A Phase-Lead Compensation Active Damping Control Method for LCL Grid-Connected Inverters

Abstract

This invention discloses a phase-lead compensation active damping control method based on capacitor current feedback, relating to the field of grid-connected inverter control technology, and solving the design problems of active damping compensators and grid-connected current outer loop controllers. The sampled capacitor current passes through the phase-lead compensator C... ic (z), generating output signal u1; the error between the sampled grid current and the given reference current is processed by the proportional resonant controller C. i2 (z), thus generating the output signal u2; subtracting u1 from u2 yields the modulation signal u. m Controlling inverter power devices. This invention proposes a capacitor current feedback phase lead compensator, provides a method for calculating the frequency point where the Nyquist curve of the grid-connected current loop crosses -180°, and obtains a method for calculating control parameters according to performance requirements. This avoids the trial-and-error process relying on experience and improves the robust stability of the grid-connected inverter in weak power grids.

Description

Technical Field

[0001] This invention relates to the field of grid-connected inverter control technology, and in particular to a phase lead compensation active damping control method for an LCL-type grid-connected inverter. Background Technology

[0002] Distributed generation based on renewable energy is one of the main ways to develop and utilize renewable energy on a large scale, solve energy and environmental problems, and achieve carbon peaking targets. Various renewable energy generation units convert DC power into high-quality AC power and input it into the grid through grid-connected inverters. To suppress high-frequency switching harmonics in the grid-connected current, a suitable output filter needs to be selected. Compared with L-type output filters, LCL-type output filters are smaller, lower in cost, and have better filtering performance. However, it is necessary to introduce control strategies to achieve active damping in LCL-type grid-connected inverters to solve the stability problems caused by LCL filter resonance.

[0003] Capacitor current proportional feedback is a widely used active damping method. It is equivalent to connecting a virtual resistor in parallel with the filter capacitor, providing good resonant damping. However, when the inverter uses digital control, due to control delay, the capacitor current proportional feedback is equivalent to a virtual impedance, which will affect the loop's frequency characteristics. In weak grids, the grid impedance will cause changes in the resonant frequency, resulting in variations at different resonant frequencies f. r Under different conditions, the system stability constraints vary greatly, especially when the resonant frequency f is... r Approaching f s / 6 o'clock (f s (This refers to the controller's sampling frequency), resulting in poor system stability.

[0004] Existing active damping methods based on capacitor current feedback typically increase the positive resistance frequency range of their equivalent impedance by designing compensators. However, since the virtual impedance is the equivalent effect of the active damping closed loop, it's difficult to directly see how adjusting the compensator changes the positive resistance characteristics of the virtual impedance. Furthermore, while increasing the positive resistance frequency range improves the system's robustness and stability, increasing it to f... s / 2 is not always necessary; rather, the design requirements of both the inner and outer loops should be considered comprehensively based on the resonant frequency range. Existing compensators all employ phase compensation strategies to improve the frequency characteristics of the equivalent impedance and enhance the robustness and stability of the system, but none of them explain the rationale for using phase lead compensation or phase lag compensation. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a phase lead compensation active damping control method for LCL-type grid-connected inverters. This method solves the problem that existing methods are difficult to design capacitor current feedback active damping compensators and grid-connected current outer loop controllers according to performance requirements, thereby improving the robust stability of grid-connected inverters in weak power grids.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a phase-lead compensation active damping control method based on capacitor current feedback, comprising the following steps:

[0007] Step 1: Sample the capacitor current i in the LCL filter c , change i c Input to phase lead compensator C ic (z), thus obtaining the phase lead compensator output signal u1;

[0008] Step 2: Sample the grid current i2, and convert the grid current reference signal i ref The error signal e is obtained by comparing it with i2; the error signal e is then input to the proportional resonant controller C. i2 (z), thus obtaining the proportional resonant controller output signal u2;

[0009] Step 3: Subtracting u1 from u2 gives the pulse width modulation signal u. m This controls the states of switching transistors S1, S2, S3, and S4.

[0010] Step 4: Based on the cutoff frequency f of the grid-connected current loop c Fundamental gain T f0 Performance requirements for phase margin (PM) and gain margin (GM), and calculation of the phase lead compensator C. ic (z) and proportional resonant controller C i2 (z) control parameters;

[0011] The phase lead compensator C ic The expression for (z) is:

[0012] ,

[0013] Where ζ and H ic As a control parameter, ζ determines the phase lead angle of the phase lead compensator, H ic Determines the gain of the phase lead compensator;

[0014] The proportional resonant controller C i2 The expression for (z) is:

[0015] ,

[0016] Where Kp and K r K is a control parameter. p The proportional coefficient K of the proportional resonant controller is determined. r The resonant coefficient of the proportional resonant controller is determined by ω0, where ω is the fundamental angular frequency. i For the resonant term bandwidth, K = 2f s f s The sampling frequency for the digital control of the grid-connected inverter;

[0017] In step 4, the control parameter K p K r ζ and H ic The calculation steps are as follows:

[0018] Step 4-1: Calculate K p The expression is:

[0019] ,

[0020] Where L1 is the inverter-side inductance value, L2 is the grid-side inductance value, and H... i2 K represents the sampling coefficient for the power grid current. PWM For inverter gain, T s =1 / f s ω is the sampling period. c =2πf c The cutoff angular frequency;

[0021] Step 4-2: Calculate K r The expression is:

[0022] ;

[0023] Step 4-3: Set the initial value of ζ to 0.01;

[0024] Step 4-4: Calculate H ic_ PM That is, H that satisfies the phase margin PM ic The expression is:

[0025] ,

[0026] in

[0027] A oh c =∠ [ ( K p K + 2 K r oh i )cos oh c T s + 2 K r oh i − K p K + j( K p K + 2 K r oh i )sin oh c T s ] ,

[0028] C oh c =∠ [ x 1 ( oh c ) + j y 1 ( oh c ) ] −∠ [ K (cos oh c T s − 1 + jsin oh c T s ) ] ,

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] Where is the resonant angular frequency, C is the filter capacitor, and L is the resonant angular frequency. g This is the inductance value of the power grid;

[0035] Steps 4-5: Calculate H to meet the gain margin requirement. ic ;

[0036] The specific calculation method for steps 4-5 is as follows:

[0037] Solve the analytical expression of the following equation using Wolfram Mathematica software:

[0038] ,

[0039] in

[0040] ,

[0041] ,

[0042] ,

[0043] ,

[0044] ;

[0045] The equation has four solutions, z1, z2, z3, and z4, where each solution corresponds to a frequency point on the Nyquist curve of the grid-connected current loop that crosses the real axis, denoted as ω. x =(arccos z x / T s ), x=1, 2, 3, 4; when ω x Make y1(ω) x )y2(ω x When ω < 0, then the ω x Let y1 be the angular frequency point that crosses -180°, where y1(ω x ) and y2(ω x The expressions for ) are as follows:

[0046] ,

[0047] ;

[0048] Based on the calculated K p The current value of ζ, and the angular frequency point ω crossing -180°. x and H ic The range of values ​​for H is used to calculate the gain across -180° of the Nyquist curve, thereby determining the H value that satisfies the gain margin requirement. ic Range; the gain expression for the Nyquist curve crossing -180° is:

[0049] ,

[0050] in

[0051] K ol ( oh x ) =− K PWM L 1 [ sin oh r T s ( 1 − cos oh x T s ) + oh r T s (cos oh x T s − cos oh r T s ) ] ( 1 + 2 g cos oh x T s + g 2 ) 2 ( L 1 + L 2 + L g )( 1 − cos oh x T s ) H i 2 ;

[0052] Steps 4-6: Increase the current value of ζ by 0.01;

[0053] Step 4-7: If ζ < 1 after increasing by 0.01, return to step 4-4; if ζ = 1 after increasing by 0.01, end the calculation and obtain ζ and H that meet the gain margin requirements. ic scope.

[0054] Furthermore, in steps 4-5, when calculating the gain of the Nyquist curve crossing -180°, H ic The range of values ​​for is as follows:

[0055] If ω r <ω b 0 <H ic_max <H ic_ PM Then H ic In (0, H) ic_max Values ​​can be taken within a range;

[0056] If ω r <ω b 0 <H ic_ PM ≤H ic_max Then H ic In (0, H) ic_ PM It takes values ​​within the range of ).

[0057] If ω r >ω b H ic_max ≤0< H ic_ PM Then H ic In (0, H) ic_ PM It takes values ​​within the range of ).

[0058] in oh b = arccos [ ( 1 − 2 g − g 2 ) / 2 ] / T s It is the critical resonant angular frequency. To ensure that the grid-connected current loop has the critical gain corresponding to the stable pole.

[0059] Furthermore, in steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows:

[0060] When the number of unstable poles in the grid-connected current loop is 0, the number of times its Nyquist curve crosses -180° may be 1, 2, 3, or 4 times; it is required that in each case, the gain of each crossing of -180° is positive and meets the given positive gain margin requirement.

[0061] Furthermore, in steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows:

[0062] When the number of unstable poles in the grid-connected current loop is 2 and the Nyquist curve crosses -180° twice, the gain of the first crossing of -180° must be positive and the gain of the second crossing of -180° must be negative, and the given positive and negative gain margin requirements must be met.

[0063] Furthermore, in steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows:

[0064] When the number of unstable poles in the grid-connected current loop is 2 and its Nyquist curve crosses -180° 3 times, the gain of the first crossing of -180° must be positive, the gain of the second crossing of -180° must be negative, and the gain of the third crossing of -180° must be positive, while satisfying the given positive and negative gain margin requirements; or the gain of the first crossing of -180° must be positive, the gain of the second crossing of -180° must be positive, and the gain of the third crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements.

[0065] Furthermore, in steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows:

[0066] When the number of unstable poles in the grid-connected current loop is 2, and its Nyquist curve crosses -180° 4 times, the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be negative, the gain for the third crossing of -180° must be positive, and the gain for the fourth crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements; or the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be positive, the gain for the third crossing of -180° must be positive, and the gain for the fourth crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements. The gain is negative, and the given positive and negative gain margin requirements are met; or the gain for the first crossing of -180° is negative, the gain for the second crossing of -180° is negative, the gain for the third crossing of -180° is positive, and the gain for the fourth crossing of -180° is negative, and the given positive and negative gain margin requirements are met; or the gain for the first crossing of -180° is positive, the gain for the second crossing of -180° is negative, the gain for the third crossing of -180° is negative, and the gain for the fourth crossing of -180° is negative, and the given positive and negative gain margin requirements are met.

[0067] The beneficial effects of this invention are: this method utilizes a phase lead compensator based on capacitor current feedback to achieve active damping, directly designs the compensator in the discrete time domain, and controls parameters ζ and H. ic The significance is clear: it can improve the robust stability of the system to changes in resonant frequency. Based on the phase margin and gain margin requirements, ζ and H can be obtained through numerical calculation. ic The range of values ​​is determined by this, avoiding a trial-and-error process that relies on experience.

[0068] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0069] Figure 1 This is a schematic diagram of the digital control of a single-phase LCL grid-connected inverter according to an embodiment of the present invention;

[0070] Figure 2 This is a control block diagram of an LCL-type grid-connected inverter according to an embodiment of the present invention;

[0071] Figure 3 This is a flowchart illustrating the calculation of control parameters according to an embodiment of the present invention;

[0072] Figure 4 This refers to the parameter range of a phase lead compensator according to an embodiment of the present invention.

[0073] Figure 5 Bode plot of the frequency response of the grid-connected current loop after adopting the control method in a specific embodiment of the present invention;

[0074] Figure 6The grid-connected current simulation waveform is shown in the specific implementation method of this invention.

[0075] Figure 7 This is a trend diagram of the change of the closed-loop poles of the grid-connected current when the grid impedance changes, after adopting the control method in a specific embodiment of the present invention. Detailed Implementation

[0076] Figure 1 This is a digital control schematic diagram of a single-phase LCL grid-connected inverter. S1, S2, S3, and S4 constitute a full-bridge inverter circuit, V... DC The input voltage is DC, v inv The inverter output voltage is represented by inductor L1, capacitor C, and inductor L2, which together form an LCL filter. i1 is the inverter-side current. c V is the capacitor current. c i1 is the capacitor voltage, i2 is the mains current, and L is the mains voltage. g For the impedance of a weak power grid, v g The voltage is the grid voltage. Since the inductor's resistance provides damping, the resistance of the filter inductor and the grid impedance are ignored, considering the worst-case scenario for system damping performance. The sampling period for the digital control of the grid-connected inverter is T. s Sampling frequency f s =1 / T s Sampling angular frequency ω s =2πf s The main control objective of the grid-connected inverter is to ensure system stability and regulate the output current i2 to track the reference current i. ref C ic (z) is a phase lead compensator based on capacitor current feedback, used to implement active damping of LCL filters. H i2 C is the sampling coefficient for the power grid current. i2 (z) is a proportional resonant controller used to adjust the output current i2. m This is the output of the digital controller, i.e., the voltage modulation signal. Finally, u m The inverter switch is controlled using the PWM method.

[0077] Figure 2 This is the control block diagram of an LCL-type grid-connected inverter, where G i2 (z) is the discrete-time transfer function from the voltage modulation signal to the grid current, and its expression is:

[0078] (1)

[0079] in The resonant angular frequency, , L1 is the inverter-side inductance value, L2 is the grid-side inductance value, C is the filter capacitor value, and L... g K represents the inductance value of the power grid. PWM Inverter gain;

[0080] G ic (z) is the discrete-time transfer function from the voltage modulation signal to the capacitor current, and its expression is:

[0081] (2)

[0082] The impedance L of a weak power grid g This will cause the resonant angular frequency ω r In (0, ω s The resonant point of the system varies within the range of / 2). r The range of influence determines this. According to the Nyquist stability criterion, the system's resonant point being located in the first or second quadrant is a necessary condition for active damping to generate stable poles. The resonant position and phase compensation requirements for active damping based on capacitor current feedback are as follows:

[0083] When f r ∈(0, f s When / 6), G ic (e jωrTs Located in the I quadrant, no phase compensation is required;

[0084] When f r =f s At 6 o'clock, G ic (e jωrTs Located in the I quadrant, phase compensation requires θ > 0°;

[0085] When f r ∈(f s / 6, f s When / 3), G ic (e jωrTs Located in quadrant IV, phase compensation requires 0° < θ ≤ 90°;

[0086] When f r =f s At 3 o'clock, G ic (e jωrTs Located in the IV quadrant, phase compensation requires θ > 90° or θ < −90°;

[0087] When f r ∈(f s / 3, f s When / 2), G ic (e jωrTsLocated in the third quadrant, the phase compensation requirement is 90° < θ ≤ 180° or −90° ≤ θ < 0°;

[0088] Based on the phase compensation requirements, a phase lead compensator C is adopted. ic (z), the expression is:

[0089] (3)

[0090] Critical resonant angular frequency oh b = arccos [ ( 1 − 2 g − g 2 ) / 2 ] / T s ;

[0091] The grid-connected current outer loop control adopts a proportional resonant controller C. i2 (z), the expression is:

[0092] (4)

[0093] Where ω i =1 rad / s, K=2f s ;

[0094] The specific embodiments of the present invention include the following steps:

[0095] Step 1: Sample the capacitor current i in the LCL filter c , change i c Input to phase lead compensator C ic (z), thus obtaining the phase lead compensator output signal u1;

[0096] Step 2: Sample the grid current i2, and convert the grid current reference signal i ref The error signal e is obtained by comparing it with i2; the error signal e is then input to the proportional resonant controller C. i2 (z), thus obtaining the proportional resonant controller output signal u2;

[0097] Step 3: Subtracting u1 from u2 gives the pulse width modulation signal u. m This controls the states of switching transistors S1, S2, S3, and S4.

[0098] Step 4: Based on the given performance specifications: cutoff frequency f c Fundamental gain T f0 Calculate the phase lead compensator C using phase margin PM and gain margin GM. ic (z) and proportional resonant controller C i2 (z) control parameter K p K r ζ and H ic ;

[0099] Step 4-1: According to f cCalculate K p ;reference Figure 2 Consider C i2 The frequency response of the grid-connected current loop when (z) = 1 is expressed as:

[0100] (5)

[0101] in

[0102] K ol ( oh x ) = − K PWM L 1 [ sin oh r T s ( 1 − cos oh x T s ) + oh r T s (cos oh x T s − cos oh r T s ) ] ( 1 + 2 g cos oh x T s + g 2 ) 2 ( L 1 + L 2 + L g )( 1 − cos oh x T s ) H i 2 (6)

[0103] (7)

[0104] (8)

[0105] (9)

[0106] (10)

[0107] Cutoff angular frequency ω c =2πf c Consider ω c Usually less than ω r When ω < ω c <ω r When, the amplitude-frequency characteristic of (1) is approximately:

[0108] (11)

[0109] When ω≥ω c When, the amplitude-frequency characteristic of (4) is approximately:

[0110] (12)

[0111] K p It is calculated by the following formula:

[0112] (13)

[0113] Step 4-2: According to T f0 Calculate K r When ω=ω0, the amplitude-frequency characteristic of the grid-connected current loop is approximately:

[0114] (14)

[0115] K r It is calculated by the following formula:

[0116] (15)

[0117] Step 4-3: Set the initial value of ζ to 0.01;

[0118] Step 4-4: Based on K p The calculation formula (13), K r The calculation formula (15), the current value of ζ, and the phase margin PM are used to calculate H. ic_ PM That is, H that meets the phase margin requirement ic ;

[0119] Because ω c>> ω0 and ω c>> ω i Therefore, when z=e jωcTs When, (4) is approximately:

[0120] (16)

[0121] Based on (5) and (16), the phase margin of the grid-connected current loop is approximately:

[0122] (17)

[0123] in

[0124] A oh c =∠ [ ( K p K + 2 K r oh i )cos oh c T s + 2 K r oh i − K p K + j( K p K + 2 K r oh i )sin oh c T s ] (18)

[0125] B oh c =∠ [ x 1 ( oh c ) + j y 1 ( oh c ) ] −∠ [ x 2 ( oh c ) + j y 2 ( oh c ) ] −∠ [ K (cos oh c T s − 1 + jsin oh c T s ) ] (19)

[0126] H ic_ PM It is calculated by the following formula:

[0127] (20)

[0128] in

[0129] C oh c =∠ [ x 1 ( oh c ) + j y 1 ( oh c ) ] −∠ [ K (cos oh c T s − 1 + jsin oh c T s ) ] (twenty one)

[0130] (twenty two)

[0131] (twenty three)

[0132] (twenty four)

[0133] Steps 4-5: Based on ω r and ω b Relationship, H ic_max and H ic_ PM The relationship, among which Determine which of the following situations applies:

[0134] Case A: ωr <ω b 0 <H ic_max <H ic_ PM When H ic ∈(0, H ic_max When H is in the grid-connected current loop, there are no unstable poles. ic ∈(H ic_max H ic_PM When the grid-connected current loop has a pair of unstable poles outside the unit circle;

[0135] Case B: ω r <ω b 0 <H ic_ PM ≤H ic_max When H ic ∈(0, H ic_ PM When the grid-connected current loop has no unstable poles, the grid-connected current loop has no unstable poles.

[0136] Case C: ω r >ω b H ic_max ≤0 <H ic_ PM When H ic ∈(0, H ic_ PM When the grid-connected current loop has a pair of unstable poles outside the unit circle;

[0137] If the judgment is case A, then in (0, H) ic_max H within the range ic Sampling, the sampling interval can be determined according to the specific range and accuracy requirements; according to K p The calculation formula (13), the current value of ζ, and H ic For each sampled value, calculate the gain of the Nyquist curve crossing -180°; determine whether the sampled value meets the gain margin requirement; after determining all sampled values, obtain the H value that meets the gain margin requirement. ic scope;

[0138] If the judgment is case B, then in (0, H) ic_ PM H within the range ic Sampling, the sampling interval can be determined according to the specific range and accuracy requirements; according to K p The calculation formula (13), the current value of ζ, and H ic For each sampled value, calculate the gain of the Nyquist curve crossing -180°; determine whether the sampled value meets the gain margin requirement; after determining all sampled values, obtain the H value that meets the gain margin requirement. ic scope;

[0139] If the judgment is case C, then in (0, H) ic_ PM H within the range icSampling, the sampling interval can be determined according to the specific range and accuracy requirements; according to K p The calculation formula (13), the current value of ζ, and H ic For each sampled value, calculate the gain of the Nyquist curve crossing -180°; determine whether the sampled value meets the gain margin requirement; after determining all sampled values, obtain the H value that meets the gain margin requirement. ic scope;

[0140] The specific calculation and judgment methods for steps 4-5 are as follows:

[0141] Solve equation (25), the expression is:

[0142] (25)

[0143] in

[0144] ,

[0145] ,

[0146] ,

[0147] ,

[0148] ;

[0149] When a0, a1, a2, a3, and a4 are all given coefficients, equation (25) has four solutions z1, z2, z3, and z4, all of which have analytical expressions. The expressions for z1, z2, z3, and z4 are directly solved using Wolfram Mathematica software, and the specific solutions are obtained by substituting the given coefficients. Each solution corresponds to a frequency point in (5) where the Nyquist curve crosses the real axis, denoted as ω. x =(arccos z x / T s ), x=1, 2, 3, 4. When ω x Make y1(ω) x )y2(ω x When ω < 0, then the ω x Let y1 be the angular frequency point that crosses -180°, where y1(ω x ) and y2(ω x The expressions for ) are as follows:

[0150] ,

[0151] ;

[0152] Based on (5), (12), and the angular frequency point ω where the Nyquist curve crosses -180°, x The gain of the Nyquist curve crossing -180° is calculated using the following expression:

[0153] (26)

[0154] Where K p Determined by expression (13),

[0155] K ol ( oh x ) = − K PWM L 1 [ sin oh r T s ( 1 − cos oh x T s ) + oh r T s (cos oh x T s − cos oh r T s ) ] ( 1 + 2 g cos oh x T s + g 2 ) 2 ( L 1 + L 2 + L g )( 1 − cos oh x T s ) H i 2 ,

[0156] ζ is a given value and ζ∈(0, 1);

[0157] Based on the gain calculation formula (26), determine H that satisfies the gain margin requirement. ic The specific requirements for the range and gain margin are as follows:

[0158] When the number of unstable poles in the grid-connected current loop is 0, the number of times its Nyquist curve crosses -180° may be 1, 2, 3, or 4 times; it is required that in each case, the gain of each crossing of -180° is positive and meets the given positive gain margin requirement.

[0159] When the number of unstable poles in the grid-connected current loop is 2 and the Nyquist curve crosses -180° twice, the gain of the first crossing of -180° is required to be positive and the gain of the second crossing of -180° is required to be negative, and the given positive and negative gain margin requirements must be met.

[0160] When the number of unstable poles in the grid-connected current loop is 2, and its Nyquist curve crosses -180° 3 times, the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be negative, and the gain for the third crossing of -180° must be positive, while satisfying the given positive and negative gain margin requirements; or the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be positive, and the gain for the third crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements.

[0161] When the number of unstable poles in the grid-connected current loop is 2, and its Nyquist curve crosses -180° 4 times, the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be negative, the gain for the third crossing of -180° must be positive, and the gain for the fourth crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements; or the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be positive, the gain for the third crossing of -180° must be positive, and the gain for the fourth crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements. The gain is negative, and the given positive and negative gain margin requirements are met; or the gain for the first crossing of -180° is negative, the gain for the second crossing of -180° is negative, the gain for the third crossing of -180° is positive, and the gain for the fourth crossing of -180° is negative, and the given positive and negative gain margin requirements are met; or the gain for the first crossing of -180° is positive, the gain for the second crossing of -180° is negative, the gain for the third crossing of -180° is negative, and the gain for the fourth crossing of -180° is negative, and the given positive and negative gain margin requirements are met.

[0162] Steps 4-6: Increase the current value of ζ by 0.01;

[0163] Step 4-7: If ζ < 1 after increasing by 0.01, return to step 4-4; if ζ = 1 after increasing by 0.01, end the calculation and obtain ζ and H that meet the gain margin requirements. ic scope.

[0164] Figure 3 The flowchart for calculating the control parameters involved in step 4 is shown.

[0165] The system parameters selected in this embodiment are as follows:

[0166] DC voltage V DC =360V, triangular wave amplitude value V tri =3V, effective value of mains voltage V g =220V, fundamental frequency f0=50Hz, output power P o =1kW, switching frequency f sw =10kHz, sampling frequency f s =20kHz, inverter-side inductance L1=3mH, filter capacitor C=1.5uF, grid-side inductance L2=270uH, grid current sampling coefficient H i2 =0.15, the effective value of the grid-connected current reference signal is 2A.

[0167] The performance requirements are: f c =1.32kHz, T f0 ≥73dB, PM≥45°, GM + ≥3dB, GM- ≤−3dB.

[0168] Based on the calculation method in step 4, K is obtained. p =1.497, K r =253.433; ζ and H ic The range of values ​​is determined by Figure 4 As shown, ζ=0.6, H ic =0.02.

[0169] Using the above control parameters, the Bode plot of the grid-connected current loop is obtained from... Figure 5 As shown, this indicates that the performance indicators meet the requirements.

[0170] Using the above control parameters, the simulated waveform of the grid-connected current is shown in the figure. Figure 6 As shown, this indicates that the grid-connected current is stable and accurately tracks the reference value.

[0171] When considering the grid impedance L g When the current varies between 0 and 3mH, the trend of the closed-loop poles of the grid-connected current changes from... Figure 7 As shown, this indicates that the system has robust stability under weak power grid conditions.

Claims

1. A phase lead compensation active damping control method for an LCL-type grid-connected inverter, comprising the following steps: Step 1: Sample the capacitor current i in the LCL filter c , change i c Input to phase lead compensator C ic (z), thus obtaining the phase lead compensator output signal u1; Step 2: Sample the grid current i2, and convert the grid current reference signal i ref The error signal e is obtained by comparing it with i2; the error signal e is then input to the proportional resonant controller C. i2 (z), thus obtaining the proportional resonant controller output signal u2; Step 3: Subtracting u1 from u2 gives us the pulse width modulation signal u. m This controls the states of switching transistors S1, S2, S3, and S4. Step 4: Based on the cutoff frequency f of the grid-connected current loop c Fundamental gain T f0 Performance requirements for phase margin (PM) and gain margin (GM), and calculation of the phase lead compensator C. ic (z) and proportional resonant controller C i2 The control parameters of (z) are characterized in that, The phase lead compensator C ic The expression for (z) is: ， Where ζ and H ic As a control parameter, ζ determines the phase lead angle of the phase lead compensator, H ic Determines the gain of the phase lead compensator; The proportional resonant controller C i2 The expression for (z) is: ， Where K p and K r K is a control parameter. p The proportional coefficient K of the proportional resonant controller is determined. r The resonant coefficient of the proportional resonant controller is determined by ω0, where ω is the fundamental angular frequency. i For the resonant term bandwidth, K = 2f s f s The sampling frequency for the digital control of the grid-connected inverter; In step 4, the control parameter K p K r ζ and H ic The calculation steps are as follows: Step 4-1: Calculate K p The expression is: ， Where L1 is the inverter-side inductance value, L2 is the grid-side inductance value, and H... i2 K represents the sampling coefficient for the power grid current. PWM For inverter gain, T s =1 / f s ω is the sampling period. c =2πf c The cutoff angular frequency; Step 4-2: Calculate K r The expression is: ； Step 4-3: Set the initial value of ζ to 0.01; Step 4-4: Calculate H ic_ PM That is, H that satisfies the phase margin PM ic The expression is: ， in ， ， ， ， ， ， ， Where is the resonant angular frequency, C is the filter capacitor, and L is the resonant angular frequency. g This is the value of the mains inductance; Steps 4-5: Calculate H to meet the gain margin requirement. ic ; The specific calculation method for steps 4-5 is as follows: Solve the analytical expression of the following equation using Wolfram Mathematica software: ， in ， ， ， ， ； The equation has four solutions, z1, z2, z3, and z4, where each solution corresponds to a frequency point on the Nyquist curve of the grid-connected current loop that crosses the real axis, denoted as ω. x =(arccos z x / T s ), x=1, 2, 3, 4; when ω x Make y1(ω) x )y2(ω x When ω < 0, then the ω x Let y1 be the angular frequency point that crosses -180°, where y1(ω x ) and y2(ω x The expressions for ) are as follows: ， ； Based on the calculated K p The current value of ζ, and the angular frequency point ω crossing -180°. x and H ic The range of values ​​for H is used to calculate the gain across -180° of the Nyquist curve, thereby determining the H value that satisfies the gain margin requirement. ic Range; the expression for calculating the gain of the Nyquist curve crossing -180° is: ， in ； Steps 4-6: Increase the current value of ζ by 0.01; Step 4-7: If ζ < 1 after increasing by 0.01, return to step 4-4; if ζ = 1 after increasing by 0.01, end the calculation and obtain ζ and H that meet the gain margin requirements. ic scope.

2. The phase lead compensation active damping control method for an LCL-type grid-connected inverter according to claim 1, characterized in that, In steps 4-5, when calculating the gain of the Nyquist curve crossing -180°, H ic The range of values ​​for is as follows: If ω r <ω b 0 <H ic_max <H ic_ PM Then H ic In (0, H) ic_max Values ​​can be taken within a range; If ω r <ω b 0 <H ic_ PM ≤H ic_max Then H ic In (0, H) ic_ PM It takes values ​​within the range of ). If ω r >ω b H ic_max ≤0< H ic_ PM Then H ic In (0, H) ic_ PM It takes values ​​within the range of ). in It is the critical resonant angular frequency. To ensure that the grid-connected current loop has the critical gain corresponding to the stable pole.

3. The phase lead compensation active damping control method for an LCL-type grid-connected inverter according to claim 1 or 2, characterized in that, In steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows: When the number of unstable poles in the grid-connected current loop is 0, the number of times its Nyquist curve crosses -180° may be 1, 2, 3, or 4 times; it is required that in each case, the gain of each crossing of -180° is positive and meets the given positive gain margin requirement.

4. A phase-lead compensation active damping control method for an LCL-type grid-connected inverter according to claim 1 or 2, characterized in that, In steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows: When the number of unstable poles in the grid-connected current loop is 2 and the Nyquist curve crosses -180° twice, the gain of the first crossing of -180° must be positive and the gain of the second crossing of -180° must be negative, and the given positive and negative gain margin requirements must be met.

5. A phase-lead compensation active damping control method for an LCL-type grid-connected inverter according to claim 1 or 2, characterized in that, In steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows: When the number of unstable poles in the grid-connected current loop is 2 and its Nyquist curve crosses -180° 3 times, the gain of the first crossing of -180° must be positive, the gain of the second crossing of -180° must be negative, and the gain of the third crossing of -180° must be positive, while satisfying the given positive and negative gain margin requirements; or the gain of the first crossing of -180° must be positive, the gain of the second crossing of -180° must be positive, and the gain of the third crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements.

6. A phase-lead compensation active damping control method for an LCL-type grid-connected inverter according to claim 1 or 2, characterized in that, In steps 4-5, H is determined to meet the gain margin requirement. ic When the range is within a certain range, the gain margin requirement for satisfying the Nyquist stability criterion is as follows: When the number of unstable poles in the grid-connected current loop is 2, and its Nyquist curve crosses -180° 4 times, the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be negative, the gain for the third crossing of -180° must be positive, and the gain for the fourth crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements; or the gain for the first crossing of -180° must be positive, the gain for the second crossing of -180° must be positive, the gain for the third crossing of -180° must be positive, and the gain for the fourth crossing of -180° must be negative, while satisfying the given positive and negative gain margin requirements. The gain is negative, and the given positive and negative gain margin requirements are met; or the gain for the first crossing of -180° is negative, the gain for the second crossing of -180° is negative, the gain for the third crossing of -180° is positive, and the gain for the fourth crossing of -180° is negative, and the given positive and negative gain margin requirements are met; or the gain for the first crossing of -180° is positive, the gain for the second crossing of -180° is negative, the gain for the third crossing of -180° is negative, and the gain for the fourth crossing of -180° is negative, and the given positive and negative gain margin requirements are met.

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