A Decoupling and Balancing Control Method for Three-Phase Power Electronic Transformer Based on Feedback Linearization

Abstract

The present invention discloses a decoupling and balancing control method for a three-phase cascaded power electronic transformer (PET) based on feedback linearization, so as to achieve the rapid stabilization of the two-stage DC voltages of the intermediate DC and output DC of the three-phase cascaded PET and the balance of the three-phase intermediate DC voltages when there are large power disturbances and unbalanced grid voltages or inconsistent three-phase parameters. The method is characterized in that the present invention adopts the state feedback linearization method to linearize and decouple the nonlinear state equations of the three-phase intermediate DC voltages and the DC grid-side output voltages of the three-phase cascaded PET, simplifies the control of each voltage quantity into a first-order differential system, and then the PI controller and the method of zero-pole configuration can be used for parameter design. This method can improve the transient performance of the PET device during large reverse power disturbances, realize the voltage and power balance among the three phases of the PET, and has good prospects for ensuring the stable control ability of the PET in a wide operating range and promoting its application in the AC-DC hybrid power grid project with a high proportion of new energy.

Description

Technical Field

[0001] The present invention relates to a control method for a three-phase power electronic transformer, in particular to a decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization, belonging to the technical field of power electronic transformer control. Background Art

[0002] A three-phase cascaded power electronic transformer (PET) based on cascaded H-bridge (CHB) and dual active bridge (DAB) converters can facilitate the input of a three-phase medium-voltage AC power grid and the output of a low-voltage high-power DC, and has the advantages of good multi-level waveform quality, fewer required components, and easy modular expansion. It is the core equipment for constructing AC-DC flexible power transmission and distribution systems and energy Internet.

[0003] Each H-bridge module of the CHB in each phase of the three-phase cascaded PET is connected to the DC stage DAB through an independent intermediate DC capacitor, and the output ends of all DAB modules in the three-phase DC stage are connected in parallel to provide high-power DC output. Therefore, the control of the three-phase cascaded PET is essentially a multi-objective strongly coupled nonlinear system, which not only needs to achieve the control of AC grid-connected current and power factor, the stable control of the output DC voltage, but also needs to achieve the stable and inter-phase balanced control of the three-phase intermediate DC average voltage, as well as the balanced control of the in-phase sub-module voltage and power.

[0004] When there are large bidirectional disturbances in the power of the PET DC grid side, the instantaneous power inside the device is unbalanced, which first causes fluctuations in the two-level DC bus voltages of the output capacitor and the intermediate capacitor. If the control response is not timely, it will lead to severe fluctuations or even instability of the DC voltages at all levels. In addition, unbalanced grid voltages or inconsistent module parameters among the three phases will cause the imbalance of the three-phase intermediate DC average voltage, and will aggravate the instability risk during power disturbances.

[0005] In terms of the DC voltage stability and balance control of each stage of the cascaded PET, most studies focus on single-phase cascaded PET. By superimposing an equalization control loop on the basis of the main control loop of each stage, the CHB duty cycle (modulation wave) or the DAB phase shift ratio is corrected to achieve the sub-module voltage equalization control, but it cannot solve the problem of unbalance between phases in the three-phase PET topology. For the three-phase PET topology, one method is based on CHB-level control. By introducing the reactive current correction component of each phase or using the zero-sequence voltage injection method, the three-phase active power is redistributed independently to achieve the purpose of equalizing the inter-phase voltage; another method is based on DAB-level independent control. By adding an input voltage equalization control loop on the basis of the DAB total output voltage control loop to achieve the inter-phase voltage equalization. However, these methods are all adding control loops on the basis of the main control loop, and there is strong coupling between the transformations and controls at all levels. Moreover, the control design is based on a small-signal approximate linearized model, and it is difficult to achieve good dynamic responses of the control objectives in the large disturbance of the full power bidirectional operation range.

[0006] The state feedback linearization method based on differential geometry theory can overcome the limitations brought by small-signal approximate linearization and achieve the exact linearization and decoupling of multi-variable non-linear strongly coupled systems. For this reason, based on the state feedback linearization method, the present invention proposes a decoupling control method applicable to the fast stability and inter-phase balance control of the DC voltage of each stage of the three-phase cascaded PET, which can solve the above problems. Summary of the Invention

[0007] The purpose of the present invention is to provide a decoupling and equalization control method for a three-phase cascaded power electronic transformer based on feedback linearization, so as to achieve the fast stability control of the intermediate DC voltage and the output DC voltage of the three-phase cascaded PET and the inter-phase voltage equalization control when the PET power changes bidirectionally in a large range and there is three-phase unbalance.

[0008] To achieve the above purpose, the technical solutions adopted by the present invention are as follows:

[0009] A decoupling and equalization control method for a three-phase cascaded power electronic transformer based on feedback linearization includes the following steps:

[0010] Step 1: Establish a mathematical model of the three-phase cascaded PET;

[0011] Step 2: According to the power conservation, obtain the non-linear coupling state equations of the average DC voltage of the three-phase intermediate of the PET and the DC grid-side output voltage;

[0012] Step 3: Assume that under the state feedback control, the non-linear coupling state equation in Step 2 is linearly decoupled into a first-order differential system, and the state feedback control law is obtained by inverse solution;

[0013] Step 4: Design a PI controller according to the first-order differential system described in Step 3 by the method of zero-pole configuration;

[0014] Step 5: According to Step 3 and Step 4, obtain the decoupling and balancing control strategy of the three-phase cascaded power electronic transformer, and output the duty cycles d a1 ~d aN ,d b1 ~d bN ,d c1 ~d cN ,as well as the phase-shift ratios D a1 ~D aN ,D b1 ~D bN ,D c1 ~D cN of each phase DAB module in the DC isolation stage, and control the three-phase cascaded PET.

[0015] In the said Step 1, by analyzing the dynamic relationship of the electrical quantities of the three-phase independent DC capacitors in the middle and the parallel output capacitors of the DAB stage of the three-phase cascaded PET, the mathematical models of the three-phase intermediate DC average voltage and the DC grid-side output voltage can be obtained as:

[0016]

[0017] In the formula, N represents the number of H-bridge modules in each phase CHB circuit; v dcj (j = a, b, c) represents the average value of the voltages of N intermediate DC capacitors in the j phase; D j (j = a, b, c) represents the average phase-shift ratio of the DAB module in the j phase; C1 is the capacitance value of the intermediate DC capacitor; C o is the equivalent capacitance value of the parallel output terminal of the DAB stage; n t is the turns ratio of the DAB high-frequency transformer; T hs is half of the working switching period of the DAB; L t is the equivalent leakage inductance of the DAB high-frequency transformer referred to the primary side; i dcj (j = a, b, c) is the average value of the currents input from the N H-bridge modules in the j phase CHB to the intermediate DC capacitor. Because the H-bridges in each phase are in series and when the same duty cycle is adopted, the input currents i dcj1 ~i dcjN of the N H-bridge modules to the intermediate DC capacitor are the same and are all equal to their average value i dcj ; v o and i o are the output voltage and output current of the PET DC grid side respectively.

[0018] In the said Step 2, when the cascaded PET operates at unity power factor, according to the power conservation, it can be obtained that:

[0019]

[0020] Wherein, v d and i d are respectively the d-axis components of the grid-connected voltage and current on the AC side of the PET; meanwhile, it is assumed that under the current inner-loop control, i d can well track its reference value i dref , simplifying the dynamic process of the current inner loop, that is, making i d = i dref ;

[0021] Substituting Equation (2) into Equation (1), the non-linear coupling state equations of the three-phase intermediate DC average voltage and the DC grid-side output voltage of the PET are obtained as follows:

[0022]

[0023] Wherein, the state vector x = [v dca v dcb v dcc v o T , the control input vector u = [M a M b M c i dref T , wherein, M j = D j (1 - |D j |), j = a, b, c.

[0024] In the said step 3, it is assumed that through the state feedback control law u = Ф(x), the non-linear coupling state equation (3) in step 2 can be linearly decoupled into the following first-order differential system:

[0025]

[0026] Wherein, v = [v1 v2 v3 v4] T is the preset control variable;

[0027] Then, according to Equation (3) and Equation (4), the state feedback control law can be obtained by back-calculation as:

[0028]

[0029] Wherein, (k x1 , k x2j , k x3 , k x4 ) = θ(v d , v dca , v dcb , v​​dcc , v o ) is a non - linear gain parameter, which is calculated and updated in real - time according to the state - variable measurement. Specifically:

[0030] In step 4, according to the first - order differential system shown in equation (4), the preset control quantity v = [v1 v2 v3 v4] T is output by the PI controller, and its frequency - domain expression is as follows:

[0031]

[0032] where G PI (s) is the transfer function of each voltage - loop PI controller; v dcref is the reference value of the three - phase intermediate DC average voltage, and v oref is the reference value of the DC grid - side output voltage;

[0033] As shown in equation (6), the reference values for tracking the three - phase intermediate DC average voltage are the same, all being v dcref , so through the error - free control of the PI controller, the balanced control of the three - phase intermediate DC average voltage can be achieved, that is, v dca = v dcb = v dcc = v dcref ;

[0034] Substituting equation (6) into equation (4), the typical second - order closed - loop transfer function of the three - phase intermediate DC average voltage and the DC grid - side output voltage of the PET can be obtained, and its expression is:

[0035]

[0036] where K p , K i are the proportional and integral coefficients of each voltage - loop PI controller respectively;

[0037] Furthermore, according to equation (7), the method of zero - pole configuration of a typical second - order system with zeros can be used to tune the parameters of the PI controller.

[0038] According to steps 3 and 4, the three - phase cascaded PET decoupling and balancing control strategy in step 5 can be obtained, including the following steps:

[0039] Step 5 - 1: Measure the electrical quantities on the AC side of the cascaded PET, and perform dq transformation to obtain the d - axis and q - axis components v d 、v q of the AC grid voltage, and the d - axis and q - axis components i d 、i q;Measure the electrical quantities of the intermediate DC bus and output DC grid side of the cascaded PET, including the intermediate DC capacitor voltage v of each phase submodule dca1 ~v dcaN , v dcb1 ~v dcbN , v dcc1 ~v dccN , and the PET DC grid side output voltage v o And the output current i o ;

[0040] Step 5-2: Calculate the average value of the DC capacitor voltages of the N submodules in each phase to obtain the three-phase DC average voltage v dca , v dcb , v dcc , the average voltage is compared with the reference value v dcref The difference is compared, and the PI controller outputs the preset control quantity v1, v2, v3; the DC grid side output voltage v o With its reference value v oref After comparison, the difference is output through the PI controller as the preset control quantity v4;

[0041] Step 5-3: According to the state variable v dca , v dcb , v dcc , v o and the grid voltage component v d , calculate the feedback gain parameter k x1 , k x2j(j＝a，b，c) , k x3 , k x4 , input state feedback control law;

[0042] Step 5-4: The preset control quantities v1, v2, v3, and v4 are controlled by the state feedback control law to output the actual control quantity u1=M of the system. a , u2=M b , u3=M c , u4=i dref ;

[0043] Step 5-5: By M a , M b , M c The inverse function f -1 =[M j =D j (1-|D j |)] -1 , j = a, b, c calculation, output each phase DAB average phase shift D a , D b , D c ; by i drefOutput the average duty cycle d of each phase of CHB through the grid-connected current inner loop control a d b d c ;

[0044] Step 5-6: According to the average duty cycles d a d b d c of the three-phase CHB and the average phase shift ratios D a D b D c of the three-phase DAB, through the in-phase sub-module equalization control, output the duty cycles d a1 ~d aN d b1 ~d bN d c1 ~d cN of the H-bridge modules in each phase of CHB in the PET rectification stage, as well as the phase shift ratios D a1 ~D aN D b1 ~D bN D c1 ~D cN of the DAB modules in each phase of the DC isolation stage to control the three-phase PET.

[0045] Compared with the existing control methods, the present invention has the following beneficial effects:

[0046] The control method of the present invention can achieve fast tracking and stable control of the DC voltages at all levels to the target values under large bidirectional power disturbances through feedback linearization decoupling control of the three-phase intermediate DC average voltage and the DC grid-side output voltage of the three-phase cascaded power electronic transformer, and the dynamic performance is significantly improved; at the same time, it can directly achieve the equalization control of the three-phase intermediate DC average voltage when the grid voltage is unbalanced or the three-phase parameters of the PET are inconsistent. Description of the Drawings

[0047] Figure 1 is the circuit structure diagram of the three-phase cascaded PET in the present invention;

[0048] Figure 2 is the decoupling and equalization control schematic diagram of a three-phase cascaded power electronic transformer based on feedback linearization provided by the present invention;

[0049] Figure 3 is the in-phase sub-module equalization control block diagram;

[0050] Figure 4 is the waveform of the three-phase intermediate DC average voltage under different control methods during power reverse disturbance and grid voltage imbalance;

[0051] Figure 5Output voltage waveforms on the DC grid side under different control methods when there is power reverse disturbance and grid voltage imbalance;

[0052] Figure 6 Grid voltage and grid-connected current waveforms under different control methods when there is power reverse disturbance and grid voltage imbalance;

[0053] Figure 7 Average DC voltage waveforms of three phases under different control methods when there is power reverse disturbance and three-phase parameter inconsistency;

[0054] Figure 8 Output voltage waveforms on the DC grid side under different control methods when there is power reverse disturbance and three-phase parameter inconsistency. Specific implementation manners

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0056] Embodiment:

[0057] As Figure 1 shown, the input side of each phase of the three-phase cascaded power electronic transformer consists of N H-bridge circuits to form a CHB rectification stage. Each H-bridge module is connected to the DC stage DAB circuit through an independent intermediate DC capacitor C1. The output ends of all DAB modules in the three-phase DC stage are connected in parallel and supply power to the DC grid through the output DC capacitor C o for the DC grid.

[0058] A decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization includes the following steps:

[0059] Step 1: According to Figure 1 the three-phase cascaded PET circuit structure shown, establish a mathematical model of the three-phase cascaded PET;

[0060] Step 2: According to power conservation, obtain the nonlinear coupling state equations of the average DC voltage of the three phases of the PET and the output voltage of the DC grid side;

[0061] Step 3: Assume that under state feedback control, the nonlinear coupling state equations in Step 2 are linearly decoupled into a first-order differential system, and inversely obtain the state feedback control law;

[0062] Step 4: Design a PI controller according to the first-order differential system described in Step 3 by the method of zero-pole configuration;

[0063] Step 5: According to Step 3 and Step 4, obtain the decoupling and balancing control strategy of the three-phase cascaded power electronic transformer. The block diagram is as Figure 2 shown, and output the duty cycles d a1 ~d aN, d b1 ~d bN , d c1 ~d cN , and the phase shift ratio D of each phase DAB module of the DC isolation stage a1 ~D aN , D b1 ~D bN , D c1 ~D cN , to control the three-phase cascaded PET.

[0064] In the said step 1, by analyzing the dynamic relationship of the electrical quantities of the three-phase independent DC capacitors in the middle of the three-phase cascaded PET and the parallel output capacitors of the DAB stage, the mathematical models of the three-phase intermediate DC average voltage and the DC grid-side output voltage can be obtained as follows:

[0065]

[0066] In the formula, N represents the number of H-bridge modules in each phase of the CHB circuit; v dcj (j = a, b, c) represents the average value of the voltages of N intermediate DC capacitors in the j phase; D j (j = a, b, c) represents the average phase shift ratio of the DAB module in the j phase; C1 is the capacitance value of the intermediate DC capacitor; C o is the equivalent capacitance value at the parallel output end of the DAB stage; n t is the turns ratio of the DAB high-frequency transformer; T hs is half of the DAB working switching period; L t is the equivalent leakage inductance of the DAB high-frequency transformer referred to the primary side; i dcj (j = a, b, c) is the average value of the currents input from the N H-bridge modules in the j phase of the CHB to the intermediate DC capacitor. Because the H-bridges in each phase are in series and the same duty cycle is adopted, the input currents i dcj1 ~i dcjN of the N H-bridge modules to the intermediate DC capacitor are the same and are all equal to their average value i dcj ; v o and i o are the DC grid-side output voltage and output current of the PET respectively.

[0067] In the said step 2, when the cascaded PET operates at unity power factor, according to power conservation, we get:

[0068]

[0069] In the formula, v d and i d are the d-axis components of the grid-connected voltage and current on the AC side of the PET respectively; at the same time, it is assumed that under the inner current loop control, i d can well track its reference value idref to simplify the dynamic process of the inner current loop, i.e., let i d = i dref ;

[0070] Substituting Equation (2) into Equation (1), the nonlinear coupling state equations of the three-phase intermediate DC average voltage and the DC grid-side output voltage of the PET are obtained as follows:

[0071]

[0072] where the state vector x = [v dca v dcb v dcc v o T , and the control input vector u = [M a M b M c i drcf T , where M j = D j (1 - |D j |), j = a, b, c.

[0073] In step 3, assuming that through the state feedback control law u = Ф(x), the nonlinear coupling state equation (3) in step 2 can be linearly decoupled into the following first-order differential system:

[0074]

[0075] where v = [v1 v2 v3 v4] T is the preset control variable;

[0076] Then, according to Equations (3) and (4), the state feedback control law can be obtained by back-calculation as:

[0077]

[0078] where (k x1 , k x2j , k x3 , k x4 ) = θ(v d , v dca , v dcb , v dcc , v o ) are the nonlinear gain parameters, which are calculated and updated in real time according to the measurement of the state variables. Specifically:

[0079] In step 4, according to the first-order differential system shown in Equation (4), its preset control quantity v = [v1 v2 v3 v4]​​T Output from the PI controller, with the frequency-domain expression as follows:

[0080]

[0081] In the formula, G PI (s) is the transfer function of each voltage-loop PI controller; v dcref is the reference value of the three-phase intermediate DC average voltage, and v oref is the reference value of the output voltage on the DC grid side;

[0082] As shown in Equation (6), the reference values tracked by the three-phase intermediate DC average voltage are the same, all being v dcref . Therefore, through the non-error control of the PI controller, the balanced control of the three-phase intermediate DC average voltage can be achieved, that is, v dca = v dcb = v dcc = v dcref ;

[0083] Substitute Equation (6) into Equation (4), and the typical second-order closed-loop transfer function of the three-phase intermediate DC average voltage and the output voltage on the DC grid side of the PET can be obtained, and its expression is:

[0084]

[0085] In the formula, K p , K i are the proportional and integral coefficients of each voltage-loop PI controller respectively;

[0086] Furthermore, according to Equation (7), the method of zero-pole configuration of a typical second-order system with a zero can be used to tune the parameters of the PI controller.

[0087] According to Step 3 and Step 4, the three-phase cascaded PET decoupling and balancing control strategy in Step 5 can be obtained, including the following steps:

[0088] Step 5-1: Measure the electrical quantities on the AC side of the cascaded PET, and perform dq transformation to obtain the d-axis and q-axis components v d , v q of the grid voltage, and the d-axis and q-axis components i d , i q of the grid-connected current; Measure the electrical quantities on the intermediate DC bus and the output DC grid side of the cascaded PET, including the intermediate DC capacitor voltages v dca1 ~v dcaN of each phase sub-module, v dcb1 ~v dcbN , v dcc1 ~v dccN , and the parallel output voltage v o and output current i o of the PET DC grid side;

[0089] Step 5-2: Calculate the average value of the intermediate DC capacitor voltages of each phase's N sub-modules to obtain the three-phase intermediate DC average voltage v dca , v dcb , v dcc , and compare the average voltages with the reference value v dcre f respectively. The differences pass through a PI controller to output the preset control quantities v1, v2, v3; Compare the output voltage v o of the DC grid side with its reference value v oref , and the difference passes through a PI controller to output the preset control quantity v4;

[0090] Step 5-3: According to the state variables v dca , v dcb , v dcc , v o and the grid voltage component v d , calculate the feedback gain parameters k x1 , k x2j(j＝a，b，c) , k x3 , k x4 , and input the state feedback control law;

[0091] Step 5-4: Pass the preset control quantities v1, v2, v3, v4 through the state feedback control law to output the actual control quantities of the system u1 = M a , u2 = M b , u3 = M c , u4 = i dref ;

[0092] Step 5-5: Calculate from M a , M b , M c through the inverse function f -1 = [M j = D j (1 - |D j |)] -1 , j = a, b, c to calculate and output the average phase shift ratio D a , D b , D c of each phase's DAB; Calculate from i dref through the grid-connected current inner loop control to output the average duty cycle d a , d b , d c of each phase's CHB;

[0093] Step 5-6: According to the average duty cycles d a , d b , d c of the three-phase CHB and the average phase shift ratios D a , Db , D c , after the in-phase sub-module balance control, the duty ratios d a1 ~ d aN , d b1 ~ d bN , d c1 ~ d cN , and the phase shift ratios D a1 ~ D aN , D b1 ~ D bN , D e1 ~ D cN of each phase DAB module in the DC isolation stage are used to control the three-phase PET.

[0094] The in-phase sub-module balance control block diagram is as shown in Figure 3 , taking phase a as an example (phases b and c are the same as phase a), it can be described as follows:

[0095] The N intermediate DC capacitor voltages v dca1 ~ v dcaN of phase a are respectively compared with their average voltage v dca . The error is output through a PI controller to obtain the phase shift ratio correction values ΔD a1 ~ ΔD aN of each DAB module in phase a. The phase shift ratio correction values are summed with the average phase shift ratio D a of phase a DAB to obtain the actual phase shift ratios D a1 ~ D aN of each DAB module in phase a; on the basis of this voltage equalization control, the H-bridge modules in the CHB of phase a in the rectifier stage are made to have the same duty ratio, that is, d a1 =... = d aN = d a , and the power balance control of the in-phase sub-modules can be directly realized.

[0096] To demonstrate the effectiveness and superiority of the feedback linearization decoupling balance control method, this specification conducts a simulation on a three-phase cascaded PET using the control strategy example based on Matlab / Simulink, and compares it with the traditional control scheme. The simulation parameters are: PET rated power 1 MW, grid line voltage effective value 690 V, three-phase intermediate DC average voltage 600 V, DC grid-side output voltage 600 V, CHB switching frequency 10 kHz, DAB switching frequency 10 kHz, grid-side inductor 15 mH, intermediate DC capacitor 50 mF, DC grid-side parallel output equivalent capacitor 150 mF, DAB high-frequency transformer turns ratio 1:1, equivalent leakage inductance of the DAB high-frequency transformer referred to the primary side 200 mH, and the number of sub-modules per phase is 2.

[0097] The traditional control scheme is to use the CHB level to control the average DC voltage in the middle of the PET, and the DAB level to control the output voltage on the DC grid side. On this basis, an intermediate DC voltage equalization control loop is added to each DAB sub-module in the three phases to achieve the equalization control of the intermediate DC voltage between phases and within phases; the H-bridge modules in each phase of the CHB level all use the same duty cycle to achieve the power equalization of the sub-modules.

[0098] In addition, to demonstrate the effect of the inter-phase equalization control, the equalization control loop in the above traditional control scheme is removed, and a set of simulation results without inter-phase equalization control in the traditional case are given.

[0099] The simulation conditions are as follows: before 0.4 s, the power of the PET is transmitted from the AC side to the DC side, and then reverses, with the power magnitude remaining unchanged; at the same time, simulations are carried out and compared under two conditions of unbalanced grid voltage and inconsistent three-phase parameters. In the former case, the grid voltage of phase a drops to 90% of the rated value, and in the latter case, the leakage inductance parameters of the three-phase DAB are set to 105%, 95%, and 90% of the rated value respectively.

[0100] Figures 4 to 6 It is the simulation waveform of the PET system under large bidirectional power disturbances and unbalanced grid voltage. Figures 7 to 8 It is the simulation waveform of the PET system under large bidirectional power disturbances and inconsistent three-phase parameters. It can be analyzed from the waveform results that: (1) Under large bidirectional power disturbances, compared with the traditional control method, under the feedback linearization decoupling control of the present invention, the average DC voltage v dca ,v dcb ,v dcc in the three phases, the output voltage v o on the DC grid side, and the AC grid side current i sabc all have smaller transient fluctuations and faster recovery times, and the dynamic performance is significantly improved; (2) When the grid voltage is unbalanced or the three-phase parameters are inconsistent, under the traditional inter-phase equalization control strategy, the average DC voltage v dca ,v dcb ,v dcc in the three phases is unbalanced, with obvious deviations, and the deviations are even larger after the power reverses, and the stability deteriorates. An equalization control loop must be added to achieve equalization and stability, as shown by the waveform of the traditional inter-phase equalization control in the figure; while under the feedback linearization decoupling control of the present invention, the average DC voltage v dca ,v dcb ,v dcc in the three phases can directly achieve equalization with good results.

Claims

1. A decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization, characterized in that, It includes the following steps: Step 1: Establish a mathematical model of a three-phase cascaded power electronic transformer (PET); Step 2: According to power conservation, obtain the non-linear coupled state equations of the three-phase intermediate DC average voltage and the DC grid-side output voltage of the PET; Step 3: Assume that under state feedback control, the non-linear coupled state equations in Step 2 are linearly decoupled into a first-order differential system, and inversely obtain the state feedback control law; Step 4: Design a PI controller according to the method of zero-pole configuration based on the first-order differential system described in Step 3; Step 5: According to Step 3 and Step 4, obtain the decoupling and balancing control strategy of the three-phase cascaded power electronic transformer, and output the duty cycles d a1 ~d aN , d b1 ~d bN , d c1 ~d cN , and the phase shift ratios D a1 ~D aN , D b1 ~D bN , D c1 ~D cN of each phase DAB module in the DC isolation stage, and control the three-phase cascaded PET.

2. The decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization according to claim 1, characterized in that: In Step 1, by analyzing the dynamic relationship of the electrical quantities of the three-phase intermediate independent DC capacitors and the DAB-stage parallel output capacitors of the three-phase cascaded PET, the mathematical models of the three-phase intermediate DC average voltage and the DC grid-side output voltage can be obtained as follows: Where, N represents the number of H-bridge modules in each phase of the CHB circuit; v dcj (j = a, b, c) represents the average value of the voltages of N intermediate DC capacitors in the j-th phase; D j (j = a, b, c) represents the average phase-shift ratio of the DAB module in the j-th phase; C1 is the capacitance value of the intermediate DC capacitor; C o is the equivalent capacitance value of the parallel output terminal of the DAB stage; n t is the turns ratio of the DAB high-frequency transformer; T hs is half of the switching period of the DAB; L t is the equivalent leakage inductance of the DAB high-frequency transformer referred to the primary side; i dcj (j = a, b, c) is the average value of the currents input from the N H-bridge modules in the j-th phase of the CHB to the intermediate DC capacitor. Since the H-bridges in each phase are connected in series and the same duty cycle is adopted, the input currents i dcj1 ~i dcjN are the same and are all equal to their average value i dcj ; v o and i o are the output voltage and output current of the PET DC grid side, respectively.

3. A decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization according to claim 2, characterized in that: In Step 2, when the cascaded PET operates at unity power factor, according to power conservation, it is obtained that: where, v d and i d are respectively the d-axis components of the grid-connected voltage and current on the AC side of the PET; meanwhile, it is assumed that under the current inner-loop control, i d can well track its command value i dref , simplifying the dynamic process of the current inner loop, that is, letting i d = i dref ; Substitute Equation (2) into Equation (1) to obtain the non-linear coupled state equations of the three-phase intermediate DC average voltage and the DC grid-side output voltage of the PET as follows: where the state vector x = [v dca v dcb v dcc v o T , and the control input vector u = [M a M b M c i dref T , where M j = D j (1 - |D j |), j = a, b, c.​​ 4. A decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization as claimed in claim 3, characterized in that: In Step 3, assume that through the state feedback control law u = Φ(x), the non-linear coupled state equation (3) in Step 2 can be linearly decoupled into the following first-order differential system: where v = [v1 v2 v3 v4] T is a preset control variable; Then, according to Equation (3) and Equation (4), the state feedback control law u = Φ(x) can be inversely obtained as: where (k x1 , k x2j , k x3 , k x4 ) = θ(v d , v dca , v dcb , v dcc , v o ) is a non-linear gain parameter, which is calculated and updated in real time according to the state variable measurement, specifically:

5. A decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization according to claim 4, characterized in that: In the said step 4, according to the first-order differential system shown in Equation (4), its preset control quantity \(v = [v_1\ v_2\ v_3\ v_4]\) T Output by the PI controller, the frequency-domain expression is as follows: where G PI (s) is the transfer function of each voltage loop PI controller; v dcref is the reference value of the three-phase intermediate DC average voltage, and v oref is the reference value of the DC grid-side output voltage; As shown in Equation (6), the reference values for tracking the average DC voltage in the three phases are the same, all being v dcref . Therefore, through the error-free control of the PI controller, the balanced control of the average DC voltage in the three phases can be achieved, that is, v dca = v dcb = v dcc = v dcref ; Substitute Equation (6) into Equation (4) to obtain the typical second-order closed-loop transfer function of the three-phase intermediate DC average voltage and the DC grid-side output voltage of the PET, and then the parameters of the PI controller can be tuned according to the method of zero-pole configuration of the second-order system.

6. A decoupling and balancing control method for a three-phase cascaded power electronic transformer based on feedback linearization according to claim 1 or 2 or 3 or 4 or 5, characterized in that: The decoupling and balancing control strategy of the three-phase cascaded PET in Step 5 includes the following steps: Step 5-1: Measure the AC-side electrical quantities of the cascaded PET, perform dq transformation, and obtain the d-axis and q-axis components v d , v q of the AC grid voltage, and the d-axis and q-axis components i d , i q of the grid-connected current; Measure the electrical quantities on the intermediate DC bus and the output DC grid side of the cascaded PET, including the intermediate DC capacitor voltages v dca1 to v dcaN , v dcb1 to v dcbN , v dcc1 to v dccN of each phase sub-module, and the output voltage v o and output current i o of the PET DC grid side; Step 5-2: Calculate the average value of the intermediate DC capacitor voltages of N sub-modules in each phase to obtain the three-phase intermediate DC average voltage v dca , v dcb , v dcc . Compare the average voltages with the reference value v dcref respectively. The differences are passed through a PI controller to output the preset control quantities v1, v2, and v3. Compare the output voltage v o of the DC grid side with its reference value v oref . The difference is passed through a PI controller to output the preset control quantity v4; Step 5-3: According to the state variables v dca , v dcb , v dcc , v o and the grid voltage component v d , calculate the feedback gain parameters k x1 , k x2j(j＝a，b，c) , k x3 , k x4 , and input the state feedback control law; Step 5-4: Output the actual control quantities u1 = M, u2 = M, u3 = M, and u4 = i of the system by passing the preset control quantities v1, v2, v3, v4 through the state feedback control law a , u2 = M b , u3 = M c , u4 = i dref ; Step 5-5: From M a , M b , M c through the inverse function f -1 = [M i = D i (1 - |D i |)] -1 , j = a, b, c are calculated, and the average phase shift ratio D of each phase DAB, namely D a , D b , D c ; is output; From i dref through the grid-connected current inner loop control, the average duty cycle d of each phase CHB, namely d a , d b , d c ; is output. Step 5-6: According to the average duty cycle d of three-phase CHB a , d b , d c and the average phase-shift ratio D of three-phase DAB a , D b , D c , through the in-phase sub-module balancing control, the duty cycles d of the H-bridge modules in each phase CHB of the PET rectifier stage are output a1 ~d aN , d b1 ~d bN , d c1 ~d cN , and the phase-shift ratios D of the DAB modules in each phase of the DC isolation stage a1 ~D aN , D b1 ~D bN , D c1 ~D cN , to control the three-phase PET.

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