Small signal model establishment method, device and equipment suitable for string type photovoltaic grid-connected system and medium

Abstract

The invention discloses a small-signal model establishment method, device and equipment suitable for a string type photovoltaic grid-connected system and a medium, and the method comprises the steps: constructing a mathematical model of a photovoltaic array, and carrying out the linearization and per-unit processing, and obtaining a state-space equation of the photovoltaic array; constructing a mathematical model of the Boost circuit and the control system thereof, and carrying out linearization and per-unit processing to obtain a state space equation of the Boost circuit and the control system thereof; constructing a mathematical model of the converter and the control system thereof, and carrying out linearization and per-unit processing to obtain a state-space equation of the converter and the control system thereof; simultaneously establishing the state space equation to obtain a complete small signal model of the string type photovoltaic grid-connected system under the dq coordinate system; and performing coordinate transformation on the small signal model to obtain a string photovoltaic grid-connected system small signal model under the xy coordinate system. The small interference stability of the string type photovoltaic grid-connected system can be accurately described, and the characteristic value can correctly reflect the stability of the string type photovoltaic grid-connected system.

Description

Technical Field

[0001] The present invention relates to the technical field of small-signal model establishment, and specifically to a method, device, equipment and medium for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system. Background Art

[0002] With the continuous expansion of the scale of photovoltaic grid connection, the photovoltaic grid-connected system faces the problem of sub-synchronous oscillation (SSO), which seriously affects the safe and stable operation of the power grid.

[0003] Most of the existing research on the oscillation stability of photovoltaic grid connection is aimed at centralized photovoltaic power stations, and there is little research on string-type photovoltaic grid-connected systems. There are significant differences in the circuit structure and control methods between string-type photovoltaics and centralized photovoltaics. Therefore, the oscillation characteristics of the two grid-connected systems may be different, and it is necessary to study the small-signal stability of the string-type photovoltaic grid-connected system.

[0004] For the research on the small-signal stability of the string-type photovoltaic grid-connected system, a small-signal model of the string-type photovoltaic grid-connected system is often established first to establish its small-signal state-space model. Based on this, the eigenvalues of the entire system are obtained through the characteristic mode analysis method, and the stability of the system is judged by the sign of the real part of the eigenvalues.

[0005] At present, most of the small-signal modeling methods for photovoltaic power stations are for centralized photovoltaic power stations. The photovoltaic inverters in centralized photovoltaic power stations mostly use single-stage photovoltaic inverters, while string-type photovoltaic inverters mostly use two-stage photovoltaic inverters. The differences in their structures result in different contents and orders of their small-signal models. Therefore, it is necessary to model the small-signal model of the string-type photovoltaic inverter. Summary of the Invention

[0006] The purpose of the present invention is to solve the above-mentioned deficiencies of the existing technology, and thus provide a method, device, equipment and medium for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system.

[0007] A method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system includes the following steps:

[0008] S1. Construct a mathematical model of the photovoltaic array, perform linearization and normalization to obtain the state-space equation of the photovoltaic array;

[0009] S2. Construct a mathematical model of the Boost circuit and its control system, perform linearization and normalization to obtain the state-space equation of the Boost circuit and its control system;

[0010] S3. Build the mathematical models of the converter and its control system, linearize and per-unitize them to obtain the state-space equations of the converter and its control system;

[0011] S4. By simultaneously solving the state-space equations of the photovoltaic array, Boost circuit and its control system, and the converter and its control system established in steps S1 - S3, obtain the complete small-signal model of the string-type photovoltaic grid-connected system in the dq coordinate system;

[0012] S5. Perform coordinate transformation on the small-signal model to obtain the small-signal model in the xy coordinate system.

[0013] Step S1 specifically includes:

[0014] S11. Build the mathematical model of the photovoltaic array

[0015] Output voltage and current equations of the photovoltaic array:

[0016] I = I sc {1 - α[exp[V / (βV oc )] - 1]} (1)

[0017] Where: α is the standard condition parameter of the photovoltaic cell, β is the actual environmental parameter, I sc is the short-circuit current of the photovoltaic cell, V oc is the open-circuit voltage, V m 、I m are the terminal voltage and output current of the photovoltaic cell at the maximum power point, V and I are the terminal voltage and output current of the photovoltaic cell;

[0018]

[0019] Given the open-circuit voltage V ocr , short-circuit current I scr , terminal voltage V mr at the maximum power point and output current I mr , introduce compensation coefficients to calculate the key parameters under any working conditions. The specific algorithm is as shown in Equation (3):

[0020]

[0021] In the formula, T ref is the reference cell temperature; S ref is the reference light intensity; T air is the air temperature, T is the cell temperature in °C, S is the light intensity in W / m 2 ; a, b, c are compensation coefficients; k is the temperature coefficient of the photovoltaic cell;

[0022] A number of photovoltaic cells are connected in series and parallel to form a photovoltaic array. Assume that the number of series-connected photovoltaic cells in the photovoltaic array is N S , and the number of parallel-connected cells is M P ; the output voltage of the photovoltaic array is U pv , and the current is I pv . Then, the external characteristics of the photovoltaic array are as follows:

[0023]

[0024] S12. Linearization and per-unitization of the mathematical model of the photovoltaic array

[0025] Linearizing Equation (4) at the steady-state point, the linearized state-space equation of the photovoltaic array can be obtained:

[0026]

[0027] ΔI pv represents the differential component of the output current of the photovoltaic array, and ΔU pv represents the differential component of the output voltage of the photovoltaic array, and U pv0 represents the steady-state operating value of the output voltage of the photovoltaic array;

[0028] Since the photovoltaic inverter includes a DC part and an AC part, setting the reference power of the AC and DC parts to be the same, the relationship between the reference values on both the AC and DC sides can be obtained as follows:

[0029]

[0030] Among them, S bac and S bdc are the reference capacities of the AC system and the DC system respectively, U bac and U bdc are the reference voltages of the AC system and the DC system respectively, I bac and I bdc are the reference currents of the AC system and the DC system respectively, S bac is taken as the rated capacity of the photovoltaic inverter, U bdc takes the reference voltage value of the DC bus voltage, and U bac takes the rated value of the output voltage of the inverter;

[0031] Per-unitizing the small-signal equation (5) of the photovoltaic array, the linearized and per-unitized state-space equation of the photovoltaic array is obtained:

[0032]

[0033] Among them: ΔI pv * represents the per-unit value of the differential component of the output current of the photovoltaic array, and I sc *Represents the per-unit value of the short-circuit current of the photovoltaic cell, V oc * Represents the per-unit value of the open-circuit voltage, U pv0 * Represents the per-unit value of the output voltage at the steady-state point of the photovoltaic array, ΔU pv * Represents the per-unit value of the differential component of the output voltage of the photovoltaic array.

[0034] Step S2 specifically includes:

[0035] S21. The mathematical model of the Boost circuit and its control system

[0036] The Boost circuit consists of the switching transistor V Q , the boost inductor L B , the DC capacitor C on the photovoltaic array side pv , the capacitor C on the inverter side dc , and the diode V D ;

[0037] The mathematical model of the Boost circuit is expressed as:

[0038]

[0039] In the formula: I pv is the output current of the photovoltaic array, I B is the current of the inductor L B , I dc is the Boost output current; U pv is the output voltage of the photovoltaic array, U dc is the Boost output voltage; D is the input duty cycle of the switching transistor; L B is the value of the boost inductor, C pv is the value of the DC capacitor on the photovoltaic array side, C dc is the value of the capacitor on the inverter side;

[0040] The input-output voltage relationship of the Boost circuit is shown in Equation (9):

[0041]

[0042] Since the output voltage is constant, it can be seen from Equation (9) that the output voltage U of the photovoltaic array pv is linearly related to the duty cycle D, and the maximum power point tracking can be achieved by controlling the duty cycle D. The voltage loop control adopts PI control and compares with the carrier to generate the PWM modulation wave; pv For U

[0043] Add a first-order measurement filter to improve the input waveform, and introduce the intermediate variables z pv and U mppt and Upvm , the state equation of the control system of the Boost circuit is as follows:

[0044]

[0045] The corresponding algebraic equation is:

[0046]

[0047] Among them, K pmppt , K imppt are the proportional gain and integral gain of the Boost voltage loop, z mppt is the intermediate variable of the Boost control, U pvm is the output voltage of the photovoltaic array after first-order filtering, U pvref is the maximum power point voltage output by the MPPT using the perturbation increment method, T udc is the measurement filtering constant of the output voltage of the photovoltaic array; u id and u iq are the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; i id and i iq are the d-axis component and q-axis component of the inverter-side current of the LCL filter;

[0048] S22, Linearization and per-unitization of the mathematical model of the Boost circuit and its control system

[0049] By performing linearization on equations (8) and (10) near the steady-state point, the state-space equations of the linearized Boost circuit and its control system can be obtained:

[0050]

[0051] In the formula, ΔI pv is the differential component of the output current of the photovoltaic array, ΔI B is the differential component of the current on the inductor L B , ΔI dc is the differential component of the Boost output current; ΔU pv is the differential component of the output voltage of the photovoltaic array, ΔU dc is the differential component of the Boost output voltage; ΔD is the differential component of the input duty cycle of the switch tube; I B0 is the steady-state point current of the inductor L B , U dc0 is the Boost steady-state point output voltage; D0 is the steady-state point operating value of the duty cycle;

[0052]

[0053] Among them, Δz mpptThe differential component of the intermediate variable for Boost control, ΔU pvm The differential component of the output voltage of the PV array after first-order filtering, ΔU pvref The differential component of the maximum power point voltage of the output of the MPPT using the perturbation increment method;

[0054] Performing per-unitization on equations (12) and (13), the state-space equations of the linearized and per-unitized Boost circuit and its control system are obtained:

[0055]

[0056] In the formula, Y bdc = I bdc / U bdc is the reference admittance of the DC system, Z bdc = U bdc / I bdc is the reference reactance of the DC system; ΔI pv * is the per-unit value of the differential component of the output current of the PV array, ΔI B * is the per-unit value of the differential component of the current of inductor L B ΔI dc * is the per-unit value of the differential component of the Boost output current; ΔU pv * is the per-unit value of the differential component of the output voltage of the PV array, ΔU dc * is the per-unit value of the differential component of the Boost output voltage; I B0 * is the per-unit value of the steady-state point current of inductor L B U dc0 * is the per-unit value of the Boost steady-state point output voltage; Δz mppt * is the per-unit value of the differential component of the intermediate variable for Boost control, ΔU pvm * is the per-unit value of the differential component of the output voltage of the PV array after first-order filtering, ΔU pvref * is the per-unit value of the differential component of the maximum power point voltage of the output of the MPPT using the perturbation increment method;

[0057] Performing linearization and per-unitization on equation (11), the per-unit linearized algebraic equation of the Boost circuit and its control system is obtained:

[0058]

[0059] Δu id* 、Δu iq * are the differentials of the per-unit values of the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; Δi id * 、Δi iq * are the differentials of the per-unit values of the d-axis component and q-axis component of the inverter-side current of the LCL filter; u id0 * 、u iq0 * are the per-unit values of the steady-state operating points of the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; i id0 * 、i iq0 * are the per-unit values of the steady-state operating points of the d-axis component and q-axis component of the inverter-side current of the LCL filter.

[0060] Step S3 specifically includes:

[0061] S31. The mathematical model of the converter and its control system

[0062] Construct the mathematical model of the inverter

[0063] The inverter circuit topology includes two series-connected capacitors C1 and C2, and the point between the two capacitors is called the midpoint Z; each phase includes four groups of insulated gate bipolar transistors / diodes Sx1, Sx2, Sx3 and Sx4 and two clamping diodes;

[0064] Its mathematical model is expressed as:

[0065]

[0066] In the formula: u id and u iq are the d-axis component and q-axis component of the inverter-side voltage of the LCL filter, u idref and u iqref are the reference d-axis component and q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter; T d is the switching delay time constant, K pwm is the equivalent gain of the PWM inverter;

[0067] Construct the mathematical model of the inverter output filter

[0068] The inverter output filter uses LCL filtering;

[0069] The control of the inverter adopts vector control based on grid voltage orientation, which belongs to dq decoupling control. Since the voltage and current components of the LCL filter circuit are correlated with the electrical quantities of the control system, it is necessary to perform dq decoupling analysis on the LCL filter components. Its mathematical model is expressed as:

[0070]

[0071] Among them, ω is the rotational angular velocity of the reference dq coordinate system; L f and L g are the filter inductance values on the inverter side and the grid side, and C f is the filter capacitor; u cd is the d-axis component of the filter capacitor voltage, and u cq is the q-axis component of the filter capacitor voltage; u gd is the d-axis component of the grid side voltage of the LCL filter, and u gq is the q-axis component of the grid side voltage of the LCL filter; i id is the d-axis component of the inverter side inductor current of the LCL filter, and i iq is the q-axis component of the inverter side inductor current of the LCL filter; i cd is the d-axis component of the filter capacitor current of the LCL filter, and i cq is the q-axis component of the filter capacitor current of the LCL filter; i gd is the d-axis component of the grid side inductor current of the LCL filter, and i gq is the q-axis component of the grid side inductor current of the LCL filter;

[0072] Construct the mathematical model of the control system

[0073] The outer loop of the d-axis of the converter controls the capacitor voltage to maintain at the command value to ensure the normal operation of the converter; the q-axis adopts constant reactive power control to make the converter output reactive power of 0 according to the command; since at power frequency, the capacitor in the LCL filter is approximately open circuit, and in the control, the LCL filter can be approximated as a single L filter, so the decoupling control structure of the current loop is the same as the L filter structure;

[0074] Introduce intermediate variables z pd , z pq , z pcd , z pcq , and the equations of the PQ decoupling control link of the inverter can be respectively expressed as:

[0075]

[0076] Among them, U dcref * is the per-unit value of the command value of the DC capacitor voltage; Q ref *is the per-unit value of the command value of reactive power, Q m * is the per-unit value of the measured reactive power output of the inverter; L * is L f and L g is the per-unit value of the sum; z pd are the intermediate variables of the outer DC voltage loop control, z pq is the intermediate variable of the outer AC reactive power loop control, z pcd is the intermediate variable of the inner d-axis current loop control, z pcq is the intermediate variable of the inner q-axis current loop control; i gdref * is the per-unit value of the reference d-axis component of the inverter output current, i gqref * is the per-unit value of the reference q-axis component of the inverter output current; u gdm * is the per-unit value of the measured filtered d-axis voltage component, u gqm * is the per-unit value of the measured filtered q-axis voltage component, i gdm * is the per-unit value of the measured filtered d-axis current component, i gqm * is the per-unit value of the measured filtered q-axis current component; u idref * 、u iqref * are the per-unit values of the reference d-axis component and q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter; ω0 * is the per-unit value of the steady-state operating value of the synchronous angular velocity on the grid side; K pd 、K id are the proportional gain and integral gain of the outer DC voltage loop control; K pq 、K iq are the proportional gain and integral gain of the outer reactive power loop control; K pcd 、K icd are the proportional gain and integral gain of the inner d-axis current loop control; K pcq 、K icq are the proportional gain and integral gain of the inner q-axis current loop control;

[0077] Considering the delay of the measurement filtering link, there is:

[0078]

[0079] In the formula, T m is the measurement filtering time constant of the inverter output voltage and current; T mqis the measurement filtering time constant of the inverter output reactive power; Q is the inverter output reactive power value; Q m is the measured value of the inverter output reactive power value; u gd * is the per-unit value of the d-axis component of the grid-side voltage of the LCL filter, u gq * is the per-unit value of the q-axis component of the grid-side voltage of the LCL filter; i gd * is the per-unit value of the d-axis component of the grid-side current of the LCL filter, i gq * is the per-unit value of the q-axis component of the grid-side current of the LCL filter;

[0080] Introduce the intermediate variable x of the phase-locked loop control, then the equation of the phase-locked loop PLL is:

[0081]

[0082] θ PLL is the phase angle output by the phase-locked loop, ω is the synchronous angular velocity of the grid side, K pPLL 、K iPLL are the proportional gain and integral gain of the phase-locked loop control; ω0 is the steady-state operating value of the synchronous angular velocity of the grid side;

[0083] For S32, the mathematical model of the converter and its control system is linearized and per-unitized to obtain the per-unit linearized state-space equation of the converter and its control system in different links;

[0084] Converter modulation link:

[0085]

[0086] In the formula, Δu idref * 、Δu iqref * are the differential components of the per-unit values of the reference d-axis component and q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter

[0087] LCL filtering link:

[0088]

[0089] Among them, Δω * is the differential component of the per-unit value of the rotational angular velocity of the reference dq coordinate system; L f * and L g * are the per-unit values of the inverter-side and grid-side filter inductance values, C f *is the per-unit value of the filtering capacitor; Δu cd * , Δu cq * are the differential components of the per-unit values of the d-axis component and q-axis component of the filtering capacitor voltage respectively; Δu gd * , Δu gq * are the differential components of the per-unit values of the d-axis component and q-axis component of the grid-side voltage of the LCL filter respectively; Δi id * , Δi iq * are the differential components of the per-unit values of the d-axis component and q-axis component of the inverter-side inductor current of the LCL filter respectively; Δi cd * , Δi cq * are the differential components of the per-unit values of the d-axis component and q-axis component of the filtering capacitor current of the LCL filter respectively; Δi gd * , Δi gq * are the differential components of the per-unit values of the d-axis component and q-axis component of the grid-side inductor current of the LCL filter respectively; ω0 * is the per-unit value of the steady-state operating value of the rotational angular velocity of the reference dq coordinate system; i id0 * , i iq0 * are the per-unit values of the steady-state operating values of the d-axis component and q-axis component of the inverter-side inductor current of the LCL filter respectively; u cd0 * , u cq0 * are the per-unit values of the steady-state operating values of the d-axis component and q-axis component of the filtering capacitor voltage respectively; i gd0 * , i gq0 * are the per-unit values of the steady-state operating values of the d-axis component and q-axis component of the grid-side inductor current of the LCL filter respectively; w b is the reference value of the rotational angular velocity of the reference dq coordinate system;

[0090] Double closed-loop control link:

[0091]

[0092] In the formula: ΔQ m * is the differential component of the per-unit value of the measured reactive power output by the inverter; Δz pd is the differential component of the intermediate variable of the DC voltage outer-loop control, Δz pqThe differential component of the intermediate variable for the AC reactive outer-loop control, Δz pcd The differential component of the intermediate variable for the d-axis current inner-loop control, Δz pcq The differential component of the intermediate variable for the q-axis current inner-loop control; Δi gdref * The differential component of the per-unit value of the reference value of the d-axis component of the inverter output current, Δi gqref * The differential component of the per-unit value of the reference value of the q-axis component of the inverter output current; Δi gdm * The differential component of the per-unit value of the measured and filtered d-axis current component, Δi gqm * The differential component of the per-unit value of the measured and filtered q-axis current component; Δi gdref * The differential component of the per-unit value of the reference value of the d-axis component of the inverter output current, Δi gqref * The differential component of the per-unit value of the reference value of the q-axis component of the inverter output current; Δu idref * 、Δu iqref * The differential components of the per-unit values of the reference d-axis component and the q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter; Δu gdm * The differential component of the per-unit value of the measured and filtered d-axis voltage component, Δu gqm * The differential component of the per-unit value of the measured and filtered q-axis voltage component;

[0093] Phase-locked loop link:

[0094]

[0095] In the formula, ω b Is the reference value of the synchronous rotation angular velocity of the AC system; Δθ PLL Is the differential component of the phase angle output by the phase-locked loop, and Δx is the differential component of the intermediate variable of the phase-locked loop control;

[0096] Measurement and filtering link:

[0097]

[0098] In the formula, ΔQ * Is the differential component of the per-unit value of the reactive power output by the converter.

[0099] Step S4 specifically includes:

[0100] Simultaneously solve the equations to establish a complete small-signal model of the string-type photovoltaic grid-connected system

[0101] By simultaneously solving equations (3), (7), (14 - 16), and (22 - 27), the 24 - order small - signal equations of the string - type photovoltaic grid - connected system in the reference dq coordinate system can be obtained:

[0102]

[0103] Among them, the state variable X = [ΔU dc * Δi id * Δi iq * Δu cd * Δu cq * Δi gd * Δi gq * Δu id * Δu iq * Δi gdm * Δi gqm * Δu gdm * Δu gqm * Δz pd Δz pcd Δz pq Δz pcq ΔQ m * ΔxΔθ pll ΔU pv * ΔI B * Δz mppt ΔU pvm * T , and the algebraic variable W = [ΔI dc * Δω * Δu idref * Δu iqref * ΔQ * ΔI pv * ΔDΔU pvref * T , and the input variable is the port voltage U in the dq coordinate system gdq = [Δu gd * Δu​​gd * T The output variable is the port current I in the dq coordinate system gdq =[Δi gd * Δi gd * T ; p is the differential operator

[0104] Step S5 specifically includes:

[0105] Transform the output variables U gdq and I gdq of the small-signal state-space model from the dq coordinate system to a unified xy coordinate system U gdq and I gdq , where U gxy =[Δu gx * Δu gy * T , I gxy =[Δi gx * Δi gy * T’ , and the coordinate transformation formula is:

[0106]

[0107] In the formula, δ is the angle between the dq reference coordinate system of the component and the unified xy reference coordinate system; Δu gx * is the differential of the per-unit value of the x-axis component of the output voltage of the LCL filter, Δu gy * is the differential of the per-unit value of the y-axis component of the output voltage of the LCL filter, Δi gx * is the differential of the per-unit value of the x-axis component of the grid-side inductor current of the LCL filter, Δi gy * is the differential of the per-unit value of the y-axis component of the grid-side inductor current of the LCL filter;

[0108] By combining Equation (29 - 30) and Equation (28), the complete small-signal model of the series-connected photovoltaic grid-connected system in the unified xy coordinate system, Equation (31), can be obtained. The input variable is the port voltage U gxy =[Δu gx * Δu gy * T , and the output variable is the port current I in the xy coordinate system​​​​​gxy =[Δi gx * Δi gy * ] T :

[0109]

[0110] The present invention also provides a small signal model construction device suitable for a string photovoltaic grid-connected system, comprising:

[0111] A photovoltaic array processing module, which is used to construct a mathematical model of the photovoltaic array, and perform linearization and normalization to obtain a photovoltaic array state space equation;

[0112] A boost circuit and a control system processing module, wherein the boost circuit and a control system processing module is used to construct a mathematical model of the boost circuit and a control system, and perform linearization and normalization to obtain a state space equation of the boost circuit and a control system;

[0113] A converter and its control system processing module, wherein the converter and its control system processing module is used to construct a mathematical model of the converter and its control system, and perform linearization and per-unit normalization to obtain a state space equation of the converter and its control system;

[0114] A combined module, wherein the combined module is used to combine the state space equations obtained by the photovoltaic array processing module, the Boost circuit and its control system processing module, and the converter and its control system processing module to obtain a complete small signal model of the string photovoltaic grid-connected system in the dq coordinate system;

[0115] A coordinate transformation module is used to transform the coordinates of the small signal model of the string photovoltaic grid-connected system in the dq coordinate system to obtain the small signal model of the string photovoltaic grid-connected system in the xy coordinate system.

[0116] The present invention also provides an electronic device, characterized in that it includes a processor and a memory, wherein the processor is used to execute a computer program stored in the memory to implement a small signal model establishment method suitable for a string-type photovoltaic grid-connected system as described in any one of claims 1 to 6.

[0117] The present invention also provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores at least one instruction, and when the at least one instruction is executed by a processor, it implements the small signal model establishment method suitable for a string-type photovoltaic grid-connected system as described in any one of claims 1 to 6.

[0118] To evaluate the grid connection stability of the string - type photovoltaic grid - connected system and analyze the instability scenarios and dominant instability factors of the string - type photovoltaic grid - connected system, the present invention proposes a small - signal modeling method for the string - type photovoltaic grid - connected system. First, based on the working principle of the string - type photovoltaic inverter, mathematical models of the photovoltaic cell array, Boost circuit and its control system, inverter and its control system, and filter circuit are established, and they are linearized and normalized to obtain the small - signal model of the photovoltaic power station. To facilitate subsequent connection with complex systems, the input voltage and output current of the model are converted to the unified xy coordinate system. Finally, an eigenvalue program is written based on the small - signal model, and the consistency between the stability and oscillation frequency of the system in the time - domain simulation of PSCAD / EMTDC and the eigenvalue program is verified, thus verifying the correctness of the small - signal program. The small - signal model established by this method correctly describes the string - type photovoltaic grid - connected system and can accurately reflect the small - disturbance stability of the system; in addition, the established small - signal model has strong unity, which is convenient for subsequent connection with other components in complex networks to analyze the small - disturbance stability of complex systems.

[0119] The advantages of the present invention are as follows: (1) According to the principle and mathematical model of the string - type photovoltaic inverter, the present invention establishes a small - signal model of the string - type photovoltaic grid - connected system, and its eigenvalues can correctly reflect the stability and oscillation frequency of the system; (2) When establishing the simultaneous equations, the present invention transforms the input voltage and output current to the unified xy coordinate system, which is convenient for connection with other systems and for small - signal stability analysis of complex systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] The accompanying drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0121] Figure 1 is a schematic flow chart of the method for establishing a small - signal model applicable to the string - type photovoltaic grid - connected system provided by an exemplary embodiment of the present invention; Figure 2 is the structure diagram of the string - type photovoltaic grid - connected system; Figure 3 is the structural block diagram of the Boost circuit; Figure 4 is the control block diagram of the Boost; Figure 5 is the circuit diagram of the NPC inverter; Figure 6 is the circuit diagram of the LCL filter; Figure 7 is the structural block diagram of the double - closed - loop control of the converter; Figure 8 is the control structural block diagram of the phase - locked loop; Figure 9 Schematic diagram of the dq reference coordinate system and the unified xy reference coordinate system for components Figure 10 Schematic diagram of a string-type photovoltaic grid-connected system Figure 11 Time-domain simulation results provided by an exemplary embodiment of the present invention Figure 12 Schematic structural diagram of a small-signal model construction device applicable to a string-type photovoltaic grid-connected system provided by an exemplary embodiment of the present invention Figure 13 Block diagram of the structure of an electronic device provided by an exemplary embodiment of the present invention Detailed implementation manners

[0123] Next, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments of the present invention. It should be understood that the present invention is not limited by the exemplary embodiments described herein.

[0124] As Figure 1 shown, a method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system of the present invention includes the following steps:

[0125] A string-type photovoltaic power station is mainly composed of multiple string-type photovoltaic inverters aggregated and equivalent. A string-type photovoltaic inverter mainly needs to consider three parts: a photovoltaic cell array, a Boost circuit and its control system, and an inverter and its control system. Its structure is as Figure 2 shown. Among them, the control scheme of the Boost circuit is: to achieve the maximum power point tracking of the output voltage of the photovoltaic array through constant voltage control; the control scheme of the inverter is: to stabilize the DC-side voltage of the converter and control the output of reactive power through dq decoupling control to ensure unity power factor output. The system takes the PCC voltage as the input quantity and the PCC terminal current as the output quantity.

[0126] The small-signal state space model of the system needs to be linearized near the steady-state operating point, and the small-signal state space equation is written in per-unit value. For the convenience of expression, in the unified variables, the subscript with 0 is the steady-state operating value, the superscript with * is the per-unit value, and the variable preceded by Δ is the differential quantity. The parameters of each part are shown in Table 1 in the appendix.

[0127] S1. Construct the mathematical model of the photovoltaic array, and perform linearization and per-unitization to obtain the state space equation of the photovoltaic array

[0128] S11. Mathematical model of the photovoltaic array

[0129] Output voltage and current equations of the photovoltaic array:

[0130] I = I sc{1 - α[exp(V / (βV oc )) - 1]} (1)

[0131] where α and β are variables related to the standard condition parameters and actual environmental parameters of the photovoltaic cell, and the specific expressions are as shown in Equation (2), and I sc is the short - circuit current of the photovoltaic cell, V oc is the open - circuit voltage, V m 、I m are the terminal voltage and output current at the maximum power point, and V and I are the terminal voltage and output current of the photovoltaic cell.

[0132]

[0133] Based on Equation (2), as long as the four key parameters under any working condition are obtained, the voltage - current characteristics of the cell under any working condition can be obtained.

[0134] Battery manufacturers often provide the key electrical parameters of photovoltaic cells under standard working conditions (open - circuit voltage V ocr , short - circuit current I scr , terminal voltage V mr at the maximum power point and output current I mr ). By introducing compensation coefficients, the key parameters under any working condition can be deduced. The specific algorithm for deducing the key parameters under any working condition is as shown in Equation (3):

[0135]

[0136] In the formula, T ref is the reference cell temperature, 25 °C; S ref is the reference light intensity, 1000 W / m 2 ; T air is the air temperature, T is the cell temperature in °C, S is the light intensity in W / m 2 ; a, b, c are compensation coefficients, generally taking a = 0.0025 (°C) -1 , b = 0.0005 (W / m 2 ) -1 , c = 0.00288 (°C) -1 ; k is the temperature coefficient of the photovoltaic cell. For common solar cell array brackets, k = 0.03 can be taken.

[0137] If several photovoltaic cells are connected in series and parallel to form a photovoltaic array, assuming the number of series - connected photovoltaic cells in the photovoltaic array is N S , and the number of parallel - connected cells is N P , and the output current and voltage of the photovoltaic array are U pv , I pv , then the external characteristics of the photovoltaic array are:

[0138]

[0139] (2) Linearization and normalization of the PV array mathematical model

[0140] By linearizing equation (4) at the steady-state point, the linearized photovoltaic array state space equation can be obtained.

[0141]

[0142] ΔI pv Represents the differential of the photovoltaic array output current, ΔU pv Represents the differential component of the photovoltaic array output voltage, U pv0 Indicates the output voltage steady-state point operating value of the photovoltaic array;

[0143] Since the photovoltaic inverter consists of a DC part and an AC part, and the electrical quantities of the two parts are interrelated, in order to facilitate the simultaneous equations, the variables on both sides need to be normalized. If the reference power of the AC and DC parts is set to be the same, the reference value relationship between the AC and DC sides can be obtained as follows:

[0144]

[0145] Among them, S bac and S bdc are the base capacities of the AC system and the DC system, U bac and U bdc are the reference voltages of the AC system and the DC system, I bac and I bdc are the reference currents for the AC system and the DC system respectively. bac Take the rated capacity of the PV inverter, U bdc Take the reference voltage value of the DC bus voltage, U bac Take the inverter output voltage rating.

[0146] By normalizing formula (5), we can obtain the normalized small signal equation of the photovoltaic array:

[0147]

[0148] In the formula, ΔI pv * Indicates the per unit value of the output current differential of the photovoltaic array, I sc * Represents the short-circuit current per unit value of the photovoltaic cell, V oc * Indicates the per unit value of the open circuit voltage, U pv0 * Indicates the per unit value of the steady-state output voltage of the photovoltaic array, ΔU pv* Represents the per-unit value of the derivative of the output voltage of the photovoltaic array.

[0149] S2. Construct the mathematical model of the Boost circuit and its control system, linearize and per-unitize it to obtain the state space equations of the Boost circuit and its control system

[0150] S21. Principle and mathematical model of the Boost circuit

[0151] The structural block diagram of the Boost circuit is as Figure 3 shown. This circuit consists of a switching transistor V Q , a boost inductor L B , a DC capacitor C on the photovoltaic array side pv , a capacitor C on the inverter side dc , and a diode V D . The control terminal of the switching transistor V Q needs to input a driving signal to control its conduction and cut-off. In engineering applications, the driving signal usually adopts the PWM method to implement.

[0152] The mathematical model of the Boost circuit is expressed as:

[0153]

[0154] In the formula: I pv is the output current of the photovoltaic array, I B is the current of the inductor L B , I dc is the Boost output current; U pv is the output voltage of the photovoltaic array, U dc is the Boost output voltage; D is the input duty cycle of the switching transistor; L B is the value of the boost inductor, C pv is the value of the DC capacitor on the photovoltaic array side, C dc is the value of the capacitor on the inverter side.

[0155] The input-output voltage relationship of the Boost circuit is as shown in Equation (9):

[0156]

[0157] Since the output voltage is constant, it can be seen from Equation (9) that the output voltage u pv of the photovoltaic array is linearly related to the duty cycle D, and the maximum power point tracking (MPPT, Maximum Power Point Tracking) can be achieved by controlling the duty cycle D. The voltage loop control adopts PI control, compares with the carrier to generate a PWM modulation wave, and the control block diagram is as pv shown. Figure 4 shown.

[0158] Add a first-order measurement filter to Upv to improve the input waveform. Introduce intermediate variables zmppt and Upwm. The state equations of the control system of the Boost circuit are as follows:

[0159]

[0160] The corresponding algebraic equations are:

[0161]

[0162] Among them, K pmppt , K imppt are the control proportional gain and integral gain of the Boost voltage loop, z mppt is the intermediate variable of Boost control, U pvm is the output voltage of the photovoltaic array after first-order filtering, U pvref is the maximum power point voltage output by the MPPT using the perturbation increment method, T udc is the measurement filter constant of the output voltage of the photovoltaic array;

[0163] Linearization and per-unitization of the mathematical models of S22, the Boost circuit and its control system

[0164] Perform linearization on equations (8) and (10) near the steady state point to obtain the linearized state space equation of the linearized Boost circuit:

[0165]

[0166] Among them: ΔI pv is the differential value of the output current of the photovoltaic array, ΔI B is the differential value of the current of the inductor L B , ΔI dc is the differential value of the Boost output current; ΔU pv is the differential value of the output voltage of the photovoltaic array, ΔU dc is the differential value of the Boost output voltage; ΔD is the differential value of the input duty cycle of the switch tube; I B0 is the steady state point current of the inductor L B , U dc0 is the Boost steady state point output voltage; D0 is the steady state operating value of the duty cycle;

[0167]

[0168] Among them, Δz mppt is the differential component of the intermediate variable of Boost control, ΔU pvm is the differential component of the output voltage of the photovoltaic array after first-order filtering, ΔU pvrefis the differential component of the maximum power point voltage of the output of the MPPT using the perturbation increment method;

[0169] Normalize equations (12) and (13) to obtain the state - space equations of the linearized and normalized Boost circuit and its control system:

[0170]

[0171] In the formula, Y bdc = I bdc / U bdc is the reference admittance of the DC system, Z bdc = U bdc / I bdc is the reference reactance of the DC system. ΔI pv * is the per - unit value of the differential component of the output current of the photovoltaic array, ΔI B * is the per - unit value of the differential component of the current of the inductor L B ; ΔI dc * is the per - unit value of the differential component of the Boost output current; ΔU pv * is the per - unit value of the differential component of the output voltage of the photovoltaic array, ΔU dc * is the per - unit value of the differential component of the Boost output voltage; I B0 * is the per - unit value of the steady - state point current of the inductor L B ; U dc0 * is the per - unit value of the Boost steady - state point output voltage; Δz mppt * is the per - unit value of the differential component of the intermediate variable of the Boost control, ΔU pvm * is the per - unit value of the differential component of the output voltage of the photovoltaic array after first - order filtering, ΔU pvref * is the per - unit value of the differential component of the maximum power point voltage of the output of the MPPT using the perturbation increment method.

[0172] Normalize and linearize equation (11) to obtain the per - unit linearized algebraic equation of the Boost and its control system:

[0173]

[0174] Δu id * 、Δu iq *are the differentials of the per-unit values of the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; Δi id * and Δi iq * are the differentials of the per-unit values of the d-axis component and q-axis component of the inverter-side current of the LCL filter; u id0 * and u iq0 * are the per-unit values of the steady-state operating points of the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; i id0 * and i iq0 * are the per-unit values of the steady-state operating points of the d-axis component and q-axis component of the inverter-side current of the LCL filter.

[0175] S3. Construct the mathematical model of the converter and its control system, and perform linearization and per-unitization to obtain the state-space equation of the converter and its control system

[0176] S31. Mathematical model of the converter and its control system

[0177] The converter includes three parts: a DC / AC inverter circuit, an LCL filter circuit, and a control system.

[0178] (1) Mathematical model of the inverter

[0179] The inverter of the 1500V PV DC system adopts a neutral point clamped (NPC) three-level topology structure, and realizes the control of multi-level voltage by introducing two clamping diodes. Compared with a two-level inverter, it has the advantages of small output voltage and current harmonics, and the voltage and switching losses borne by the switching devices are halved, etc., which can effectively reduce the volume and weight of passive devices such as filters. Therefore, the three-level NPC inverter has gradually moved from high-power medium-voltage applications to grid-connected inverter systems for low-voltage 1500V PV, wind power, and energy storage systems. Its three-level topology is as Figure 5 shown:

[0180] This topology structure includes two series-connected capacitors C1 and C2. The point between the two capacitors is called the neutral point Z. Therefore, the neutral point clamped inverter is also called a diode clamped inverter; each phase includes four groups of IGBT / Diode (Insulated Gate Bipolar Transistor / Diode) Sx1, Sx2, Sx3, and Sx4 and two clamping diodes (x = a, b, and c).

[0181] Its mathematical model is expressed as:

[0182]

[0183] That is, the switching control dynamics refers to the inverter pulse width modulation process, which is approximately simulated by a first-order inertial delay link of the inverter output voltage relative to the reference voltage command. Where: u id and u iq are the d-axis component and q-axis of the inverter output voltage, u idref and u iqref are the reference d-axis component and q-axis component of the inverter-side voltage output by the inverter control system. T d is the switching delay time constant, usually taken as 1 to 1.5 times the switching frequency. K pwm is the equivalent gain of the PWM inverter.

[0184] (2) Mathematical model of inverter output filtering

[0185] The inverter output filtering adopts LCL filtering, and its circuit model is as Figure 6 shown.

[0186] The control of the inverter adopts vector control based on grid voltage orientation, which belongs to dq decoupling control. Since the voltage and current components of the LCL filtering circuit are correlated with the electrical quantities of the control system, it is necessary to perform dq decoupling analysis on the LCL filtering components, and its mathematical model is expressed as:

[0187]

[0188] Among them, ω is the rotational angular velocity of the reference dq coordinate system; L f and L g are the filtering inductance values on the inverter side and grid side, C f is the filtering capacitor; u cd and u cq 、u gd and u gq are the d-axis component and q-axis component of the filtering capacitor voltage and the grid side voltage of the LCL filter; i id and i iq 、i cd and i cq 、i gd and i gq are the d-axis component and q-axis component of the inverter-side inductance current, filtering capacitor current, and grid-side inductance current of the LCL filter. All the electrical quantities in this formula are nominal values.

[0189] (3) Mathematical model of the converter control system

[0190] The outer loop of the d-axis of the converter controls the capacitor voltage to maintain it at the commanded value, ensuring the normal operation of the converter; the q-axis adopts a constant reactive power control, enabling the converter to output reactive power of 0 according to the command. Since at power frequency, the capacitor in the LCL filter is approximately open-circuited, the LCL filter can be approximated as a single-L filter in control, so the decoupling control structure of the current loop is the same as that of the L filter structure. The control structure is as Figure 7 shown, and in the control system, the per-unit values of the variables are all controlled.

[0191] Introduce an intermediate variable z in the integral link of the PI control pd ,z pq ,z pcd ,z pcq , and the equations of the decoupling control link of the inverter PQ can be respectively expressed as:

[0192]

[0193] Among them, U dcref is the commanded value of the DC capacitor voltage; Q ref is the commanded value of the reactive power, and Q m is the measured value of the reactive power output by the inverter; L is the sum of L f and L g ; z pd are respectively the intermediate variables of the DC voltage outer loop control, z pq is the intermediate variable of the AC reactive power outer loop control, z pcd is the intermediate variable of the d-axis current inner loop control, and z pcq is the intermediate variable of the q-axis current inner loop control; i gdref and i gqref are the reference values of the d-axis component and q-axis component of the inverter output current; u gdm and u gqm are the d-axis and q-axis components of the measured filtered output voltage, and i gdm and i gqm are the d-axis and q-axis components of the measured filtered output current; K pd , K id are the proportional gain and integral gain of the DC voltage outer loop control; K pq , K iq are the proportional gain and integral gain of the reactive power outer loop control; K pcd , K icd are the proportional gain and integral gain of the d-axis current inner loop control; K pcq , K icq are the proportional gain and integral gain of the q-axis current inner loop control;

[0194] Considering the delay of the measurement and filtering link, there is:

[0195]

[0196] Wherein, T m is the measurement filtering time constant of the output voltage and current of the inverter; T mq is the measurement filtering time constant of the output reactive power of the inverter; Q is the output reactive power value of the inverter; Q m is the measured value of the output reactive power value of the inverter; u gd * is the per-unit value of the d-axis component of the grid-side voltage of the LCL filter, u gq * is the per-unit value of the q-axis component of the grid-side voltage of the LCL filter; i gd * is the per-unit value of the d-axis component of the grid-side current of the LCL filter, i gq * is the per-unit value of the q-axis component of the grid-side current of the LCL filter;

[0197] The phase-locked loop control structure is as Figure 8 shown, u ga , u gb and u gc are the three-phase voltages at the grid connection point, ω0 is the grid synchronous rotation angular velocity, and θ PLL is the phase angle output by the phase-locked loop.

[0198] Introduce an intermediate variable x, then the equation of the PLL is:

[0199]

[0200] S32. Linearize and per-unitize the mathematical model of the converter and its control system to obtain the per-unit linearized state-space equations of different links of the converter and its control system

[0201] Linearize and per-unitize the mathematical model equations (17)-(21) of the above links. Since the DC voltage reference value and the reactive power reference value of the outer loop are both constant values, they can be directly ignored during the linearization process to obtain the per-unit linearized equations of different links.

[0202] Converter modulation link:

[0203]

[0204] LCL filter link:

[0205]

[0206] Dual closed-loop control link:

[0207]

[0208] The algebraic equation is expressed as:

[0209]

[0210] Phase-locked loop section:

[0211]

[0212] Measurement and filtering section:

[0213]

[0214] S4. By simultaneously solving the state space equations of the photovoltaic array, Boost circuit and its control system, and converter and its control system established in steps S1 - S3, a complete small-signal model of the string-type photovoltaic grid-connected system in the dq coordinate system is obtained

[0215] By simultaneously solving equations (3), (7), (14 - 16), and (22 - 27) in S1 - S3, a 24th-order small-signal model of the string-type photovoltaic power station is established, as shown in equation (28). Among them, the state variable X = [ΔU dc * Δi id * Δi iq * Δu cd * Δu cq * Δi gd * Δi gq * Δu id * Δu iq * Δi gdm * Δi gqm * Δu gdm * Δu gqm * Δz pd Δz pcd Δz pq Δz pcq ΔQ m * ΔxΔθ pll ΔU pv * ΔI B * Δz mppt ΔU pvm * T , and the algebraic variable W = [ΔI dc * ​Δω * Δu idref * Δu iqref * ΔQ * ΔI pv * ΔDΔU pvref * T The input variable is the terminal voltage U in the dq coordinate system gdq =[Δu gd * Δu gd * T The output variable is the terminal current I in the dq coordinate system gdq =[Δi gd * Δi gd * T ;

[0216]

[0217] Where p is the differential operator

[0218] S5. Perform a coordinate transformation on the small-signal model to obtain the small-signal model in the xy coordinate system

[0219] To facilitate the connection of the state equation of the string-type PV power station to the external system, establish the state-space equation of the entire system (including the PV power station and the external AC network), and transform the output variables U gdq and I gdq of the small-signal model in Equation (28) from the dq coordinate system to a unified xy coordinate system U gdq and I gdq . At this time, the relationship between the reference dq coordinate system of the component PV inverter and the unified xy reference coordinate system is as Figure 9 shown, and the coordinate transformation formula is as shown in Equations (29 - 30).

[0220]

[0221] Where δ is the angle between the component dq reference coordinate system and the unified xy reference coordinate system; u gx is the x-axis component of the output voltage of the LCL filter, u gy is the y-axis component of the output voltage of the LCL filter, i gx is the x-axis component of the grid-side inductor current of the LCL filter, and i gy is the y-axis component of the grid-side inductor current of the LCL filter

[0222] ​​​By simultaneously solving equations (28) and (29 - 30), the complete small-signal model of the series-connected photovoltaic grid-connected system in the unified xy coordinate system is obtained as shown in equation (31). The input variable is the port voltage U in the xy coordinate system gxy = [Δu gx * Δu gy * T , and the output variable is the port current I in the xy coordinate system gxy = [Δi gx * Δi gy * T :

[0223]

[0224] Characteristic analysis and verification of the small-signal model of the series-connected photovoltaic inverter system

[0225] Calculate the eigenvalues of the A matrix of the above small-signal model. According to the positive or negative real part of the eigenvalue calculation results, judge the stability of the system, and judge the oscillation frequency of the system from the imaginary part. Then, build an electromagnetic transient simulation model in PSCAD / EMTDC to conduct time-domain simulation to verify the correctness of the eigenvalue program calculation results of the small-signal model

[0226] Build the system shown in Figure 10 in PSCAD / EMTDC. A 100 MW photovoltaic power station is connected to the AC network through a box transformer and a primary step-up transformer. The photovoltaic power station is equivalent to a parallel aggregation of several photovoltaic inverters

[0227] Under the condition of photovoltaic output of 0.7 pu and weak grid, the short circuit ratio (SCR) of the system is taken as 2. Solve the eigenvalues of the system, and the oscillation modes of the system can be obtained, as shown in Table 1. There is a group of unstable subsynchronous oscillation modes with a positive real part in the oscillation modes of the system, λ 16,17 (5.80 ± j2π×31.37).

[0228] Table 1 Calculation results of eigenvalues of the series-connected photovoltaic grid-connected system

[0229]

[0230] To verify the eigenvalue analysis results, in the electromagnetic transient simulation software PSCAD / EMTDC, change the system short circuit ratio from 3 to 2 at 2 s. The time-domain simulation results are as shown in Figure 11 . Figure 11 (a) in is the time-domain simulation waveform of the system output power Figure 11 ​​(b) in the figure is the FFT analysis result of the system active power output waveform. It can be seen from the figure that the system has a power oscillation of 31.4Hz, which is consistent with the result of the eigenvalue analysis, verifying the accuracy of the small signal model.

[0231] A schematic diagram of a small signal model building device for a string photovoltaic grid-connected system provided by an exemplary embodiment of the present invention. Figure 12 As shown, the device 200 includes:

[0232] The photovoltaic array processing module 201 is used to construct a mathematical model of the photovoltaic array, and perform linearization and normalization to obtain a photovoltaic array state space equation;

[0233] The Boost circuit and its control system processing module 202 is used to construct a mathematical model of the Boost circuit and its control system, and perform linearization and normalization to obtain a state space equation of the Boost circuit and its control system;

[0234] The converter and its control system processing module 203 is used to construct a mathematical model of the converter and its control system, and perform linearization and normalization to obtain a state space equation of the converter and its control system;

[0235] A combined module 204 is used to combine the state space equations obtained by the photovoltaic array processing module, the boost circuit and its control system processing module, and the converter and its control system processing module to obtain a complete small signal model of the string photovoltaic grid-connected system in the dq coordinate system;

[0236] The coordinate transformation module 205 is used to transform the coordinates of the small signal model of the string photovoltaic grid-connected system in the dq coordinate system to obtain the small signal model of the string photovoltaic grid-connected system in the xy coordinate system.

[0237] Figure 13 A structural block diagram of an electronic device provided by an exemplary embodiment of the present invention. Figure 13 As shown, the electronic device 300 includes one or more processors 301 and a memory 302 .

[0238] The processor 301 may be a central processing unit (CPU) or other forms of processing units having data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions.

[0239] The memory 302 may include one or more computer program products, and the computer program products may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include random access memory (RAM), cache memory, etc. The non-volatile memory may include read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage media, and the processor 301 may run the program instructions to implement the methods of the software programs of the various embodiments of the present invention described above and / or other desired functions. In one example, the electronic device may further include: an input device 303 and an output device 304, and these components are interconnected through a bus system and / or other forms of connection mechanisms (not shown).

[0240] In addition, the input device 303 may further include a keyboard, a mouse, etc.

[0241] The output device 304 may output various information to the outside. The output device 304 may include a display, a speaker, a printer, and a communication network and its connected remote output devices, etc.

Claims

1. A method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system, characterized in that, The following steps are involved: S1. Construct a mathematical model of the photovoltaic array, perform linearization and normalization, and obtain the state space equation of the photovoltaic array; S2. Construct a mathematical model of the Boost circuit and its control system, perform linearization and normalization, and obtain the state space equation of the Boost circuit and its control system; S3. Construct a mathematical model of the converter and its control system, perform linearization and normalization, and obtain a state space equation of the converter and its control system; S4, by combining the state space equations of the photovoltaic array, the boost circuit and its control system, and the converter and its control system established in steps S1-S3, a complete small signal model of the string photovoltaic grid-connected system in the dq coordinate system is obtained; S5. Perform coordinate transformation on the small signal model to obtain the small signal model in an xy coordinate system.

2. The method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system according to claim 1, wherein Step S1 specifically includes: S11. Constructing a mathematical model of a photovoltaic array Photovoltaic array output voltage and current equation: I = I sc {1 - α]exp]V(βV oc )] - 1]}(1) Where: α is the standard condition parameter of the photovoltaic cell, β is the actual environmental parameter, I sc is the short-circuit current of the photovoltaic cell, V oc is the open-circuit voltage, V m 、I m are the terminal voltage and output current of the photovoltaic cell at the maximum power point, V and I are the terminal voltage and output current of the photovoltaic cell; Open-circuit voltage V under standard conditions ocr , short-circuit current I scr , terminal voltage V at the maximum power point mr and output current I mr , introducing a compensation coefficient, the key parameters under any working conditions are deduced, and the specific algorithm is as shown in Equation (3): Where, T ref is the reference cell temperature; S ref is the reference light intensity; T air is the air temperature, T is the cell temperature in °C, S is the light intensity in W / m 2 ; a, b, c are compensation coefficients; k is the temperature coefficient of the photovoltaic cell; A number of photovoltaic cells are connected in series and parallel to form a photovoltaic array. Assume that the number of series-connected photovoltaic cells in the photovoltaic array is N S , and the number of parallel-connected cells is N P ; the output voltage of the photovoltaic array is U pv , and the current is I pv , then the external characteristics of the photovoltaic array are as follows: S12. Linearization and normalization of the mathematical model of photovoltaic arrays By linearizing equation (4) at the steady-state point, the linearized photovoltaic array state space equation can be obtained: ΔI pv represents the differential component of the output current of the photovoltaic array, Δ U pv represents the differential component of the output voltage of the photovoltaic array, represents the operating value at the steady-state point of the output voltage of the photovoltaic array; Since the photovoltaic inverter consists of a DC part and an AC part, the reference power of the AC and DC parts is set to be consistent, and the relationship between the reference values ​​on both sides of the AC and DC can be obtained as follows: Among them, S bac and S bdc are the base capacities of the AC system and the DC system respectively, U bac and U bdc are the base voltages of the AC system and the DC system respectively, I bac and I bdc are the base currents of the AC system and the DC system respectively, S bac is taken as the rated capacity of the PV inverter, U bdc takes the reference voltage value of the DC bus voltage, U bac takes the rated value of the inverter output voltage; The small signal equation (5) of the photovoltaic array is normalized to obtain the linearized and normalized photovoltaic array state space equation: Where: ΔI pv * represents the per-unit value of the differential component of the output current of the photovoltaic array, I sc * represents the per-unit value of the short-circuit current of the photovoltaic cell, V oc * represents the per-unit value of the open-circuit voltage, U pv0 * represents the per-unit value of the output voltage at the steady-state point of the photovoltaic array, ΔU pv * represents the per-unit value of the differential component of the output voltage of the photovoltaic array.

3. The method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system according to claim 1, wherein Step S2 specifically includes: Mathematical Model of S21, Boost Circuit and Its Control System The Boost circuit consists of a switching transistor V Q , a boost inductor L B , a DC capacitor C on the photovoltaic array side pv , a capacitor C on the inverter side dc , a diode V D ; The mathematical model of the Boost circuit is expressed as: Where: I pv is the output current of the photovoltaic array, I B is the current of the inductor L B and I dc is the Boost output current; U pv is the output voltage of the photovoltaic array, U dc is the Boost output voltage; D is the input duty cycle of the switch tube; L B is the value of the boost inductor, C pv is the value of the DC capacitor on the photovoltaic array side, C dc is the value of the capacitor on the inverter side; The input and output voltage relationship of the Boost circuit is shown in formula (9): Since the output voltage is constant, it can be seen from Equation (9) that the output voltage U of the photovoltaic array pv is linearly related to the duty cycle D, and U can be made by controlling the duty cycle D pv to achieve maximum power point tracking. The voltage loop control adopts PI control and compares with the carrier wave to generate a PWM modulation wave; For U pv Add a first-order measurement filter to improve the input waveform and introduce an intermediate variable z mppt and U pvm , the state equation of the control system of the Boost circuit is as follows: The corresponding algebraic equation is: Among them, K pmppt , K imppt are the proportional gain and integral gain of the Boost voltage loop, z mppt is the intermediate variable of Boost control, U pvm is the output voltage of the photovoltaic array after first-order filtering, U pvref is the maximum power point voltage output by the MPPT using the perturbation increment method, T udc is the measurement filtering constant of the photovoltaic array output voltage; u id and u iq are the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; i id and i iq are the d-axis component and q-axis component of the inverter-side current of the LCL filter; Linearization and normalization of mathematical models of S22, Boost circuits and their control systems By linearizing equations (8) and (10) near the steady-state point, the linearized state space equation of the Boost circuit and its control system can be obtained: Where, ΔI pv is the differential component of the output current of the photovoltaic array, ΔI B is the differential component of the current on the inductor L B ; ΔI dc is the differential component of the Boost output current; ΔU pv is the differential component of the output voltage of the photovoltaic array, ΔU dc is the differential component of the Boost output voltage; ΔD is the differential component of the input duty cycle of the switching tube; I B0 is the steady-state point current of the inductor L B ; U dc0 is the Boost steady-state point output voltage; D0 is the steady-state point operating value of the duty cycle; where, Δz mppt is the differential component of the intermediate variable of Boost control, ΔU pvm is the differential component of the output voltage of the photovoltaic array after first-order filtering, ΔU pvref is the differential component of the maximum power point voltage of the output of MPPT using the perturbation increment method; By normalizing equations (12) and (13), we can obtain the linearized and normalized state space equations of the Boost circuit and its control system: where Y bdc = I bdc / U bdc is the reference admittance of the DC system, and Z bdc = U bdc / I bdc is the reference reactance of the DC system; ΔI pv * is the per-unit value of the differential component of the output current of the photovoltaic array, and ΔI B * is the per-unit value of the differential component of the current of the inductor L B ; ΔI dc * is the per-unit value of the differential component of the output current of Boost; ΔU pv * is the per-unit value of the differential component of the output voltage of the photovoltaic array, and ΔU dc * is the per-unit value of the differential component of the output voltage of Boost; I B0 * is the per-unit value of the current at the steady-state point of the inductor L B ; U dc0 * is the per-unit value of the output voltage at the steady-state point of Boost; Δz mppt * is the per-unit value of the differential component of the intermediate variable of the Boost control, and ΔU pvm * is the per-unit value of the differential component of the output voltage of the photovoltaic array after first-order filtering, and ΔU pvref * is the per-unit value of the differential component of the maximum power point voltage of the output of the MPPT using the perturbation and incremental method; By linearizing and normalizing equation (11), we can obtain the normalized linearized algebraic equation of the Boost circuit and its control system: Δu id * and Δu iq * are the differential components of the per-unit values of the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; Δi id * and Δi iq * are the differential components of the per-unit values of the d-axis component and q-axis component of the inverter-side current of the LCL filter; u id0 * and u iq0 * are the per-unit values of the steady-state operating points of the d-axis component and q-axis component of the inverter-side voltage of the LCL filter; i id0 * and i iq0 * are the per-unit values of the steady-state operating points of the d-axis component and q-axis component of the inverter-side current of the LCL filter.

4. The method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system according to claim 1, characterized in that, Step S3 specifically includes: S31, Mathematical model of converter and its control system Constructing a mathematical model of the inverter The inverter circuit topology includes two capacitors C1 and C2 connected in series, and the point between the two capacitors is called the midpoint Z; each phase includes four sets of insulated gate thyristors / diodes Sx1, Sx2, Sx3 and Sx4 and two clamping diodes; Its mathematical model is expressed as: Where: u id and u iq are the d-axis component and q-axis component of the inverter-side voltage of the LCL filter, u idref and u iqref are the reference d-axis component and q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter; T d is the switching delay time constant, K pwm is the equivalent gain of the PWM inverter; Constructing a mathematical model for inverter output filtering The inverter output filter adopts LCL filtering; The inverter control adopts grid voltage-oriented vector control, which belongs to dq decoupling control. Since the voltage and current components of the LCL filter circuit are interrelated with the electrical quantities of the control system, it is necessary to analyze the dq decoupling of the LCL filter components. The mathematical model is expressed as follows: where ω is the rotational angular velocity in the reference dq coordinate system; L f and L g are the filter inductance values on the inverter side and the grid side, and C f is the filter capacitor; u cd is the d-axis component of the filter capacitor voltage, and u cq is the q-axis component of the filter capacitor voltage; u gd is the d-axis component of the grid side voltage of the LCL filter, and u gq is the q-axis component of the grid side voltage of the LCL filter; i id is the d-axis component of the inverter side inductor current of the LCL filter, and i iq is the q-axis component of the inverter side inductor current of the LCL filter; i cd is the d-axis component of the filter capacitor current of the LCL filter, and i cq is the q-axis component of the filter capacitor current of the LCL filter; i gd is the d-axis component of the grid side inductor current of the LCL filter, and i gq is the q-axis component of the grid side inductor current of the LCL filter; Constructing a mathematical model of the control system The voltage of the capacitor controlled by the outer loop of the converter d-axis is maintained at the command value to ensure the normal operation of the converter; the q-axis adopts constant reactive power control to make the converter output reactive power of 0 according to the command; because the capacitor in the LCL filter is approximately open-circuited under the power frequency, the LCL filter can be approximately a single L filter in the control, so the decoupling control structure of the current loop is the same as the L filter structure; Introduce an intermediate variable z in the integral link of PI control pd , z pq , z pcd , z pcq , the equations of the inverter PQ decoupling control link can be respectively expressed as: Among them, U dcref * is the per-unit value of the reference value of the DC capacitor voltage; Q ref * is the per-unit value of the reference value of the reactive power, and Q m * is the per-unit value of the measured value of the reactive power output by the inverter; L * is the per-unit value of L f and L g The sum of; z pd are the intermediate variables of the DC voltage outer-loop control respectively, and z pq is the intermediate variable of the AC reactive power outer-loop control, z pcd is the intermediate variable of the d-axis current inner-loop control, and z pcq is the intermediate variable of the q-axis current inner-loop control; i gdref * is the per-unit value of the reference value of the d-axis component of the inverter output current, and i gqref * is the per-unit value of the reference value of the q-axis component of the inverter output current; u gdm * is the per-unit value of the measured filtered d-axis voltage component, and u gqm * is the per-unit value of the measured filtered q-axis voltage component, and i gdm * is the per-unit value of the measured filtered d-axis current component, and i gqm * is the per-unit value of the measured filtered q-axis current component; u idref * 、u iqref * are the per-unit values of the reference d-axis component and q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter; ω0 * is the per-unit value of the steady-state operating value of the synchronous angular velocity on the grid side; K pd 、K id are the proportional gain and integral gain of the DC voltage outer-loop control; K pq 、K iq are the proportional gain and integral gain of the reactive power outer-loop control; K pcd 、K icd are the proportional gain and integral gain of the d-axis current inner-loop control; K pcq 、K icq are the proportional gain and integral gain of the q-axis current inner-loop control; Considering the delay of the measurement filter link, we have: where, T m is the measurement filtering time constant of the inverter output voltage and current; T mq is the measurement filtering time constant of the inverter output reactive power; Q is the value of the inverter output reactive power; Q m is the measured value of the inverter output reactive power value; u gd * is the per-unit value of the d-axis component of the grid-side voltage of the LCL filter, u gq * is the per-unit value of the q-axis component of the grid-side voltage of the LCL filter; i gd * is the per-unit value of the d-axis component of the grid-side current of the LCL filter, i gq * is the per-unit value of the q-axis component of the grid-side current of the LCL filter; Introducing the intermediate variable x of the phase-locked loop control, the equation of the phase-locked loop PLL is: θ PLL is the phase angle output by the phase-locked loop, ω is the synchronous angular velocity on the grid side, K pPLL , K iPLL are the proportional gain and integral gain controlled by the phase-locked loop; ω0 is the steady-state operating value of the synchronous angular velocity on the grid side; S32, linearizing and per-unit processing of the mathematical model of the converter and its control system, and obtaining per-unit linearized state space equations of the converter and its control system at different links; Converter modulation link: where Δu idref * and Δu iqref * are the differential components of the per-unit values of the reference d-axis component and q-axis component of the inverter-side voltage of the LCL filter output by the control system of the inverter LCL filtering link: where, Δω * is the differential component of the per-unit value of the rotational angular velocity in the reference dq coordinate system; L f * and L g * are the per-unit values of the filter inductance values on the inverter side and the grid side, and C f * is the per-unit value of the filter capacitor; Δu cd * and Δu cq * are respectively the differential components of the per-unit values of the d-axis component and the q-axis component of the filter capacitor voltage; Δu gd * and Δu gq * are respectively the differential components of the per-unit values of the d-axis component and the q-axis component of the grid-side voltage of the LCL filter; Δi id * and Δi iq * are respectively the differential components of the per-unit values of the d-axis component and the q-axis component of the inverter-side inductor current of the LCL filter; Δi cd * and Δi cq * are respectively the differential components of the per-unit values of the d-axis component and the q-axis component of the filter capacitor current of the LCL filter; Δi gd * and Δi gq * are respectively the differential components of the per-unit values of the d-axis component and the q-axis component of the grid-side inductor current of the LCL filter; ω0 * is the per-unit value of the steady-state operating value of the rotational angular velocity in the reference dq coordinate system; i id0 * and i iq0 * are respectively the per-unit values of the steady-state operating values of the d-axis component and the q-axis component of the inverter-side inductor current of the LCL filter; u cd0 * and u cq0 * are respectively the per-unit values of the steady-state operating values of the d-axis component and the q-axis component of the filter capacitor voltage; i gd0 * and i gq0 * are respectively the per-unit values of the steady-state operating values of the d-axis component and the q-axis component of the grid-side inductor current of the LCL filter; w b is the reference value of the rotational angular velocity in the reference dq coordinate system; Double closed-loop control link: where: ΔQ m * is the differential component of the per-unit value of the reactive power measurement at the inverter output; Δz pd is the differential component of the intermediate variable in the outer DC voltage loop control, Δz pq is the differential component of the intermediate variable in the outer AC reactive power loop control, Δz pcd is the differential component of the intermediate variable in the inner d-axis current loop control, Δz pcq is the differential component of the intermediate variable in the inner q-axis current loop control; Δi gdref * is the differential component of the per-unit value of the reference d-axis component of the inverter output current, Δi gqref * is the differential component of the per-unit value of the reference q-axis component of the inverter output current; Δi gdm * is the differential component of the per-unit value of the measured and filtered d-axis current component, Δi gqm * is the differential component of the per-unit value of the measured and filtered q-axis current component; Δi gdref * is the differential component of the per-unit value of the reference d-axis component of the inverter output current, Δi gqref * is the differential component of the per-unit value of the reference q-axis component of the inverter output current; Δu idref * 、Δu iqref * are the differential components of the per-unit values of the reference d-axis and q-axis components of the inverter-side voltage of the LCL filter output by the control system of the inverter; Δu gdm * is the differential component of the per-unit value of the measured and filtered d-axis voltage component, Δu gqm * is the differential component of the per-unit value of the measured and filtered q-axis voltage component; Phase-locked loop link: where ω b is the reference value of the synchronous rotating angular velocity of the AC system; Δθ PLL is the differential component of the phase angle output by the phase-locked loop, and Δx is the differential component of the intermediate variable controlled by the phase-locked loop; Measurement filtering link: where ΔQ * is the differential component of the per-unit value of the reactive power output by the converter.

5. A method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system according to claim 1, characterized in that Step S4 specifically includes: Simultaneous equations to establish a complete small signal model of the string photovoltaic grid-connected system By combining equations (3)(7)(14-16)(22-27), the 24th-order small signal equation of the string photovoltaic grid-connected system in the reference dq coordinate system can be obtained: where the state variable X = [ΔU dc * Δi id * Δi iq * Δu cd * Δu cq * Δi gd * Δi gq * Δu id * Δu iq * Δi gdm * Δi gqm * Δu gdm * Δu gqm * Δz pd Δz pcd Δz pq Δz pcq ΔQ m * ΔxΔθ pll ΔU pv * ΔI B * Δz mppt ΔU pvm * T , and the algebraic variable W = [ΔI dc * Δω * Δu idref * Δu iqref * ΔQ * ΔI pv * ΔDΔU pvref * T , the input variable is the terminal voltage U in the dq coordinate system gdq = [Δu gd * Δu gd * T , and the output variable is the terminal current I in the dq coordinate system gdq = [Δi gd * Δi gd * T ; p is the differential operator.​​​​ 6. The method for establishing a small-signal model applicable to a string-type photovoltaic grid-connected system according to claim 1, wherein Step S5 specifically includes: The output variables U gdq and I gdq of the small-signal state-space model are transformed from the dq coordinate system to a unified xy coordinate system U gdq and I gdq , where U gxy = [Δu gx * Δu gy * T , I gxy = [Δi gx * Δi gy * T， , and the coordinate transformation formula is:​​ where δ is the angle between the dq reference coordinate system of the component and the unified xy reference coordinate system; Δu gx * is the differential of the per-unit value of the x-axis component of the output voltage of the LCL filter, Δu gy * is the differential of the per-unit value of the y-axis component of the output voltage of the LCL filter, Δi gx * is the differential of the per-unit value of the x-axis component of the grid-side inductor current of the LCL filter, Δi gy * is the differential of the per-unit value of the y-axis component of the grid-side inductor current of the LCL filter; Combining equations (29-30) and equation (28) gives the complete small-signal model of the series-connected photovoltaic grid-connected system in the unified xy coordinate system, equation (31), with the input variable being the port voltage U in the xy coordinate system gxy = [Δu gx * Δu gy * T , and the output variable being the port current I in the xy coordinate system gxy = [Δi gx * Δi gy * T :​​ 7. A small-signal model construction device applicable to a string-type photovoltaic grid-connected system, characterized in that include: A photovoltaic array processing module, which is used to construct a mathematical model of the photovoltaic array, and perform linearization and normalization to obtain a photovoltaic array state space equation; A boost circuit and a control system processing module, wherein the boost circuit and a control system processing module is used to construct a mathematical model of the boost circuit and a control system, and perform linearization and normalization to obtain a state space equation of the boost circuit and a control system; A converter and its control system processing module, wherein the converter and its control system processing module is used to construct a mathematical model of the converter and its control system, and perform linearization and per-unit normalization to obtain a state space equation of the converter and its control system; A combined module, wherein the combined module is used to combine the state space equations obtained by the photovoltaic array processing module, the Boost circuit and its control system processing module, and the converter and its control system processing module to obtain a complete small signal model of the string photovoltaic grid-connected system in the dq coordinate system; A coordinate transformation module is used to transform the coordinates of the small signal model of the string photovoltaic grid-connected system in the dq coordinate system to obtain the small signal model of the string photovoltaic grid-connected system in the xy coordinate system.

8. An electronic device, characterized in that, It comprises a processor and a memory, wherein the processor is used to execute a computer program stored in the memory to implement a small signal model establishment method applicable to a string-type photovoltaic grid-connected system as claimed in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, and when the at least one instruction is executed by the processor, the method for establishing a small signal model applicable to a string photovoltaic grid-connected system as described in any one of claims 1 to 6 is implemented.

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