Transient stability analysis method of grid-connected inverter based on iterative equal-area rule

Abstract

The present invention relates to power electronics technology, and specifically to a transient stability analysis method for grid-connected inverters based on the iterative equal-area rule, including establishing a mathematical model of a VSC connected to a weak power grid system, proposing a model correction term caused by a sudden change in the angular velocity of a phase-locked loop, and analyzing the influence of ignoring the sudden change in angular velocity on the synchronous stability of the system; iteratively calculating the power angle-damping function under the critical state, quantitatively analyzing the influence of damping on the stability of the system, and calculating a more accurate power angle stability range; and analyzing the influence of different controller parameters and network parameters on the stability of the system through the iterative equal-area method. This method effectively improves the analytical conservatism caused by the inability to quantitatively analyze the variable damping term in previous methods. The power angle-damping function under the critical state is estimated iteratively to achieve a quantitative analysis of the negative damping effect, and a relatively accurate estimate of the stability domain is obtained, which has good development potential and promotion space.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics, and in particular relates to a transient stability analysis method for a grid-connected inverter based on an iterative equal-area rule. Background Art

[0002] As the power system gradually develops towards a dual-high power system, VSC is widely used as an important interface for connecting new energy to the power grid. The synchronous instability problem of VSC connected to weak power grid systems is being widely studied and discussed.

[0003] At present, the research on VSC synchronous stability mainly includes time domain simulation method, phase diagram method, energy function-based method (Lyapunov method and Hamiltonian energy function), and equal area method. Among them, the time domain simulation method and phase diagram method are intuitive but cannot obtain the stability domain boundary in analytical form. Although the Lyapunov function can give an estimate of the stability domain in analytical form, the construction of the Lyapunov function is difficult, and the Lyapunov method is conservative. Although the traditional equal area method is simple and effective, it may lead to misjudgment of stability because it ignores the sudden change of angular velocity and cannot quantitatively analyze the impact of negative damping on system stability. For example, the patent with application publication number CN113612254A and invention name "Grid-connected inverter transient stability analysis method and related equipment" also quantitatively calculates the impact of nonlinear negative damping on system stability, but it involves the scaling process of the maximum angular velocity and ignores part of the energy consumed by the positive damping work. The obtained stability boundary is still quite conservative. Therefore, the large signal stability analysis method suitable for complex VSC systems still needs further research. Summary of the invention

[0004] In view of the problems existing in the background technology, the present invention provides a transient stability analysis method for a grid-connected inverter based on an iterative equal-area rule.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solution: a transient stability analysis method of a grid-connected inverter based on an iterative equal-area rule, characterized in that it includes the following steps:

[0006] Step 1: Establish a mathematical model of VSC connected to a weak power grid system, and determine a modified VSC second-order mathematical model according to a phase-locked loop angular velocity mutation correction term;

[0007] Step 2: Use the iterative equal-area method to analyze the system synchronization stability and estimate the power angle stability range by the iterative equal-area method;

[0008] Step 3: Use the iterative equal-area method to obtain the stability region of the system under different controller parameters and network parameters.

[0009] In the above-mentioned grid-connected inverter transient stability analysis method based on iterative equal-area rule, the implementation of step 1 includes the following steps:

[0010] Step 1.1, establish the second-order mathematical model of the VSC system;

[0011] (1)

[0012] (2)

[0013] in, V g is the amplitude of the weak grid, i g is the phase angle of the weak grid, R g is the equivalent resistance of the weak grid, L g is the equivalent inductance of the weak grid, V PCCq is the q-axis voltage at the common input terminal PCC of the phase-locked loop, V PCCd is the d-axis voltage at the common input terminal PCC of the phase-locked loop, f is the power factor of the line, φ=arctan ( i d * / i q * ), I g is the amplitude of the line current, and i gd =I g cosφ , i gq =I g sinφ are the dq axis components of the line current, and are the dq axis components of the current reference value, respectively, where i PLL is the reference phase of the phase-locked loop output;

[0014] (3)

[0015] Combine equations (2) and (3) and define d = i PLL - i g is the power angle of the system, K p andK i They are the proportional coefficient and integral parameter of the PI controller respectively; x 1 =d , x 2 =dδ / dt , and we get the following formula:

[0016] (4)

[0017] in:

[0018] (5);

[0019] Step 1.2, establishing a modified VSC second-order mathematical model;

[0020] The phase-locked loop has:

[0021] (6)

[0022] Among them, Δ V PCCq and Δ oh PLL Respectively V PCCq and oh PLL The mutation value of

[0023] Take the increments at both ends of equation (2) and substitute them into equation (6) to obtain Δ oh PLL The analytical expression of is:

[0024] (7)

[0025] Among them, Δ V g , Δ d , Δ L g and Δ I g Respectively V g , d , L g and I g The amount of mutation;

[0026] Combining (4) and (7), we can get the modified VSC second-order mathematical model:

[0027] (8).

[0028] In the above-mentioned grid-connected inverter transient stability analysis method based on iterative equal-area rule, the implementation of step 2 includes the following steps:

[0029] Step 2.1: Calculate the right boundary of the stable power angle d max ;

[0030] (9)

[0031] From formula (9), we can see that regardless of the positive or negative system damping, the right boundary of the power angle stability region in the transient process of the system is d max :

[0032] (10)

[0033] Step 2.2: Use the iterative equal-area method to calculate the left boundary of the stable power angle d min ;

[0034] The iterative equal-area method is implemented by iterating oh and D eq ( d ) Calculate a set of angular velocity and power angle functions oh ( d ):

[0035] (11)

[0036] in d min satisfy:

[0037] (12)

[0038] Calculate a set oh ( d ) as d The function satisfies: k 1- k 2- D eq ( d ) oh ( d ) in each d The acceleration and deceleration effect produced at oh ( d ) matches, and finally d max Slow down to oh =0;

[0039] Step 2.3, solve equations (11) and (12) by iterative method;

[0040] The angular velocity distribution without considering the damping effect is taken as the initial value oh 0( d ); iterative calculation oh i ( d ), consider D eq ( d ) oh i-1 ( d ) on the system motion, i Iteration cycle d mini satisfy: oh i-1 ( d mini )=Δ oh ( d mini );when d mini Converge to d min When (11)-(12) are approximately satisfied; exit the iteration, the estimate of the stable domain is [ d min , d max ]; The specific iteration process is as follows:

[0041] (13)

[0042] i =1 satisfies the following formula:

[0043] (14)

[0044] i = i +1 satisfies the following formula:

[0045] (15)

[0046] If formula (15) is satisfied, then:

[0047] (16)

[0048] If formula (15) is not satisfied, return to formula (14).

[0049] In the above-mentioned grid-connected inverter transient stability analysis method based on iterative equal-area rule, the implementation of step 3 includes the following steps:

[0050] Step 3.1, calculate the stability region of different controller parameters;

[0051] Changing the proportional coefficient of the phase-locked loop PI controller K p , using the iterative equal area method described in step 2, we can obtain different proportional coefficients K p Stable region under the condition of changing the integral parameter of the phase-locked loop PI controller K i , and obtain different integral parameters K i The stability domain below;

[0052] Step 3.2, calculate the stability region of different network parameters;

[0053] Changing the line current amplitude I g , using the iterative equal area method described in step 2, we can obtain different current amplitudes I g Stable domain under the change of grid voltage amplitude V g , get different voltage amplitudes V g The stability domain below.

[0054] Compared with the prior art, the present invention has the following beneficial effects: the present invention proposes a method for analyzing the synchronous stability of a grid-connected inverter based on a phase-locked loop by using an iterative equal-area rule, determines a modified VSC second-order mathematical model according to the phase-locked loop angular velocity mutation correction term, improves the shortcomings of the original model, and uses the iterative equal-area rule to obtain a relatively accurate estimate of the stability domain, greatly improving the conservatism of the original equal-area rule applied to the VSC system.

[0055] The present invention modifies the model. The second-order mathematical model in the prior art does not take into account the q-axis voltage at the PCC at the moment of mutation. V pccq The application derives a specific expression for the frequency mutation amount due to the frequency mutation caused by the mutation.

[0056] The iterative equal-area method proposed in this application has extremely high estimation accuracy for stability and can be theoretically non-conservative. The iterative equal-area method can accurately estimate the adverse effect of variable negative damping on system stability by iterating the angular velocity. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a flow chart of a method for analyzing transient stability of a grid-connected inverter based on the iterative equal-area rule according to an embodiment of the present invention;

[0058] Figure 2 A schematic diagram of a grid-connected inverter connected to an AC weak power grid system according to an embodiment of the present invention;

[0059] Figure 3 A schematic diagram of the structure of an SRF phase-locked loop according to an embodiment of the present invention;

[0060] Figure 4 A comparison diagram of transient waveforms of a circuit model, a model before correction, and a model after correction according to an embodiment of the present invention;

[0061] Figure 5 It is a flowchart of an iterative equal area method according to an embodiment of the present invention;

[0062] Figure 6 The proportional coefficients of different phase-locked loop PI controllers according to an embodiment of the present invention are K p Schematic diagram of the corresponding system stability domain;

[0063] Figure 7 The integral parameters of different phase-locked loop PI controllers according to an embodiment of the present invention are as follows: K i Schematic diagram of the corresponding system stability domain;

[0064] Figure 8 The current amplitudes of different lines in one embodiment of the present invention are shown in FIG. I g Schematic diagram of the corresponding system stability domain;

[0065] Figure 9 Different grid voltage amplitudes according to an embodiment of the present invention V g Schematic diagram of the corresponding system stability domain. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0068] The present invention will be further described below in conjunction with specific embodiments, but the present invention is not limited thereto.

[0069] This embodiment makes an iterative improvement to the traditional equal-area rule to adapt it to the particularity of the VSC system, thereby effectively improving the shortcomings of the traditional equal-area method in analyzing the synchronous stability of the VSC system. Considering that the VSC system is different from the SG system in terms of variable equivalent damping (even negative damping) and angular velocity mutation, the power angle-damping function in the critical state is estimated through the iterative equal-area calculation method, thereby achieving the purpose of using the equal-area rule to analyze the transient stability of the VSC under the conditions of negative damping and angular velocity mutation. This method uses the equal-area rule to effectively improve the analytical conservatism caused by the inability to quantitatively analyze the variable damping term in the previous method. Using an iterative process of negative feedback convergence, the power angle-damping function in the critical state is estimated, and the quantitative analysis of the negative damping effect is achieved, and a relatively accurate estimate of the stability domain is obtained, which greatly improves the conservatism of the original equal-area rule applied to the VSC system.

[0070] This embodiment is implemented by the following technical solutions: Figure 1 As shown in the figure, a transient stability analysis method for grid-connected inverters based on the iterative equal-area rule is proposed, including establishing a mathematical model of VSC connected to a weak power grid, proposing a correction term for angular velocity mutation, and proposing and using the iterative equal-area method to calculate the estimation of the transient stability domain of the system. The iterative equal-area method is used to analyze the influence of different controller parameters and network parameters on the transient stability of the system. The specific steps are as follows:

[0071] S1. Establish a mathematical model of VSC connected to a weak power grid system, propose the model correction term caused by the sudden change of angular velocity of the phase-locked loop, and analyze the adverse impact of ignoring the sudden change of angular velocity on the synchronization stability of the system;

[0072] S1.1 mathematical modeling of VSC connected to weak grid system;

[0073] Consider Figure 2 The VSC system shown in the figure is connected through an L-type filter with amplitude and phase angle respectively. V g and i g The equivalent resistance and inductance of the grid are 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 uses the q-axis voltage at the input common terminal PCC to control the current. V PCCq , achieving synchronization with the power grid.

[0074] The basic structure of a phase-locked loop is as follows: Figure 3As shown in the figure, the phase-locked loop (SRF-PLL) in a typical rotating reference coordinate system consists of a PARK converter and a PI controller. K p and K i are the proportional coefficient and integral parameter of the PI controller respectively. In general, considering that the dynamic response speed of the current loop and the line is much faster than that of the PLL, the dynamics of the two are ignored, and equations (1) to (2) can be derived:

[0075] (1)

[0076] (2)

[0077] in, f is the power factor of the line, φ=arctan ( i d * / i q * ), I g is the amplitude of the line current, and i gd = I g cosφ , i gq =I g sinφ are the dq axis components of the line current, and are the dq axis components of the current reference value respectively. For the phase-locked loop PLL, there is formula (3), where i PLL is the reference phase of the phase-locked loop output. Combining equations (2) and (3), and defining d = i PLL - i g , is the power angle of the system. x 1 =d , x 2 =dδ / dt , we can get formula (4):

[0078] (3)

[0079] (4)

[0080] in:

[0081] (5)

[0082] The above is the traditional second-order mathematical model of the VSC system.

[0083] S1.2 Although (4) is widely used in the existing VSC system synchronization stability, Figure 4 As shown, there is a significant error between the transient response waveform of (4) and the actual circuit model, which is mainly reflected in the overshoot and time delay. For (4), the angular velocity x 2 cannot mutate, which is limited by However, in the VSC system V PCCq Under the condition of large disturbance, it will change suddenly, and the phase-locked loop has:

[0084] (6)

[0085] Where Δ V PCCq and Δ oh PLL Respectively V PCCq and oh PLL The mutation value of .

[0086] This mutation is caused by the existence of the proportional link 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 change suddenly, while the output angular frequency of the synchronous motor cannot change suddenly. Ignoring the frequency mutation will lead to misjudgment of stability. The reason why there is no misjudgment of stability in the prior art is that the conservatism brought about by scaling and the energy consumed by ignoring the positive damping work are greater than the initial kinetic energy that is not considered. That is, for the actual phase-locked loop controller, its output angular velocity changes suddenly at the moment of disturbance, rather than the rotor angular velocity of the SG changing by the integral of acceleration.

[0087] Take the increments on both ends of equation (2) and substitute them into (6), and we can get Δ oh PLL The analytical expression of is:

[0088] (7)

[0089] Among them, Δ V g , Δ d , Δ L g and Δ I g Respectively V g , d , L g and I g The amount of mutation.

[0090] Combining equations (4) and (7), we can obtain the modified VSC second-order mathematical model:

[0091] (8)

[0092] like Figure 4 As shown, the revised mathematical model has a significant improvement in accuracy. Although there are still some errors, these errors are mainly caused by ignoring the current loop dynamics and line current dynamics.

[0093] S2. A synchronous stability analysis method for grid-connected inverters based on the iterative equal-area method is proposed. The power angle-damping function under the critical state is calculated iteratively, the influence of damping on system stability is quantitatively analyzed, and a more accurate power angle stability range is calculated.

[0094] S2.1 Calculate the right boundary of the stable power angle d max ;

[0095] From the analysis of S1.1, it can be seen that for the VSC system, the damping D eq = k 3+ k 4cos x 1 is variable and can even be negative. When the power angle reaches a certain value, the system damping may be negative, and negative damping is not conducive to the transient stability of the system. In the existing literature that uses the equal area rule to analyze the transient stability of VSC, the negative damping area is ignored or directly discarded, and it is believed that the system will become unstable once it enters the negative damping area, which will undoubtedly lead to excessive conservatism in the obtained stability domain. Or the variable damping term is directly ignored, but this will undoubtedly lead to the adverse effect of negative damping on the stability of the system, which may cause the obtained power angle stability domain to be too optimistic, leading to misjudgment of stability.

[0096] Regardless of the damping term D eq When the system moves to the rightmost end, the angular velocity of the system is zero. At this time, the damping term no longer affects the motion stability of the system, and we have:

[0097] (9)

[0098] From formula (9), we can see that regardless of the positive or negative system damping, the right boundary of the power angle stability region in the transient process of the system is d max :

[0099] (10).

[0100] S2.2 Calculate the left boundary of the stable power angle d min ;

[0101] The damping torque affects the angular velocity of the system in the dynamic process by doing work, and it is also affected by the angular velocity. The core of the iterative equal-area method is to iterate oh and D eq ( d ) Calculate a set of angular velocity ~ power angle functions oh ( d ):

[0102] (11)

[0103] in d min satisfy:

[0104] (12)

[0105] That is, calculate a set oh ( d ) as d The function satisfies: k 1- k 2- D eq ( d ) oh ( d ) in each d The acceleration and deceleration effect produced at oh ( d ) matches, and finally d max Slow down to oh = 0. In addition, the sudden change of angular velocity after disturbance is also considered: the initial angular velocity Δ oh ( d min ) and the initial power angle before disturbance d min Equation (12) uses the variable lower bound integral opposite to the actual physical process. That is, the initial state of the motion can be inferred from the final state of the system motion.

[0106] The main content of the iterative equal area method is to solve equations (11)-(12) through iteration. The flowchart of the iteration process is shown in the figure. Figure 5 As shown. The angular velocity distribution without considering the damping effect is taken as the initial value oh 0( d ). Iterative calculation ohi ( d ), consider D eq ( d ) oh i-1 ( d ) on the system motion, in the i-th iteration cycle d mini satisfy: oh i-1 ( d mini )=Δ oh ( d mini ).when d mini Converge to d min When , (11)-(12) are approximately satisfied. Exit the iteration, the estimation of the stable domain is [ d min , d max ].

[0107] S3. Through the iterative equal-area method proposed in S2, the influence of different controller parameters and network parameters on system stability is analyzed.

[0108] S3.1 first changes the proportional coefficient of the phase-locked loop PI controller K p , using the iterative equal-area method proposed in S2 multiple times, different K p The estimation of the stability region under Figure 6 Similarly, the integral parameter of the phase-locked loop PI controller is changed K i , you can get different K i The stability region estimate under Figure 7 shown.

[0109] S3.2 First change the line current amplitude I g , using the iterative equal-area method proposed in S2 multiple times, different I g The estimation of the stability region under Figure 8 Similarly, changing the grid voltage amplitude V g , you can get different V g The stability region estimate under Figure 9 shown.

[0110] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the specification of the present invention should be included in the protection scope of the present invention.

Claims

1. A transient stability analysis method for grid-connected inverters based on iterative equal-area rule, characterized by: The following steps are involved: Step 1: Establish a mathematical model of the VSC connected to a weak power grid system, and determine a modified VSC second-order mathematical model according to the phase-locked loop angular velocity mutation correction term; Step 2: Use the iterative equal-area method to analyze the system synchronization stability and estimate the power angle stability range by the iterative equal-area method; Step 3: Use the iterative equal area method to obtain the stability region of the system under different controller parameters and network parameters; The implementation of step 1 includes the following steps: Step 1.1, establish the second-order mathematical model of the VSC system; （1） （2） in, V g is the amplitude of the weak grid, θ g is the phase angle of the weak grid, R g is the equivalent resistance of the weak grid, L g is the equivalent inductance of the weak grid, V PCCq is the q-axis voltage at the common input terminal PCC of the phase-locked loop, V PCCd is the d-axis voltage at the common input terminal PCC of the phase-locked loop, φ is the power factor of the line, φ=arctan ( i d * / i q * ), I g is the amplitude of the line current, and i gd = I g cosφ , i gq =I g sinφ are the dq axis components of the line current, and are the dq axis components of the current reference value, respectively, where θ PLL is the reference phase of the phase-locked loop output; （3） Combine equations (2) and (3) and define δ = θ PLL - θ g is the power angle of the system, K p and K i They are the proportional coefficient and integral parameter of the PI controller respectively; x 1 =δ , x 2 =dδ / dt , we get the following formula: （4） in: （5）； Step 1.2, establishing a modified VSC second-order mathematical model; The phase-locked loop has: （6） Among them, Δ V PCCq and Δ ω PLL Respectively V PCCq and ω PLL The mutation value of Take the increments at both ends of equation (2) and substitute them into equation (6) to obtain Δ ω PLL The analytical expression of is: （7） Among them, Δ V g , Δ δ , Δ L g and Δ I g Respectively V g , δ , L g and I g The amount of mutation; Combining (4) and (7), we can get the modified VSC second-order mathematical model: （8）； The implementation of step 2 includes the following steps: Step 2.1: Calculate the right boundary of the stable power angle δ max ; （9） From formula (9), we can see that regardless of the positive or negative system damping, the right boundary of the power angle stability region in the transient process of the system is δ max : （10） Step 2.2: Use the iterative equal-area method to calculate the left boundary of the stable power angle δ min ; The iterative equal-area method is implemented by iterating ω and D eq ( δ ) Calculate a set of angular velocity and power angle functions ω ( δ ): （11） in δ min satisfy: （12） Calculate a set ω ( δ ) as δ The function satisfies: k 1- k 2- D eq ( δ ) ω ( δ ) in each δ The acceleration and deceleration effect produced at ω ( δ ) matches, and finally δ max Slow down to ω =0; Step 2.3, solve equations (11) and (12) by iterative method; The angular velocity distribution without considering the damping effect is taken as the initial value ω 0( δ ); iterative calculation ω i ( δ ), consider D eq ( δ ) ω i-1 ( δ ) on the system motion, i Iteration cycle δ mini satisfy: ω i-1 ( δ mini )=Δ ω ( δ mini );when δ mini Converge to δ min When (11)-(12) are approximately satisfied; exit the iteration, the estimate of the stable domain is [ δ min , δ max ]; The specific iteration process is as follows: （13） i =1 satisfies the following formula: （14） i = i +1 satisfies the following formula: (15) If formula (15) is satisfied, then: (16) If formula (15) is not satisfied, return to formula (14).

2. The transient stability analysis method for grid-connected inverter based on iterative equal-area rule according to claim 1, characterized in that: The implementation of step 3 includes the following steps: Step 3.1, calculate the stability region of different controller parameters; Changing the proportional coefficient of the phase-locked loop PI controller K p , using the iterative equal area method described in step 2, we can obtain different proportional coefficients K p Stable region under the condition of changing the integral parameter of the phase-locked loop PI controller K i , and obtain different integral parameters K i The stability domain below; Step 3.2, calculate the stability region of different network parameters; Changing the line current amplitude I g , using the iterative equal area method described in step 2, we can obtain different current amplitudes I g Stable domain under the change of grid voltage amplitude V g , get different voltage amplitudes V g The stability domain below.

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