A single-phase inverter multi-resonant control system design method

Abstract

The application discloses a single-phase inverter multi-resonance control system design method. Through the equivalence of a multi-quasi-resonance controller and an odd-harmonic repetitive controller, the design parameter system of the odd-harmonic repetitive controller is mapped to the equivalent multi-quasi-resonance controller, so that the controller design is simplified and the robustness is improved. Through the method, the design process can be simplified under the condition of guaranteeing the system performance and stability, and the method is suitable for deployment and application in a digital control system.

Description

Technical Field

[0001] This invention relates to DC-AC conversion and inverter output voltage control technology. More specifically, it relates to a single-phase inverter output voltage control method in the field of power electronics, used to output AC power with low total harmonic distortion and high waveform output quality. Background Technology

[0002] In power grid systems, batteries store energy in direct current (DC), while inverters play a crucial role in converting DC to alternating current (AC). High-performance inverters, due to their stable output voltage amplitude and frequency characteristics, are widely used in uninterruptible power supplies (UPS), reactive power compensation in distributed generation, electric aircraft power systems, and industrial applications. Currently, the design of high-performance inverters needs to achieve two main technical goals: first, to suppress harmonic distortion to reduce the total harmonic distortion (THD) of the AC voltage output, thereby improving power quality; and second, to ensure continuous, stable, and high-quality AC power delivery under complex operating conditions to meet increasingly stringent industrial and residential power demands.

[0003] However, in actual operation, inverters face multiple harmonic interference challenges. On the one hand, uncertainties in parameters such as the turn-on / turn-off timing deviation of switching devices, on-state voltage drop, and unmodeled dynamics such as dead-time effects introduce non-ideal harmonic components. On the other hand, nonlinear loads (such as rectifier capacitor filter loads) and external interference further exacerbate harmonic distortion. Although traditional passive filters can suppress high-frequency switching ripple, their effect on suppressing harmonics near the fundamental frequency is limited.

[0004] At the control strategy level, traditional feedback control schemes (such as deadbeat control, sliding mode control, and lag control) can improve dynamic response speed, but they struggle to achieve accurate tracking of periodic signals and effective suppression of harmonic distortion. Compensation methods based on disturbance estimation (such as disturbance observers and active disturbance rejection control) can handle parameter uncertainties and nonlinear load disturbances, but their parameter tuning process is complex. Model predictive control achieves multi-objective coordination through rolling time-domain optimization, but its high computational complexity limits its applicability in real-time systems. Against this backdrop, repetitive control, with its unique periodic error compensation mechanism, has become a prominent solution. Based on the internal model principle, the repetitive controller stores the tracking error of the previous cycle and superimposes it onto the current control signal, generating a closed-loop error accumulation effect, thereby significantly enhancing the suppression of periodic harmonics, especially suitable for constant voltage and constant frequency PWM inverters.

[0005] Nevertheless, the design process of traditional resonant controllers is quite complex, limiting their widespread application in practice. Therefore, simplifying the design process of resonant controllers has become a core issue of concern for engineers in this field. Summary of the Invention

[0006] To address the shortcomings and improvement needs of existing technologies, this invention provides a design method for a multi-resonant control system for a single-phase inverter, aiming to reduce the total harmonic distortion rate of the output voltage of the single-phase inverter and improve the waveform output quality.

[0007] To achieve the above objectives, this invention provides a design method for a multi-resonant control system of a single-phase inverter. The single-phase inverter includes switching transistors S1-S4 (composed of controllable switching transistors and diodes connected in anti-parallel), an inductor L, a capacitor C, an inductor equivalent resistance r, and a load R. load The positive input terminal (+) of the single-phase inverter is connected to the drains of switching transistors S1 and S3. The source of switching transistor S1 is connected to the drain of S2, and the source of switching transistor S3 is connected to the drain of S4. The sources of switching transistors S3 and S4 are both connected to the negative input terminal (-) of the single-phase inverter. A resistor r, an inductor L, and a capacitor C are connected in series between the connection point of switching transistors S1 and S3 and the connection point of S2 and S4. One end of capacitor C is connected to the common terminal of inductor L and resistor r, and the other end is connected to the load R. Load It includes the following steps:

[0008] S1. Based on the parameters of inductance L and capacitance C in the single-phase inverter, establish the mathematical model of the equivalent circuit of the single-phase inverter.

[0009] S2, In order to reduce the impact of load changes on the control system, a virtual impedance R is constructed. v , making i o =u o / R Load + u o / R v And the complete mathematical function H(s) of the controlled object containing virtual impedance is derived: ;

[0010] S3. Using the backward difference method, the transfer function H(s) of the controlled object containing virtual impedance in the continuous domain is converted into the transfer function H(z) in the discrete domain. A notch filter H is then designed based on the resonance peak of the controlled object's transfer function. f (z) to cancel the resonance peak in the function H(z), and the notch filter transfer function H is obtained by using the Tustin discretization method with pre-twisting. f (z);

[0011] S4, plot function H f Bode plot of (z)×H(z), design phase lead compensator z m In m, z m-1.5 ×H f (z)×H(z) has near-zero phase characteristics in the low-frequency range;

[0012] S5. Let the odd harmonic repetitive controller be G. o-RC G0(z)=zm G o-RC (z)H f (z), H0(z)=z -1.5 H(z), introduce an additional controller G1(z), under constraints Internally, a PD controller G1(z) is designed to be connected in parallel with G0(z) so that the phase margin of the open-loop transfer function is greater than 60 degrees;

[0013] S6, with the following structure The multi-resonant controller, based on ω0=2π / T0 and ω c =(− ln Q) / T0, the odd harmonic repetitive controller G o-RC The parameters in the original text are equivalently transformed into the parameters in the multi-resonant controller, resulting in the transfer function of the odd-harmonic repetitive controller. ;

[0014] S7, based on the rotation factor e jφh Phase lead compensator z m Combined with multi-resonant controller , where ω k =(2k−1)ω0,φ k =mω k T s .

[0015] Furthermore, step S1 uses a PWM drive voltage signal u PWM The input is the actual output voltage u. o The result of the subtraction is input to the transfer function 1 / (Ls+r), and the output is the current i flowing through the inductor L. L i L Subtract the load current i on the load side o The input is then passed to the transfer function 1 / Cs, and the output is u. o u o Divide the equivalent load resistance by R Load After that, we get i o Where Ls represents the output inductance value, r represents the inductance equivalent resistance, and Cs represents the output capacitance value.

[0016] Furthermore, in step S1, the output voltage expression is derived by constructing a state-space average mathematical model of the single-phase inverter using the state-space averaging method. Construct R v The expression after that is , where R Load Indicates the output load, u o (s) represents the output voltage, u PWM (s) represents the PWM voltage pulse output by the inverter bridge.

[0017] Furthermore, in step S4, the phase lead compensator z m A phase lead θ = m × (ω / ω) can be introduced at angular frequency ω. N )×180°.

[0018] Furthermore, the transfer function of the input and output of the additional controller G1(z) in step S5 is: It is necessary to ensure that all eigenvalues ​​remain within the unit circle, that is, it is necessary to satisfy... .

[0019] Furthermore, step S6 uses mathematical derivation to calculate that the odd-harmonic repetitive controller and the multi-resonant controller are equivalent, ultimately... In the formula, ω0 = 2π / T0, ω c =(−lnQ) / T0.

[0020] Furthermore, the load R mentioned above... load The load is either a resistor or a rectifier, wherein the rectifier load is a load inductor L connected in series after a diode bridge consisting of four diodes. r Load capacitance C r and load resistance R r .

[0021] In general, the above-described technical solutions conceived in this invention can achieve the following beneficial effects.

[0022] (1) Simplified design process: By establishing an equivalent mapping relationship between the odd harmonic repetitive controller and the multi-quasi-resonant controller, the complex parameter tuning process of the traditional multi-quasi-resonant controller is effectively avoided, enabling designers to directly reuse the mature design experience of the odd harmonic repetitive controller, which significantly reduces the technical threshold and implementation difficulty of engineering applications.

[0023] (2) Guarantee control performance: The equivalent multi-quasi-resonant controller constructed based on the method proposed in this invention can achieve accurate tracking and suppression of periodic harmonic signals. Its harmonic suppression performance is basically equivalent to that of the odd harmonic repetitive controller, ensuring high-quality power output.

[0024] (3) Enhanced system stability: Through the coordinated design of notch filter, phase lead compensator and PD controller, the system phase lag is effectively compensated, ensuring that the system phase margin is greater than 60 degrees and the system stability is strong.

[0025] (4) Strong physical feasibility: By introducing a rotation factor, the physical implementation problem of the phase lead compensator is solved, making the controller structure easy to implement in digital signal processors or microcontrollers, which is very suitable for deployment and application in digital control systems. Attached Figure Description

[0026] Figure 1 This is a flowchart of the design method of the present invention;

[0027] Figure 2 This is a schematic diagram of the single-phase inverter structure of the present invention;

[0028] Figure 3 This is a block diagram of the state-space average model of the single-phase inverter of the present invention;

[0029] Figure 4 Bode plots of the single-phase inverter of the present invention under different loads;

[0030] Figure 5 The state-space average model block diagram of the single-phase inverter after virtual impedance was designed;

[0031] Figure 6 Bode plots of the inverter under different loads were designed after virtual impedance was calculated.

[0032] Figure 7 The system amplitude-frequency response curves under different orders of compensation;

[0033] Figure 8 This is a schematic diagram of the overall structure of the control system of the present invention;

[0034] Figure 9 The amplitude-frequency response curve of a PD controller connected in series with an inverter with digital delay;

[0035] Figure 10 A comparison of the equivalent amplitude-frequency response curves before and after the lead element;

[0036] Figure 11 The output voltage and current waveforms of a single-phase inverter;

[0037] Figure 12 The THD result is for the output voltage of a single-phase inverter. Detailed Implementation

[0038] The specific embodiments of the present invention will now be described in conjunction with the accompanying drawings and examples to enable those skilled in the art to better understand the present invention.

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0040] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0041] This invention discloses a design method for a multi-resonant control system for a single-phase inverter, which aims to solve the problems of poor stability of existing multi-quasi-resonant controllers and complex implementation of repetitive controllers. Figure 1 The diagram shown is a flowchart of the design method for a single-phase inverter multi-resonant control system in an embodiment of the present invention. (See also...) Figure 1 , combined Figures 2-11 The design method in this embodiment will be described in detail.

[0042] Figure 2 The single-phase inverter shown includes switching transistors S1 to S4, which consist of controllable switching transistors and diodes connected in anti-parallel, an inductor L, a capacitor C, an inductor equivalent resistance r, and a load R. load The positive input terminal (+) of the single-phase inverter is connected to the drains of switching transistors S1 and S3. The source of switching transistor S1 is connected to the drain of S2, and the source of switching transistor S3 is connected to the drain of S4. The sources of switching transistors S3 and S4 are both connected to the negative input terminal (-) of the single-phase inverter. A resistor r, an inductor L, and a capacitor C are connected in series between the connection point of switching transistors S1 and S3 and the connection point of S2 and S4. One end of capacitor C is connected to the common terminal of inductor L and resistor r, and the other end is connected to the load R. Load In this embodiment, the load R Load The rectifier load consists of a diode bridge composed of four diodes, followed by a load inductor L connected in series. r Load capacitance C r and load resistance R r In this prototype, the output inductance L = 1mH, the output capacitance C = 200uF, and the equivalent internal resistance of the inductor r = 0.02Ω.

[0043] Operate S1 to establish a mathematical model of the equivalent circuit of the single-phase inverter based on the electrical parameters in the single-phase inverter.

[0044] Drive voltage signal u with PWM PWM The input is the actual output voltage u. o The result of the subtraction is input to a stage with a transfer function of 1 / (Ls+r), where Ls represents the output inductance value and r represents the equivalent resistance of the inductor. The output of this stage is the current i flowing through the inductor. L i L Subtract the load current i on the load side o The input is then fed into a stage with a transfer function of 1 / Cs, where Cs represents the output capacitor value. The output of this stage is u. o u o Divide the equivalent load resistance by R Load After that, we get io

[0045] See Figure 3 It shows the block diagram of the single-phase inverter output voltage system, combined with Figure 2 The single-phase inverter structure shown was used to construct a 10 kVA prototype to verify the effectiveness of the invention, and will be used to further explain the technical features and advantages of the invention.

[0046] See Figure 3 Based on the block diagram of the single-phase inverter output voltage system, the expression for the output voltage can be derived as follows: , where R Load Indicates the output load, u o (s) represents the output voltage, u PWM (s) represents the PWM voltage pulse output by the inverter bridge.

[0047] In operation S2, a virtual impedance R is introduced to reduce the impact of load changes on the control system. v , making i o =u o / R Load + u o / R v And the complete mathematical function H(s) of the controlled object containing virtual impedance is derived.

[0048] See Figure 4 When the load changes, the system's transfer function is altered, leading to changes in the system's resonant peak and resonant frequency, which is detrimental to subsequent notch filter design. Therefore, refer to... Figure 5 A virtual impedance R is constructed in the control system. v To reduce the impact of inverter output resistance on the system, the output voltage expression becomes... In this embodiment, R v =5Ω.

[0049] See Figure 6 Considering the virtual impedance R v Subsequently, when the load changes, the system's resonant peak and resonant frequency change very little, and the resonant peak value drops significantly, which is beneficial for subsequent design.

[0050] Operation S3 is used to design a notch filter to cancel the resonance peak in the mathematical function H(s), and the notch filter transfer function H is obtained by using the Tustin discretization method with pre-twisting. f (z).

[0051] Using the backward difference method, the virtual impedance R in the continuous domain is... vThe transfer function H(s) of the controlled object is converted into the transfer function H(z) in the discrete domain. A notch filter H is designed based on the resonance peak of the transfer function H(s) of the controlled object. f (z) to cancel the resonance peak in the mathematical function H(s), and to obtain the notch filter transfer function H using the Tustin discretization method with pre-distortion. f (z).

[0052] In this embodiment, the notch filter H f The resonant peak frequency of (z) is 355Hz, and the center frequency ω 0f With a damping rate of 2π × 355 rad / s, damping coefficients ζ1 and ζ2 are chosen to be 0.04348 and 0.7692, respectively, to achieve the desired frequency-selective attenuation. The Tustin discretization method with pre-distortion is used to obtain... .

[0053] Operation S4, plot function H f Bode plot of (z)×H(z), design phase lead compensator z m In m, z m-1.5 ×H f (z)×H(z) exhibits near-zero phase characteristics in the low-frequency range. Phase lead compensator z m A phase lead θ = m × (ω / ω) can be introduced at angular frequency ω. N )×180°.

[0054] See Figure 7 The z-shaped graph was drawn. m-1.5 ×H f (z)×H(z) amplitude-frequency response curves under different compensator orders. When m=16, the controlled object of the odd harmonic repetitive controller has close-to-zero phase characteristics.

[0055] Operation S5, assuming the odd harmonic repetitive controller is... Where T0 represents the control period, and Q = 0.95 or the transfer function of a first-order low-pass filter. Let G0(z) = z m ×G o-RC (z)×H f (z), H0(z)=z -1.5 ×H(z), introducing an additional controller G1(z), under constraints Internally, design a PD controller G1(z) in parallel with G0(z) to make the open-loop transfer function... The phase margin is greater than 60 degrees.

[0056] See Figure 8Although the odd-harmonic repetitive controller has good periodic disturbance suppression capability, its dynamic performance is poor. To enhance the dynamic response of the system, an additional controller G1(z) is added along with the odd-harmonic repetitive controller G... o-RC Parallel connection. Furthermore, to ensure the stability of the odd-harmonic repetitive controller, a notch filter (H) must be used. f (z) Filter out resonance peaks and use a phase lead compensator z m Compensation system delay. When m=1.5, z -1.5 This represents the combined delay of one sampling period and the additional half-cycle delay introduced by PWM modulation in digital control.

[0057] The introduction of the PD controller G1(z) improves the dynamic performance of the system, but it is necessary to ensure that the parameters of G1(z) do not affect the stability of the system. The input-output transfer function is... ,like Figure 9 As shown.

[0058] To ensure the stable operation of the system, it is necessary to ensure that all eigenvalues ​​remain within the unit circle, that is, it is necessary to satisfy... This condition can be transformed into: when the sampling frequency is lower than half of the Nyquist frequency, if the amplitude of |G0(z)H0(z)| is lower than the amplitude of |1+G1(z)H0(z)|, the system is definitely stable. This formula greatly simplifies the controller design process because the PD controller G1(z) only needs to consider the design of H0(z).

[0059] In this embodiment, a PD controller structure is adopted. .

[0060] See Figure 9 The phase margin of the system, after being connected in series with the designed PD controller and the inverter mathematical model H0(z) with digital delay, always exceeds 60 degrees under all load conditions, thus ensuring system stability.

[0061] When the sampling frequency is below half the Nyquist frequency, if the amplitude of |G0(z)H0(z)| is lower than the amplitude of |1+G1(z)H0(z)|, the system will definitely be stable. This formula greatly simplifies the controller design process because G1(z) only needs to consider the design of H0(z).

[0062] Construct a multi-resonant controller by operating S6. According to ω0=2π / T0 and ω c =(− ln Q) / T0, the odd harmonic repetitive controller G o-RC The parameters in the original text are equivalently converted into the parameters in the multi-resonant controller, resulting in the odd-harmonic repetitive controller. .

[0063] Through mathematical derivation, it can be calculated that the odd-harmonic repetitive controller and the multi-resonant controller are equivalent, and the final expression is: In the formula, ω0 = 2π / T0, ω c =(− ln Q) / T0.

[0064] This structure is similar to that of a multiresonant controller, so the odd-harmonic repetitive controller can be completely equivalently converted into a multiresonant controller through mathematical transformation.

[0065] Through step S6, the odd-harmonic repetitive controller is completely equivalently converted into a multi-resonant controller, while the notch filter H... f (z) and the PD controller G1(z) can be directly applied to the control system, but because z m Due to the physical unrealizability of the control architecture, a twiddle factor e is required to ensure functional equivalence between control architectures. jφh .

[0066] Operation S7, based on the rotation factor e jφh The phase lead compensator z m Combined with a multi-resonant controller, the combined expression G EMQ-RSC (s) is , where ω k =(2k−1)ω0,φ k =mω k T s .

[0067] The merged expression G EMQ-RSC (s) becomes G after the backward difference method. EMQ-RSC (z), and notch filter H f Multiplying (z) yields the equivalent resonant controller G0'(z). The transfer function of the designed control system is G0'(z) + G1(z).

[0068] See Figure 9 The phase margin of the system is always greater than 60 degrees under all load conditions after the designed PD controller G1(z) and the inverter mathematical model H0(z) with digital delay are connected in series, thus ensuring system stability.

[0069] See Figure 10 To maintain the requirements of the actual coefficient system, an auxiliary function was constructed such that its numerator is related to s=jω. h Rotational molecular matching at the point of origin allows for the maintenance of phase compensation characteristics while satisfying realizability constraints.

[0070] To verify the practicality of the control method in this embodiment, based on, as shown in the example... Figure 2 The control method for the single-phase inverter shown is illustrated, and a prototype based on this control method has been established. (See reference...) Figure 11 and Figure 12 Experimental results show that the system performance of the multi-resonant controller designed by this method is comparable to that of the odd-harmonic repetitive controller, confirming its functional equivalence in this respect.

[0071] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a multi-resonant control system of a single-phase inverter, wherein the single-phase inverter comprises switching transistors S1 to S4 consisting of controllable switching transistors and diodes connected in anti-parallel, an inductor L, a capacitor C, an inductor equivalent resistance r, and a load R. load The positive input terminal of the single-phase inverter is connected to the drains of switching transistors S1 and S3. The source of switching transistor S1 is connected to the drain of S2, and the source of switching transistor S3 is connected to the drain of S4. The sources of switching transistors S3 and S4 are both connected to the negative input terminal. A resistor r, an inductor L, and a capacitor C are connected in series between the connection point of switching transistors S1 and S3 and the connection point of S2 and S4. One end of capacitor C is connected to the common terminal of inductor L and resistor r, and the other end is connected to the load R. Load Its features are: Includes the following steps S1. Based on the parameters of inductance L and capacitance C in the single-phase inverter, establish the mathematical model of the equivalent circuit of the single-phase inverter. S2, constructing a virtual impedance R v make i o =u o / R Load + u o / R v To obtain the complete mathematical function of the controlled object. ； S3. Using the backward difference method, the function H(s) in the continuous domain is transformed into the transfer function H(z) in the discrete domain, and a notch filter H is designed. f (z) to cancel the resonance peak in the function H(z), and the notch filter transfer function H is obtained by using the Tustin discretization method with pre-twisting. f (z); S4, plot function H f Bode plot of (z)×H(z), design phase lead compensator z m In m, z m-1.5 ×H f (z)×H(z) has near-zero phase characteristics in the low-frequency range; S5. Let the odd harmonic repetitive controller be G. o-RC G0(z)=z m G o-RC (z)H f (z), H0(z)=z -1.5 H(z), under the constraints Internally, a PD controller G1(z) is designed to be connected in parallel with G0(z) so that the phase margin of the open-loop transfer function is greater than 60 degrees; S6, with the following structure The multi-resonant controller, based on ω0=2π / T0 and ω c =(− ln Q) / T0, the odd harmonic repetitive controller G o-RC The parameters in the original text are equivalently transformed into the parameters in the multi-resonant controller, resulting in the transfer function of the odd-harmonic repetitive controller. ； S7, based on the rotation factor e jφh Phase lead compensator z m Combined with multi-resonant controller , among them k =(2k−1)ω0 ,φ k =mω k T s 。 2. The design method for a multi-resonant control system of a single-phase inverter according to claim 1, characterized in that, Step S1 uses a PWM drive voltage signal u PWM The input is the actual output voltage u. o The result of the subtraction is input to the transfer function 1 / (Ls+r), and the output is the current i flowing through the inductor L. L Subtract the load current i o The input is then passed to the transfer function 1 / Cs, and the output is u. o Where Ls represents the output inductance value, r represents the inductance equivalent resistance, and Cs represents the output capacitance value.

3. The design method for a multi-resonant control system of a single-phase inverter according to claim 2, characterized in that, In step S1, the output voltage expression is derived based on the mathematical model as follows: , where u o (s) represents the output voltage, u PWM (s) represents the PWM voltage pulse output by the inverter.

4. The design method for a multi-resonant control system of a single-phase inverter according to claim 3, characterized in that, In step S4, the phase lead compensator z m Introducing a phase lead θ = m × (ω / ω) at angular frequency ω N )×180°.

5. The design method for a multi-resonant control system of a single-phase inverter according to claim 4, characterized in that, The input-output transfer function of the PD controller G1(z) in step S5 is: , .

6. The design method for a multi-resonant control system of a single-phase inverter according to claim 5, characterized in that, In step S6, the transfer function of the odd-harmonic repetitive controller is mathematically derived to be equivalent to that of the multi-resonant controller, thus obtaining... In the formula, ω0 = 2π / T0, ω c =(−lnQ) / T0.

7. The design method for a multi-resonant control system of a single-phase inverter according to claim 6, characterized in that, The load R load The load is either a resistor or a rectifier, wherein the rectifier load is a load inductor L connected in series after a diode bridge consisting of four diodes. r Load capacitance C r and load resistance R r .

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