estimated value is calculated.

  In the generator frequency estimation unit 19, the substation frequency 28, the generator internal voltage estimate 26, the system voltage estimate 23, the reactance 24 from the generator to the substation, the reactance 25 from the substation to the system, the generator internal phase angle Using the initial value 29, the substation bus phase angle initial value 30, and the system bus phase angle initial value 31, the generator frequency estimation value is calculated based on Equation 33. The differential operation unit 20 inputs the generator frequency estimation value and outputs the differential value. The control amount calculation unit 21 uses the outputs of the generator internal phase angle estimation unit 17, the generator internal voltage estimation unit 18, the generator frequency estimation unit 19, and the differential calculation unit 20 to calculate the control amount for power fluctuation suppression. 24 based on the calculation.

  FIG. 10 is a configuration diagram of a nonlinear controller 2 that is Embodiment 2 of the present invention. The present embodiment shows a case where the reactive power compensator 1 is installed at the power plant end of the power system.

  As shown in FIG. 10, the non-linear control device 2 is configured by, for example, a general purpose or dedicated digital controller, and functionally includes a generator internal phase angle estimation unit 17, a generator internal voltage estimation unit 18, a differential calculation unit. 20 and a control amount calculation unit 21.

  When installed at the end of the power plant, the generator frequency is assumed to be readily available, and the generator frequency estimation unit is omitted. In the generator internal phase angle estimator 17, the power plant bus voltage 34, the system voltage estimated value 23, the reactance 35 from the power generator 6 to the power plant bus 33, the reactance 36 from the power plant bus 33 to the system side substation bus 11, Using the generator internal voltage estimated value 26, the generator internal phase angle estimated value 41 is calculated based on Equation 27.

  Next, the generator internal voltage estimation unit 18 uses the power plant bus voltage 34, the generator current 38, and the reactance 35 from the generator 6 to the power plant bus 33 to calculate the generator internal voltage estimated value based on Equation 28. Calculate. The differential calculation unit 20 inputs the generator frequency 32 and outputs the differential value. The control amount calculation unit 21 uses the generator internal phase angle estimation unit 17, the generator internal voltage estimation unit 18, the generator frequency 32, and the output 37 of the differential calculation unit 20 to calculate the control amount for suppressing power fluctuations in Expression 24. Calculate based on

  According to the embodiment of the present invention, the control amount is calculated in consideration of the influence due to the non-linear characteristics of the system, so the control amount conforms to the actual system, and the installation capacity of the reactive power compensator is minimized. Therefore, the power fluctuation can be converged quickly and accurately by the stabilization control. In addition, even if the optimum value of the control gain for system stabilization changes due to changes in the system configuration of the power system, the opening of the transmission line due to failure removal, or changes in the generator output, etc. Can be easily reset automatically.

  Moreover, optimal system stabilization control can be performed by the reactive power compensator at all operating points. Further, the optimum value of the system stabilization control gain changes due to the change in the system configuration of the power system, the opening of the transmission line due to the failure removal, the change in the generator output, and the like. Even with such a change in operating conditions, an optimum stabilization control system can be reset by adjusting the control gain by inputting generator information and system information.

  In addition, the internal phase angle of the generator can be estimated from the information available at the substation, the optimal control gain can be calculated, the generator phase angle fluctuation becomes large, and even if the fluctuation of the generator active power enters the nonlinear region, it is optimal A stable control gain and power fluctuation can be suppressed.

  Especially for unstable power systems caused by power system failures, etc., applied to nonlinear control devices that implement stabilization control to maintain the generator phase angle and substation bus voltage within predetermined values. .

DESCRIPTION OF SYMBOLS 1 Reactive power compensator 2 Nonlinear controller 3 Voltage control block 4 Auxiliary transformer 5 Load 6 Generator 7 Automatic voltage controller 8 Generator bus 9 Generator transformer 10 Substation bus 11 System side substation bus 12 Main system 13 Load transformer

Claims (5)

  A reactive power compensator that includes a reactive power output circuit that is connected to the power system, supplies reactive power to the power system, and adjusts the voltage of the power system; and a control device that controls the reactive power output circuit. In addition to maintaining the voltage of the power system, the control device is capable of estimating a generator active power output estimated value, a generator internal voltage estimated value, a generator frequency estimated value, a generator internal phase angle estimated value, a system voltage estimated value, and A nonlinear system stabilization apparatus comprising a control gain adjustment unit of the reactive power output circuit for calculating a control amount based on an estimated system impedance value and suppressing power fluctuations by the calculated control amount .   2. The control device according to claim 1, wherein the control device optimizes the gain of the linear controller by strictly linearizing the non-linear power system by input conversion based on differential geometry, dynamic linearization feedback, and coordinate conversion. Non-linear system stabilizer.   Instead of using the generator internal phase angle, the controller estimates the generator internal phase angle based on substation bus voltage fluctuation, generator internal voltage estimate, grid voltage estimate and grid reactance estimate. The nonlinear system stabilization apparatus according to claim 1, wherein a control amount is calculated.   The control device calculates an optimum control amount by estimating the generator internal voltage based on the substation bus voltage, the system reactance estimated value, and the generator current estimated value, instead of using the generator internal voltage. The nonlinear system stabilization device according to claim 1.   The control device is based on substation bus frequency, generator internal voltage estimate, grid voltage estimate, grid reactance estimate, generator internal phase angle initial value and bus phase angle initial value instead of using generator frequency. The nonlinear system stabilization apparatus according to claim 1, wherein an optimal control amount is calculated by estimating a generator frequency.

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