Equivalent Modeling Method for Feedforward Discontinuous Current Ripple in Cascade Power Converters

Abstract

The present invention relates to the technical field of cascade power converters, and in particular to an equivalent modeling method for feedforward discontinuous current ripples in cascade power converters, including: using a source converter and a Sigmoid pulsating current generator as equivalent to a load converter to jointly construct an equivalent cascade power converter; using two switch states and a switch state sequence of the equivalent cascade power converter to perform equivalent reduced-order dynamics simulation. The present invention eliminates the multiple switch state sequences introduced by the discontinuous input current of the load converter, and reduces the complexity of dynamic modeling and stability analysis of the cascade power converter.

Description

Technical Field

[0001] The invention relates to the technical field of cascade power converters, and in particular to an equivalent modeling method for feedforward discontinuous current ripples in cascade power converters. Background Art

[0002] With the continuous development of modern power supply technology, distributed power systems provide more efficient, reliable and flexible solutions for various applications such as medical facilities, data centers, electric vehicles, etc. In distributed power systems, the cascade connection of switching converters is a typical connection method. As the application of distributed power systems becomes more and more extensive, the stability of cascade power converters has also received more and more attention.

[0003] In a cascade power converter, the output voltage of the front-stage converter (also called the source converter) is used as the input voltage of the rear-stage converter (also called the load converter), and the input current of the rear-stage converter determines the output current of the front-stage converter. In this way, the input current ripple of the load converter is fed forward to the output capacitor of the source converter, interacting with the current ripple of the source converter, significantly affecting the stability of the cascade power converter. Under the interaction of switching ripples, the cascade power converter is a high-order dynamic system with multiple switching state sequences, which makes its dynamic modeling and stability analysis more complicated. Since the load converter contains a low-pass filter, the amplitude of the interactive switching ripple at the common coupling point has been greatly attenuated before entering the output end of the load converter, and the impact on the stability of the load converter is small and can often be ignored. For this reason, we can focus on the impact of the switching ripple on the stability of the source converter. According to the substitution theorem, the load converter can be replaced by its input current, thereby reducing the modeling order of the cascade power converter.

[0004] The input current of the load converter is closely related to its topological structure. For the load converter topology with a switching device at the input end, the input current is intermittent. This current also carries information such as the switching cycle and duty cycle of the load converter. To study the stability effect of the switching ripple interaction between the source and load converters, it is still necessary to consider the multi-switch state sequence, which increases the difficulty of dynamic modeling and stability analysis of cascaded power converters. Summary of the invention

[0005] In view of the shortcomings of the existing methods, the present invention eliminates the multi-switch state sequence introduced by the discontinuous input current of the load converter, and reduces the complexity of dynamic modeling and stability analysis of the cascade power converter.

[0006] The technical solution adopted by the present invention is: an equivalent modeling method for feedforward discontinuous current ripple in a cascade power converter comprises the following steps:

[0007] Step 1, using the source converter and the Sigmoid pulsating current generator as the load converter to jointly construct an equivalent cascade power converter;

[0008] Step 2, performing equivalent reduced-order dynamics simulation using two switching states and one switching state sequence of an equivalent cascade power converter;

[0009] A pulsating current load is constructed using a Sigmoid pulsating current generator and is used to equivalently replace the discontinuous input current of the load converter.

[0010] As a preferred embodiment of the present invention, the equivalent cascade power converter includes: a switch tube S1, a diode D1, an inductor L1, a capacitor C1, a comparator U1, a trigger RS1 and a Sigmoid pulsating current generator, the source of S1 is respectively connected to the negative electrode of D1 and the left end of L1, the right end of L1 is respectively connected to one end of C1, the same-direction input end of U1, and one end of the Sigmoid pulsating current generator, the gate of S1 is connected to the Q end of RS1, the R end of RS1 is connected to the output end of U1, and the other end of the Sigmoid pulsating current generator is respectively connected to the other end of C1 and the positive electrode of D1.

[0011] As a preferred embodiment of the present invention, the two switching states include:

[0012] The first switch state after equivalent is: the switch tube S1 is turned on, and the diode D1 is turned off;

[0013] The equivalent second switch state is: the switch tube S1 is turned off, and the diode D1 is turned on.

[0014] As a preferred embodiment of the present invention, the equations for the two switching states are:

[0015]

[0016] In the formula, y(t)=[i L1 ,v C1 ] T is the state variable vector, i o1 =I m S{a[cos(ωt+θ-Dπ)-cos(Dπ)]} is the expression of Sigmoid pulsating current, a is the Sigmoid function S(x) = 1 / (1+e -x )’s steepness coefficient, I m , ω, θ and D are i o1 The amplitude, angular velocity, initial phase and duty cycle, t k-1 and t k They represent the starting time of the kth switch state, P k is the coefficient matrix, Q kand Q o are all input matrices.

[0017] As a preferred implementation of the present invention, a switch state sequence is: the first equivalent switch state evolves into the second equivalent switch state.

[0018] As a preferred implementation of the present invention, the model of the comparator U1 is LM319.

[0019] As a preferred implementation of the present invention, the trigger RS1 is of model 74HC02.

[0020] As a preferred embodiment of the present invention, an equivalent modeling system for feedforward discontinuous current ripple in a cascade power converter includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement an equivalent modeling method for feedforward discontinuous current ripple in a cascade power converter.

[0021] As a preferred embodiment of the present invention, a computer readable medium stores computer program code, and when the computer program code is executed by a processor, an equivalent modeling method of feedforward discontinuous current ripple in a cascade power converter is implemented.

[0022] Beneficial effects of the present invention:

[0023] 1. The Sigmoid function is used to construct a continuous and smooth pulsating current equivalent to replace the discontinuous input current of the load converter. On the one hand, it eliminates the multi-switch state sequence introduced by the switching ripple interaction and significantly reduces the modeling complexity of the cascade power converter; on the other hand, it retains the key characteristics of the discontinuous input current of the load converter. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is the schematic diagram of the cascaded peak voltage controlled Buck converter;

[0025] Figure 2 It is the intermittent non-continuous input current of the load converter;

[0026] Figure 3 It is a continuous smooth pulsating current constructed using the Sigmoid function;

[0027] Figure 4 The equivalent circuit diagram of the cascaded peak voltage controlled Buck converter;

[0028] Figure 5 (a) and (b) are the time domain waveforms of the source converter output voltage and inductor current before and after the equivalent circuit, respectively;

[0029] Figure 6(a) and (b) are the bifurcation diagrams of the source converter inductor current before and after equivalent with the change of the source converter inductance value L1;

[0030] Figure 7 (a) and (b) are the bifurcation diagrams of the inductor current of the source converter before and after the equivalent process as the parasitic resistance r1 changes. DETAILED DESCRIPTION

[0031] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.

[0032] like Figure 1 As shown, the equivalent modeling method of the feedforward discontinuous current ripple in the cascade power converter includes the following steps:

[0033] The circuits before and after the cascade peak voltage control Buck converter are dynamically modeled. The dynamic model before the equivalent is:

[0034] Before equivalence, the circuit structure schematic diagram of the cascade peak voltage control Buck converter is as follows: Figure 1 As shown in the figure, the cascade peak voltage control Buck converter is dynamically modeled, where both the source converter and the load converter operate in continuous conduction mode. i (i=1,2) and diode D i (i=1,2) working state, there are four switch states, namely:

[0035] Switch state 1: S1 is on, D1 is off; S2 is on, D2 is off;

[0036] Switch state 2: S1 is on, D1 is off; S2 is off, D2 is on;

[0037] Switch state 3: S1 is off, D1 is on; S2 is on, D2 is off;

[0038] Switch state 4: S1 is off, D1 is on; S2 is off, D2 is on.

[0039] The state equation of the mth (m=1,2,3,4) switch state is:

[0040]

[0041] In the formula, x(t)=[i L1 ,v C1 ,i L2 ,v C2 ] T is the state variable vector, t m-1 and t mRespectively represent the starting moment of the m-th switch state, A m and B m Are the coefficient matrix and the input matrix respectively, and the corresponding expressions are respectively:

[0042]

[0043] B1 = B2 = [1 / L1 0 0 0] T , B3 = B4 = [0 0 0 0] T ,

[0044] Assume that the steady-state duty cycles of the source and load converters are D1 and D2 respectively; according to the steady-state duty cycle relationship of the source and load converters, three switch state sequences (the evolution order of switch states within one switching period) can be determined as:

[0045] When D1 > D2, the switch state evolution order is: 1 → 2 → 4, denoted as switch state sequence 1;

[0046] When D1 = D2, the switch state evolution order is: 1 → 4, denoted as switch state sequence 2;

[0047] When D1 < D2, the switch state evolution order is: 1 → 3 → 4, denoted as switch state sequence 3.

[0048] From Figure 1 The circuit modeling process shows that the dynamic model of the cascaded peak voltage control Buck converter is 4-dimensional, including 4 switch states and 3 switch state sequences; such as Figure 2 Is the input current of the load converter.

[0049] Step 1: Use the source converter and the Sigmoid pulsating current generator to equivalently construct an equivalent cascaded power converter with the load converter;

[0050] The equivalent dynamic model: After equivalence, the circuit structure schematic diagram of the cascaded peak voltage control Buck converter is as Figure 4 Shown. Conduct dynamic modeling on the peak voltage control Buck converter with a Sigmoid pulsating current load, where the peak voltage control Buck converter operates in continuous conduction mode. According to the working states of the switch tube S1 and the diode D1, there are two switch states, which are respectively as follows:

[0051] Equivalent switch state 1: S1 is conducting, D1 is cut off;

[0052] Equivalent switch state 2: S1 is cut off, D1 is conducting.

[0053] The state equation of the k-th (k = 1, 2) switch state is:

[0054]

[0055] In the formula, y(t)=[i L1 ,v C1 ] T is the state variable vector, i o1 =I m S{a[cos(ωt+θ-Dπ)-cos(Dπ)]} is the expression of Sigmoid pulsating current, a is the Sigmoid function S(x) = 1 / (1+e -x )’s steepness coefficient, I m , ω, θ and D are i o1 The amplitude, angular velocity, initial phase and duty cycle, t k-1 and t k They represent the starting time of the kth switch state, P k is the coefficient matrix, Q k and Q o are all input matrices, and the corresponding expressions are:

[0056]

[0057] like Figure 3 Schematic diagram of continuous smooth pulsating current constructed by Sigmoid function.

[0058] Step 2, performing equivalent reduced-order dynamics simulation using two switching states and one switching state sequence of an equivalent cascade power converter;

[0059] The evolution order of the switch state is: equivalent switch state 1 → equivalent switch state 2.

[0060] Depend on Figure 4 From the modeling process, we can see that the dynamic model of the equivalent circuit is 2-dimensional, including 2 switching states and 1 switching state sequence.

[0061] contrast Figure 4 and Figure 1 It can be seen from the dynamic model of the circuit shown that not only the multi-switch state sequence brought by the load converter is eliminated, but also the complexity of the dynamic modeling of the cascade power converter is reduced.

[0062] like Figure 4 As shown, the equivalent cascade power converter includes: switch tube S1, diode D1, inductor L1, capacitor C1, comparator U1 can be implemented by LM319 comparator chip, trigger RS1 can be implemented by OR gate chip 74HC02 and Sigmoid pulsating current generator, the drain of S1 is connected to the DC voltage V in The positive connection, V inThe negative electrode of S1 is grounded, the source of S1 is connected to the negative electrode of D1 and the left end of L1 respectively, the right end of L1 is connected to the upper end of C1, the same-direction input end of comparator U1, and one end of the Sigmoid pulsating current generator respectively, and the reverse input end of comparator U1 is connected to V ref1 , the gate of S1 is connected to the Q end of RS1, the R end of RS1 is connected to the output end of U1, the S end of RS1 is connected to the clock signal, and the other end of the Sigmoid pulsating current generator is connected to the other end of C1, the positive electrode of D1 and V in negative connection.

[0063] Simulation results analysis:

[0064] In this simulation experiment, the source converter is a peak voltage controlled Buck converter. Before equivalence, the load converter is a peak voltage controlled Buck converter; after equivalence, the load converter is replaced by a Sigmoid pulsating current load. Simulation conditions: Input voltage V in =12V, source converter inductor L1 = 120μH, output capacitor C1 = 470μF, output capacitor equivalent series resistance (ESR) r1 = 60mΩ, reference voltage V ref1 =8V, clock frequency f S1 =100kHz, load converter inductor L2 = 500μH, output capacitor C2 = 470μF, output capacitor ESR r2 = 20mΩ, reference voltage V ref2 =2V, clock frequency f S2 =100kHz, load resistance R = 0.5Ω; the amplitude of the sigmoid pulsating current load is I m =4A, angular frequency ω = 2πf S2 rad / s, initial phase θ=0rad, duty cycle D2=0.125, steepness coefficient a=100.

[0065] Figure 5 is the equivalent front and rear source converter output voltage v o1 , inductor current i L1 , control pulse V S1 And the PSIM circuit simulation time domain waveform of the clock signal CLK1. Among them, Figure 5 (a) is the equivalent front-source converter v o1 、i L1 、V S1 and the time domain waveform of CLK1; Figure 5 (b) is the equivalent source converter v o1 、i L1 、V S1 and the time domain waveform of CLK1.

[0066] Figure 6(a) and (b) are the bifurcation diagrams of the source converter before and after the equivalent circuit with the change of inductance L1. Figure 6 (a) is the equivalent front-source converter inductor current i L1 The bifurcation diagram of ; Figure 6 (b) is the equivalent rear source converter inductor current i L1 The bifurcation diagram of .

[0067] Figure 7 (a) and (b) are the bifurcation diagrams of the source converter before and after the equivalent circuit with the change of output capacitance ESRr1. Figure 7 (a) is the equivalent front-source converter inductor current i L1 The bifurcation diagram of ; Figure 7 (b) is the equivalent rear source converter inductor current i L1 The bifurcation diagram of .

[0068] By comparing the time domain waveforms and bifurcation diagrams of the source converter before and after the equivalent, it can be seen that the Sigmoid pulsating current load can effectively replace the actual load converter for dynamic analysis.

[0069] The present invention first establishes a high-order dynamic model of four switching states and three switching state sequences of a cascaded peak voltage-controlled Buck converter; secondly, the intermittent input current of the load converter is equivalent to a pulsating current load constructed based on a Sigmoid function, thereby the cascaded power converter is equivalent to a source converter connected to a Sigmoid pulsating current load, and an equivalent reduced-order dynamic model of two switching states and one switching state sequence is established; then, the complexity of the dynamic model of the cascaded peak voltage-controlled Buck converter before and after the equivalence is compared to demonstrate the superiority of the equivalent method proposed in the present invention; finally, the time domain waveforms of the cascaded peak voltage-controlled Buck converter under different parameters before and after the equivalence and the bifurcation diagrams varying with given parameters are compared to demonstrate the effectiveness of the equivalent method proposed in the present invention.

[0070] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. An equivalent modeling method for feedforward discontinuous current ripple in a cascade power converter, characterized in that: The following steps are involved: Step 1, using the source converter and the Sigmoid pulsating current generator as the load converter to jointly construct an equivalent cascade power converter; The pulsating current load is constructed by using the Sigmoid pulsating current generator to replace the intermittent input current of the load converter. Step 2, performing equivalent reduced-order dynamics simulation using two switching states and one switching state sequence of an equivalent cascade power converter; The equivalent cascade power converter includes: a switch tube S1, a diode D1, an inductor L1, a capacitor C1, a comparator U1, a trigger RS1 and a Sigmoid pulsating current generator, the source of S1 is respectively connected to the negative electrode of D1 and the left end of L1, the right end of L1 is respectively connected to one end of C1, the same-direction input end of U1, and one end of the Sigmoid pulsating current generator, the gate of S1 is connected to the Q end of RS1, the R end of RS1 is connected to the output end of U1, and the other end of the Sigmoid pulsating current generator is respectively connected to the other end of C1 and the positive electrode of D1; The two switch states include: The first switch state after equivalent is: the switch tube S1 is turned on, and the diode D1 is turned off; The second switch state after equivalent is: the switch tube S1 is turned off, and the diode D1 is turned on; The equations for the two switching states are: In the formula, y(t)=[i L1 ,v C1 ] T , y(t) is the state variable vector; V in is the DC voltage; i o1 =I m S{a[cos(ωt+θ-Dπ)-cos(Dπ)]},i o1 is the expression of Sigmoid pulsating current, a is the steepness coefficient of Sigmoid function, S(x)=1 / (1+e -x );I m , ω, θ and D are i o1 The amplitude, angular velocity, initial phase and duty cycle of t k represents the starting time of the kth switch state, t k-1 represents the starting time of the k-1th switch state; P k is the coefficient matrix, Q k and Q o are all input matrices; V in is the DC voltage; r1 is the equivalent series resistance of the capacitor.

2. The equivalent modeling method of feedforward discontinuous current ripple in a cascade power converter according to claim 1, characterized in that: A switch state sequence is: the first equivalent switch state evolves into the second equivalent switch state.

3. The equivalent modeling method of feedforward discontinuous current ripple in a cascade power converter according to claim 1, characterized in that: The model of comparator U1 is LM319.

4. The equivalent modeling method of feedforward discontinuous current ripple in a cascade power converter according to claim 1, characterized in that: The trigger RS1 model is 74HC02.

5. An equivalent modeling system for feedforward discontinuous current ripple in a cascade power converter, characterized in that: include: a memory for storing instructions executable by a processor; A processor, configured to execute instructions to implement an equivalent modeling method for feedforward discontinuous current ripple in a cascade power converter as described in any one of claims 1 to 4.

6. A computer readable medium storing computer program code, characterized in that: The computer program code, when executed by a processor, implements an equivalent modeling method for feedforward discontinuous current ripple in a cascade power converter as claimed in any one of claims 1 to 4.

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