Inverter global asymptotic stability control method, nonlinear controller and inverter

Abstract

The invention belongs to the technical field of inverters, and particularly relates to an inverter global asymptotic stability control method, a nonlinear controller and an inverter, a passivity-based three-phase voltage source type inverter double-loop controller is deduced on the basis of a passive current controller, and effective compensation for harmonic voltage is realized. In a current inner ring controller, an absolute value item of a voltage error is introduced, and the buffeting problem introduced by an inner ring sliding mode item is effectively suppressed. In the passive current inner loop controller, a nonlinear control item is introduced, the robustness of the system is enhanced, and the harmonic voltage can be effectively compensated even under 50% parameter disturbance. In addition, the controller provided by the invention only needs two control parameters, so that the system design and parameter setting process is greatly simplified.

Description

Technical Field

[0001] The present invention belongs to the technical field of inverters, and particularly relates to a global asymptotic stability control method for an inverter, a non-linear controller, and an inverter. Background Art

[0002] The grid-forming inverter (GFM) is increasingly regarded as a solution to promote the large-scale grid integration of inverter-based resources and achieve a 100% power electronics-based power system. The GFM consists of a power control loop, a voltage-current double closed loop, and a modulation module. A large number of studies have been conducted on the power control loop of the grid-forming inverter for research and improvement to enhance the power angle stability of the GFM during transients. However, these studies have ignored the impact of the voltage-current double closed loop control on the performance of the GFM, especially the problem of achieving harmonic voltage compensation in the case of filter parameter perturbation and non-linear loads.

[0003] To address the above problems, in the voltage-current double closed loop controller, the most widely used are the traditional PI controller and the PR controller. However, the PI controller has no compensation effect on harmonic voltage. The PR controller can effectively compensate specific harmonic voltages, such as the 5th, 7th, and 11th harmonics, but the number of parameters required by the PR controller increases with the increase in the number, making parameter tuning more challenging. Although this problem has been solved by proposing a selective pole placement and elimination method for PR controller design in VSI, which simplifies the parameter design process, the PR controller is highly sensitive to changes in filter parameters, and its harmonic compensation effect is poor.

[0004] Compared with traditional linear controllers, non-linear controllers have enhanced robustness to external disturbances and parameter perturbations. For example, a robust model predictive controller is designed based on a super-local model, and differential algebra and an extended state observer are used to estimate external disturbances caused by parameter mismatches, but both the model predictive controller and the state observer require a large amount of digital signal processor (DSP) resources. Another example is that a reference adaptive controller based on adaptive super-twisting sliding mode control has robustness to harmonic compensation, but the complexity of its parameter design limits its general applicability. Summary of the Invention

[0005] The present invention aims to provide a global asymptotic stability control method for a three-phase voltage source inverter and an inverter to solve the problems of parameter perturbation and harmonic voltage compensation of the inverter under different load conditions, so as to achieve limited compensation for high-order harmonic voltages.

[0006] To achieve the above object, one aspect of the present invention provides a technical solution: a global asymptotic stability control method for a three-phase voltage source inverter and an inverter, comprising the following steps:

[0007] Voltage and current detection: Detect the inductor current I Labc and detect the output voltage V oabc ;

[0008] Coordinate system transformation: Transform from the abc coordinate system to the αβ coordinate system to obtain the I Lαβ , V oαβ required for double closed-loop control;

[0009] Parameter tuning: Tune the voltage outer loop K2 and the current inner loop parameter K1 to optimize the system control effect;

[0010] Voltage outer loop control: Obtain the reference value of the filter inductor current through the voltage outer loop The control equation of the voltage outer loop is:

[0011]

[0012] Current inner loop control: Input the current reference value into the current inner loop control, and obtain the inverter modulation signal S in the αβ coordinates through the inner loop control invx(x＝α,β) , where the control equation of the current inner loop is:

[0013]

[0014] Three-phase AC output: Convert the modulation signal to S in the abc coordinates invz(z＝a,b,c) , and output the PWM drive signal of the inverter switching device through carrier modulation to drive the inverter to output three-phase alternating current;

[0015] In the parameter tuning step, the current inner loop parameter K1 and the voltage outer loop parameter K2 are tuned using the filter KVL equation and KCL equation:

[0016]

[0017] In the parameter tuning step, according to the Input-to-State Stability (ISS) theory, it is realized by constructing a Lyapunov function. The Lyapunov function is:

[0018]

[0019] The ISS theory expression is:

[0020]

[0021] Among them, x1 is the voltage error, x2 is the first derivative of the voltage error with respect to time, L1 is the inductor of the LC filter, C is the capacitor of the LC filter, r is the parasitic resistance, and b = (1 + rK2) / L1C.

[0022] Optionally, in the voltage and current detection step, the inductor current I is detected by a filter inductor current sensor Labc , and the output voltage V is detected by a filter capacitor voltage sensor oabc .

[0023] Optionally, in the parameter tuning step, the system differential equation is linearized around the steady-state operating point, and the linearized system differential equation becomes:

[0024]

[0025] Another aspect of the present invention is to provide another technical solution: a non-linear double closed-loop controller, the control method of which adopts the aforementioned global asymptotic stability control method for a three-phase voltage source inverter

[0026] Another aspect of the present invention is to provide another technical solution: an inverter, which adopts the aforementioned non-linear double closed-loop controller

[0027] Another aspect of the present invention is to provide another technical solution: an inverter, the control method of which adopts the aforementioned global asymptotic stability control method for a three-phase voltage source inverter

[0028] The working principle of the present invention is that: the filter inductor current sensor detects the inductor current I Labc , and the filter capacitor voltage sensor detects the output voltage V oabc . By converting from the abc coordinate system to the αβ coordinate system, the I Lαβ , V oαβ required by the control method are obtained. Through the voltage outer loop, the reference value of the filter inductor current is obtained The current reference value is input to the current inner loop controller. The absolute value of the voltage error is introduced into the current inner loop, and is used to replace the in the inner loop of the original passive control method to solve the chattering problem caused by the sliding mode term. Through the current inner loop control, the modulation signal S in the αβ coordinates is obtained invx(x＝α,β) , and the modulation signal is converted to S in the abc coordinates invz(z＝a,b,c) . Finally, the PWM drive signal of the inverter switching device is output through the carrier modulation method. Through the action of the PWM drive signal, the inverter outputs three-phase alternating current

[0029] The beneficial effects of the present invention are as follows:

[0030] 1. Based on the passive current inner loop controller (PBC), a non-linear double closed-loop controller and control method are proposed, which ensure the global asymptotic stability of the system under parameter perturbation and different loads

[0031] 2. The absolute value term of the voltage error is introduced into the current inner loop controller, effectively suppressing the inherent chattering problem in traditional sliding mode control.

[0032] 3. A non-linear control term is introduced into the passive current inner loop controller, enhancing the system robustness, and effectively compensating for harmonic voltage even under 50% parameter perturbation.

[0033] 4. The proposed control method eliminates the integral term added in the super-twisting sliding mode controller, enhancing the anti-interference ability of the controller;

[0034] 5. The proposed control method only requires two control parameters, simplifying the parameter design. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the overall control framework of the non-linear double-loop controller in the embodiment of the present invention;

[0036] Figure 2 It is the system control block diagram of the non-linear double-loop controller in the embodiment of the present invention;

[0037] Figure 3 It is the topological structure of the non-linear double-loop controller in the embodiment of the present invention;

[0038] Figure 4 It is the comparison diagram of the output phase voltage and phase A current waveforms before and after the filter parameters are reduced by 50% under different load conditions of the non-linear double-loop controller in the embodiment of the present invention;

[0039] Figure 5 It is the THD frequency component of the non-linear double-loop controller in the embodiment of the present invention under standard parameters and different load conditions;

[0040] Figure 6 It is the tracking effect diagram of the phase A phase voltage to the reference voltage of the non-linear double-loop controller in the embodiment of the present invention under standard parameters and different load conditions;

[0041] Figure 7 It is the output waveform diagram of the three-phase phase voltage and phase A current of the inverter under different load conditions when the output voltage frequency is 60Hz and other experimental parameters remain unchanged for the non-linear double-loop controller in the embodiment of the present invention;

[0042] Figure 8 It is the waveform diagram of the output three-phase phase voltage and phase A line current when the non-linear double-loop controller in the embodiment of the present invention transitions from a linear load to a non-linear load and the reference voltage transitions from 110V to 220V. DETAILED DESCRIPTION OF THE INVENTION

[0043] The following is a further detailed description through specific embodiments:

[0044] The marks in the attached drawings of the specification include:

[0045] Embodiment

[0046] This embodiment is basically as Figure 1 and Figure 2 shown: A global progressive stability control method, a non - linear controller and an inverter for an inverter. The basic parameters of the experiment to verify this method are as follows:

[0047] ω = 2πf o , f o = 50Hz, V dc = 800V, f sw = 100KHz, L1 = 340μH, L2 = 22μH, C = 4.7μF, r snubber = 0.55Ω, r = 0.2Ω, C dc1 = C dc2 = 600μF.

[0048] ω is the output voltage angular frequency, f o is the output voltage frequency, V dc is the DC voltage, is the reference voltage, f sw is the switching frequency, L1 and L2 are filter inductors, r snubber is the Snubber resistor, r is the parasitic resistor of the filter inductor L1, C dc1 , C dc2 are the DC - side capacitors, K1 and K2 are controller parameters

[0049] The whole method includes the following steps:

[0050] Voltage and current detection: The filter inductor current sensor detects the inductor current I Labc , and the filter capacitor voltage sensor detects the output voltage V oabc .

[0051] Coordinate system transformation: Convert from the abc coordinate system to the αβ coordinate system to obtain I Lαβ , I oαβ , V oαβ required for double - closed - loop control;

[0052] Parameter tuning: Tune the current inner - loop parameter K1 and the voltage outer - loop parameter K2; The specific process is as follows:

[0053] KVL equation of the filter:

[0054]

[0055] KCL equation of the filter:

[0056]

[0057] In this embodiment, the power control loop is not included. Therefore, for the control method in this embodiment, the situations of the α-axis and the β-axis are the same and independent of each other. Thus, the subscripts α and β are omitted in the stability proof. Combine the inner current loop control equation and Equation (1):

[0058]

[0059] Combine the outer voltage loop control equation and Equation (2):

[0060]

[0061] Let the voltage error Combining (3) and (4) gives:

[0062]

[0063] Define the state variables:

[0064]

[0065] Transforming (5) into the state space equation gives:

[0066]

[0067] where,

[0068] Define the sliding surface:

[0069] s(x) = Cx2 + K2x1 (8)

[0070] Next, prove the global asymptotic stability of the system differential equation, including the sliding term proof and the reaching term stability proof.

[0071] First, analyze the stability of the sliding term. That is, the case of s(x) = 0. On the sliding surface, the equivalent control of the nonlinear control is called Φ eq， If Φ can be found eq such that then it means that the system state will always remain on the sliding surface, which proves the stability of the sliding term. Now assume that the system is stable, that is, s(x) = 0 and That is:

[0072]

[0073] Substitute (9) into (7) to get:

[0074]

[0075] Substituting the system parameters into Equation (10), Φ can be calculated as follows: eq , and the dynamic equation of the system on the sliding surface is as follows:

[0076]

[0077] When K2 > 0, the system is globally exponentially stable on the sliding surface.

[0078] Then, the stability of the reaching term is analyzed. Since the system is globally exponentially stable on the sliding surface when K2 > 0, assume K2 = 1. Combining Equations (7) and (8), we get:

[0079]

[0080] Construct the Lyapurov function of the reaching term:

[0081]

[0082] Substituting Equation (12) into Equation (13), we get:

[0083]

[0084] Since we obtain:

[0085]

[0086] There is only one negative term in Equation (15). When is large enough, it can make where η > 0. Therefore, a lower bound of K1 needs to be found.

[0087] From Equation (8), we know that:

[0088]

[0089] Since both |x1| and |x2| in the system have lower bounds, we may assume:

[0090]

[0091] where M1 and M2 are positive constants. Then Equation (15) can be written as:

[0092]

[0093] To make it is required that:

[0094]

[0095] As can be seen from Equation (19), an appropriate K1 can always be found to make the approaching term globally asymptotically stable. When K2 = 0.3, through Matlab simulation, K1 ≥ 20 is obtained.

[0096] Next, the system differential equation will be linearized near the steady-state operating point, and combined with the controller bandwidth to determine the upper bounds of K1 and K2. Near the steady-state operating point, there is So there is:

[0097]

[0098] The linearized system differential equation is:

[0099]

[0100] Taking the Laplace transform of Equation (21) gives:

[0101] L1Cs 2 +(L1K2 + rC)s+(1 + rK2 + K1)e = 0 (22)

[0102] Observing Equation (22), it can be found that this is a second-order linear system, and the natural frequency and damping ratio of the system are:

[0103]

[0104] Since the switching frequency f of the system sω = 100KHz, to avoid high-frequency oscillations in the system, the natural frequency ω n is usually restricted to be between 1 / 5 and 1 / 3 of the switching frequency f sω . So there is When K2 = 0.3, K1 ≤ 69 is obtained. Thus: 20 ≤ K1 ≤ 69.

[0105] Since K2 is proportional to the closed-loop bandwidth of the system, and the closed-loop bandwidth of the system should be between 1 / 5 and 1 / 3 of the delay frequency. On the other hand, for a first-order or second-order system, the bandwidth f bω of the system is inversely proportional to the time constant τ, and the capacitance C is proportional to the time constant τ. Thus:

[0106]

[0107] In this embodiment, the delay frequency So there is Therefore: 0 ≤ K2 ≤ 0.3.

[0108] Voltage outer loop control: I Laβ 、V oαβ The reference value of the filter inductor current is obtained through the voltage outer loop The control equation of the voltage outer loop is as follows:

[0109]

[0110] Inner current loop control: Input the current reference value into the inner current loop control method, and obtain the inverter modulation signal S in the αβ coordinate system through the inner loop control method invx(x＝α,β) , where the control equation of the inner current loop is as follows:

[0111]

[0112] Three-phase AC output: Convert the modulation signal to the abc coordinate system as S invz(z＝a,b,c) , and output the PWM drive signal of the inverter switching device through carrier modulation to drive the inverter to output three-phase alternating current.

[0113] The inverter topology used in the experiment is as Figure 3 shown. In this embodiment, a 10KW GaN / Si hybrid MOSFET ANPC inverter prototype is used to verify the control method. Among them, the red ones are GaN MOSFETs, and the blue ones are Si MOSFETs. It should be noted that, on the one hand, due to the decoupling of the controller and the modulation module proposed in this embodiment, it is also applicable to other three-phase voltage source inverters, including two-level inverters and other types of three-level inverters such as TNPC type inverters or NPC type inverters. On the other hand, the ANPC prototype used in this embodiment adopts an LCL type filter, and a snubber resistor is added to the filter capacitor of the LCL filter, effectively suppressing the resonance peak of the LCL. And only the current on the filter inductor L1 and the voltage on the filter capacitor C are used in the derivation and simulation of the above control method equation, and the filter inductor L2 is not involved. Therefore, it is reasonable and effective to use the GaN / Si hybrid ANPC with a snubber resistor to experimentally verify the proposed control method.

[0114] Figure 4 Waveform diagrams of the three-phase phase voltage and phase current of phase A output by the inverter before and after the filter parameters change under different load conditions. Figure 4 (a)(c)(e) are waveform diagrams of the three-phase phase voltage and phase current of phase A output by the inverter under the conditions of no change in filter parameters, linear load, linear load with non-linear components, and RCD non-linear load respectively. Figure 4(b), (d), and (f) show the waveforms of the three-phase phase voltage and the phase current of phase A at the inverter output under the conditions of a linear load, a linear load with a non-linear component, and an RCD non-linear load when the filter parameters are reduced by 50%. The THD value of the inverter output voltage is used to evaluate the quality of the inverter output voltage before and after the filter parameters change under different load conditions. By Figure 4 comparing (a) with (b), (c) with (d), and (e) with (f), it can be seen that when the filter parameters are reduced, the THD value of the output voltage under each different load condition increases, and the influence of the non-linear component under the load condition on the increase in THD when the filter parameters are reduced also becomes greater and greater. This is because the reduction of the filter parameters results in a higher cut-off frequency, increasing the THD by reducing the harmonic attenuation ability in the low-frequency range. And it is observed that when the filter parameters are reduced under the non-linear RCD load condition, the THD value of the output voltage of the proposed controller is only 3.43%. Thus, it effectively proves the robustness of the proposed controller in harmonic voltage compensation under filter parameter perturbations.

[0115] Figure 5 It is shown that by Figure 4 analyzing the THD frequency components shown in (a), (c), and (e), the influence of different types of loads on the THD value of the inverter output voltage can be evaluated in more detail. It can be seen that compared with the resistive load, the non-linear RCD load mainly increases the 5th, 7th, and 11th harmonics of the output. The harmonic compensation performance of the proposed controller can be based on Figure 6 what is observed in Figure 4 the tracking effect of the phase voltage VAO waveform of phase A on the corresponding reference voltage VAOref waveform obtained under different load conditions in (a), (c), and (e). From Figure 6 the waveforms magnified at the peak points in (b), (d), and (f), the peak error of the output phase voltage is controlled within ±1.95%, verifying that the proposed controller has a good harmonic compensation effect.

[0116] The robustness of the proposed controller to the change in the output voltage frequency can be evaluated based on the waveforms of the three-phase phase voltage and phase current at the inverter output under the conditions of a linear load, a linear load with a non-linear load component, and a non-linear RCD load when the output voltage frequency is 60 Hz while other experimental parameters remain unchanged, as shown in Figure 7 (a), (b), and (c) respectively. Comparing these results with Figure 4 the corresponding results in (a), (c), and (e), it can be found that under different voltage frequencies, the variation of the THD value of the output voltage under different load conditions is basically the same. Therefore, it shows that the proposed PBC scheme has almost the same harmonic voltage compensation performance under different output voltage frequencies.

[0117] Figures (8)(a) and (b) respectively show the changes in the inverter output waveform when transitioning from a linear load to a nonlinear load and when the reference voltage transitions from 110V to 220V. It can be observed that the proposed controller has good robustness against changes in the load type or reference voltage, and can achieve the stabilization of the output waveform within 2.4 ms.

Claims

1. A global progressive stability control method for an inverter, characterized in that: The following steps are involved: Voltage and current detection: detect the inductor current I Labc , detect output voltage V oabc ; Coordinate system conversion: Convert the abc coordinate system to the αβ coordinate system to obtain the I required for double closed-loop control Lαβ 、V oαβ ; Parameter setting: set the voltage outer loop K2 and current inner loop parameter K1 to optimize the system control effect; Voltage outer loop control: The filter inductor current reference value is obtained through the voltage outer loop The control equation of the voltage outer loop is: Current inner loop control: The current reference value is input into the current inner loop control, and the inverter modulation signal S under the αβ coordinates is obtained through the inner loop control. invx(x＝α,β) , where the control equation of the inner current loop is: Three-phase AC output: Convert the modulated signal to S in abc coordinates invz(z＝a,b,c) , outputting PWM drive signals of inverter switching devices by carrier modulation to drive the inverter to output three-phase AC power; In the parameter setting step, the current inner loop parameter K1 and the voltage outer loop parameter K2 are set using the filter KVL equation and KCL equation: In the parameter tuning step, according to the input-to-state stability (ISS) theory, the Lyapunov function is constructed. The Lyapunov function is: The theoretical expression of ISS is: Wherein, x1 is the voltage error, x2 is the first-order derivative of the voltage error with respect to time, L1 is the LC filter inductance, C is the LC filter capacitance, r is the parasitic resistance, and b=(1+rK2) / L1C.

2. The inverter global progressive stability control method according to claim 1, characterized in that: In the voltage and current detection step, the filter inductor current sensor is used to detect the inductor current I Labc , use the filter capacitor voltage sensor to detect the output voltage V oabc .

3. The inverter global progressive stability control method according to claim 1, characterized in that: In the parameter tuning step, the system differential equation is linearized near the steady-state operating point, and the linearized system differential equation becomes:

4. A nonlinear controller, characterized in that: The control method thereof adopts the control method as described in any one of claims 1 to 3.

5. An inverter, characterized in that: It adopts the nonlinear double closed-loop controller as claimed in claim 4.

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