Method for determining stability region of main circuit parameters of low-ripple adjustable DC regulated power supply based on Buck-Boost inverter circuit

Abstract

The present invention discloses a method for determining the stability domain of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit. The method comprises the following steps: establishing a mathematical model of the main circuit of the DC regulated power supply; using the capacitor voltage and inductor current in the inverter circuit as state variables, and using the PWM modulated DC voltage and the inverter circuit output current as the input and output variables of the inverter circuit, establishing a state differential equation for the three-phase Buck-Boost inverter circuit; establishing an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit; obtaining a discrete iterative mapping model of the DC regulated power supply based on the mathematical model of the PWM modulated DC voltage, the state differential equation of the three-phase Buck-Boost inverter circuit, and the equivalent mathematical model of the three-phase uncontrolled rectifier circuit; and using numerical simulation to obtain the value range of the main circuit parameters of the DC regulated power supply when the DC regulated power supply is in stable operation, thereby achieving stable operation of the DC regulated power supply.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronic system stability analysis, and particularly relates to a method for determining the stability domain of main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit. Background Art

[0002] A low-ripple, adjustable DC power supply based on a Buck-Boost inverter circuit is a novel, simple DC power supply topology consisting of a three-phase PWM rectifier circuit, a three-phase Buck-Boost inverter circuit, and a three-phase uncontrolled rectifier circuit. However, because this DC power supply is a highly nonlinear variable-structure system, bifurcation and chaos can occur under certain conditions, leading to unstable operation. Therefore, stability research on this DC power supply is of great significance.

[0003] At present, relevant research has been carried out on the stability analysis of Buck-Boost converters, especially DC regulated power supplies based on Buck-Boost converters. Among them, the paper "Study on the Nonlinear Characteristics of Buck-Boost Converters Based on Pulse Input Voltage" (Journal of System Simulation, 2017, 29(5): 1021-1027) studies the stability of Buck-Boost converters under the action of pulse voltages of equal amplitude and width; and the patent "Method for Determining the Stability Region of the Main Circuit Parameters of a DC Chopper Power Supply Based on Buck-Boost Inverter" (Chinese Patent: CN118573020B) studies the stability of a DC chopper power supply composed of a three-phase Buck-Boost inverter circuit and a three-phase uncontrolled rectifier circuit under the action of a constant DC voltage, and determines the stability region of its main circuit parameters. However, the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit studied in this application has a three-phase PWM rectifier circuit that outputs a PWM-modulated DC voltage, which is a pulse voltage sequence with variable pulse amplitude and duty cycle that changes according to a certain rule. When this variable amplitude and variable duty cycle pulse voltage is used as the input voltage of the three-phase Buck-Boost inverter circuit, the above-mentioned mathematical modeling and analysis methods for system stability are no longer applicable. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a mathematical modeling method for a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit and a method for determining the stability domain of its main circuit parameters. The present invention can determine the stability domain range of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit.

[0005] The technical solution of the present invention to solve the above technical problems is: a method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit, comprising the following steps:

[0006] (1) Establish a mathematical model for a three-phase PWM rectifier circuit to output a PWM modulated DC voltage; specifically, the three-phase PWM rectifier circuit adopts a space vector modulation strategy without a zero vector, and the resulting PWM modulated DC voltage is a pulse voltage sequence whose pulse voltage amplitude and duty cycle vary with time. The mathematical model of the pulse voltage sequence is:

[0007] The high and low level values of the i-th pulse voltage are:

[0008] (1);

[0009] Among them: U Hi is the high level amplitude of the i-th (i=1,2,3…) pulse voltage, U L is the low level voltage value of the pulse voltage, V m and ω are the effective value and angular frequency of the input AC voltage of the three-phase PWM rectifier circuit respectively, t i and t i+1 are the starting time of the i-th and i+1-th pulse voltages, t i ’ is the falling edge moment of the i-th pulse voltage;

[0010] The duty cycle of the i-th pulse voltage is:

[0011] (2);

[0012] (2) Establish the state differential equation of the three-phase Buck-Boost inverter circuit;

[0013] (3) Establish an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit;

[0014] (4) obtaining a discrete iterative mapping model of the DC regulated power supply based on the mathematical model obtained in step (1), the state differential equation obtained in step (2), and the equivalent mathematical model obtained in step (3);

[0015] (5) Within the range of pulse voltage with variable amplitude and duty cycle corresponding to the PWM modulated DC voltage, a set of pulse voltage amplitudes and duty cycles are randomly selected and, according to the discrete iterative mapping model obtained in step (4), a range of values of the main circuit parameters of the DC regulated power supply when the DC regulated power supply is in stable operation under the set of pulse voltage amplitudes and duty cycles is obtained through numerical simulation;

[0016] (6) sequentially changing the pulse voltage amplitude and duty cycle at a certain interval, and obtaining n sets of value ranges of the main circuit parameters when the DC regulated power supply is in stable operation under the pulse voltage amplitude and duty cycle in the same manner as step (5);

[0017] (7) According to the n groups of pulse voltage amplitudes and duty cycles obtained in step (6), the range of values of the main circuit parameters and their corresponding pulse voltage amplitudes and duty cycles when the DC regulated power supply is in stable operation are obtained, and a numerical fitting method is used to obtain a functional relationship between the range of values of each main circuit parameter and the pulse voltage amplitude and duty cycle;

[0018] (8) Based on the functional relationship of the value ranges of the main circuit parameters obtained above and the pulse voltage amplitude and duty cycle on the input side of the Buck-Boost inverter circuit of the DC regulated power supply during actual operation, the value ranges of the main circuit parameters under the pulse voltage amplitude and duty cycle for achieving stable operation of the power supply are obtained.

[0019] Preferably, the specific steps of establishing the state differential equation of the three-phase Buck-Boost inverter circuit in step (2) are:

[0020] Since the three-phase Buck-Boost inverter circuit consists of three sets of Buck-Boost DC / DC converters with the same structure, the following analysis takes phase A as an example, and the other two phases are the same;

[0021] The two power switches Q1 and Q2 in the A-phase converter are in complementary working states. The state differential equations are established for the two complementary working states, which are:

[0022] State I: Q1 is on, Q2 is off:

[0023] (3);

[0024] State II: Q1 is off, Q2 is on:

[0025] (4);

[0026] Where: is the system state vector, is the input and output state vector, i L is the inductor current, u C is the capacitor voltage, U in is the pulse voltage at the input side of the converter, i o is the converter output current, A1, A2, B1, B2 are all real-valued matrices, specifically:

[0027] , ;

[0028] , .

[0029] Where: R on is the equivalent resistance of the power switch tube in the on-state, R L is the inductor equivalent resistance, L and C are the inductance and capacitance values respectively.

[0030] Preferably, the specific steps of establishing an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit in step (3) are:

[0031] The three-phase uncontrolled rectifier circuit is equivalent to a dead zone module and an adjustment gain module, and its equivalent mathematical model is:

[0032] (5);

[0033] Where: i o and u o are the output current and output voltage of the three-phase Buck-Boost inverter circuit, where u o =U m sinωt;u z is the limit value of the dead zone module, To adjust the gain value, u z and The optimal value of is obtained by numerical simulation method.

[0034] Preferably, the specific steps of obtaining the discrete iterative mapping model in step (4) are:

[0035] The discrete iterative mapping mathematical model of the DC regulated power supply is obtained from equations (1), (2), (3), (4) and (5):

[0036] (6);

[0037] Where: i n+1 and u n+1 are the inductor current and capacitor voltage of the converter at (n+1)T time; T is the switching period of the power switch tube in the converter; α, β, e, X, and Y are all intermediate variables, respectively: ; ; ; ; ; ; ; ;t a is the on-time of the power switch Q1 in the (n+1)th switching cycle T, t bis the off time of the power switch Q1 in the (n+1)th switching cycle T, i Lref is the inductor reference current, u Cref is the capacitor reference voltage, i n and u n are the inductor current and capacitor voltage of the converter at time nT respectively.

[0038] Preferably, the specific steps of step (5) are:

[0039] Step (5-1): Set system parameters, including: equivalent resistance R of inductor L L , the power switch tube on-state equivalent resistance R on , switching cycle T, maximum number of iterations K, deviation value between two adjacent iteration variables , capacitor reference voltage u Cref , the initial value of the number of iterations n is 1;

[0040] Step (5-2): Set the input pulse voltage amplitude and duty cycle to U H and d0;

[0041] Step (5-3): Assume that the main circuit inductance of the Buck-Boost converter remains unchanged and is set to L. The capacitor C in the Buck-Boost converter is used as a variable parameter, with its initial value set to 0, and ΔC as the change step size.

[0042] Step (5-4): Calculate the inductor current i at time (n+1)T according to formula (6): n+1 and capacitor voltage u n+1 ;

[0043] Step (5-5): Determine whether both and ; If so, the system is in a stable state and execute step (5-8); otherwise, execute step (5-6);

[0044] Step (5-6): Determine whether the number of iterations n is greater than K. If so, execute step (5-7); otherwise, increase the number of iterations n by 1 and return to step (5-4);

[0045] Step (5-7): The capacitance value C is added to the set step size ΔC, the number of iterations n is reset to 1 and returns to step (5-4);

[0046] Step (5-8): Let the corresponding capacitance value at this time be the lower limit value C of its stable domain min ;

[0047] Step (5-9): within the capacitance stability domain determined in step (5-8), any capacitance value C is selected and kept constant, and the inductance L is used as the variable parameter, with its initial value set to 0, the number of iterations n is returned to 1, and ΔL is used as the step size of the change;

[0048] Steps (5-10): Calculate the inductor current i at time (n+1)T according to formula (6): n+1 and capacitor voltage u n+1 ;

[0049] Steps (5-11): Determine whether and ; If so, the system is in a stable state and execute step (5-12); otherwise, execute step (5-13);

[0050] Step (5-12): Add the set step length ΔL to the inductance value L, return the number of iterations n to 1, and return to step (5-10);

[0051] Step (5-13): Let the corresponding inductance value at this time be the upper limit value L of its stable region max .

[0052] Preferably, the specific steps of step (7) are as follows:

[0053] The functional relationship of the lower limit of capacitance is:

[0054] (7);

[0055] Where: U H is the high level amplitude of the pulse input voltage, d0 is the duty cycle of the pulse input voltage, All are constant coefficients;

[0056] The functional relationship of the inductance upper limit is:

[0057] (8);

[0058] In the formula: b0, b1, b2, b3, b4, b5 are constant coefficients.

[0059] Compared with the prior art, the technical effect of the present invention is as follows: the present invention establishes a mathematical model of a three-phase PWM rectifier circuit outputting a PWM modulated DC voltage; then, using the capacitor voltage and the inductor current in the three-phase Buck-Boost inverter circuit as state variables, and using the PWM modulated DC voltage output by the three-phase PWM rectifier circuit and the output current of the Buck-Boost inverter circuit as the input and output variables of the Buck-Boost inverter circuit, a state differential equation of the three-phase Buck-Boost inverter circuit is established; at the same time, based on the structural characteristics of the three-phase uncontrolled rectifier circuit, an equivalent mathematical model between its input current and input voltage is established; based on the above-established mathematical model of the PWM modulated DC voltage, the state differential equation of the three-phase Buck-Boost inverter circuit, and the equivalent mathematical model of the three-phase uncontrolled rectifier circuit, a discrete iterative mapping model of the DC regulated power supply is obtained; based on the obtained discrete iterative mapping model, numerical simulation is used to obtain the value range of the main circuit parameters of the DC regulated power supply when it achieves stable operation, thereby laying a foundation for achieving stable operation of the power supply and optimizing the design of its main circuit parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a topological diagram of the main circuit of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit provided by the present invention.

[0061] Figure 2 This is a flow chart of a method for determining the stability domain of main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit provided by the present invention.

[0062] Figure 3 This is the equivalent circuit structure diagram of the A-phase Buck-Boost DC / DC converter provided by the present invention.

[0063] Figure 4 The bifurcation diagram provided by the present invention uses capacitance as the bifurcation parameter.

[0064] Figure 5 The bifurcation diagram provided by the present invention uses inductance as the bifurcation parameter.

[0065] Figure 6 The figure is a fitting curve diagram of the functional relationship between the capacitance lower limit value, the pulse voltage amplitude and the duty cycle provided by the present invention.

[0066] Figure 7 This is a fitting curve diagram of the functional relationship between the inductance upper limit value, pulse voltage amplitude and duty cycle provided by the present invention.

[0067] Figure 8 This is an output voltage waveform diagram corresponding to the parameters taken within the main circuit parameter stability domain provided by the present invention.

[0068] Figure 9 This is the output voltage waveform corresponding to the parameters taken outside the stable region of the main circuit parameters provided by the present invention. DETAILED DESCRIPTION

[0069] The present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0070] Figure 1 This is a topology diagram of the main circuit of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit provided by the present invention. This topology includes a three-phase PWM rectifier circuit, a three-phase Buck-Boost inverter circuit, and a three-phase uncontrolled rectifier circuit. Among them:

[0071] The three-phase PWM rectifier circuit consists of six fully controlled power switches, S1 through S6. The emitters of power switches S1, S3, and S5 are connected to the collectors of S2, S4, and S6, respectively, forming three bridge arms. These three bridge arms are connected in parallel to form a three-phase PWM rectifier circuit. The three-phase input AC power is connected to the midpoints of the three bridge arms. The collectors of power switches S1, S3, and S5 are connected to form the positive output DC voltage of the PWM rectifier circuit, while the emitters of power switches S2, S4, and S6 are connected to form the negative output DC voltage of the PWM rectifier circuit.

[0072] The three-phase Buck-Boost inverter circuit consists of three identical Buck-Boost boost / buck circuits connected in parallel in a phase-interleaved manner, including fully controlled power switches Q1 to Q6, inductors L1 to L3, and capacitors C1 to C3. The on-state equivalent resistance of the power switches Q1 to Q6 is R on1 ~R on6 , the equivalent resistance of the inductor is R L1 ~R L3 ; The fully-controlled power switches Q1~Q6 are intended to use MOS tubes; taking the phase A circuit as an example: the drain of the Q1 tube is connected to the positive electrode of the DC power supply, the source of the Q1 tube is connected to one end of the inductor L1 and the drain of the Q2 tube, the other end of the inductor L1 is connected to the negative electrode of the DC power supply, the source of the Q2 tube is connected to one end of the capacitor C1, and the other end of the capacitor C1 is connected to the other end of the inductor L1.

[0073] The three-phase uncontrolled rectifier circuit consists of six rectifier diodes D1 to D6 and a filter capacitor C0. The anodes of the rectifier diodes D1, D3, and D5 are respectively connected to the cathodes of the diodes D2, D4, and D6 and are respectively connected to the output end of the three-phase Buck-Boost inverter circuit. The cathodes of the diodes D1, D3, and D5 are connected together as the positive terminal of the rectifier output, and the anodes of the diodes D2, D4, and D6 are connected together as the negative terminal of the rectifier output. The positive and negative terminals of the rectifier output are connected to the filter capacitor C0 and the load resistor R0.

[0074] Since the circuit structures of each phase of the three-phase Buck-Boost inverter circuit are exactly the same, and the parameters of the corresponding components in the circuit are exactly the same, the on-state equivalent resistance of each power switch tube is set to R in the following calculation. on , the equivalent resistance of the inductor is R L .

[0075] Figure 2 This is a flow chart of a method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit provided by the present invention. The method includes the following steps:

[0076] Step (1): Establish a mathematical model of a three-phase PWM rectifier circuit outputting a PWM modulated DC voltage. The three-phase PWM rectifier circuit adopts a space vector modulation strategy without a zero vector. The resulting PWM modulated DC voltage is a pulse voltage sequence whose pulse voltage amplitude and duty cycle vary with time. The mathematical model of the pulse voltage sequence is:

[0077] The high and low level values of the i-th pulse voltage are:

[0078] (1);

[0079] Among them: U Hi is the high level amplitude of the i-th (i=1,2,3…) pulse voltage, U L is the low level voltage value of the pulse voltage (constant), V m and ω are the effective value and angular frequency of the input AC voltage of the three-phase PWM rectifier circuit respectively, t i and t i+1 are the starting time of the i-th and i+1-th pulse voltages, t i ’ is the falling edge moment of the i-th pulse voltage.

[0080] The duty cycle of the i-th pulse voltage is:

[0081] (2);

[0082] Step (2): Establish the state differential equation of the three-phase Buck-Boost inverter circuit, specifically:

[0083] Since the three-phase Buck-Boost inverter circuit consists of three groups of Buck-Boost DC / DC converters with exactly the same structure, the following analysis takes phase A as an example, and the other two phases are the same.

[0084] Figure 3The figure shows the equivalent circuit structure of the A-phase Buck-Boost DC / DC converter provided by the present invention. For the two power switches in the A-phase converter in a complementary working state, their state differential equations are established respectively, which are:

[0085] State I: Q1 is on, Q2 is off:

[0086] (3);

[0087] State II: Q1 is off, Q2 is on:

[0088] (4);

[0089] Where: is the system state vector, is the input and output state vector, i L is the inductor current, u C is the capacitor voltage, U in is the pulse voltage at the input side of the converter, i o is the converter output current, A1, A2, B1, B2 are all real-valued matrices, specifically:

[0090] , ;

[0091] , .

[0092] Where: R on is the equivalent resistance of the power switch tube in the on-state, R L is the inductor equivalent resistance, L and C are the inductance and capacitance values respectively.

[0093] Step (3): Establish an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit, where the input current and input voltage of the three-phase uncontrolled rectifier circuit are also the output current and output voltage of the three-phase Buck-Boost inverter circuit. The equivalent mathematical model is specifically:

[0094] The three-phase uncontrolled rectifier circuit is equivalent to a dead zone module and an adjustment gain module, and its equivalent mathematical model is:

[0095] (5);

[0096] Where: i o and u o are the output current and output voltage of the three-phase Buck-Boost inverter circuit, where u o =U m sinωt;u zis the limit value of the dead zone module, To adjust the gain value, u z and The optimal value of is obtained by numerical simulation method.

[0097] Step (4): Based on the mathematical model obtained in step (1), the state differential equation obtained in step (2), and the equivalent mathematical model obtained in step (3), a discrete iterative mapping model of the DC regulated power supply is obtained, specifically:

[0098] According to equations (1), (2), (3), (4) and (5), the discrete iterative mapping mathematical model of the DC regulated power supply is obtained as follows:

[0099] (6);

[0100] Where: i n+1 and u n+1 are the inductor current and capacitor voltage of the converter at (n+1)T time; T is the switching period of the power switch tube in the converter; α, β, e, X, and Y are all intermediate variables, respectively: ; ; ; ; ; ; ; ;t a is the on-time of the power switch Q1 in the (n+1)th switching cycle T, t b is the off time of the power switch Q1 in the (n+1)th switching cycle T, i Lref is the inductor reference current, u Cref is the capacitor reference voltage, i n and u n are the inductor current and capacitor voltage of the converter at time nT respectively.

[0101] Step (5): Within the range of pulse voltage with variable amplitude and duty cycle corresponding to the PWM modulated DC voltage, a set of pulse voltage amplitudes and duty cycles are randomly selected and, based on the discrete iterative mapping model obtained in step (4), the range of values of the main circuit parameters of the DC regulated power supply when the DC regulated power supply is in stable operation under the set of pulse voltage amplitudes and duty cycles is obtained through numerical simulation. The specific steps are as follows:

[0102] Step (5-1): Set system parameters, including: equivalent resistance R of inductor L L , the power switch tube on-state equivalent resistance R on , switching cycle T, maximum number of iterations K, deviation value between two adjacent iteration variables , capacitor reference voltage u Cref, the initial value of the number of iterations n is 1;

[0103] Step (5-2): Set the input pulse voltage amplitude and duty cycle to U H and d0;

[0104] Step (5-3): Assume that the main circuit inductance of the Buck-Boost converter remains unchanged and is set to L. The capacitor C in the Buck-Boost converter is used as a variable parameter, with its initial value set to 0, and ΔC as the change step size.

[0105] Step (5-4): Calculate the inductor current i at time (n+1)T according to formula (6): n+1 and capacitor voltage u n+1 ;

[0106] Step (5-5): Determine whether both and ; If so, the system is in a stable state and execute step (5-8); otherwise, execute step (5-6);

[0107] Step (5-6): Determine whether the number of iterations n is greater than K. If so, execute step (5-7); otherwise, increase the number of iterations n by 1 and return to step (5-4);

[0108] Step (5-7): The capacitance value C is added to the set step size ΔC, the number of iterations n is reset to 1 and returns to step (5-4);

[0109] Step (5-8): Let the corresponding capacitance value at this time be the lower limit value C of its stable domain min ;

[0110] Step (5-9): within the capacitance stability domain determined in step (5-8), any capacitance value C is selected and kept constant, and the inductance L is used as the variable parameter, with its initial value set to 0, the number of iterations n is returned to 1, and ΔL is used as the step size of the change;

[0111] Steps (5-10): Calculate the inductor current i at time (n+1)T according to formula (6): n+1 and capacitor voltage u n+1 ;

[0112] Steps (5-11): Determine whether and ; If so, the system is in a stable state and execute step (5-12); otherwise, execute step (5-13);

[0113] Step (5-12): Add the set step length ΔL to the inductance value L, return the number of iterations n to 1, and return to step (5-10);

[0114] Step (5-13): Let the corresponding inductance value at this time be the upper limit value L of its stable region max ;

[0115] Step (6): Select n groups of pulse voltage amplitudes and duty cycles in sequence at a certain interval, and obtain the corresponding n groups of main circuit parameter value ranges using the same method as step (5).

[0116] Step (7): Based on the n groups of main circuit parameter value ranges and their corresponding pulse voltage amplitudes and duty cycles obtained in step (6), a numerical fitting method is used to obtain a functional relationship between each main circuit parameter value range and the pulse voltage amplitude and duty cycle; the numerical fitting method adopts a multivariate linear regression numerical fitting method; the functional relationship between each main circuit parameter value range and the pulse voltage amplitude and duty cycle is as follows:

[0117] (1) The functional relationship of the lower limit of capacitance is:

[0118] (7);

[0119] Where: U H is the high level amplitude of the pulse input voltage, d0 is the duty cycle of the pulse input voltage, are all constant coefficients.

[0120] (2) The functional relationship of the inductance upper limit is:

[0121] (8);

[0122] In the formula: b0, b1, b2, b3, b4, b5 are constant coefficients.

[0123] In this embodiment, in order to verify the effect of the method for determining the stability region of the main circuit parameters of the low ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit provided by the present invention, the main technical parameters of the power supply are taken as shown in Table 1.

[0124] Table 1 Main technical parameters

[0125]

[0126] According to the discrete iterative mapping model obtained by formula (6) and the technical parameters shown in Table 1, first, the capacitance C is used as the variable parameter and the inductance remains unchanged. The corresponding bifurcation diagram is obtained by numerical simulation using Matlab, as shown below:

[0127] Set the pulse voltage high level amplitude and duty cycle to: U H =400V, d0=0.5; any inductance L=6×10 -6 H remains unchanged; let the initial value of capacitor C be 0, and take 5×10-8 F is the capacitance change step; according to the above parameters, numerical simulation is performed to obtain the bifurcation diagram as follows: Figure 4 As shown. Figure 4 The capacitance value of the bifurcation point is C=3.10×10 -6 F, when the capacitance value C>3.10×10 -6 After F, the converter no longer bifurcates, that is, the system enters a stable working state. The capacitance value at this bifurcation point is the lower limit value C of its stable domain. min .

[0128] Select 9 groups of pulse voltage amplitudes and duty cycles in sequence at a certain interval, and use the same method as above to obtain the corresponding lower limit value of capacitance C for achieving stable operation of the system. min , as shown in Table 2.

[0129] Table 2 Capacitance lower limit C corresponding to different pulse voltage amplitudes and duty cycles min

[0130]

[0131] According to the 9 sets of data obtained in Table 2, the capacitance lower limit C is obtained by using the multivariate linear regression numerical fitting method. min With the pulse voltage amplitude U H And the functional relationship between the duty cycle d0 is specifically:

[0132] (7);

[0133] Where: a0=2.06×10 -8 ; a1=-2.67×10 -7 ; a2=1.13×10 -10 ; a3=4.7×10 -5 ; a4=1.86×10 -10 ; a5=-1.92×10 -7 .

[0134] Similarly, within the capacitance stability range, any capacitance C=1×10 -5 F remains unchanged, inductance is used as the variable parameter, and its initial value is 0, and 5×10 -8 H is the inductance change step size, and other technical parameters remain unchanged. The bifurcation diagram obtained through numerical simulation is as follows Figure 5 According to the 9 groups of pulse voltage amplitudes and duty cycles selected above, the same method is used to obtain the corresponding inductance upper limit L when the system is running stably. max , as shown in Table 3.

[0135] Table 3 Inductance upper limit L corresponding to different pulse voltage amplitudes and duty cyclesmax

[0136]

[0137] According to the 9 sets of data obtained in Table 3, the upper limit value of inductance L is obtained by using the multivariate linear regression numerical fitting method. max With the pulse voltage amplitude U H And the functional relationship between the duty cycle d0 is specifically:

[0138] (8);

[0139] Where: b0=4.30×10 -8 ; b1 = -3.67 × 10 -7 ; b2=2.11×10 -10 ; b3 = -5.27 × 10 -5 ; b4=1.70×10 -10 ; b5=-8.87×10 -9 .

[0140] According to formula (7) and (8), the corresponding fitting curves are as follows: Figure 6 、 7 shown.

[0141] In order to verify the validity of the above functional relationship, a set of main circuit parameters is randomly selected inside and outside the determined main circuit parameter stability domain. For example, the main circuit parameters randomly selected within the stability domain are: L=8×10 -6 H, C = 1 × 10 -5 F, the main circuit parameters outside the stable region are: L=6×10 -6 H, C = 2 × 10 -6 F, other main technical parameters are still as shown in Table 1, the above two sets of main circuit parameters are simulated and analyzed respectively, and the corresponding output voltage waveforms are as follows Figure 8 、 9 As shown in the figure, it can be seen that the output voltage waveform corresponding to the main circuit parameters taken within the stable domain is relatively smooth, indicating that the system is in a stable state; while the output voltage waveform corresponding to the main circuit parameters taken outside the stable domain has large harmonics, indicating that the system has oscillated and is in an unstable state. This further proves that the stable domain of the main circuit parameters determined in this application is effective.

Claims

1. A method for determining the parameter stability region of a main circuit of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit, wherein the DC regulated power supply main circuit includes a three-phase PWM rectifier circuit, a three-phase Buck-Boost inverter circuit, and a three-phase uncontrolled rectifier circuit; characterized in that: The method for determining the main circuit parameter stability region comprises the following steps: (1) Establish a mathematical model for a three-phase PWM rectifier circuit to output a PWM modulated DC voltage; specifically, the three-phase PWM rectifier circuit adopts a space vector modulation strategy without a zero vector, and the resulting PWM modulated DC voltage is a pulse voltage sequence whose pulse voltage amplitude and duty cycle vary with time. The mathematical model of the pulse voltage sequence is: The high and low level values of the i-th pulse voltage are: （1）； Among them: U Hi is the high level amplitude of the i-th (i=1,2,3…) pulse voltage, U L is the low level voltage value of the pulse voltage, V m and ω are the effective value and angular frequency of the input AC voltage of the three-phase PWM rectifier circuit respectively, t i and t i+1 are the starting time of the i-th and i+1-th pulse voltages, t i ’ is the falling edge moment of the i-th pulse voltage; The duty cycle of the i-th pulse voltage is: （2）； (2) Establish the state differential equation of the three-phase Buck-Boost inverter circuit; (3) Establish an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit; (4) obtaining a discrete iterative mapping model of the DC regulated power supply based on the mathematical model obtained in step (1), the state differential equation obtained in step (2), and the equivalent mathematical model obtained in step (3); (5) Within the range of pulse voltage with variable amplitude and duty cycle corresponding to the PWM modulated DC voltage, a set of pulse voltage amplitudes and duty cycles are randomly selected and, according to the discrete iterative mapping model obtained in step (4), a range of values of the main circuit parameters of the DC regulated power supply when the DC regulated power supply is in stable operation under the set of pulse voltage amplitudes and duty cycles is obtained through numerical simulation; (6) sequentially changing the pulse voltage amplitude and duty cycle at a certain interval, and obtaining n sets of value ranges of the main circuit parameters when the DC regulated power supply is in stable operation under the pulse voltage amplitude and duty cycle in the same manner as step (5); (7) According to the n groups of pulse voltage amplitudes and duty cycles obtained in step (6), the range of values of the main circuit parameters and their corresponding pulse voltage amplitudes and duty cycles when the DC regulated power supply is in stable operation are obtained, and a numerical fitting method is used to obtain a functional relationship between the range of values of each main circuit parameter and the pulse voltage amplitude and duty cycle; (8) Based on the functional relationship of the value ranges of the main circuit parameters obtained above and the pulse voltage amplitude and duty cycle on the input side of the Buck-Boost inverter circuit of the DC regulated power supply during actual operation, the value ranges of the main circuit parameters under the pulse voltage amplitude and duty cycle for achieving stable operation of the power supply are obtained.

2. The method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit according to claim 1, characterized in that: In step (2), the state differential equation of the three-phase Buck-Boost inverter circuit is established, specifically: Since the three-phase Buck-Boost inverter circuit consists of three sets of Buck-Boost DC / DC converters with the same structure, the following analysis takes phase A as an example, and the other two phases are the same; The two power switches Q1 and Q2 in the A-phase converter are in complementary working states. The state differential equations are established for the two complementary working states, which are: State I: Q1 is on, Q2 is off: （3）； State II: Q1 is off, Q2 is on: （4）； Where: is the system state vector, is the input and output state vector, i L is the inductor current, u C is the capacitor voltage, U in is the pulse voltage at the input side of the converter, i o is the converter output current, A1, A2, B1, B2 are all real-valued matrices, specifically: ， ； ， ； Where: R on is the equivalent resistance of the power switch tube in the on-state, R L is the inductor equivalent resistance, L and C are the inductance and capacitance values respectively.

3. The method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit according to claim 2, characterized in that: The specific steps of establishing the equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit in step (3) are: The three-phase uncontrolled rectifier circuit is equivalent to a dead zone module and an adjustment gain module, and its equivalent mathematical model is: （5）； Where: i o and u o are the output current and output voltage of the three-phase Buck-Boost inverter circuit, where u o =U m sinωt;u z is the limit value of the dead zone module, a is the adjustment gain value, u z The optimal values of and a are obtained using numerical simulation methods.

4. The method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit according to claim 3, characterized in that: The specific steps of obtaining the discrete iterative mapping model in step (4) are: The discrete iterative mapping mathematical model of the DC regulated power supply is obtained from equations (1), (2), (3), (4) and (5): （6）； Where: i n+1 and u n+1 are the inductor current and capacitor voltage of the converter at (n+1)T time; T is the switching period of the power switch tube in the converter; α, β, e, X, and Y are all intermediate variables, respectively: ; ; ; ; ; ; ; ;t a is the on-time of the power switch Q1 in the (n+1)th switching cycle T, t b is the off time of the power switch Q1 in the (n+1)th switching cycle T, i Lref is the inductor reference current, u Cref is the capacitor reference voltage, i n and u n are the inductor current and capacitor voltage of the converter at time nT respectively.

5. The method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit according to claim 4, characterized in that: The specific steps of step (5) are: Step (5-1): Set system parameters, including: equivalent resistance R of inductor L L , the power switch tube on-state equivalent resistance R on , switching cycle T, maximum number of iterations K, deviation value between two adjacent iteration variables , capacitor reference voltage u Cref , the initial value of the number of iterations n is 1; Step (5-2): Set the input pulse voltage amplitude and duty cycle to U H and d0; Step (5-3): Assume that the main circuit inductance of the Buck-Boost converter remains unchanged and is set to L. The capacitor C in the Buck-Boost converter is used as a variable parameter, with its initial value set to 0, and ΔC as the change step size. Step (5-4): Calculate the inductor current i at time (n+1)T according to formula (6): n+1 and capacitor voltage u n+1 ; Step (5-5): Determine whether both and ; If so, the system is in a stable state and execute step (5-8); otherwise, execute step (5-6); Step (5-6): Determine whether the number of iterations n is greater than K. If so, execute step (5-7); otherwise, increase the number of iterations n by 1 and return to step (5-4); Step (5-7): The capacitance value C is added to the set step size ΔC, the number of iterations n is reset to 1 and returns to step (5-4); Step (5-8): Let the corresponding capacitance value at this time be the lower limit value C of its stable domain min ; Step (5-9): within the capacitance stability domain determined in step (5-8), any capacitance value C is selected and kept constant, and the inductance L is used as the variable parameter, with its initial value set to 0, the number of iterations n is returned to 1, and ΔL is used as the step size of the change; Steps (5-10): Calculate the inductor current i at time (n+1)T according to formula (6): n+1 and capacitor voltage u n+1 ; Steps (5-11): Determine whether and ; If so, the system is in a stable state and execute step (5-12); otherwise, execute step (5-13); Step (5-12): Add the set step length ΔL to the inductance value L, return the number of iterations n to 1, and return to step (5-10); Step (5-13): Let the corresponding inductance value at this time be the upper limit value L of its stable region max .

6. The method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit according to claim 1, characterized in that: The specific steps of step (7) are as follows: The functional relationship of the lower limit of capacitance is: （7）； Where: U H is the high level amplitude of the pulse input voltage, d0 is the duty cycle of the pulse input voltage, All are constant coefficients; The functional relationship of the inductance upper limit is: （8）； In the formula: b0, b1, b2, b3, b4, b5 are constant coefficients.

Images