Fractional order modeling method for single-phase power spring

Abstract

The invention discloses a fractional order modeling method for a single-phase power spring, and belongs to the technical field of power electronic system modeling. The modeling method comprises the step of establishing a fractional order mathematical model of a fractional order filter inductor and a fractional order filter capacitor, a fractional order mathematical model of a single-phase power spring and a fractional order small signal model of the single-phase power spring. In order to solve the problem that a large deviation exists between modeling and analysis results and an actual system due to the fact that an existing single-phase power spring model is usually an integer-order model established by adopting integer-order inductance and capacitance, the fractional-order characteristics of actual inductance and capacitance are considered, and the models are established; the method can be conveniently used for analyzing the operating characteristics of the single-phase power spring and designing a fractional order controller of the single-phase power spring, and the operating performance and the control effect are improved. Compared with an integer order model, the fractional order model can achieve high-precision simulation of output waveforms, the difference value between the fractional order model and an actual system is small, and the essence of the actual system can be better reflected.

Description

Technical Field

[0001] The invention relates to the technical field of power electronic system modeling, and in particular to a fractional order modeling method for a single-phase power spring. Background Art

[0002] With the large-scale and high-proportion integration of renewable energy into the power grid, there may be a mismatch between load demand and power generation, causing harmonic pollution, voltage fluctuations and frequency flicker. Large power grids have a certain self-regulation ability for voltage fluctuations; while small isolated microgrids have weaker regulation capabilities, and voltage fluctuations will have an adverse effect on electrical equipment, and in severe cases will damage key equipment. In response to the above situation, Shu Yuen (Ron) Hui's team proposed the concept of "Electric Spring (ES)".

[0003] Power Spring is a distributed voltage control technology. Its core idea is to respond to the fluctuation of intermittent renewable energy generation by adjusting non-critical loads in the power grid, thereby maintaining the stability of critical loads. It changes the traditional operation mode of the power system where power generation is subject to power consumption, and forms a new operation mode where power consumption automatically matches power generation.

[0004] At present, the models of electric springs are all linear integer-order models established using integer-order inductance and integer-order capacitance, for example:

[0005] 1) "T. Yang, T. Liu, J. Chen, S. Yan and SY Rhui, Dynamic Modular Modeling of Smart Loads As Sociated With Electric Springs and Control", IEEE Transactions on Power Electronics, 2018, 33(12): 10071-10085. ("Dynamic Modular Modeling of Smart Loads As Sociated With Electric Springs and Control"), published in IEEE Transactions on Power Electronics in 2018, 33(12): 10071-10085. This paper proposes a modular, dynamic electric spring model to improve the flexibility of the model. However, the model combines the controller design with the circuit dynamic characteristics, making the model too complex.

[0006] 2) "Yang, Y., Ho, SS, Tan, SC, Hui, SYR. Small-signal model and stability of electric springs in power grids", IEEE Trans. Smart Grid, 2018, 9: 857-865. This paper develops a frequency-domain linearized state-space model of electric springs for stability analysis of distribution networks with multiple electric springs, but this model is incompatible with standard stability models of other components.

[0007] 3) "Areed, EF, Abido, MA and Al-Awami, AT, Switching model analysis and implementation of electric spring for voltage regulation in smart grids", published in IET Generation Transmission & Distribution in 2017, 11: 3703-3712. ("Switching model analysis and implementation of electric spring for voltage regulation in smart grids") This paper proposes that the linearized state space model of electric spring based on vector control can be integrated with other components into the stability model of distribution network and microgrid, but ignores the dynamic characteristics of DC link voltage.

[0008] In summary, the prior art has the following problems:

[0009] 1) The modeling methods for single-phase electric springs are all based on linear integer-order mathematical models established based on integer-order filter inductors and integer-order filter capacitors, ignoring the fact that the impedance of actual inductors and actual capacitors presents fractional-order characteristics, resulting in the problem of inaccurate models.

[0010] 2) None of the existing inventions have proposed a solution for establishing a nonlinear fractional-order model by considering the fractional-order characteristics of actual inductance and actual capacitance to improve the accuracy of the model. Summary of the invention

[0011] The technical problem to be solved by the present invention is that the traditional single-phase electric spring modeling method does not take into account the fractional-order characteristics of actual inductance and actual capacitance, and there is a problem that the model is not accurate enough.

[0012] The technical solution of the present invention is as follows:

[0013] A fractional-order modeling method for a single-phase power spring, the method involves a topological structure including a single-phase power spring, a non-critical load, a critical load, a line impedance and a renewable energy microgrid, wherein the topological structure of the single-phase power spring includes a DC power supply, a main inverter, a fractional-order filter inductor and a fractional-order filter capacitor, the main inverter input end is connected in parallel with the DC power supply, the positive pole of the main inverter output end is connected in series with the fractional-order filter inductor, the other end of the fractional-order filter inductor is connected to the positive pole of the fractional-order filter capacitor, the positive pole of the critical load and the line impedance, and the other end of the line impedance is connected to the positive pole of the renewable energy microgrid; the negative pole of the main inverter output end is connected to the negative pole of the fractional-order filter capacitor and the positive pole of the non-critical load, and the negative pole of the non-critical load is connected to the negative pole of the critical load and the negative pole of the renewable energy microgrid;

[0014] The fractional-order modeling method includes establishing a fractional-order mathematical model of a fractional-order filter inductor and a fractional-order filter capacitor, a fractional-order mathematical model of a single-phase power spring, and a fractional-order small signal model of a single-phase power spring. The specific steps are as follows:

[0015] Step 1: Sampling

[0016] The following parameters are sampled: The voltage of the DC power supply is recorded as the DC side voltage V dc , inverter output port voltage v in ; Impedance Z of non-critical load NC , the voltage across the non-critical load v NC , the current i flowing through the non-critical load NC , the impedance of the critical load is Z CL , the voltage across the critical load is recorded as the critical load voltage v s , the current i flowing through the critical load CL , line impedance Z g , the voltage of the renewable energy power generation grid connection point v g , grid current i g ; The inductance value L of the fractional-order filter inductor, the current flowing through the fractional-order filter inductor is recorded as the fractional-order filter inductor current i Lα , the voltage v across the fractional-order filter inductor L , the capacitance value C of the fractional filter capacitor β , the current i flowing through the fractional filter capacitor Cβ , the voltage across the fractional filter capacitor is recorded as the fractional filter capacitor voltage v ES , where α is the order of the fractional filter inductor and satisfies 0<α<1, β is the order of the fractional filter capacitor and satisfies 0<β<1;

[0017] Step 2: Establish the fractional-order mathematical model of the fractional-order filter inductor and fractional-order filter capacitor

[0018] Considering the fractional-order characteristics of actual inductance and actual capacitance, based on the fractional-order calculus theory, the fractional-order mathematical model of fractional-order filter inductance and fractional-order filter capacitance is established, and its expression is:

[0019]

[0020] Where, d α i Lα / dt α is the fractional-order filter inductor current i Lα Take the fractional order differential form of the fractional order filter inductor order α, d β v ES / dt β is the fractional filter capacitor voltage v ES Take the fractional differential form of the order of the fractional filter capacitor β;

[0021] Step 3: Establish a fractional-order mathematical model of a single-phase electric spring

[0022] According to the mathematical model of fractional-order filter inductor and fractional-order filter capacitor, combined with Kirchhoff's voltage and current law, the fractional-order mathematical model of single-phase power spring is established, and its expression is:

[0023]

[0024] Where σ is the switching function of the power switch in the main inverter. <t<dT s When σ=1, when dT s <t <T s When σ=0, T S is the switching cycle, t is the operating time, and d is the duty cycle;

[0025] Step 4: Establish a fractional-order small signal model of a single-phase power spring

[0026] The single-phase electric spring with fractional-order inductance and fractional-order capacitance is a nonlinear system. It is linearized by small signal analysis to simplify the analysis process. The fractional-order small signal model of the single-phase electric spring is established, and its expression is:

[0027]

[0028] In the formula, is the fractional inductor current i Lα The disturbance amount, is the voltage across the fractional capacitor v ES The disturbance amount, is the DC side voltage V dc The disturbance amount, is the grid voltage v g The disturbance amount, is the critical load voltage v s The disturbance amount, is the disturbance of duty cycle d, is the fractional-order inductor current disturbance Take the fractional differential form of the fractional inductor order α; is the voltage disturbance across the fractional capacitor Take the fractional differential form of the fractional capacitor order β; A is the state matrix, B is the input matrix, C is the output matrix, and E is the output input matrix.

[0029] Preferably, the non-critical load refers to a dissipative load, and the critical load refers to a load requiring precise terminal voltage.

[0030] Preferably, the expressions of the state matrix A, input matrix B, output matrix C, and output input matrix E in step 4 are respectively:

[0031]

[0032] Where D is the duty cycle of the static operating point.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. The traditional modeling methods for single-phase power springs are all based on linear integer-order mathematical models established by integer-order filter inductors and integer-order filter capacitors, ignoring the fact that the impedance of actual inductors and actual capacitors presents fractional-order characteristics, and there is a problem that the model is not accurate enough. The present invention takes into account the fractional-order characteristics of actual inductors and actual capacitors, and proposes a fractional-order modeling method for single-phase power springs, which is different from the traditional integer-order modeling method, is very simple and has innovative significance;

[0035] 2. The present invention provides a fractional-order circuit simulation model of a single-phase electric spring. Compared with an integer-order circuit simulation model, the high-precision simulation waveform of the single-phase electric spring output by the fractional-order model has a smaller deviation from the actual system waveform and can more accurately describe the essence of the actual system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a main circuit structure diagram of the single-phase power spring with fractional-order characteristics adopted by the present invention.

[0037] Figure 2 is the fractional-order transfer function for different order α Bode plot of .

[0038] Figure 3 is the fractional-order transfer function for different order α The step response curve.

[0039] Figure 4 is the fractional transfer function for different order β Bode plot of .

[0040] Figure 5 is the fractional transfer function for different order β The step response curve.

[0041] Figure 6 is the equivalent circuit model of fractional-order inductance and fractional-order capacitance.

[0042] Figure 7 Output of critical load voltage waveforms for a single-phase power spring integer-order model simulation.

[0043] Figure 8 Output of critical load voltage waveforms for a single-phase power spring fractional-order model simulation.

[0044] Fig. 9 It is a curve diagram of the difference ΔU1 (ΔU2) between the integer-order model (fractional-order model) and the actual system. DETAILED DESCRIPTION

[0045] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings.

[0046] Figure 1 This is a main circuit structure diagram of the single-phase power spring used in the present invention. As can be seen from the figure, the topological structure involved in the modeling method of the present invention includes a single-phase power spring, a non-critical load, a critical load, a line impedance and a renewable energy microgrid, wherein the topological structure of the single-phase power spring includes a DC power supply, a main inverter, a fractional-order filter inductor and a fractional-order filter capacitor. The input end of the main inverter is connected in parallel with the DC power supply, the positive pole of the output end of the main inverter is connected in series with the fractional-order filter inductor, the other end of the fractional-order filter inductor is connected to the positive pole of the fractional-order filter capacitor, the positive pole of the critical load, and the line impedance, and the other end of the line impedance is connected to the positive pole of the renewable energy microgrid; the negative pole of the output end of the main inverter is connected to the negative pole of the fractional-order filter capacitor and the positive pole of the non-critical load, and the negative pole of the non-critical load is connected to the negative pole of the critical load and the negative pole of the renewable energy microgrid.

[0047] In this embodiment, the non-critical load refers to a dissipative load, and the critical load refers to a load that requires precise terminal voltage.

[0048] The dissipative loads include electric kettles, electric stoves, lighting systems, etc. The critical loads include medical equipment for monitoring vital signs, data centers, monitoring and ventilation equipment in coal mines, etc.

[0049] Considering the fractional-order characteristics of the filter inductor and the filter capacitor, a fractional-order modeling method for a single-phase power spring is provided. The fractional-order modeling method includes establishing a fractional-order mathematical model of the fractional-order filter inductor and the fractional-order filter capacitor, a fractional-order mathematical model of the single-phase power spring, and a fractional-order small signal model of the single-phase power spring. The specific steps are as follows:

[0050] Step 1: Sampling

[0051] The following parameters are sampled: The voltage of the DC power supply is recorded as the DC side voltage V dc , inverter output port voltage v in ; Impedance Z of non-critical load NC , the voltage across the non-critical load v NC , the current i flowing through the non-critical load NC , the impedance of the critical load is Z CL , the voltage across the critical load is recorded as the critical load voltage v s , the current i flowing through the critical load CL , line impedance Z g , the voltage of the renewable energy power generation grid connection point v g , grid current i g ; The inductance value L of the fractional-order filter inductor α , the current flowing through the fractional-order filter inductor is recorded as the fractional-order filter inductor current i Lα , the voltage v across the fractional-order filter inductor L , the capacitance value C of the fractional filter capacitor β , the current i flowing through the fractional filter capacitor Cβ , the voltage across the fractional filter capacitor is recorded as the fractional filter capacitor voltage v ES , where α is the order of the fractional-order filter inductor and satisfies 0<α<1, and β is the order of the fractional-order filter capacitor and satisfies 0<β<1.

[0052] In the present embodiment, V dc =480V, L α =3mH, C β =50Mf.

[0053] Step 2: Establish the fractional-order mathematical model of the fractional-order filter inductor and fractional-order filter capacitor

[0054] Considering the fractional-order characteristics of actual inductance and actual capacitance, based on the fractional-order calculus theory, the fractional-order mathematical model of fractional-order filter inductance and fractional-order filter capacitance is established, and its expression is:

[0055]

[0056] Where, d α i Lα / dt α is the fractional-order filter inductor current i Lα Take the fractional order differential form of the fractional order filter inductor order α, d β v ES / dt β is the fractional filter capacitor voltage v ES The order is taken as the fractional differential form of the fractional filter capacitor order β.

[0057] Step 3: Establish a fractional-order mathematical model of a single-phase electric spring

[0058] According to the mathematical model of fractional-order filter inductor and fractional-order filter capacitor, combined with Kirchhoff's voltage and current law, the fractional-order mathematical model of single-phase power spring is established, and its expression is:

[0059]

[0060] Where σ is the switching function of the power switch in the main inverter. <t<dT s When σ=1, when dT s <t <T s When σ=0, T S is the switching period, t is the operating time, and d is the duty cycle.

[0061] Step 4: Establish a fractional-order small signal model of a single-phase power spring

[0062] The single-phase electric spring with fractional-order inductance and fractional-order capacitance is a nonlinear system. It is linearized by small signal analysis to simplify the analysis process. The fractional-order small signal model of the single-phase electric spring is established, and its expression is:

[0063]

[0064] In the formula, is the fractional inductor current i Lα The disturbance amount, is the voltage across the fractional capacitor v ES The disturbance amount, is the DC side voltage V dc The disturbance amount, is the grid voltage v g The disturbance amount, is the critical load voltage v s The disturbance amount, is the disturbance of duty cycle d, is the fractional-order inductor current disturbance Take the fractional differential form of the fractional inductor order α; is the voltage disturbance across the fractional capacitor Take the fractional differential form of the fractional capacitor order β; A is the state matrix, B is the input matrix, C is the output matrix, and E is the output input matrix.

[0065] In this embodiment, the expressions of the state matrix A, input matrix B, output matrix C, and output input matrix E are respectively:

[0066]

[0067] Where D is the duty cycle of the static operating point.

[0068] In this embodiment, the fractional order transfer function of duty cycle to output critical load voltage is also plotted. The Bode plot and step response curve of the single-phase power spring fractional order model are used to perform stability analysis to verify the effectiveness of the model. The fractional order transfer function from the duty cycle to the output key load voltage is The fractional order transfer function The fractional order transfer function The establishment includes the following steps:

[0069] S1, in order to effectively improve the efficiency of system characteristic analysis and control design, the fractional-order small signal model of the single-phase power spring in the time domain is converted into the s domain by Laplace transform, and the disturbance of the duty cycle d in the s domain is recorded as The critical load voltage v in the s domain s The disturbance is recorded as

[0070] S2, the main function of the power spring system is to maintain the critical load voltage v s The stability of the fractional order transfer function is established Reflecting the performance of the system, its expression is:

[0071]

[0072] S3, plot fractional order transfer function Bode plot and step response curve, and analyze the stability and dynamic performance of the system.

[0073] Figure 2 is the fractional-order transfer function for different order α The Bode plot of Figure 3 is the fractional-order transfer function for different order α The step response curve of Figure 4 is the fractional transfer function for different order β The Bode plot of Figure 5 is the fractional transfer function for different order β The step response curve is Figures 2 to 5 Analyzing the influence of fractional order α and order β on the stability and dynamic performance of the system, it can be seen that: with the increase of the values ​​of fractional order α and order β, the peak gain increases and the phase margin decreases; with the increase of the values ​​of fractional order α and order β, the peak time and adjustment time of the step response increase, and the dynamic performance deteriorates; therefore, fractional order α and order β will affect the stability and dynamic performance of the system, and the greater the distance of order α and order β deviating from 1, the greater the impact.

[0074] In the embodiment of the present invention, in order to verify the beneficial effects of the present invention, a dynamic response simulation is also performed.

[0075] In the simulation, a simulation circuit based on an integer-order model and a simulation circuit based on a fractional-order model of a single-phase power spring were built. In the simulation circuit of the integer-order single-phase power spring, its filter inductance and capacitance adopt an integer-order model; in the simulation circuit of the single-phase power spring based on a fractional-order model, α=0.8, β=0.8, that is, the filter inductance adopts a fractional-order filter inductance L with an order α of 0.8. 0.8 The filter capacitor uses a fractional filter capacitor C with an order β of 0.8. 0.8 The fractional-order filter inductor L is constructed by standard RC passive synthesis based on the Zeroup approximation principle. 0.8 And the fractional order filter capacitor C 0.8 The fifth-order equivalent circuit model is as follows Figure 6 As shown, it includes equivalent resistance R0, equivalent resistance R1, equivalent resistance R2, equivalent resistance R3, equivalent resistance R4, equivalent resistance R5, equivalent inductance L1, equivalent inductance L2, equivalent inductance L3, equivalent inductance L4, equivalent inductance L5, equivalent capacitance C1, equivalent capacitance C2, equivalent capacitance C3, equivalent capacitance C4 and equivalent capacitance C P .

[0076] The simulation output of the single-phase power spring based on the integer-order model shows the key load voltage waveform as follows Figure 7 As shown; the simulation output of the single-phase power spring based on the fractional order model is as follows: Figure 8 shown.

[0077] In order to further compare the deviations between the integer-order model and the fractional-order model and the actual system, the change curve of the relative difference ΔU1 (ΔU2) between the output voltage of the integer-order model (fractional-order model) and the output voltage of the actual system at the same time is shown as follows: Fig. 9 As shown. Fig. 9 It can be seen that compared with the integer-order model, the difference between the output voltage of the fractional-order model and the output voltage of the actual system is smaller, and the fractional-order model can capture and describe the dynamic characteristics of the system more carefully and reflect the essence of the actual system. That is, the correctness and necessity of the fractional-order model constructed by the present invention are verified.

Claims

1. A fractional order modeling method for a single-phase power spring, the topology involved in the method includes a single-phase power spring, a non-critical load, a critical load, a line impedance and a renewable energy microgrid, wherein: The topological structure of the single-phase power spring includes a DC power supply, a main inverter, a fractional-order filter inductor and a fractional-order filter capacitor. The input end of the main inverter is connected in parallel with the DC power supply, the positive pole of the output end of the main inverter is connected in series with the fractional-order filter inductor, the other end of the fractional-order filter inductor is connected to the positive pole of the fractional-order filter capacitor, the positive pole of the critical load, and the line impedance, and the other end of the line impedance is connected to the positive pole of the renewable energy microgrid; the negative pole of the output end of the main inverter is connected to the negative pole of the fractional-order filter capacitor and the positive pole of the non-critical load, and the negative pole of the non-critical load is connected to the negative pole of the critical load and the negative pole of the renewable energy microgrid; It is characterized in that the fractional-order modeling method includes establishing a fractional-order mathematical model of a fractional-order filter inductor and a fractional-order filter capacitor, a fractional-order mathematical model of a single-phase power spring, and a fractional-order small signal model of a single-phase power spring, and the specific steps are as follows: Step 1: Sampling The following parameters are sampled: The voltage of the DC power supply is recorded as the DC side voltage V dc , inverter output port voltage v in ; Impedance Z of non-critical load NC , the voltage across the non-critical load v NC , the current i flowing through the non-critical load NC , the impedance of the critical load is Z CL , the voltage across the critical load is recorded as the critical load voltage v S , the current i flowing through the critical load CL , line impedance Z g , the voltage of the renewable energy power generation grid connection point v g , grid current i g ; The inductance value L of the fractional-order filter inductor α , the current flowing through the fractional-order filter inductor is recorded as the fractional-order filter inductor current i Lα , the voltage v across the fractional-order filter inductor L , the capacitance value C of the fractional filter capacitor β , the current i flowing through the fractional filter capacitor Cβ , the voltage across the fractional filter capacitor is recorded as the fractional filter capacitor voltage v ES , where α is the order of the fractional filter inductor and satisfies 0<α<1, β is the order of the fractional filter capacitor and satisfies 0<β<1; Step 2: Establish the fractional-order mathematical model of the fractional-order filter inductor and fractional-order filter capacitor Considering the fractional-order characteristics of actual inductance and actual capacitance, based on the fractional-order calculus theory, the fractional-order mathematical model of fractional-order filter inductance and fractional-order filter capacitance is established, and its expression is: Where, d α i Lα / dt α is the fractional-order filter inductor current i Lα Take the fractional order differential form of the fractional order filter inductor order α, d β v ES / dt β is the fractional filter capacitor voltage v ES Take the fractional differential form of the order of the fractional filter capacitor β; Step 3: Establish a fractional-order mathematical model of a single-phase electric spring According to the mathematical model of fractional-order filter inductor and fractional-order filter capacitor, combined with Kirchhoff's voltage and current law, the fractional-order mathematical model of single-phase power spring is established, and its expression is: Where σ is the switching function of the power switch in the main inverter. <t<dT s When σ=1, when dT s <t <T s When σ=0, T S is the switching cycle, t is the operating time, and d is the duty cycle; Step 4: Establish a fractional-order small signal model of a single-phase power spring The single-phase electric spring with fractional-order inductance and fractional-order capacitance is a nonlinear system. It is linearized by small signal analysis to simplify the analysis process. The fractional-order small signal model of the single-phase electric spring is established, and its expression is: In the formula, is the fractional inductor current i Lα The disturbance amount, is the voltage across the fractional capacitor v ES The disturbance amount, is the DC side voltage V dc The disturbance amount, is the grid voltage v g The disturbance amount, is the critical load voltage v s The disturbance amount, is the disturbance of duty cycle d, is the fractional-order inductor current disturbance Take the fractional differential form of the fractional inductor order α; is the voltage disturbance across the fractional capacitor Take the fractional differential form of the fractional capacitor order β; A is the state matrix, B is the input matrix, C is the output matrix, and E is the output input matrix.

2. The fractional order modeling method of a single-phase power spring according to claim 1, characterized in that: The non-critical load refers to a dissipative load, and the critical load refers to a load that requires precise terminal voltage.

3. The fractional order modeling method of a single-phase power spring according to claim 1 is characterized in that: The expressions of the state matrix A, input matrix B, output matrix C, and output input matrix E in step 4 are respectively: Where D is the duty cycle of the static operating point.

Images