CN114938029A - Grid-connected inverter transient stability analysis method based on iteration equal-area rule - Google Patents
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Abstract
The invention relates to the power electronic technology, in particular to a grid-connected inverter transient stability analysis method based on an iterative equal-area rule, which comprises the steps of establishing a mathematical model of a VSC (voltage source converter) connection weak grid system, providing a model correction term brought by angular velocity mutation of a phase-locked loop, and analyzing and ignoring the influence of the angular velocity mutation on the system synchronization stability; calculating a power angle-damping function in a critical state through iteration, quantitatively analyzing the influence of damping on the stability of the system, and calculating a more accurate power angle stable range; and analyzing the influence of different controller parameters and network parameters on the stability of the system by an iteration equal-area method. The method effectively improves the analysis conservation caused by the fact that the variable damping term cannot be quantitatively analyzed in the past method. The power angle-damping function under the critical state is estimated by iteration, the quantitative analysis of the negative damping effect is realized, a relatively accurate estimation of a stable domain is obtained, and the method has good development potential and popularization space.
Description
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to a grid-connected inverter transient stability analysis method based on an iteration equal-area rule.
Background
With the trend of power systems towards dual high power systems. VSC is widely used as an important interface for new energy to access a power grid. The problem of synchronous instability of VSC grid systems is being widely studied and discussed.
At present, the research on the VSC synchronization stability mainly comprises a time domain simulation method, a phase diagram method, a method based on an energy function (a Lyapunov method and a Hamilton energy function), an equal area method and the like. Although the time domain simulation method and the phase diagram method are intuitive, the boundary of the stable domain in the analytic form cannot be obtained, and although the Lyapunov function can give an estimation of the stable domain in the analytic form, the Lyapunov function is high in construction difficulty and strong in conservation of the Lyapunov method. Although the traditional equal area is simple and effective, because the influence of angular velocity mutation and the fact that negative damping cannot be quantitatively analyzed on the stability of the system is ignored, the misjudgment of the stability can be brought, for example: the patent with the application publication number of CN113612254A entitled "grid-connected inverter transient stability analysis method and related equipment" relates to a scaling process of the maximum angular velocity and neglects partial energy consumed by positive damping work, although the influence of nonlinear negative damping on the system stability is also quantitatively calculated, and the obtained stable boundary still has small conservatism. Therefore, a large signal stability analysis method suitable for a complex VSC system still needs to be further researched.
Disclosure of Invention
Aiming at the problems in the background art, the invention provides a grid-connected inverter transient stability analysis method based on an iteration equal-area rule.
In order to solve the technical problems, the invention adopts the following technical scheme: the grid-connected inverter transient stability analysis method based on the iteration equal-area rule is characterized by comprising the following steps of: the method comprises the following steps:
and 3, obtaining the stable domains of the system under different controller parameters and network parameters by using an iterative equal-area method.
In the grid-connected inverter transient stability analysis method based on the iterative equal-area rule, the implementation of the step 1 comprises the following steps:
step 1.1, establishing a second-order mathematical model of the VSC system;
wherein, V g Amplitude of weak grid, theta g Phase angle of weak grid, R g Is a weak grid equivalent resistance, L g Is a weak grid equivalent inductance, V PCCq Passing the q-axis voltage, V, at the input common terminal PCC for a phase locked loop PCCd For the phase locked loop to pass the d-axis voltage at the input common terminal PCC,
is the power factor of the line and,
I g is the amplitude of the line current and has
Respectively the dq-axis component of the line current,
and
dq-axis components of the current reference values, respectively, where θ PLL Is the reference phase of the phase-locked loop output;
formula (2) and formula (3) are combined, and δ ═ θ is defined PLL -θ g Is the power angle of the system, K p And K i Proportional coefficients and integral parameters of the PI controller are respectively; get x 1 ＝δ，x 2 D δ,/dt, giving the formula:
wherein:
step 1.2, establishing a corrected VSC second-order mathematical model;
the phase-locked loop comprises:
Δω PLL ＝K p ΔV PCCq (6)
wherein, is Δ V PCCq And Δ ω PLL Respectively represent V PCCq And omega PLL The mutation value of (a);
the two ends of the formula (2) are increased and substituted into the formula (6) to obtain delta omega PLL The analytical expression of (1):
wherein, is Δ V g ,Δδ,ΔL g And Δ I g Respectively represent V g ,δ,L g And I g The amount of mutation of (a);
and (4) and (7) are combined to obtain a corrected VSC second-order mathematical model:
in the grid-connected inverter transient stability analysis method based on the iterative equal-area rule, the step 2 comprises the following steps:
step 2.1, calculating the right boundary delta of the stable power angle max ；
As can be seen from the equation (9), the right boundary of the power angle stability domain in the transient process of the system is delta no matter whether the damping of the system is positive or negative max ：
δ max ＝arctan(k 1 /k 2 ) (10)
Step 2.2, calculating the left boundary delta of the stable power angle by using an iterative equal area method min ；
Iterative equal area method by iterating ω and D eq (δ) calculating a set of angular velocity and power angle functions ω (δ):
wherein delta min Satisfies the following conditions:
calculating a set of ω (δ) as a function of δ, satisfying: k is a radical of 1 -k 2 -D eq (δ) ω (δ) acceleration/deceleration produced at each δEffect, matching ω (δ) and finally δ max Decelerating to omega 0;
2.3, solving the formulas (11) and (12) by an iterative method;
the angular velocity distribution without considering the damping effect is taken as the initial value ω 0 (δ); iterative computation of omega i (δ) when considering D eq (δ)ω i-1 (delta) influence on System motion, delta in the ith iteration cycle mini Satisfies the following conditions: omega i-1 (δ mini )＝Δω(δ mini ) (ii) a When delta mini Converge to delta min When (11) - (12) are approximately satisfied; exit iteration, estimate of stable domain is [ delta ] min ,δ max ](ii) a The specific iterative process is as follows:
i 1 satisfies the following formula:
i +1 satisfies the following formula:
|δ mini -δ mini-1 |≤ε ？ (15)
if equation (15) is satisfied:
δ min ＝δ mini (16)
if equation (15) is not satisfied, equation (14) is returned.
In the above method for analyzing transient stability of a grid-connected inverter based on an iterative equal-area rule, the step 3 includes the following steps:
step 3.1, calculating stable domains of different controller parameters;
changing the proportionality coefficient K of a phase-locked loop PI controller p Obtaining different proportionality coefficients K by using the iterative equal-area method in the step 2 p A lower stability domain; changing an integral parameter K of a phase-locked loop PI controller i To obtain different integral parameters K i A lower stability domain;
step 3.2, calculating stable domains of different network parameters;
varying the amplitude I of the line current g Obtaining different current amplitudes I by using the iterative equal-area method in the step 2 g A lower stability domain; changing the voltage amplitude V of the network g To obtain different voltage amplitudes V g The lower stable domain.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a method for analyzing synchronization stability of a grid-connected inverter based on a phase-locked loop by using an iterative equal-area rule, wherein a corrected VSC second-order mathematical model is determined according to a phase-locked loop angular velocity mutation correction term, the defects of the original model are improved, a relatively accurate stable domain estimation is obtained by using the iterative equal-area rule, and the conservatism of the original equal-area rule applied to a VSC system is greatly improved.
The invention modifies the model, and the second-order mathematical model in the prior art does not consider the q-axis voltage V at PCC at the moment of mutation pccq The application deduces a specific expression of the frequency mutation.
The stability estimation precision of the iteration equal-area method is extremely high, and no conservatism can be achieved theoretically. The iteration equal-area rule can accurately estimate the adverse effect of the variable negative damping on the stability of the system through iteration of angular velocity.
Drawings
Fig. 1 is a flowchart of a grid-connected inverter transient stability analysis method based on an iterative equal-area rule according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a grid-connected inverter connected to an AC low-current grid system according to an embodiment of the invention;
FIG. 3 is a schematic diagram of an SRF phase-locked loop structure according to an embodiment of the present invention;
FIG. 4 is a graph showing a comparison of transient waveforms of a circuit model, a pre-modification model and a post-modification model in accordance with an embodiment of the present invention;
FIG. 5 is a flow chart of an iterative equal area method according to one embodiment of the present invention;
FIG. 6 shows different PLLs according to an embodiment of the present inventionProportional coefficient K of controller p A corresponding system stability domain schematic;
FIG. 7 shows an integration parameter K of different PLL PI controllers according to an embodiment of the present invention i A corresponding system stability domain schematic;
FIG. 8 shows different line current amplitudes I according to an embodiment of the present invention g A corresponding system stability domain schematic;
FIG. 9 shows different grid voltage amplitudes V according to an embodiment of the present invention g Corresponding system stability domain schematic.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the following embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The present invention is further illustrated by the following examples, which are not intended to limit the scope of the invention.
The embodiment effectively overcomes the defects of the traditional equal-area method in the analysis of the synchronization stability of the VSC system by performing an iterative improvement on the traditional equal-area method to adapt to the particularity of the VSC system. Considering variable equivalent damping (even negative damping) and angular velocity sudden change of the VSC system different from the SG system, estimating a power angle-damping function in a critical state by an iterative equal area calculation method, thereby realizing the purpose of analyzing the transient stability of the VSC under the condition of considering the negative damping and the angular velocity sudden change by using an equal area rule. The method selects the equal-area rule to effectively improve the analysis conservation caused by the fact that the variable damping term cannot be quantitatively analyzed in the conventional method. An iterative process of negative feedback convergence is used for estimating a power angle-damping function in a critical state, quantitative analysis of a negative damping effect is realized, a relatively accurate estimation of a stable domain is obtained, and the conservatism of the VSC system applied by the original equal-area rule is greatly improved.
The embodiment is realized by the following technical scheme, as shown in fig. 1, a grid-connected inverter transient stability analysis method based on an iterative equal-area rule includes establishing a VSC weak grid mathematical model, providing an angular velocity abrupt change correction term, and providing and using an iterative equal-area method to calculate the estimation of a transient stability domain of a system. And the influence of different controller parameters and network parameters on the transient stability of the system is analyzed by using an iterative equal-area method. The method comprises the following specific steps:
s1, establishing a mathematical model of the VSC connection weak current grid system, providing a model correction term brought by angular velocity mutation of a phase-locked loop, and analyzing and neglecting the adverse effect of the angular velocity mutation on the system synchronization stability;
s1.1, performing mathematical modeling on the VSC weak current grid system;
consider a VSC system as shown in figure 2, which passes an L-type filter with a magnitude and phase angle of V respectively g And theta g The equivalent resistance and inductance of the power grid are respectively R g And L g . The control part of the VSC uses a phase locked loop PLL and a current control loop. The phase-locked loop passes a q-axis voltage V at an input common terminal PCC PCCq And synchronization with the power grid is realized.
The basic structure of the phase-locked loop is shown in fig. 3, and a typical phase-locked loop (SRF-PLL) under a rotating reference frame consists of a PARK converter and a PI controller, where K is p And K i Respectively, the proportional coefficient and the integral parameter of the PI controller. In general, considering that the dynamic response speed of the current loop and the line is much faster than that of the PLL, equations (1) to (2) can be derived by neglecting the dynamics of the current loop and the line
Wherein the content of the first and second substances,
is the power factor of the line and,
I g is the amplitude of the line current and has
Respectively the dq-axis component of the line current,
and
dq-axis components, respectively, of the current reference value, for a phase-locked loop PLL, there is equation (3), where θ PLL Is the reference phase of the phase-locked loop output. Formula (2) and formula (3) are combined, and δ ═ θ is defined PLL -θ g The power angle of the system. Take x below 1 ＝δ，x 2 Given d δ,/dt, formula (4) can be obtained:
wherein:
the above is a traditional second order mathematical model of the VSC system.
S1.2 though(4) The formula is widely applied to the synchronization stability of the existing VSC system, but as shown in FIG. 4, transient response waveforms of the formula (4) and an actual circuit model have obvious errors, which are mainly reflected in overshoot and time delay. For the formula (4), the angular velocity x 2 Is not mutable, which is limited by
Is well-defined. However in VSC systems V PCCq Under the condition of large disturbance, the phase-locked loop is sudden change, and the phase-locked loop comprises the following components:
Δω PLL ＝K p ΔV PCCq (6)
wherein Δ V PCCq And Δ ω PLL Respectively represent V PCCq And omega PLL The mutation value of (2).
The sudden change is caused by the presence of the proportional loop of the PI controller in the phase locked loop. It is also an essential difference between the grid-connected inverter system and the synchronous motor: the output angular frequency of the grid-connected inverter can be suddenly changed, and the output angular frequency of the synchronous motor cannot be suddenly changed. Neglecting the frequency mutation can cause the misjudgment of stability, and the misjudgment of stability does not occur in the prior art because the conservatism caused by scaling and the energy consumed by neglecting the positive damping work application are larger than the initial kinetic energy which is not considered. That is, for a practical phase-locked loop controller, its output angular velocity is abrupt at the disturbed instant, rather than the SG-like rotor angular velocity being varied by the acceleration integral.
The increment is taken from the two ends of the formula (2) and substituted into the formula (6), thus obtaining the delta omega PLL The analytical expression of (c):
wherein, is Δ V g ,Δδ,ΔL g And Δ I g Respectively represent V g ,δ,L g And I g The amount of mutation of (c).
And (3) combining the formula (4) and the formula (7) to obtain a corrected VSC second-order mathematical model:
as shown in fig. 4, the corrected mathematical model has a large improvement in accuracy, and although there are some errors, these errors are mainly caused by neglecting the current loop dynamics and the line current dynamics.
S2, providing a synchronization stability analysis method of the grid-connected inverter based on an iteration equal-area method, calculating a power angle-damping function in a critical state through iteration, quantitatively analyzing the influence of damping on the stability of the system, and calculating a more accurate power angle stability range;
s2.1 calculating the right boundary delta for calculating the stable power angle max ；
From S1.1 analysis, it can be seen that for VSC systems, the damping is D eq ＝k 3 +k 4 cosx 1 The damping of the system may be negative when the power angle reaches a certain value, and the negative damping is not good for the transient stability of the system. In the existing literature for analyzing the transient stability of the VSC by applying an equal area law, a negative damping region is also or directly omitted, and the system is considered to be unstable once entering the negative damping region, which undoubtedly results in excessive conservation of the obtained stable region. The variable damping term is also directly ignored, but this will definitely cause the negative damping to have an adverse effect on the system stability, so that the resulting power angle stable region may be too optimistic, resulting in a stable misjudgment.
Irrespective of the damping term D eq When the system moves to the rightmost endpoint, the angular velocity of the system is zero, and the damping term does not influence the motion stability of the system any more, and the method comprises the following steps:
as can be seen from the equation (9), the right boundary of the power angle stability domain in the transient process of the system is delta no matter whether the damping of the system is positive or negative max ：
δ max ＝arctan(k 1 /k 2 ) (10)。
S2.2 calculating the left boundary delta of the Stable Power Angle min ；
The damping moment influences the angular speed of the system in the dynamic process by acting, and is influenced by the angular speed, and the core of the iteration equal-area method is that omega and D are iterated eq (δ) calculating a set of angular velocity-power angle functions ω (δ):
wherein delta min Satisfies the following conditions:
that is, a set of ω (δ) is calculated as a function of δ, satisfying: k is a radical of formula 1 -k 2 -D eq (delta) omega (delta) the acceleration and deceleration effect produced at each delta can be matched to omega (delta) and finally at delta max And decelerated to ω ═ 0. Furthermore, abrupt changes in the angular velocity after the disturbance are also considered: initial angular velocity Δ ω (δ) min ) And initial power angle delta before disturbance min It is relevant. (12) The equation uses a variable lower bound integral that is inverse to the actual physical process. I.e. to reverse the initial state of the motion from the final state of the system motion.
The main content of the iterative equal-area method is to solve equations (11) - (12) by an iterative method. A flow chart of the iterative process is shown in fig. 5. The angular velocity distribution without considering the damping effect is taken as the initial value ω 0 (δ). Iterative computation of omega i (δ) when considering D eq (δ)ω i-1 (delta) influence on System motion, delta in the ith iteration cycle mini Satisfies the following conditions: omega i-1 (δ mini )＝Δω(δ mini ). When delta mini Converge to delta min When (11) - (12) are satisfied approximately. Exit iteration, estimate of stable domain is [ delta ] min ,δ max ]。
S3, the influence of different controller parameters and network parameters on the system stability is analyzed through an iterative equal-area method provided by S2.
S3.1 first of all, the proportionality coefficient K of the phase-locked loop PI controller is changed p And different K can be obtained by repeatedly using the iterative equal-area method provided in S2 p The estimation of the next stable domain is shown in fig. 6. Similarly changing the integral parameter K of the phase locked loop PI controller i Can obtain different K i The following stable domain estimation is shown in fig. 7.
S3.2 first of all the line current amplitude I is changed g And repeatedly using the iterative equal-area method provided in S2 to obtain different I g The estimation of the lower stable domain is shown in fig. 8. Similarly changing the grid voltage amplitude V g Different V can be obtained g The following stable domain estimation is shown in fig. 9.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.
Claims (4)
1. The grid-connected inverter transient stability analysis method based on the iteration equal-area rule is characterized by comprising the following steps of: the method comprises the following steps:
step 1, establishing a mathematical model of the VSC connection weak grid system, and determining a corrected VSC second-order mathematical model according to a phase-locked loop angular velocity sudden change correction term;
step 2, analyzing the system synchronization stability by using an iterative equal-area method, and estimating a power angle stability range by using the iterative equal-area method;
and 3, obtaining the stable domains of the system under different controller parameters and network parameters by using an iterative equal-area method.
2. The grid-connected inverter transient stability analysis method based on the iterative equal-area rule according to claim 1, characterized in that: the implementation of step 1 comprises the following steps:
step 1.1, establishing a second-order mathematical model of the VSC system;
wherein, V g Amplitude of weak grid, theta g Phase angle of weak grid, R g Is a weak grid equivalent resistance, L g Is a weak grid equivalent inductance, V PCCq Passing the q-axis voltage, V, at the input common terminal PCC for a phase locked loop PCCd For the phase locked loop to pass the d-axis voltage at the input common terminal PCC,
is the power factor of the line and,
I g is the amplitude of the line current and has
Respectively the dq-axis component of the line current,
and
dq-axis components of the current reference values, respectively, where θ PLL Is the reference phase of the phase-locked loop output;
formula (2) and formula (3) are combined, and δ ═ θ is defined PLL -θ g Is the power angle of the system, K p And K i Proportional coefficients and integral parameters of the PI controller are respectively; get x 1 ＝δ，x 2 D δ,/dt, gives the following formula:
wherein:
step 1.2, establishing a corrected VSC second-order mathematical model;
the phase-locked loop comprises:
Δω PLL ＝K p ΔV PCCq (6)
wherein, is Δ V PCCq And Δ ω PLL Respectively represent V PCCq And ω PLL The mutation value of (a);
adding the increment of the two ends of the formula (2) and substituting the increment into the formula (6) to obtain delta omega PLL The analytical expression of (c):
wherein, is Δ V g ,Δδ,ΔL g And Δ I g Respectively represent V g ,δ,L g And I g The amount of mutation of (a);
and (4) and (7) are combined to obtain a corrected VSC second-order mathematical model:
3. the grid-connected inverter transient stability analysis method based on the iterative equal-area rule according to claim 1, characterized in that: the implementation of step 2 comprises the following steps:
step 2.1, calculating the right boundary delta of the stable power angle max ；
As can be seen from the equation (9), the right boundary of the power angle stability domain in the transient process of the system is delta no matter whether the damping of the system is positive or negative max ：
δ max ＝arctan(k 1 /k 2 ) (10)
Step 2.2, calculating the left boundary delta of the stable power angle by using an iterative equal area method min ；
Iterative equal area method by iterating ω and D eq (δ) calculating a set of angular velocity and power angle functions ω (δ):
wherein delta min Satisfies the following conditions:
calculating a set of ω (δ) as a function of δ, satisfying: k is a radical of formula 1 -k 2 -D eq (δ) ω (δ) the acceleration and deceleration effect produced at each δ, matching ω (δ) and finally δ (δ) max Decelerating to omega 0;
2.3, solving the formulas (11) and (12) by an iterative method;
the angular velocity distribution without considering the damping effect is taken as the initial value ω 0 (δ); iterative computation of omega i (δ) when considering D eq (δ)ω i-1 (delta) influence on System motion, delta in the ith iteration cycle mini Satisfies the following conditions: omega i-1 (δ mini )＝Δω(δ mini ) (ii) a When delta mini ConvergenceTo delta min When (11) - (12) are approximately satisfied; exit iteration, estimate of stable domain is [ delta ] min ,δ max ](ii) a The specific iterative process is as follows:
i 1 satisfies the following formula:
i +1 satisfies the following formula:
|δ mini -δ mini-1 |≤ε？ (15)
if equation (15) is satisfied:
δ min ＝δ mini (16)
if equation (15) is not satisfied, equation (14) is returned.
4. The grid-connected inverter transient stability analysis method based on the iterative equal-area rule according to claim 1, characterized in that: the implementation of step 3 comprises the following steps:
step 3.1, calculating stable domains of different controller parameters;
changing the proportionality coefficient K of a phase-locked loop PI controller p Obtaining different proportionality coefficients K by using the iterative equal-area method in the step 2 p A lower stability domain; changing an integral parameter K of a phase-locked loop PI controller i To obtain different integral parameters K i A lower stability domain;
step 3.2, calculating stable domains of different network parameters;
varying the amplitude of the line current I g Obtaining different current amplitudes I by using the iterative equal-area method in the step 2 g A lower stability domain; changing the voltage amplitude V of the network g To obtain different voltage amplitudes V g The lower stable domain.
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