A harmonic modeling method for dc distribution network based on substitution theorem

Abstract

The application relates to a DC power distribution network harmonic modeling method based on a substitution theorem, and comprises the following steps: classifying each key device in a DC power distribution network according to the function of electric energy transformation; processing the input end and the output end of each type of device; writing the state space average equation of each device; obtaining the exponential Fourier coefficients of each variable in the state space average equation and bringing the exponential Fourier coefficients into the state space equation to obtain the harmonic state space model of each type of device, and then converting the frequency domain expression of each variable into a time domain expression through a Fourier series expansion formula; and building a harmonic model of the DC power distribution network according to the substitution theorem. Compared with the prior art, the application adopts a harmonic modeling method to perform harmonic analysis on each variable in the DC power distribution network system, and solves the problem that the harmonic state space modeling method is not suitable for large and complex systems.

Description

Technical Field

[0001] This invention belongs to the field of power systems, specifically relating to a harmonic modeling method for DC distribution networks based on the substitution theorem. Background Technology

[0002] Due to the overexploitation and use of energy resources, in order to compensate for energy shortages, a large amount of new energy sources are connected to DC distribution network systems through various power electronic devices. This places more stringent requirements on the power quality and reliability of DC distribution networks. In an ideal DC distribution network, electrical energy is supplied to users with constant amplitude voltage and current. However, due to the connection of a large number of nonlinear power electronic devices, voltage and current distortion occurs, resulting in DC distribution networks containing not only DC components but also a large number of harmonics. Therefore, to better manage harmonics in DC distribution networks, it is necessary to perform harmonic modeling of the DC distribution network.

[0003] DC distribution networks are large and complex systems that supply power to various loads through numerous nonlinear power electronic devices. Simultaneously, they require the integration of distributed energy sources and energy storage into the grid via these devices. Harmonic modeling of DC distribution networks is complex, computationally intensive, and difficult to extend. Therefore, a new method is needed to reduce model complexity and facilitate extension while retaining the necessary harmonic analysis techniques. Summary of the Invention

[0004] To address the problem that harmonic state-space models are unsuitable for analyzing complex DC distribution networks, this invention provides a harmonic modeling method for DC distribution networks based on substitution theorems. This method circumvents the shortcomings of harmonic state-space models and is easily extended to large and complex DC distribution networks. The technical solution is as follows:

[0005] A harmonic modeling method for DC distribution networks based on the substitution theorem includes the following steps:

[0006] Step 1: Classify the key equipment in the DC distribution network according to their power conversion functions;

[0007] Step 2: Process the input and output terminals of various devices;

[0008] Step 3: Write the state-space average equations for various types of equipment based on the physical mechanisms;

[0009] Step 4: Perform Fourier series decomposition on the variables in the state-space average equation, obtain the exponential Fourier coefficients of each variable, and substitute them into the state-space equation to obtain the harmonic state-space model of various devices. Then, transform the frequency domain expression of each variable into the time domain expression through the Fourier series expansion.

[0010] Step 5: Represent the internal circuits of various devices using the harmonic state-space models of various devices, and use the substitution theorem to establish the external circuits of various devices to construct the harmonic model of the DC distribution network.

[0011] Furthermore, in step 1, the key equipment in the DC distribution network is divided into rectifiers, inverters, and DC converters according to their power conversion functions. Among them, the three-phase AC power generated by the AC grid and wind farm is converted into DC power by the rectifier and connected to the distribution network. The photovoltaic power station, energy storage equipment, and DC load are connected to the distribution network through the DC converter. The AC load is converted into AC power by the inverter to supply power.

[0012] Furthermore, in step 2, various types of equipment and the power grid equipment connected to them are disconnected, and the electrical quantities at the disconnection point are represented by voltage and current values, wherein the voltage and current values ​​are the voltage and current values ​​of the DC bus, the distributed energy input equipment, or the voltage and current values ​​provided by the equipment to the load.

[0013] Furthermore, in step 3, the unidirectional DC converter is a buck converter, and its state-space average equation is as shown in equation (1); the bidirectional DC converter is a bidirectional buck-boost converter, and its state-space average equation is as shown in equation (2); the VSC inverter is an LC filter converter, and its state-space average equation is as shown in equation (3).

[0014]

[0015]

[0016]

[0017] In equation (1), x1 is the inductor current and x2 is the inductor voltage. Let U represent the derivatives of x1 and x2 respectively. i I0 is the input voltage, I0 is the output current, d is the duty cycle of the buck converter, L is the inductance, and C is the capacitance; in equation (2), L1, L2, and LC are the input voltage, I0 is the output current, d is the duty cycle of the buck converter, L is the inductance, and C is the capacitance; s C1 and C2 are capacitors, R1 and R2 are inductors and resistors, x3 is the current through inductor L1, and x4 is the current through inductor L2. s x5 is the current through capacitor C1, x6 is the current through inductor L2, and x7 is the voltage across capacitor C2. Let d be the derivatives of x3, x4, x5, x6, and x7 respectively. s L is the duty cycle of the bidirectional buck-boost converter, and u1 and u2 are the voltages at the input and output terminals, respectively; in equation (3), L a1 L b1 L c1R is the filter inductor for phases A, B, and C. a1 R b1 R c1 The filter inductors and resistors for phases A, B, and C are shown in Figure C. a2 C b2 C c2 For the filter capacitors of phases A, B, and C, R a2 R b2 R c2 The filter capacitors and resistors for phases A, B, and C are x8, x9, and x 10 x represents the filter inductor currents for phases A, B, and C. 11 x 12 x 13 These are the filter capacitor voltages for phases A, B, and C. They are x8, x9, and x 10 x 11 x 12 x 13 The derivative of u dc i is the input DC voltage. a i b i c For the output currents of phases A, B, and C, g a g b g c For the switching function S a S b S c The function composed of g a =(2s a -s b -s c ) / 3, g b =(-s a +2s b -s c ) / 3, g c =(-s a -s b +2s c ) / 3.

[0018] Furthermore, in step 4, the exponential form of the Fourier series decomposition expression for each variable is:

[0019]

[0020] Where y(t) is a function of various variables related to time t, Y n Let ω be the fourr coefficient of the nth exponential form of the function of variables, T be the angular frequency of the device, Z be the period of the device, and Z be the set of integers.

[0021] Furthermore, the state-space equation in step 4 is:

[0022]

[0023] Where x(t) represents the variable in the state-space average equation, Let x(t) be the derivative of x(t), A(t) be the coefficient matrix of the state-space equation, B(t) be the control matrix of the state-space equation, and u(t) be the input variable of the state-space equation.

[0024] Furthermore, the general form of the harmonic state-space model in step 4 is:

[0025] sX=(A-Λ)X+BU, (6)

[0026] in,

[0027]

[0028] X = [X] -h … X -1 X0 X1 … X h ] T ,

[0029]

[0030] s is a complex variable, h represents the order of harmonic decomposition, matrix B has the same form as matrix A, column vector U has the same form as vector X, and I is an identity matrix of (2h+1)×(2h+1).

[0031] Furthermore, in step 4, the harmonic state-space model of the buck converter is as shown in equation (7), the harmonic state-space model of the bidirectional buck-boost converter is as shown in equation (8), and the harmonic state-space model of the three-term LC filter converter is as shown in equation (9):

[0032]

[0033]

[0034]

[0035] Where O is the zero matrix of (2h+1)×(2h+1), D is the Toplitz matrix of the duty cycle of the Buck converter, and D s Let be the Toplitz matrix of the duty cycle of the bidirectional buck-boost converter.

[0036] Further, in step 5, according to the substitution theorem, a controlled voltage source is used to replace the power grid to provide the grid-side input voltage to the rectifier, inverter, and DC converter, and its value is the voltage value provided by the power grid to the rectifier, inverter, and DC converter; a controlled current source is used to replace the load to provide the load-side input current to the rectifier, inverter, and DC converter, and its value is the current value flowing from the load into the rectifier, inverter, and DC converter; on the grid side, a controlled current source is used to replace the rectifier, inverter, and DC converter, and its current value is the current value flowing from the equipment into the power grid; on the load side, a controlled voltage source is used to replace the rectifier, inverter, and DC converter to provide the input voltage to the load, and its value is the voltage value provided by the rectifier, inverter, and DC converter to the load.

[0037] Furthermore, a controlled voltage source is used to replace the grid and load output voltage to the bidirectional DC converter; a controlled current source is used to replace the bidirectional DC converter output current to the grid and load.

[0038] The beneficial effects of this invention are: it discloses a harmonic modeling method for DC distribution networks based on the substitution theorem, and uses the harmonic modeling method to perform harmonic analysis on various variables in the DC distribution network system, thus solving the problem that the harmonic state-space modeling method is not applicable to large and complex systems. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the implementation of the method disclosed in this invention.

[0040] Figure 2 This is a system structure diagram of a DC distribution network.

[0041] Figure 3 This is a topology diagram of a bidirectional buck-boost converter.

[0042] Figure 4 This is a topology diagram of the Buck converter.

[0043] Figure 5 This is a topology diagram of a three-phase LC filter converter.

[0044] Figure 6 This is a diagram showing the grid connection method for a bidirectional buck-boost converter.

[0045] Figure 7 This is a diagram showing the grid connection method for a buck converter.

[0046] Figure 8 This is a diagram showing the grid connection method for a three-phase LC filter converter.

[0047] Figure 9 A comparison chart of simulation results for the output voltage of the Buck converter.

[0048] Figure 10 The figure shows a comparison of the simulation results of the output voltage of the three-phase LC filter converter.

[0049] Figure 11 This is a comparison chart of the simulation results for the energy storage current.

[0050] Figure 12 This is a comparison chart of the simulation results for photovoltaic voltage. Detailed Implementation

[0051] The invention will now be described in further detail with reference to the accompanying drawings.

[0052] Please refer to Figure 1 This embodiment mainly includes the following steps:

[0053] Step 1: Classify the various key devices in the DC distribution network according to their power conversion functions. Specifically, classify the key devices into rectifiers, inverters, and DC converters. Three-phase AC power generated by the AC grid and wind farms can be converted into DC power by rectifiers and connected to the DC distribution network; photovoltaic power stations, energy storage devices, and DC loads need to be connected to the grid through DC converters; AC loads can be powered by inverters that convert DC power from the DC distribution network into AC power.

[0054] Step 2: Process the input and output terminals of various devices. Specifically, disconnect each device from the power grid equipment connected to it, and express the electrical quantities at the disconnection point in terms of voltage and current. The voltage and current values ​​are the voltage and current values ​​of the DC bus, the distributed energy input device, or the voltage and current values ​​provided by the device to the load.

[0055] Step 3: Write the state-space average equations for various types of equipment based on the physical mechanism. Among them, the unidirectional DC converter uses a buck converter, and its state-space average equation is shown in equation (1). The bidirectional DC converter uses a bidirectional buck-boost converter, and its state-space average equation is shown in equation (2). The VSC inverter uses a three-phase LC filter converter, and its state-space average equation is shown in equation (3).

[0056] Step 4: Perform exponential Fourier series decomposition on the variables in each state-space average equation to obtain the exponential Fourier coefficients of the variables. Substitute these coefficients into the state-space equations to obtain the harmonic state-space model of each device. Then, convert the frequency domain expression of each variable into the time domain expression through Fourier series expansion. The exponential Fourier series decomposition of each variable is shown in Equation (4), the state-space equation is shown in Equation (5), and the general form of the harmonic state-space model is shown in Equation (6). Specifically, the harmonic state-space model of the buck converter is shown in Equation (7), the harmonic state-space model of the bidirectional buck-boost converter is shown in Equation (8), and the harmonic state-space model of the three-term LC filter converter is shown in Equation (9).

[0057] Step 5: Represent the internal circuits of various devices using their harmonic state-space models, and establish the external circuits of each device using the substitution theorem to construct a harmonic model of the DC distribution network. Specifically, a controlled voltage source replaces the grid as the grid-side input voltage of the rectifier, inverter, and DC converter, and its value is the voltage provided by the grid to the aforementioned devices. A controlled current source replaces the load as the load-side input current of the rectifier, inverter, and DC converter, and its value is the current flowing from the load into the aforementioned devices. On the grid side, a controlled current source replaces the aforementioned devices, and its value is the current flowing from the devices into the grid. On the load side, a controlled voltage source replaces the aforementioned devices as the input voltage of the load, and its value is the voltage provided by the devices to the load. In particular, for the bidirectional DC converter, according to the harmonic state-space model, the input variables on both the grid side and the load side are voltages, so a controlled voltage source replaces the grid and the load. Similarly, the bidirectional DC converter outputs current to the grid and the load, so a controlled current source connects the grid and the load to replace the bidirectional DC converter.

[0058] Figure 2 The topology of a DC distribution network is given, in which the DC converters connected to photovoltaic and energy storage systems are bidirectional buck-boost converters, and their topology is as follows: Figure 3 As shown; the DC converter connected to the DC load is a Buck converter, and its topology is as follows. Figure 4 As shown; the VSC inverter connected to the AC load uses a three-phase LC filter converter, and its topology is as follows. Figure 5 As shown in Table 1, the parameters of the bidirectional buck-boost converter, buck converter, and three-phase LC filter converter are shown in Table 1. The connection diagrams of the bidirectional buck-boost converter, buck converter, and three-phase LC filter converter under their substitution theorem are shown in Table 1. Figure 6 , Figure 7 , Figure 8 As shown.

[0059] Table 1 Circuit Component Parameters

[0060]

[0061]

[0062] To verify the effectiveness of the method proposed in this invention, simulations were performed, and the simulation results were compared with the simulation waveforms of a DC distribution network built using Simulink. The comparison results are as follows: Figures 9-12 As shown in the figure, the modeling method of this invention is consistent with the actual simulation results.

[0063] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for harmonic modeling of DC distribution networks based on the substitution theorem, characterized in that, Includes the following steps: Step 1: Classify the key equipment in the DC distribution network according to their power conversion functions; Step 2: Process the input and output terminals of various devices; Step 3: Write out the state-space average equations of various devices based on the physical mechanism; the unidirectional DC converter uses a buck converter, and its state-space average equation is shown in equation (1); the bidirectional DC converter uses a bidirectional buck-boost converter, and its state-space average equation is shown in equation (2); the VSC inverter uses an LC filter converter, and its state-space average equation is shown in equation (3). ，（1） ，（2） ，（3） In equation (1), For inductor current, Inductor voltage, , They represent , The derivative of Input voltage, For output current, The duty cycle of the buck converter. For inductance, For capacitor; in equation (2), , , For inductance, , For capacitors, , For inductors and resistors, For inductance The current, For inductance The current, For capacitor voltage, For inductance The current, For capacitor voltage, , , , , They are respectively , , , , The derivative of The duty cycle of the bidirectional buck-boost converter. , The voltages at the input and output terminals are; in equation (3), , 、 These are the filter inductors for phases A, B, and C. , 、 For phases A, B, and C, use filter inductors and resistors. , 、 These are the filter capacitors for phases A, B, and C. , 、 These are the filter capacitors and resistors for phases A, B, and C. 、 、 The filter inductor currents for phases A, B, and C are... 、 、 These are the filter capacitor voltages for phases A, B, and C. , , , , , They are respectively 、 、 , 、 、 The derivative of The input DC voltage. , , The output currents for phases A, B, and C are... , , For switching functions , , The function composed of , , ; Step 4: Perform Fourier series decomposition on the variables in the state-space average equation, obtain the exponential Fourier coefficients of each variable, and substitute them into the state-space equation to obtain the harmonic state-space model of various devices. Then, transform the frequency domain expression of each variable into the time domain expression through the Fourier series expansion. Step 5: Represent the internal circuits of various devices using the harmonic state-space models of various devices, and use the substitution theorem to establish the external circuits of various devices to construct the harmonic model of the DC distribution network.

2. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 1, characterized in that, In step 1, the key equipment in the DC distribution network is divided into rectifiers, inverters and DC converters according to their power conversion functions. Among them, the three-phase AC power generated by the AC grid and wind farm is converted into DC power by the rectifier and connected to the distribution network. The photovoltaic power station, energy storage equipment and DC load are connected to the distribution network through the DC converter. The AC load is converted into AC power from the DC power in the distribution network by the inverter for power supply.

3. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 1, characterized in that, In step 2, various types of equipment and the power grid equipment connected to them are disconnected, and the electrical quantities at the disconnection point are represented by voltage and current values. The voltage and current values ​​are the voltage and current values ​​of the DC bus, the distributed energy input equipment, or the voltage and current values ​​provided by the equipment to the load.

4. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 1, characterized in that, In step 4, the exponential Fourier series decomposition expressions for each variable are as follows: ，（4） in, For each and time Related variable functions, The first function of the variable Fourier coefficients in exponential form, The device's angular frequency. For the equipment cycle, Represents the set of integers.

5. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 1, characterized in that, The state-space equation in step 4 is: ，（5） in, Describes the variables in the state-space average equation. for The derivative of This is the coefficient matrix of the state-space equations. The control matrix of the state-space equations, These are the input variables for the state-space equations.

6. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 5, characterized in that, The general form of the harmonic state-space model in step 4 is as follows: ，（6） in, ，（6-1） ，（6-2） ，（6-3） For complex variables, The order of harmonic decomposition is represented by matrix B, which has the same form as matrix A, and column vector U, which has the same form as vector X. for The identity matrix.

7. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 6, characterized in that, In step 4, the harmonic state-space model of the buck converter is shown in equation (7), the harmonic state-space model of the bidirectional buck-boost converter is shown in equation (8), and the harmonic state-space model of the three-term LC filter converter is shown in equation (9): ，（7） ，（8） ，（9） in, for The zero matrix, Let be the Toplitz matrix of the duty cycle of the Buck converter. Let be the Toplitz matrix of the duty cycle of the bidirectional buck-boost converter.

8. The method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 7, characterized in that, In step 5, according to the substitution theorem, a controlled voltage source is used to replace the power grid to provide the grid-side input voltage to the rectifier, inverter, and DC converter, and its value is the voltage value provided by the power grid to the rectifier, inverter, and DC converter; a controlled current source is used to replace the load to provide the load-side input current to the rectifier, inverter, and DC converter, and its value is the current value flowing from the load into the rectifier, inverter, and DC converter; on the grid side, a controlled current source is used to replace the rectifier, inverter, and DC converter, and its current value is the current value flowing from the equipment into the power grid; on the load side, a controlled voltage source is used to replace the rectifier, inverter, and DC converter to provide the input voltage to the load, and its value is the voltage value provided by the rectifier, inverter, and DC converter to the load.

9. A method for harmonic modeling of DC distribution networks based on the substitution theorem according to claim 8, characterized in that, A controlled voltage source replaces the grid and load output voltage to the bidirectional DC converter; a controlled current source replaces the bidirectional DC converter output current to the grid and load.

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