KR20110067946A - Nonlinear feedback control method for statbility of the internal dynamics in static synchronous compensator - Google Patents

Abstract

PURPOSE: A nonlinear feedback control method for stabilizing the inner dynamics of a static synchronous compensator is provided to increase the lifetime of a capacitor by decreasing impact applied to the capacitor. CONSTITUTION: A reactive current outputted from a static synchronous compensator is fed back and is added to a reactive current reference value(Iqref). The added value multiplied by the gain of a proportional controller is inputted to a static synchronous compensator. A firing angle of a voltage controlling the inverter of the input and output linearized static synchronous compensator is added to a derivative term. The derivative term is the time of an active current multiplied by a variable gain coefficient to damp a control signal.

Description

Nonlinear Feedback Control Method for Stabilization of Internal Dynamics in Stationary Synchronous Ancestors

The present invention relates to a non-linear feedback control method for stabilizing internal dynamics in a stationary synchronous throttle, more specifically, to a control signal through a closed loop feedback control method in a static synchronous throttle (hereinafter referred to as STATCOM). The present invention relates to a nonlinear feedback control method for stabilization of internal dynamics in a stationary synchronous throttle that can improve the stability of internal dynamics by adding nonlinear damping.

STATCOM is a synchronous voltage source that acts like a generator. The 3-phase inverter is connected in parallel with the AC system. It is designed to compensate for reactive power in the AC transmission system to maximize the transmission capacity of existing lines while maintaining the safety and efficiency of the system. It is a device having.

In analyzing STATCOM, which is a non-linear system, a second internal dynamic of the active current (Id) and the DC voltage (Vdc) appears through the input / output linearization technique. STATCOM's voltage control method and transient stability improvement method have been studied for a long time, and STATCOM's internal dynamics instability has been studied in terms of tracking performance and stabilization of closed loop system.

Here, nonlinear controller based on I / O linearization through closed loop feedback has improved performance than proportional integral controller using fixed gain, but nonlinear controller using I / O linearization technique guarantees stable output characteristics over the entire operating range of STATCOM. But internal dynamics can have large vibrations.

Let's take a look at the characteristics of STATCOM system.

1 is a circuit diagram showing an equivalent circuit of STATCOM.

As shown in FIG. 1, the STATCOM 100 converts an output voltage of three phases by adjusting a DC voltage of an input terminal using the voltage inverter 10. Here, the resistor Rs connected in series with the AC line represents the conduction loss between the voltage inverter 10 and the transformer, and the inductance Ls represents the leakage impedance of the transformer. In addition, the resistor Rp connected in parallel with the capacitor C represents the switching loss of the inverter.

Among the inverter control methods of the STATCOM system, the PWM method simultaneously adjusts the factor K indicating the magnitude relationship between the firing angle of the voltage (hereinafter referred to as α) and the peak voltage of the DC voltage to the AC voltage stage, but here only the α is used as the inverter method. Based on the considerations, the mathematical state equation model of STATCOM using the equivalent circuit of FIG. 1 is given by Equation 1 below.

[Equation 1]

here

[A] =

As shown in Equation 1, the STATCOM system has nonlinearity due to the trigonometric term for α, but it can be solved by linearizing the Iq following control problem using the input / output linearization technique.

FIG. 2A is a system structure diagram of a STATCOM having an internal dynamics using an input / output linearization technique, and FIG. 2B is a system structure diagram of a STATCOM having a following closed loop structure.

As shown in FIG. 2A, since the STATCOM system to which the input / output linearization technique is applied has a relative degree of 1, the relationship between the new input υ and the output Iq can be represented through a single integrator. It has a secondary subsystem that includes the dynamic active current Id and the DC voltage Vdc. The internal dynamics are not observable at the reactive current Iq, which is the output of STATCOM, and do not affect the output.

In STATCOM having the following closed loop of FIG. 2B, the firing angle α of the voltage which is the inverter control input in Equation 1 is equal to Equation 2.

[Equation 2]

Where the new input υ is

이다.

to be.

Where L = transformer leakage inductance, Id = active current, Vdc = DC voltage at the input terminal, Rs = conduction loss between the inverter and transformer, C = capacitor at DC stage, Iq = reactive current, λ = proportional controller gain, Iqref = Reactive current reference value, Wb = frequency, k = value indicating magnitude relationship between peak voltage of DC voltage and AC voltage terminal.

Here, the equation of the STATCOM system where the input / output linearization is applied by applying a proportional (P) controller having a gain of λ for simple development of the equation is shown in Equation 3 below.

[Equation 3]

The exact mathematical model of Equation 3 is described in the reference formula below.

[Reference Formula]

The proportional controller of Equation 2 applied to the system of the STATCOM having the following closed loop structure of FIG. 2b allows the input / output linearized STATCOM system to estimate the desired Iq. However, the proportional controller of Equation 2 has internal dynamics (Id, Vdc). ) Does not affect stabilization.

In other words, the ripple of the internal dynamics corresponds to the current ripple of the capacitor (C in FIG. 1) of the DC stage, so that the large overshoot and slow response speed of the current ripple is the lifetime of the capacitor C of the DC stage. There is a problem that shortens.

The present invention has been made to solve the above problems, it is possible to improve the stability of the internal dynamics by adding nonlinear damping to the control signal through the closed loop feedback control method in the STATCOM It is an object of the present invention to provide a non-linear feedback control method for stabilization of internal dynamics in a stationary synchronous ancestor.

Nonlinear feedback control method for stabilization of the internal dynamics in the stationary synchronous ancestor of the present invention for achieving the above object is for stabilization of the internal dynamics in the stationary synchronous ancestor having a closed loop control method applying the input and output linearization technique A nonlinear feedback control method comprising the steps of: feeding back a reactive current (Iq) which is an output of a stationary synchronous ancestor to add an reactive current reference value (Iqref) to an addition (Iqref-Iq); Inputting a value (υ) obtained by multiplying the addition value (Iqref-Iq) by the proportional controller gain (λ) to the stationary synchronous ancestor; And the firing angle α ₂ of the voltage controlling the inverter of the input / output linearized stationary synchronous compensator is a derivative of the effective current (Id) multiplied by a coefficient having a variable gain to damp the control signal (dId / dt). It characterized in that it comprises a step of adding).

Also, the firing angle α ₂ of the voltage controlling the inverter of the input / output linearized stationary synchronous compensator is calculated by Equation 5 below, and the variable gain of the derivative with respect to the time of the active current is g (Iq−Iqx). It is characterized by.

[Equation 5]

here

이다.

to be.

Where L = transformer leakage inductance, Id = active current, Vdc = DC voltage at input, Rs = conduction loss between inverter and transformer, C = capacitor at DC, Iq = reactive current, g = real constant, Iqx = The value varies depending on the value of Vdc, Wb = frequency, and k = a value representing the magnitude relationship between the peak voltage of the DC voltage and the AC voltage terminal.

In addition, the nonlinear feedback control method for stabilizing the internal dynamics in the stationary synchronous squirrel includes a firing angle of the voltage to which the derivative term dId / dt is added to the time of the effective current Id multiplied by the coefficient having the variable gain. α ₂ ) to improve the stability of the internal dynamics by moving the poles of the internal dynamics to the left _half surface LHP.

According to the present invention, according to the non-linear feedback control method for stabilizing the internal dynamics in a stationary synchronous squirrel, by applying the gain value varying for each operating point to the derivative value with respect to the time of the active current, It can be seen that the settling time is shortened and overshoot is reduced. In other words, as the ripple of the capacitor in the DC stage is reduced, it has the advantage of increasing the life of the capacitor by reducing the impact on the capacitor.

Hereinafter, the configuration and operation of the preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings. Here, the same reference numerals will be used for the same components as the prior art.

Here, the nonlinear feedback control method (II) will be described first, and the nonlinear feedback control method (III) for stabilization of the internal dynamics in the stationary synchronous ancestor of the present invention will be described by comparing with the nonlinear feedback control method (II).

The nonlinear track control method (II) is expressed by Equation 4 below, which is obtained by multiplying the derivative of the effective current ld of the firing angle α of the voltage of the formula 2 by the product of the constant gain δ. do.

[Equation 4]

here

이다.

to be.

In the nonlinear feedback control method (II), the larger the gain of the constant gain δ, the larger the movement range of the pole of the internal dynamics according to the change of the operating point. Depending on the operating point, the larger the constant gain δ, the more stable or unstable the internal dynamics may be. For example, in the inductive mode region, the larger the constant gain δ, the more unstable the internal dynamics.

Hereinafter, a non-linear feedback control method (III) for stabilizing internal dynamics in a stationary synchronous precipitator of the present invention is disclosed.

The nonlinear feedback control method (III) for stabilizing the internal dynamics in the stationary synchronous ancestor of the present invention is defined as in Equation 5 below.

[Equation 5]

here

이다.

to be.

Where L = transformer leakage inductance, Id = active current, Vdc = DC voltage at input, Rs = conduction loss between inverter and transformer, C = capacitor at DC, Iq = reactive current, g = real constant, Iqx = Vdc The value varies depending on the value of Wb = frequency, k = the value representing the magnitude relationship between the peak voltage of the DC voltage and the AC voltage terminal.

The controller output according to the nonlinear feedback control method (III) of the present invention has an added term compared with Equation 2. In other words, the derivative term (dId / dt term) with respect to the time of ld is multiplied by a gain g (Iq-Iqx) that varies depending on the operating point. Where g is a real constant and Iqx is a value that changes with the value of Vdc.

Compared with the nonlinear feedback control method (II), the nonlinear feedback control method (II) has a fixed constant gain (δ) with respect to the derivative term with respect to the time of ld, but the nonlinear feedback control method (III) of the present invention As the varying gain g (Iq-Iqx) is multiplied, it moves the pole of the internal diner mix from the imaginary axis to the left plane. On the other hand, the nonlinear feedback control method (II) is for improving the damping of the response, while the nonlinear feedback control method (III) of the present invention is for the stability of the internal dynamics.

Hereinafter, the effects of the nonlinear feedback control method (II) and the nonlinear feedback control method (III) of the present invention will be described through the pole analysis of the closed loop STATCOM system.

When I / O linearization is first performed, the closed loop STATCOM system has three poles. The real pole is one equal to the proportional controller gain (λ) and the other two are poles of the internal dynamics independent of the proportional controller gain (λ).

3 is a graph showing the poles at each operating point for each constant gain δ of the nonlinear feedback control method II.

As shown in Fig. 3, for each constant gain δ in the operating region of -1 [pu] to 1 [pu], the real pole exactly matches the controller gain when the constant gain δ is not zero. But not within the range of ± 0.5. If the constant gain (δ) is positive, the pole will be in the right plane (RHP). Since the real pole is five times larger than the complex pole, the position of the complex pole can predict the response of the internal dynamics (Id, Vdc).

When the operating range is from -1.0 [pu] to 0.6 [pu], the smaller the constant gain δ, the larger the real size of the complex pole of the internal dynamics. On the other hand, when the operating range is 0.6 [pu] to 1.0 [pu], the internal dynamics have the most unstable characteristic when the constant gain (δ) = -0.06 and the settling time (Ts) decreases as the constant gain (δ) decreases. It gets longer and the overshoot gets bigger.

It can be concluded from the pole distribution diagram of FIG. 3 by the nonlinear track control method II that the constant gain δ varying at each operating point is required to improve the performance and stability of the internal dynamics.

Fig. 4 is a graph showing the poles at each operating point for varying gain g (Iq-Iqx) of the nonlinear track control method III according to the present invention.

The nonlinear track control method (III) of the present invention applying an appropriate real constant (g) value has a stable internal dynamics in all operating regions. When applying the nonlinear track control method (III), the pole of real number does not coincide completely with the controller gain and varies with a large range depending on the operating point. It also does not always have a value greater than the complex pole. However, the position of the complex poles can be expected to have improved performance when the controller is applied.

In other words, when the nonlinear track control method (III) of the present invention is applied, the real root portion of the pole of the internal dynamics has a value 1.5 to 129 times larger than when the nonlinear track control method (II) is applied. Therefore, when the nonlinear track control method (III) using the variable gain [g (Iq-Iqx)] at each operating point is applied to the STATCOM system, the settling time (Ts) of Id and Vdc becomes shorter and the overshoot becomes smaller. It can be expected that the response characteristics will be improved.

In order to prove a control method in an ideal environment of a STATCOM system constructed in a MATLAB / simulink environment, a proportional control method (P controller), a nonlinear feedback control method (Controller 1), and a nonlinear feedback control method of the present invention (Controller) through an averaged model The settling time Ts according to 2) is compared with the overshoot.

Control performance criteria are defined as Ts <16 [ms], ess <5 [%], and% OS <10 [%].

When Iq reference (Iqref: reactive current reference value) is 0.8 [pu], FIG. 5 is a graph showing the vibration of the internal dynamics Id, and FIG. 6 is a graph showing the vibration of the internal dynamics Vdc.

As shown in FIG. 5 and FIG. 6, when the nonlinear track control method (Controller 2) of the present invention is used, the vibrations of Id and Vdc are reduced the fastest. Since the poles of the internal dynamics according to the nonlinear track control method (Controller 2) of the present invention are far to the left than the poles according to the proportional control method (P controller) and the nonlinear track control method (Controller 1), they are internal at all operating points. It can be seen that the performance is excellent for the dynamics.

That is, it can be seen that the stability of the internal dynamics of the STATCOM system can be improved through the nonlinear track control method (Controller 2) of the present invention by the gain [g (Iq-Iqx)] changing in FIGS. 5 and 6.

FIG. 7 is a graph comparing gains multiplied with derivative terms for time of an effective current of the nonlinear feedback control method (III) and the nonlinear feedback control method (II) of the present invention. As shown in Fig. 7, the gain of the nonlinear feedback control method (II) is fixed to δ while the gain g (Iq-Iqx) of the nonlinear feedback control method (III) of the present invention changes with each operating point. Can be.

It is apparent to those skilled in the art that the present invention is not limited to the above embodiments and can be practiced in various ways without departing from the technical spirit of the present invention. will be.

1 is a circuit diagram showing an equivalent circuit of STATCOM.

FIG. 2A is a system structure diagram of a STATCOM having internal dynamics using an input / output linearization technique, and FIG. 2B is a system structure diagram of a STATCOM having a following closed loop structure.

3 is a graph showing the poles at each operating point for each constant gain δ of the nonlinear feedback control method II.

Fig. 4 is a graph showing the poles at each operating point for varying gain g (Iq-Iqx) of the nonlinear track control method III according to the present invention.

5 is a graph showing the vibration of the internal dynamics Id, and FIG. 6 is a graph showing the vibration of the internal dynamics Vdc.

FIG. 7 is a graph comparing gains multiplied with derivative terms for time of an effective current of the nonlinear feedback control method (III) and the nonlinear feedback control method (II) of the present invention.

<Description of the symbols for the main parts of the drawings>

10: Inverter 100: Stop type synchronous compensator

200: proportional controller

Claims (3)

In the nonlinear feedback control method for stabilization of internal dynamics in a stationary synchronous ancestor having a closed loop control method using an input / output linearization technique, Feeding back the reactive current Iq, which is the output of the stationary synchronous compensator, and adding the reactive current reference value Iqref to Iqref-Iq; Inputting a value (υ) obtained by multiplying the addition value (Iqref-Iq) by the proportional controller gain (λ) to the stationary synchronous ancestor; And The firing angle (α ₂ ) of the voltage controlling the inverter of the input / output linearized stationary synchronous compensator is the derivative term (dId / dt) with respect to the time of the effective current (Id) multiplied by a coefficient having a variable gain in order to damp the control signal. Nonlinear feedback control method for the stabilization of the internal dynamics in the stationary synchronous ancestor characterized in that it comprises a step of adding. The method of claim 1, The firing angle α ₂ of the voltage controlling the inverter of the input / output linearized stationary synchronous compensator is calculated by Equation 5 below, and the variable gain of the derivative with respect to the time of the active current is g (Iq−Iqx). Nonlinear feedback control method for stabilization of internal dynamics in a stationary synchronous ancestor. [Equation 5]

,

. Where L = transformer leakage inductance, Id = active current, Vdc = DC voltage at input, Rs = conduction loss between inverter and transformer, C = capacitor at DC, Iq = reactive current, g = real constant, Iqx = The value varies depending on the value of Vdc, Wb = frequency, and k = a value representing the magnitude relationship between the peak voltage of the DC voltage and the AC voltage terminal. The method according to claim 1 or 2, The nonlinear feedback control method for stabilizing the internal dynamics in a stationary synchronous compensator has a firing angle (α ₂ ) of a voltage added with a derivative term (dId / dt) with respect to the time of the effective current (Id) multiplied by the variable gain coefficient. Nonlinear feedback control method for stabilization of internal dynamics in a stationary synchronous ancestor, characterized by improving the stability of the internal dynamics by moving the pole of the internal dynamics to the left half surface (LHP).

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