CN105279368A - Non-damping stability analysis method for three-phase grid-connection system - Google Patents

Abstract

The invention relates to the field of system stability analysis and provides a non-damping stability analysis method for a three-phase grid-connection system. According to an embodiment of the invention, a mathematic model of a system in a discrete digital domain is established, then a ratio relationship between a zero pole position and a resonant control frequency of the discrete system is obtained according to the mathematic model, and the system is subjected to non-damping stability analysis according to the ratio relationship, so that the grid-connection system can be improved in stability and working efficiency.

Description

The method of a kind of three-phase grid system undamped stability analysis

Technical field

The invention belongs to system stability analysis field, particularly relate to the method for a kind of three-phase grid system undamped stability analysis.

Background technology

In recent years, along with the aggravation of environmental pollution, fossil energy problem in short supply, the development and utilization of regenerative resource receives the concern of increasing country, and distributed generation system becomes a kind of new forms of energy comprehensive utilization mode of great development market owing to having the features such as initial stage hypothesis investment is low, generation mode is flexible.Grid-connected converter, as the energy interface unit between distributed generation system and electrical network public access point, is extremely important ingredient in distributed generation system.

Because grid-connected converter adopts high frequency PWM technique usually, in grid-connected current, can higher hamonic wave be contained, therefore need to adopt this harmonic noise of wave filter filtering.Adopt LCL filter not only can obtain good filter effect, can reduce costs simultaneously, raising system dynamic responding speed, but because LCL filter is a third-order system, resonance spikes can be there is in resonance frequency place amplitude-versus-frequency curve, phase-frequency characteristic curve has the phase angle sudden change of-180 °, this can cause system oscillation even unstable.In order to suppress the harm of resonance, need to carry out damping control to resonance spikes, traditional method has: 1), passive Damping Schemes changes system matrix by increasing passive damping resistance, increase system damping, suppress resonance spikes, but the method can increase system loss, reduce system effectiveness.2), active damping schemes is detect other state variables to introduce multi partitioning control system, thus increases system damping, and the method needs extra sensor, increases cost, and multi partitioning parameter designing is complicated simultaneously.

Between LCL filter parameters, contact closely, certain impact all can be produced on the important parameter such as filter effect, resonance frequency value, current attenuation ratio of system, simultaneously, in the process of design, the restrictive condition that needs consider is also a lot, as cost, volume, efficiency, loss, reactive power exchange etc., therefore the parameter designing of LCL filter is complicated.Traditional design method is all in the LCL filter parameter not considering to design under system stability condition, adopts passive damping or active damping stability control program to improve the stability of system after having designed.

Summary of the invention

The object of this invention is to provide the method for a kind of three-phase grid system undamped stability analysis, solve the above-mentioned problems in the prior art.

The technical scheme that the present invention solves the problems of the technologies described above is as follows: the method for a kind of three-phase grid system undamped stability analysis, is characterized in that, said method comprising the steps of:

Set up the mathematical model under the discrete digital territory of system;

The zero pole point position of discrete system and the ratio relation of resonance controlled frequency is obtained according to described mathematical model;

According to described ratio relation, undamped stability analysis is carried out to system.

Further, the step of the mathematical model under the described discrete digital territory setting up system, comprising:

Open-loop transfer function according to following formula computing system:

$G_k\left(z\right)={\mathrm{aK}}_p(1+\frac{1}{T_i}\frac{T_{s}z}{z-1})\frac{z^2-2bz+1}{z(z-1)(z^2-2z\cos ({\mathrm{\ω}}_{res}{T}_s)+1)};$

Wherein:

$a=\frac{{\mathrm{\ω}}_{res}{T}_s-sin\left({\mathrm{\ω}}_{res}{T}_s\right)}{(L+L_g){\mathrm{\ω}}_{res}};$

$b=\frac{sin\left({\mathrm{\ω}}_{res}{T}_s\right)-{\mathrm{\ω}}_{res}{T}_{c}cos\left({\mathrm{\ω}}_{res}{T}_s\right)}{{\mathrm{\ω}}_{res}{T}_s-sin\left({\mathrm{\ω}}_{res}{T}_s\right)};$

represent the resonance angular frequency of LCL filter;

The scale factor getting system resonance frequencies and sample frequency is k, that is:

$k=\frac{{\mathrm{\ω}}_{res}}{{\mathrm{\ω}}_s}$

The discrete open-loop transfer function then going up plane system can be reduced to following formula:

$G_k\left(z\right)={\mathrm{aK}}_p(1+\frac{1}{T_i}\frac{T_{s}z}{z-1})\frac{z^2+2bz+1}{z(z-1)(z^2-2zcos(2\mathrm{\π}k)+1)}$

Wherein:

$a=\frac{2\mathrm{\π}k-sin\left(2\mathrm{\π}k\right)}{k(L+L_g){\mathrm{\ω}}_s};$

$b=\frac{sin\left(2\mathrm{\π}k\right)-2\mathrm{\π}kcos\left(2\mathrm{\π}k\right)}{2\mathrm{\π}k-sin\left(2\mathrm{\π}k\right)};$

L represents current transformer side filter inductance; L _grepresent grid side filter inductance; C _frepresent filter capacitor; R represents the equivalent damping resistance on inverter side actual inductance model; r _grepresent the equivalent series resistance on grid side actual inductance model and the resistance on grid-connected circuit; C ₊represent positive direct-current bus capacitor; C _-represent negative dc-link capacitance, K _p, T _iproportional gain and the integration time constant of pi regulator respectively, T _srepresent the sampling period of discrete system.

Further, described step of according to described ratio relation, system being carried out to undamped stability analysis, comprising:

As k=0.1, along with system open loop gain K _pincrease, the element branches of root locus trends towards infinity from unit circle, and root locus is positioned at outside unit circle, and system does not exist stable interval;

As k=0.25, along with open-loop gain K _pincrease, the root locus element branches of system has and is positioned within unit circle, and system exists stable possibility;

As k=0.4, root locus plot is positioned within unit circle, along with K _pincrease root locus away from unit circle;

Namely along with the increase of k, system can be transitioned into conditional stability from instability.

The invention has the beneficial effects as follows: the present invention is by the mathematical model under the discrete digital territory of setting up system, then the zero pole point position of discrete system and the ratio relation of resonance controlled frequency is obtained according to described mathematical model, and according to described ratio relation, undamped stability analysis is carried out to system, make grid-connected system to improve stability, submit work efficiency to.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the method for the three-phase grid system undamped stability analysis that the embodiment of the present invention provides;

Fig. 2 is the three-phase grid-connected converter physical topological structure based on LCL filtering;

Fig. 3 is three-phase grid-connected converter system architecture control block diagram;

Fig. 4 is system discrete domain open-loop transfer function root locus plot figure under different value of K.

Embodiment

Be described principle of the present invention and feature below in conjunction with accompanying drawing, example, only for explaining the present invention, is not intended to limit scope of the present invention.

Below in conjunction with specific embodiment, specific implementation of the present invention is described in detail:

Fig. 1 shows the flow process of the method for the three-phase grid system undamped stability analysis that the embodiment of the present invention provides, and for convenience of explanation, only list the part relevant to the embodiment of the present invention, details are as follows:

The method of the three-phase grid system undamped stability analysis that the embodiment of the present invention provides, comprises the following steps:

Step S10, sets up the mathematical model under the discrete digital territory of system;

Step S20, obtains the zero pole point position of discrete system and the ratio relation of resonance controlled frequency according to described mathematical model;

Step S30, carries out undamped stability analysis according to described ratio relation to system.

As Fig. 2,3,4, as one embodiment of the present invention, according to the possibility that the root locus analysis system undamped of system open loop discrete domain transport function is stable.Set up the mathematical model under the discrete digital territory of system, draw the control structure block diagram of discrete system as shown in Figure 3, current inner loop system adopts pi regulator to control, and particularly, the implementation of step S10 is:

Open-loop transfer function according to following formula computing system:

$G_k\left(z\right)={\mathrm{aK}}_p(1+\frac{1}{T_i}\frac{T_{s}z}{z-1})\frac{z^2-2bz+1}{z(z-1)(z^2-2z\cos ({\mathrm{\ω}}_{res}{T}_s)+1)};$

Wherein:

$a=\frac{{\mathrm{\ω}}_{res}{T}_s-sin\left({\mathrm{\ω}}_{res}{T}_s\right)}{(L+L_g){\mathrm{\ω}}_{res}};$

$b=\frac{sin\left({\mathrm{\ω}}_{res}{T}_s\right)-{\mathrm{\ω}}_{res}{T}_{c}cos\left({\mathrm{\ω}}_{res}{T}_s\right)}{{\mathrm{\ω}}_{res}{T}_s-sin\left({\mathrm{\ω}}_{res}{T}_s\right)};$

represent the resonance angular frequency of LCL filter;

The scale factor getting system resonance frequencies and sample frequency is k, that is:

$k=\frac{{\mathrm{\ω}}_{res}}{{\mathrm{\ω}}_s}$

The discrete open-loop transfer function then going up plane system can be reduced to following formula:

$G_k\left(z\right)={\mathrm{aK}}_p(1+\frac{1}{T_i}\frac{T_{s}z}{z-1})\frac{z^2+2bz+1}{z(z-1)(z^2-2zcos(2\mathrm{\π}k)+1)}$

Wherein:

$a=\frac{2\mathrm{\π}k-sin\left(2\mathrm{\π}k\right)}{k(L+L_g){\mathrm{\ω}}_s};$

$b=\frac{sin\left(2\mathrm{\π}k\right)-2\mathrm{\π}kcos\left(2\mathrm{\π}k\right)}{2\mathrm{\π}k-sin\left(2\mathrm{\π}k\right)};$

T ₁-T ₆it is the power switch pipe of 3-phase power converter; L represents current transformer side filter inductance; L _grepresent grid side filter inductance; C _frepresent filter capacitor; R represents the equivalent damping resistance on inverter side actual inductance model; r _grepresent the equivalent series resistance on grid side actual inductance model and the resistance on grid-connected circuit; C ₊represent positive direct-current bus capacitor; C _-represent negative dc-link capacitance, K _p, T _iproportional gain and the integration time constant of pi regulator respectively, T _srepresent the sampling period of discrete system.

As the preferred embodiment of the present invention, in step S30, the implementation that system carries out undamped stability analysis is specially:

As k=0.1, along with the increase of system open loop gain, the element branches of root locus trends towards infinity from unit circle, and root locus is positioned at outside unit circle, and system does not exist stable interval;

As k=0.25, along with the increase of open-loop gain Kp, the root locus element branches of system has and is positioned within unit circle, and system exists stable possibility;

As k=0.4, root locus plot is positioned within unit circle, along with the increase root locus of Kp is away from unit circle;

Namely along with the increase of k, system can be transitioned into conditional stability from instability.

For the converter control system of reality, if sample frequency fixed, then resonance frequency can be regarded as is a variable element.Can be known by open-loop transfer function, the zero pole point position of discrete system is only relevant with the ratio k value of resonance controlled frequency, and other coefficients only affect the gain of open-loop transfer function.

In embodiments of the present invention, in embodiments of the present invention, by the mathematical model under the discrete digital territory of setting up system, then the zero pole point position of discrete system and the ratio relation of resonance controlled frequency is obtained according to described mathematical model, and according to described ratio relation, undamped stability analysis is carried out to system, make grid-connected system to improve stability, submit work efficiency to.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1. a method for three-phase grid system undamped stability analysis, is characterized in that, said method comprising the steps of:

Set up the mathematical model under the discrete digital territory of system;

The zero pole point position of discrete system and the ratio relation of resonance controlled frequency is obtained according to described mathematical model;

According to described ratio relation, undamped stability analysis is carried out to system.

2. method according to claim 1, is characterized in that, the step of the mathematical model under the described discrete digital territory setting up system, comprising:

Open-loop transfer function according to following formula computing system:

$G_k\left(z\right)={\mathrm{aK}}_p(1+\frac{1}{T_i}\frac{T_{s}z}{z-1})\frac{z^2-2bz+1}{z(z-1)(z^2-2z\cos ({\mathrm{\ω}}_{res}{T}_s)+1)};$

Wherein:

$a=\frac{{\mathrm{\ω}}_{res}{T}_s-sin\left({\mathrm{\ω}}_{res}{T}_s\right)}{(L+L_g){\mathrm{\ω}}_{res}};$

$b=\frac{sin\left({\mathrm{\ω}}_{res}{T}_s\right)-{\mathrm{\ω}}_{res}{T}_{c}cos\left({\mathrm{\ω}}_{res}{T}_s\right)}{{\mathrm{\ω}}_{res}{T}_s-sin\left({\mathrm{\ω}}_{res}{T}_s\right)};$

represent the resonance angular frequency of LCL filter;

The scale factor getting system resonance frequencies and sample frequency is k, that is:

$k=\frac{{\mathrm{\ω}}_{res}}{{\mathrm{\ω}}_s}$

The discrete open-loop transfer function then going up plane system can be reduced to following formula:

$G_k\left(z\right)={\mathrm{aK}}_p(1+\frac{1}{T_i}\frac{T_{s}z}{z-1})\frac{z^2+2bz+1}{z(z-1)(z^2-2zcos(2\mathrm{\π}k)+1)}$

Wherein:

$a=\frac{2\mathrm{\π}k-sin\left(2\mathrm{\π}k\right)}{k(L+L_g){\mathrm{\ω}}_s};$

$b=\frac{sin\left(2\mathrm{\π}k\right)-2\mathrm{\π}kcos\left(2\mathrm{\π}k\right)}{2\mathrm{\π}k-sin\left(2\mathrm{\π}k\right)};$

L represents current transformer side filter inductance; L _grepresent grid side filter inductance; C _frepresent filter capacitor; R represents the equivalent damping resistance on inverter side actual inductance model; r _grepresent the equivalent series resistance on grid side actual inductance model and the resistance on grid-connected circuit; C ₊represent positive direct-current bus capacitor; C _-represent negative dc-link capacitance, K _p, T _iproportional gain and the integration time constant of pi regulator respectively, T _srepresent the sampling period of discrete system.

3. method according to claim 1, is characterized in that, described step of according to described ratio relation, system being carried out to undamped stability analysis, comprising:

As k=0.1, along with system open loop gain K _pincrease, the element branches of root locus trends towards infinity from unit circle, and root locus is positioned at outside unit circle, and system does not exist stable interval;

As k=0.25, along with open-loop gain K _pincrease, the root locus element branches of system has and is positioned within unit circle, and system exists stable possibility;

As k=0.4, root locus plot is positioned within unit circle, along with K _pincrease root locus away from unit circle;

Namely along with the increase of k, system can be transitioned into conditional stability from instability.