A method for modeling the input impedance of a switched-capacitor DAB-type solid-state transformer
By constructing a small-signal model of a switched-capacitor DAB-type solid-state transformer, the problems of computational complexity and limited accuracy in existing technologies are solved, high-precision input impedance analysis is achieved, and the stability of the DC distribution network is ensured.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-01-29
- Publication Date
- 2026-06-02
Smart Images
Figure CN122137257A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of DC solid-state converter modeling, and more specifically, relates to a method for modeling the input impedance of a switched capacitor DAB type solid-state transformer. Background Technology
[0002] With the rapid development of DC power grids and the widespread application of renewable energy and energy storage systems, medium-voltage DC and low-voltage DC distribution networks have become important development directions. Solid-state transformers play a crucial role in enabling bidirectional power flow and regulation in DC distribution networks. However, in long-distance DC distribution scenarios, the interaction between the input impedance of the solid-state transformer and the equivalent impedance of the line can easily lead to insufficient damping or system oscillations. Therefore, as a load port, the input impedance characteristics of the solid-state transformer are a critical factor determining whether the DC distribution network can maintain long-term stable operation.
[0003] Oscillations in DC power distribution systems are usually caused by impedance mismatch in the circuit. Small disturbance stability analysis is often an effective method for analyzing such problems and provides a theoretical basis for the optimization design of system stability. For switched capacitor DAB (Switched Capacitor DC Transformer-Dual Active Bridge, SCDCT-DAB) type solid-state transformers, the existing input impedance modeling methods still have the following shortcomings: (1) Cascaded solid-state transformers have the structural characteristics of mixed series and parallel modules. At present, the relevant analysis is mostly based on the equivalence of cascaded ports, and there is a lack of research on the interaction mechanism between the transformer and the system equivalent impedance from the whole machine level. In addition, due to the complexity of SCDCT-DAB control and the large number of electrical parameters, the influence mechanism of small disturbances of state variables on SCDCT-DAB is unclear, resulting in relatively limited existing research on its input impedance. (2) The state generalized average modeling method adopted by DAB involves complex matrix transformations, resulting in a large amount of computation and a relatively complex implementation. In addition, only the first-order component after Fourier decomposition is retained in the modeling process, which limits the accuracy of the model. Therefore, the problem of input impedance modeling for the SCDCT-DAB type solid-state transformer urgently needs to be solved. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention provides a method for modeling the input impedance of a switched capacitor DAB-type solid-state transformer, constructing an accurate input impedance model applicable to different numbers of modules and clarifying the impact of electrical control parameters on the converter.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention proposes a method for modeling the input impedance of a switched-capacitor DAB-type solid-state transformer, comprising the following steps: (1) Based on the switching averaging method and power balance relationship, the equivalent averaging circuit and basic control strategy of the switched capacitor DAB type solid transformer are derived; the switched capacitor DAB type solid transformer includes M SC modules and M DAB modules, where M is an integer greater than or equal to 2. (2) Establish a state equation containing capacitor voltage and inductor current through the equivalent average circuit, and solve the steady-state operating point of the state equation through matrix transformation to obtain the static stable value of the solid transformer. (3) The state equation is linearized by combining the static stability value of the solid-state transformer, and a small-signal equivalent circuit model of the power stage is established to obtain the small-signal transfer function relationship between the input quantity, the control quantity and the state quantity. (4) Linearize the control block diagram of the basic control strategy, and construct the whole machine small signal model by combining the power stage small signal equivalent circuit model and the small signal transfer function relationship; (5) Based on the small-signal model of the whole machine, calculate the ratio of the small-signal input voltage of the DC bus to the small-signal input current to obtain the input impedance model of the switched capacitor DAB type solid transformer.
[0006] The beneficial effects of this invention are as follows: This invention provides a method for modeling the input impedance of an SCDCT-DAB type solid-state transformer. It proposes modeling based on the entire transformer, where the steady-state model of the subsequent DAB stage is established through power relationships. The phase shift angle can be directly solved based on a given power and the selected modulation scheme. Therefore, the model itself is not limited by the modulation strategy and can naturally cover various modulation methods of SCDCT-DAB, such as single-phase, double-phase, and extended phase-shifting. The resulting complete transformer model has strong applicability and is easy to analyze for impedance matching with external circuits.
[0007] Furthermore, the expressions in the overall modeling have a clear analytical form. The modeling process, apart from necessary linearization, did not introduce any other approximations, thus ensuring the accuracy of the impedance model to the greatest extent possible. The resulting model combines high accuracy with good generalization ability. Attached Figure Description
[0008] Figure 1 This is a flowchart of the input impedance modeling method for a switched capacitor DAB type solid-state transformer provided in an embodiment of the present invention.
[0009] Figure 2 It is the topology of a switched capacitor DAB type solid-state transformer (SCDCT-DAB).
[0010] Figure 3 It is a whole-machine control method.
[0011] Figure 4 It is the equivalent average circuit of a solid-state transformer.
[0012] Figure 5 This is the small-signal control block diagram of SCDCT-DAB.
[0013] Figure 6 This is a graph showing the results of frequency sweep impedance verification of a solid-state transformer. Detailed Implementation
[0014] The present invention will be further described and illustrated below with reference to specific embodiments. The embodiments described are merely examples of the content of this disclosure and do not limit the scope of the invention. The technical features of each embodiment in the present invention can be combined accordingly, provided that there is no mutual conflict.
[0015] Figure 1 A flowchart illustrating the input impedance modeling method for a switched-capacitor DAB-type solid-state transformer provided in this embodiment of the invention. (See also...) Figure 1 , combined Figures 2-6 The input impedance modeling method of the switched capacitor DAB type solid-state transformer in this embodiment is described in detail, and the method includes S1-S5.
[0016] S1. Based on the switching averaging method and power balance relationship, the equivalent circuit and basic control strategy of the solid-state transformer are derived. See Figure 2 The topology of the switched capacitor DAB type solid-state transformer (hereinafter referred to as SCDCT-DAB) includes: a medium-voltage side DC voltage source. There are M switched-capacitor (SC) modules and M dual active bridge (DAB) modules. The M SC modules are connected in series and are mainly used to divide the medium-voltage DC port, resulting in M discrete capacitor DC ports that are connected to the M DAB modules respectively. The other end of the DAB modules is connected to the low-voltage DC bus in parallel, realizing high-efficiency power conversion with a large transformation ratio between medium and low voltage. The low-voltage side includes supporting capacitors. and equivalent load resistance .
[0017] The switching frequency of SCDCT-DAB is Transmission power is On the series side, the input DC bus current is... The input-side inductance is On the parallel side, the output low-voltage side DC voltage is All discrete capacitors at the output terminals of the SC are kept consistent. Let the discrete capacitor at the j-th SC output terminal be denoted as... , This refers to the voltage across the discrete capacitor at the output of SC. These are the voltages of the first and Mth discrete capacitors, respectively. All M discrete capacitor voltages have the same value. The high-frequency transformer turns ratio in all DAB modules Transmission inductance value Keeping them the same, the input current and output current of the j-th DAB module are... and .
[0018] The overall control method is as follows Figure 3 As shown, where for The average value, i.e., the voltage equalization of discrete capacitors; This is a given reference value for voltage equalization of discrete capacitors. The external voltage equalization ring equalizes the voltage of the discrete capacitors. Reference value for voltage equalization with discrete capacitors The comparison yields an error signal that is then passed through the equalizing loop controller. Adjustments are made to output a reference value for the DC bus input current, which serves as the reference signal for the inner current loop. The inner current loop collects the DC bus input current. and compare it with the reference signal of the inner current loop. The comparison is performed, and the resulting current error is controlled by the current loop controller. Compensation is performed to ultimately generate the duty cycle signal of the SC module. To complete closed-loop control, the specific mathematical relationships of the SC module control are shown in formulas (1)-(3).
[0019] (1) (2) (3) The DAB module control consists of two parts: the Output Voltage Control (OVC) loop and the Discrete Capacitor Voltage Decoupling Control (VBC) loop. The OVC is responsible for regulating the low-voltage side output voltage at the output port. This refers to the actual detected low-voltage side output voltage. The low-voltage side output voltage reference value is calculated. and The error signal obtained from the difference is then processed by the output voltage controller. After processing, the reference phase shift angle of the system is generated. This phase shift angle applies simultaneously to each DAB module to ensure uniform power distribution across all modules. VBC is used to achieve precise capacitor voltage equalization. In this strategy, the first to the (M-1)th DAB modules calculate the deviation between their corresponding discrete capacitor voltage and the discrete capacitor equalization voltage. This deviation is then processed by the decoupling controller. After processing and taking the negative value, the shift ratio increment of each DAB module is obtained. . Used to correct the reference shift ratio to suppress voltage imbalance between DAB modules, combined with get The shift ratio of the Mth DAB module is incremental. The incremental algebra of the first M-1 DAB modules is then used to determine the dynamic decoupling between the main output voltage loop and the capacitor voltage decoupling loop in the control structure. The phase shift angle signal finally applied to the M DAB modules is determined by OVC and VBC. The specific mathematical relationship of the DAB modules is shown in formulas (4)-(6).
[0020] (4) (5) (6) The core basic relationships of the SC module are: (7) A single DAB module can be controlled by its transmission power. Modeling: (8) Input current and output current The average value can be expressed by formula (9), where: (9) The equivalent average circuit of a solid-state transformer can be obtained from the above, such as... Figure 4 As shown.
[0021] S2, establish a state equation containing capacitor voltage and inductor current through an equivalent averaging circuit, and solve the steady-state operating point of the state equation through matrix transformation to obtain the steady-state average value of the solid-state transformer.
[0022] Establish the overall state equations: (10) in, Represents state variables. It is the voltage of the Mth discrete capacitor. It is the low-voltage side output voltage. It is the DC bus input current. Indicates the input quantity. This indicates the input voltage of the solid-state transformer. This represents the equivalent load voltage output from the low-voltage side.
[0023] This represents the system state matrix, where K is the high-frequency transformer transformation ratio in the DAB module, and f is the switching frequency of the DAB module. This is the capacitance value of a discrete capacitor. It is the duty cycle signal of the SC module. It is the phase shift angle signal of the j-th DAB module. It is the transmission inductance value of the DAB module. It is the low-voltage side support capacitor of the DAB module. It is the equivalent load resistance on the low-voltage side of the DAB module; This represents the input matrix.
[0024] In steady state, Then the static operating point of the state variable is: (11) in, It is a given steady-state input. It is a steady-state quantity; S3. By combining the static stability value of the solid-state transformer, the state equation is linearized, and a small-signal equivalent circuit model of the power stage is established to obtain the small-signal transfer function relationship between the input quantity, the control quantity and the state quantity.
[0025] In this embodiment, a small signal of state variable is added to the above equation (10). By linearizing the circuit, we can obtain the small-signal equivalent circuit model of the power stage: (12) in, Represents a small signal of a state variable. Indicates the small signal of the input variable. This represents the small phase shift angle signal of the 1st, 2nd...Mth DAB module. The duty cycle of the SC module is a small signal. Matrix A is the system state matrix, matrix B is the input matrix, and matrices C and D are both transition matrices. , .
[0026] definition The transfer function to the state variable is , The transfer function to the state variable is The transfer function from input to state is: Thus, the transfer function description of the influence of each input disturbance on the state quantity can be obtained, as shown in formula (13).
[0027] (13) in, It is the identity matrix, and s is the Laplace operator.
[0028] S4, linearize the control block diagram of the basic control strategy, and construct the whole machine small-signal model by combining the power stage small-signal equivalent circuit model and the small-signal transfer function relationship; In this embodiment, formula (12) is combined with... Figure 3 The control loop shown is illustrated in the small-signal control block diagram of SCDCT. Figure 5 As shown, according to Figure 5 (a) The small-signal expression of the SC module after control is: (14) (15) (16) (17) in, This is the transfer function from the preceding control variables to the input inductor current. It is the transfer function from input voltage to input inductor current, and also the open-loop input admittance. Let be the transfer function of the control variable shift ratio of the j-th DAB module to the input inductor current. This is the transfer function from the output load disturbance to the input inductor current. The transfer function for the discrete capacitor voltage input to the j-th DAB module from the preceding control variables. The transfer function for the input voltage to the discrete capacitor voltage of the j-th DAB module. The transfer function for shifting the control variables of the i-th DAB module to the input discrete capacitor voltage of the j-th DAB module is given. G is the transfer function for the output load disturbance to the discrete capacitor voltage at the input of the j-th DAB module. d This is the time delay function.
[0029] Combination Figure 5 (b) and formula (9) yield the j-th... Small signal model of a DAB module: (18) (19) (20) (twenty one) The small-signal model of the Mth DAB module is: (twenty two) in: (twenty three) in, This is the transfer function from the DAB module control variables to the module input current. This is the transfer function from the DAB module's output voltage to its input current. This is the transfer function from the DAB module control variables to the module output current. This is the transfer function from the input voltage to the output current of the DAB module.
[0030] S5. Based on the small-signal model of the whole machine, the input impedance model of the transformer is obtained by calculating the ratio of the small-signal input voltage of the DC bus to the small-signal input current.
[0031] Combining formulas (20) and (22), we obtain: (twenty four) Summing formula (16) for each module, we get: (25) Combining formulas (19) and (22), the output current is obtained. , The expression is given by formulas (26) and (27): (26) (27) Combining formulas (14)-(15), (17), and (24)-(27), the input impedance model can be obtained: (28) in, , , ; This is the fifth transition term. This is the 6th transition term. This is the 7th transition term. This is the 8th transition item.
[0032] Based on the input impedance model obtained above, the frequency sweep impedance of the solid-state transformer is verified using MATLAB software, such as... Figure 6 As shown, the accuracy of impedance modeling was verified, and DC-DC conversion under various stable operating conditions was realized.
[0033] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. Those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.
Claims
1. A method for modeling the input impedance of a switched-capacitor DAB-type solid-state transformer, characterized in that, Includes the following steps: (1) Based on the switching averaging method and power balance relationship, the equivalent averaging circuit and basic control strategy of the switched capacitor DAB type solid transformer are derived; the switched capacitor DAB type solid transformer includes M SC modules and M DAB modules, where M is an integer greater than or equal to 2. (2) Establish a state equation containing capacitor voltage and inductor current through the equivalent average circuit, and solve the steady-state operating point of the state equation through matrix transformation to obtain the static stable value of the solid transformer. (3) The state equation is linearized by combining the static stability value of the solid-state transformer, and a small-signal equivalent circuit model of the power stage is established to obtain the small-signal transfer function relationship between the input quantity, the control quantity and the state quantity. (4) Linearize the control block diagram of the basic control strategy, and construct the whole machine small signal model by combining the power stage small signal equivalent circuit model and the small signal transfer function relationship; (5) Based on the small-signal model of the whole machine, calculate the ratio of the small-signal input voltage of the DC bus to the small-signal input current to obtain the input impedance model of the switched capacitor DAB type solid transformer.
2. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 1, characterized in that, The equivalent averaging circuit includes the SC module section and the DAB module section; The equivalent average circuit relationship of the SC module is as follows: ； in, This represents the average value of the discrete capacitor voltages at the output of the SC module. This indicates the input voltage of the solid-state transformer. This indicates the duty cycle signal of the SC module. This represents the voltage of the Mth discrete capacitor; The equivalent average circuit relationship of the DAB module is as follows: ； Where K is the high-frequency transformer turns ratio in the DAB module, and f is the switching frequency of the DAB module. This refers to the transmission inductance value of the DAB module. This refers to the low-voltage side output voltage of the switched-capacitor DC transformer. Let j be the phase shift angle signal of the j-th DAB module. , These are the input current and output current of the j-th DAB module, respectively. It is the transmission power of the j-th DAB module. It is the voltage of the j-th discrete capacitor.
3. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 1, characterized in that, Basic control strategies include: The SC module is controlled using an external voltage equalization loop and an internal current loop. The voltage equalization loop compares the voltage equalization of the discrete capacitors with a reference value, and the resulting error signal is used by the voltage equalization loop controller to generate a reference signal for the internal current loop. The internal current loop compares the DC bus input current on the series side with the reference signal, and the resulting error signal is used by the current loop controller to generate the duty cycle signal for the SC module. ; The DAB module's control includes an output voltage control loop and a discrete capacitor voltage decoupling control loop. The output voltage control loop compares the low-voltage side output voltage with a low-voltage side output voltage reference value, and the resulting error signal is used by the voltage controller to generate a reference phase shift angle. The discrete capacitor voltage decoupling control loop compares the voltages of the first M-1 discrete capacitors with the voltage equalization of the discrete capacitors. The resulting error signal is used by the decoupling controller to generate the phase shift increment of the first M-1 DAB modules. The final phase shift angle signal of the M DAB modules is obtained by combining the reference phase shift angle and the phase shift increment of the first M-1 DAB modules.
4. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 3, characterized in that, The final phase shift angle signal of the first M-1 DAB modules is the difference between the reference phase shift angle and the phase shift increment of the corresponding DAB module, and the phase shift angle signal of the Mth DAB module is the sum of the reference phase shift angle and the phase shift increment of the first M-1 DAB modules.
5. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 1, characterized in that, The state equation is: ； in, It is a state variable. It is the voltage of the Mth discrete capacitor. It is the low-voltage side output voltage. It is the DC bus input current. It is the input quantity. This indicates the input voltage of the solid-state transformer. This represents the equivalent load voltage output from the low-voltage side. The superscript T indicates transpose. Matrices A and B are the system state matrix and input matrix, respectively. The steady-state operating point of the state equation is obtained through the formula Please solve. It is a given steady-state input. It is a steady-state quantity.
6. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 5, characterized in that, Step (3) includes: By adding a small perturbation and linearizing the state equation, we obtain the small-signal equivalent circuit model of the power stage: ； The small-signal transfer function relationships between input quantities, control quantities, and state quantities are as follows: ； in, It is the small duty cycle signal of the SC module. Transfer function to state variables, It is the small signal of the phase shift angle of the DAB module. Transfer function to state variables, It is a small input signal Transfer function to state variables, These are small-signal state variables, and C and D are transition matrices. It is the identity matrix, and s is the Laplace operator.
7. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 1, characterized in that, The overall small-signal model includes an SC module and a DAB module. The small-signal model of the SC module is as follows: ； ； ； ； in, It is the j-th discrete capacitor voltage small signal. It is a discrete capacitor voltage equalization small signal. It is a small signal of DC bus input current. It is the small duty cycle signal of the SC module. It is the small signal of the input voltage of the solid-state transformer. It is the small phase shift angle signal of the j-th DAB module. It is the small signal of the equivalent load voltage output from the low-voltage side. It is a control variable The transfer function to the input inductor current. It is the transfer function from the medium-voltage side input voltage to the input inductor current. yes The transfer function to the input inductor current. It is the transfer function from the output load disturbance to the input inductor current. It is the transfer function from the preceding control variables to the discrete capacitor voltage input to the j-th DAB module. It is the transfer function from the medium-voltage side input voltage to the input discrete capacitor voltage of the j-th DAB module. It is the transfer function of shifting the control variable of the i-th DAB module to the input discrete capacitor voltage of the j-th DAB module. It is the transfer function of the output load disturbance to the input discrete capacitor voltage of the j-th DAB module. It is the voltage controller of the SC module. It is the inner loop control function of the SC module current. It is a time delay function; The small-signal model of the DAB module is as follows: When j=1,2,…,M-1: ； ； ； ； When j=M: ； in, This is the transfer function from the DAB module control quantity to the module input current. This is the transfer function from the DAB module's output voltage to its input current. This is the transfer function from the DAB module control quantity to the module output current. This is the transfer function from the input voltage to the output current of the DAB module. , These are the input current small signal and output current small signal of the j-th DAB module, respectively. It is the small signal of the low-voltage side output voltage of the SCDCT. It is the small phase shift angle signal of the DAB module. The shift ratio of the DAB module is smaller than the incremental signal. It is a time delay function. It is a DAB module voltage equalization controller. It is the output voltage controller of the DAB module.
8. The input impedance modeling method for a switched-capacitor DAB-type solid-state transformer according to claim 1, characterized in that, The input impedance model is: ； in, For input impedance, This is the small signal of the input voltage for the solid-state transformer. This is the inner loop control function for the SC module current. For delay function, The transfer function for the discrete capacitor voltage input to the j-th DAB module from the preceding control variables. This is the transfer function from the input voltage on the medium-voltage side to the input inductor current. The transfer function is given for the input voltage on the medium-voltage side to the input discrete capacitor voltage of the j-th DAB module. This is the 8th transition item.