Damping Analysis Method for the Generation Mechanism of Low-Frequency Oscillations in Microgrids Based on Equivalent Circuits

Abstract

The present invention discloses a damping analysis method for the generation mechanism of low-frequency oscillations in a microgrid based on an equivalent circuit. (1) Determine the control strategy of the inverter in the microgrid; (2) Establish an equivalent circuit model of the PI controller; (3) Establish an equivalent circuit model of the voltage-current double closed-loop control; (4) Establish an equivalent circuit model of the droop power control; (5) Establish a mathematical model of the overall equivalent circuit of the droop control inverter; (6) Analyze the low-frequency oscillation mechanism; (7) Discriminate and verify the oscillation mechanism. It can intuitively and clearly reflect the physical meaning of each part of the system, and can analyze the low-frequency oscillation from a mathematical perspective to determine its internal generation mechanism.

Description

Technical Field

[0001] The present invention relates to the technical field of low-frequency oscillation damping analysis methods, and in particular to a damping analysis method for a low-frequency oscillation generation mechanism of a microgrid based on an equivalent circuit. Background Art

[0002] Microgrids contain a variety of micro sources, which are generally connected to microgrids through inverters. Therefore, inverter control is the core of microgrid research. Among the various inverter control methods, droop control has become the mainstream control strategy for inverter parallel connection because it fully meets the plug-and-play characteristics of distributed power sources. Droop control adds a power outer loop on the basis of the voltage and current double closed loop to achieve autonomous power sharing of parallel inverters, but droop control cannot change the low inertia characteristics of the inverter. When the parallel system is subject to small disturbances, it will produce oscillation in the low-frequency mode, making the microgrid system difficult to work or even unstable.

[0003] Studying the generation mechanism of low-frequency oscillation is the starting point for suppressing low-frequency oscillation. Different suppression measures are taken according to different generation mechanisms to improve the stability of the microgrid system. There are two widely recognized mechanism explanations for low-frequency oscillation in power systems: one is the negative damping mechanism, and the other is the forced power oscillation based on the resonance mechanism. In the context of microgrids, the current research hotspots are mostly on analysis methods and various suppression measures such as eigenvalue analysis and impedance analysis. However, both eigenvalue analysis and impedance analysis are difficult to intuitively and clearly reflect the physical meaning of the system, and cannot give the internal mechanism of low-frequency oscillation. There is a lack of detailed mathematical explanation for the generation mechanism of low-frequency oscillation in microgrids. It can be seen that it is very necessary to study the generation mechanism of low-frequency oscillation in microgrids.

[0004] At present, domestic and foreign scholars have done a lot of research on the detailed mechanism analysis of low-frequency oscillation in microgrid systems. Some literatures calculate the inherent resonance point of the machine-grid system by treating the proportional integral link of the current controller as a virtual resistor and a virtual capacitor, thereby explaining the mechanism of electrical oscillation of the machine-grid system. However, this literature only uses the concept of "RLC equivalent circuit" and does not really establish an RLC equivalent circuit model. There are also literatures that study the equivalent circuit models of off-grid inverters in voltage control mode and grid-connected inverters in current control mode, which also include PI controllers and PR controllers. However, none of the existing literatures have equivalent the droop power loop, which is not suitable for the establishment of a droop control system model, and the established equivalent circuit model has not been further applied to more intuitively reveal the internal mechanism of low-frequency oscillation. Summary of the invention

[0005] In view of the above-mentioned technical deficiencies, the purpose of the present invention is to provide a damping analysis method for the low-frequency oscillation generation mechanism of a microgrid based on an equivalent circuit, which can intuitively and clearly reflect the physical meaning of each part of the system, analyze the low-frequency oscillation from a mathematical perspective, and determine its internal generation mechanism.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] The present invention provides a damping analysis method for a microgrid low-frequency oscillation generation mechanism based on an equivalent circuit, comprising the following steps:

[0008] (1) Determine the control strategy of the inverter in the microgrid: the droop control strategy of the “droop power loop-voltage loop-current loop”, where the droop control equation is:

[0009]

[0010]

[0011] In the formula, ω * and ω 0 are the inverter output voltage angular frequency and rated angular frequency, ω c is the cut-off frequency of the low-pass filter, U o * and U 0 are the inverter output voltage amplitude and rated voltage amplitude respectively, p and q are the instantaneous values ​​of the inverter output active power and reactive power, P and P 0 Divided into filter output active power and rated active power, Q and Q 0 are the filter output reactive power and rated reactive power, respectively, and m and n are the droop coefficients of P~f and Q~U, respectively;

[0012] The voltage loop-current loop control equation is:

[0013]

[0014]

[0015] In the formula, G PI,V and G PI,C is the PI regulator of the voltage loop and current loop, k vp and k vi is the proportional gain and integral gain of the voltage loop PI control, k cp and k ci is the proportional gain and integral gain of the current loop PI control; v d,q is the dq component of the inverter output voltage; i d,q is the dq component of the inverter output current; u *d,q is the dq component of the voltage loop PI modulation output; v * d,q is the dq component of the current loop PI modulation output; i dref and i qref is the output setting of the voltage loop; U * od,q is the dq component of the output voltage given by reactive droop control; v dref and v qref is the output of the current loop, C f and L f are the capacitance and inductance values ​​of LC filtering;

[0016] (2) performing equivalent circuit modeling of the PI controller according to the control strategy determined in step (1);

[0017] (3) performing equivalent circuit modeling of voltage and current dual closed-loop control according to the equivalent circuit model of the PI controller established in step (2);

[0018] (4) performing equivalent circuit modeling of droop power control according to the control strategy determined in step (1);

[0019] (5) establishing a mathematical model of the overall equivalent circuit of the droop control inverter based on the equivalent circuit model of the droop power control established in step (4) and the equivalent circuit model of the voltage and current dual closed-loop control established in step (3);

[0020] (6) analyzing the low-frequency oscillation mechanism based on the mathematical model of the overall equivalent circuit of the droop control inverter established in step (5);

[0021] (7) According to the low-frequency oscillation mechanism analysis results of step (6), the oscillation mechanism is identified and verified.

[0022] Preferably, the PI controller in step (2) includes a current tracking PI controller and a voltage tracking PI controller, wherein the current tracking PI controller is used to adjust the output current i and the command current i of the controlled object. ref The deviation signal i e Input to the PI controller for adjustment to obtain the output control voltage signal u i , the control voltage signal u i The calculation is done using the following formula:

[0023]

[0024] The voltage tracking PI controller is used to track the command value u through the output voltage u feedback of the controlled object. ref , the voltage deviation signal u eTo adjust the output current i of the controller, the output current i is calculated using the following formula:

[0025]

[0026] Preferably, the transfer function of the dual closed-loop control of the equivalent circuit model of the voltage and current dual closed-loop control is as follows:

[0027]

[0028] In the formula, u * and u o It is the given voltage and output voltage of the inverter double closed-loop control.

[0029] Preferably, the given voltage u of the inverter double closed-loop control * And the output voltage u o The amplitude and phase difference are:

[0030]

[0031] Preferably, the simplified third-order mathematical model of the overall equivalent circuit of the droop control inverter is:

[0032]

[0033] Where: u Cf is the filter capacitor voltage in the LC filter.

[0034] The beneficial effects of the present invention are:

[0035] 1. The present invention establishes an equivalent RLC circuit of a complete droop control inverter system, and uses the established equivalent circuit to obtain a system mathematical model, which can analyze the low-frequency oscillation mechanism of the system in detail.

[0036] 2. The present invention can break through the limitation of unclear physical meaning of eigenvalue analysis and impedance analysis. The equivalent circuit can intuitively give the actual physical meaning of each parameter of each part of the system, which is conducive to analyzing the internal mechanism of low-frequency oscillation.

[0037] 3. The present invention can provide new ideas for the analysis of low-frequency oscillation mechanisms in microgrids, and at the same time provide theoretical support for the research on low-frequency oscillation suppression measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0039] Figure 1 is a block diagram of a droop control inverter system of the present invention;

[0040] Figure 2 is an equivalent circuit of the current tracking PI controller of the present invention;

[0041] Figure 3 is an equivalent circuit of the voltage tracking PI controller of the present invention;

[0042] Figure 4 is a controller equivalent circuit model of the voltage source inverter of the present invention;

[0043] Figure 5 It is the equivalent circuit model of the voltage and current double closed loop of the present invention;

[0044] Figure 6 is an equivalent circuit model of the droop power control of the present invention;

[0045] Figure 7 is the overall equivalent circuit model of the droop control inverter system of the present invention;

[0046] Figure 8 An equivalent circuit model of a basic unit of the present invention;

[0047] Fig. 9 is an equivalent circuit model of a simplified droop control inverter of the present invention;

[0048] Fig.10 is a graph of different types of low frequency oscillations of the present invention;

[0049] Fig.11 The m of the present invention 2 =5.5×10 -5 The output active power of the inverter system at the time;

[0050] Fig.12 The m of the present invention 2 =5.5×10 -5 The waveform of the maximum output current of the inverter system when ;

[0051] Fig.13 The m of the present invention 2 =5.5×10 -5FFT analysis of inverter output power oscillation. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in 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.

[0053] like Figures 1 to 13 As shown, this embodiment provides a damping analysis method for the low-frequency oscillation generation mechanism of a microgrid based on an equivalent circuit, comprising the following steps:

[0054] (1) Determine the control strategy of the inverter in the microgrid: the droop control strategy of “droop power loop-voltage loop-current loop”, establish the mathematical model of the three-phase voltage source inverter, and the system block diagram is as follows: Figure 1 As shown in the figure, the droop control strategy realizes the regulation of voltage and frequency by simulating the primary frequency regulation and primary voltage regulation process of the synchronous generator in the power system. In order to suppress the fluctuation of output power, a low-pass filter is used to filter out the high-frequency component of the output instantaneous power. The droop control equation is:

[0055]

[0056]

[0057] In the formula, ω * and ω 0 are the inverter output voltage angular frequency and rated angular frequency, ω c is the cut-off frequency of the low-pass filter, U o * and U 0 are the inverter output voltage amplitude and rated voltage amplitude respectively, p and q are the instantaneous values ​​of the inverter output active power and reactive power, P and P 0 Divided into filter output active power and rated active power, Q and Q 0 are the filter output reactive power and rated reactive power, respectively, and m and n are the droop coefficients of P~f and Q~U, respectively;

[0058] The voltage loop and the current loop form a dual closed-loop controller, in which the inverter output voltage tracks the reference given by the droop power loop output voltage, and the current loop outputs the command voltage vector to the SVPWM module to improve the dynamic response characteristics of the system and enhance the system's anti-disturbance ability. The voltage loop-current loop control equation is:

[0059]

[0060]

[0061] In the formula, G PI,V and G PI,C is the PI regulator of the voltage loop and current loop, k vp and k vi is the proportional gain and integral gain of the voltage loop PI control, k cp and k ci is the proportional gain and integral gain of the current loop PI control; v d,q is the dq component of the inverter output voltage; i d,q is the dq component of the inverter output current; u * d,q is the dq component of the voltage loop PI modulation output; v * d,q is the dq component of the current loop PI modulation output; i dref and i qref is the output setting of the voltage loop; U * od,q is the dq component of the output voltage given by reactive droop control; v dref and v qref is the output of the current loop, C f and L f are the capacitance and inductance values ​​of LC filtering;

[0062] (2) performing equivalent circuit modeling of the PI controller according to the control strategy determined in step (1);

[0063] (3) performing equivalent circuit modeling of voltage and current dual closed-loop control according to the equivalent circuit model of the PI controller established in step (2);

[0064] (4) performing equivalent circuit modeling of droop power control according to the control strategy determined in step (1);

[0065] (5) establishing a mathematical model of the overall equivalent circuit of the droop control inverter based on the equivalent circuit model of the droop power control established in step (4) and the equivalent circuit model of the voltage and current dual closed-loop control established in step (3);

[0066] (6) analyzing the low-frequency oscillation mechanism based on the mathematical model of the overall equivalent circuit of the droop control inverter established in step (5);

[0067] (7) According to the low-frequency oscillation mechanism analysis results of step (6), the oscillation mechanism is identified and verified.

[0068] According to the difference between the voltage loop and current loop reference instructions, there are two types of PI controllers, namely current tracking type and voltage tracking type. For the current tracking type PI controller, such as Figure 2 As shown in (a), the controller converts the output current i of the controlled object and the command current i ref The deviation signal i e Input to the PI controller for adjustment to obtain the output control voltage signal u i .like Figure 2 As shown in (b), for a series RC circuit, if the current flowing through each component is i e , then the voltage expression of the branch is the same as the mathematical model expression of the current tracking PI control unit, and its expression is shown in formula (5). There is a dual relationship between the parameters of the two, that is, k cp =R, k ci =1 / C.

[0069]

[0070] For voltage tracking PI controller, such as Figure 3 As shown in (a), the output voltage u of the controlled object is fed back and its command value u is tracked. ref , the voltage deviation signal u e To adjust the output current i of the controller. Use GL parallel branch to simulate, such as Figure 3 (b), its expression is shown in formula (6), and the parameter duality relationship between the two is: vp =G,k vi =1 / L.

[0071]

[0072] The classic voltage and current dual closed-loop control block diagram is as follows: Figure 4 As shown in (a), by combining two PI controllers, the three-phase two-level inverter is regarded as a controlled voltage source, and its equivalent circuit model is as follows: Figure 4 (b) As shown. Considering that the inverter adopts LC filter, the equivalent circuit model of voltage and current double closed-loop control established in step (2) can be obtained, as shown in Figure 5 As shown; the transfer function of the double closed-loop control is as follows:

[0073]

[0074] In the formula, u * and u o is the given voltage and output voltage of the inverter double closed-loop control. Corresponding to the power frequency fundamental voltage, the amplitude and phase difference between the two are:

[0075]

[0076] Therefore, the inverter bridge arm output voltage u o and u * There is little difference between them, and they can be approximated to each other. The parameter duality relationship is: G u =k vp , L u =1 / k cv , R c =k cp , C i =1 / k ci .

[0077] According to the droop control equation in step (1), the low-pass filter can be equivalent to an RC circuit and satisfies RC = 1 / ω c , assuming R = 1, then C = 1 / ω c , the equivalent circuit model of droop power control can be obtained, as Figure 6 Combined with the equivalent circuit model of the dual closed-loop control established in step (2), the overall equivalent circuit model of the droop control inverter system can be obtained, as shown in Figure 7 shown.

[0078] Consider the inverter equivalent circuit with dual closed-loop controller in step (3) as a basic unit, such as Figure 8 As shown, the circuit is analyzed and according to Kirchhoff's law, we can get:

[0079]

[0080] In the formula, u 1 is the parallel voltage of the voltage loop equivalent circuit, the equivalent voltage u Lf is the filter inductor voltage in the LC filter. By simplifying the above formula, the third-order mathematical model of the basic unit can be obtained as shown below.

[0081]

[0082] Combining the droop power control equation in step 1) with equation (10), we can obtain:

[0083]

[0084] By simplifying the above formula, we can get the fourth-order mathematical model of the complete droop control inverter system, as shown below.

[0085]

[0086] The order of equations (10) and (12) is reduced; U mentioned in equation (2) * ois a constant. According to the characteristics of capacitors “blocking DC and passing AC” and inductors “passing DC and blocking AC”, the capacitors are open-circuited and the inductors are short-circuited. The third-order mathematical model of the complete droop control inverter system can be obtained by simplification, as shown in formula (13), where u Cf is the filter capacitor voltage in the LC filter. The simplified equivalent circuit model of the droop control inverter system is as follows: Fig. 9 shown.

[0087]

[0088] The characteristic equation and characteristic root can be obtained from formula (13). Analysis of the characteristic root shows that the low-frequency oscillation caused by the droop control strategy is mainly related to the power control part, and its damping is affected by the droop parameter. According to the different characteristics of the negative damping mechanism and the resonance mechanism, the low-frequency oscillation caused by the droop control strategy does not conform to the resonance mechanism, and it does not have a continuous periodic small disturbance with a frequency consistent with the system's natural oscillation frequency; it conforms to the negative damping mechanism. As the value of the droop coefficient changes, the power control part will affect the damping of the system until an oscillation phenomenon occurs.

[0089] The differences in the upper envelope and spectrum characteristics of the low-frequency oscillation curves caused by the negative damping mechanism and the resonance mechanism are used to distinguish the two mechanisms, and the mechanism of low-frequency oscillation caused by the droop control strategy is further determined. Fig.10 is a graph of different types of low-frequency oscillations, where Fig.10 (a) and Fig.10 (b) is a negatively damped power oscillation, and the shape of the upper envelope is mainly a concave curve or a straight line; Fig.10 (c) and Fig.10 (d) is the forced power oscillation. The shape of the upper envelope is mainly a convex curve. There are obvious differences in the upper envelope curves of power oscillations caused by different oscillation mechanisms.

[0090] The present embodiment is simulated, verified and analyzed in Matlab / Simulink. The simulation system includes two inverters. The active power droop parameter of one inverter is fixed. The active power droop parameter of the other inverter is changed. The low-frequency instability waveform is observed to analyze its characteristics. Fig.11 and Fig.12 is m 2 =5.5×10 -5 The waveforms of the maximum active power and output current of the two inverters at . It can be found that the active power waveforms of the two inverters are both oscillating with increasing amplitude, and the amplitude gradually increases. At this time, the system is unstable, and the upper envelope of the active power oscillation curve is a concave curve, which is consistent with Fig.10 (a) The shape characteristics of the upper envelope in the negatively damped power oscillation curve are consistent. Fig.13 is m 2 =5.5×10 -5From the FFT analysis of power oscillation, it can be seen from the power spectrum that there are a lot of harmonics in the active power below 10Hz, and except for the DC component, the two sides are evenly distributed decreasingly with 4Hz as the center, and the maximum value is obtained at the low-frequency oscillation frequency. At this time, there is a low-frequency negative damping oscillation.

[0091] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. Damping analysis method for the generation mechanism of low-frequency oscillations in a microgrid based on an equivalent circuit, characterized in that, it includes the following steps: (1) Determine the control strategy of the inverter in the microgrid: the droop control strategy of "droop power loop - voltage loop - current loop", where the droop control equation is: ； ； Wherein, ω * and ω 0 are respectively the angular frequency of the inverter output voltage and the rated angular frequency, ω c is the cut-off frequency of the low-pass filter, U o * and U 0 are respectively the amplitude of the inverter output voltage and the rated voltage amplitude, p and q are the instantaneous values of the active power and reactive power output by the inverter, P and P 0 are respectively the active power output by the filter and the rated active power, Q and Q 0 are respectively the reactive power output by the filter and the rated reactive power, m is the active power output by the filter The droop coefficient of P; n is the reactive power output by the filter Q is the droop coefficient; The control equations of the voltage loop - current loop are: ； ； Wherein, G PI,V and G PI,C are the PI regulators of the voltage loop and the current loop, k vp and k vi are the proportional gain and integral gain of the PI control of the voltage loop, k cp and k ci are the proportional gain and integral gain of the PI control of the current loop; v d,q is the dq component of the inverter output voltage; U * od,q are the dq components of the output voltage reference of the reactive power droop control; i d,q is the dq component of the inverter output current; u * d,q is the dq component of the output of the PI modulation of the voltage loop; v * d,q is the dq component of the output of the PI modulation of the current loop; i dref and i qref are the output references of the voltage loop; v dref and v qref are the outputs of the current loop, C f and L f are LC the capacitance value and inductance value of the filter; (2) Perform equivalent circuit modeling of the PI controller according to the control strategy determined in step (1); (3) Perform equivalent circuit modeling of the voltage-current double closed-loop control according to the equivalent circuit model of the PI controller established in step (2); (4) Perform equivalent circuit modeling of the droop power control according to the control strategy determined in step (1); (5) Establish a mathematical model of the overall equivalent circuit of the droop control inverter based on the equivalent circuit model of the droop power control established in step (4) and the equivalent circuit model of the voltage-current double closed-loop control established in step (3); (6) Perform low-frequency oscillation mechanism analysis according to the mathematical model of the overall equivalent circuit of the droop control inverter established in step (5); (7) Perform oscillation mechanism discrimination and verification according to the results of the low-frequency oscillation mechanism analysis in step (6).

2. The damping analysis method for the generation mechanism of low-frequency oscillations in a microgrid based on an equivalent circuit according to claim 1, characterized in that, The PI controller in step (2) includes a current tracking PI controller and a voltage tracking PI controller. The current tracking PI controller is used to control the output current of the controlled object. i and command current i ref The deviation signal i e Input to the PI controller for adjustment to obtain the output control voltage signal u i , the control voltage signal u i The calculation is done using the following formula: ； The voltage-tracking PI controller is used to feedback through the output voltage of the controlled object and track its command value u and regulate the output current of the controller by the voltage deviation signal u ref u e The output current is calculated by the following formula: i i ​​​ 。 3. The damping analysis method for the generation mechanism of low-frequency oscillations in a microgrid based on an equivalent circuit according to claim 1, characterized in that, The transfer function of the double closed-loop control of the equivalent circuit model of the voltage-current double closed-loop control is as follows: ； In the formula, u * and u o are the given voltage and output voltage of the dual closed-loop control of the inverter.

4. The damping analysis method for the generation mechanism of low-frequency oscillations in a microgrid based on an equivalent circuit according to claim 3, characterized in that, The given voltage of the double closed-loop control of the inverter u * and the output voltage u o The amplitude and phase difference are as follows: 。 5. The damping analysis method for the generation mechanism of low-frequency oscillations in a microgrid based on an equivalent circuit according to claim 1, characterized in that, The simplified third-order mathematical model of the mathematical model of the overall equivalent circuit of the droop control inverter is: ； Where: u Cf is the voltage of the filtering capacitor in the LC filter.

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