A branch energy balance analysis method for hexagonal modular multilevel AC-AC converter

Abstract

The present invention discloses a branch energy balance analysis method for a hexagonal modular multilevel AC-AC converter, comprising the following steps: Step 1: establishing a branch power equation based on Kirchhoff's law according to the circuit topology; Step 2: dividing the sub-converters A, B, C and U, V, and W from the perspectives of the input phase unit and the output phase unit, respectively, and using the total power, the power deviation between the sub-converters, and the power deviation between two branches within the sub-converter to represent the energy imbalance of the six branches, thereby achieving hierarchical decomposition of the branch power; Step 3: further calculating the hierarchical power equation obtained in Step 2, and establishing a hierarchical model of the branch power through coordinate transformation and positive and negative sequence decomposition of the grid current; Step 4: proposing a Hexverter branch energy control strategy based on the established branch power model. The present invention can reduce the difficulty of controller design, quickly calculate balance parameters, and achieve branch energy balance of the Hexverter.

Description

Technical Field

[0001] The present invention relates to a power supply control method, in particular to a branch energy balance analysis method of a hexagonal modular multi-level AC-AC converter. Background Art

[0002] The Hexagonal Modular Multilevel AC / AC Converter (Hexverter) performs direct three-phase AC / AC conversion. Compared to the Modular Multilevel Matrix Converter (M3C), it not only offers advantages such as modularity and a higher number of levels, but also requires fewer capacitors and inductors. This makes it a smaller and more cost-effective solution suitable for low-frequency operating environments.

[0003] Hexverter consists of 6 identical branches arranged in a hexagonal shape, such as Figure 1a As shown, each branch consists of a current limiting inductor L r It is composed of N H-bridge submodules connected in series. Each submodule consists of four power electronic switching devices IGBT and one capacitor C. The IGBT acts as the bridge arm of the H-bridge, and the capacitor C is connected across the bridge arm. The structure of expanding the Hexverter topology and using it for low-frequency transmission of offshore wind power is as follows. Figure 1b As shown, each of the three-phase input (A, B, C) on the left is connected to two of the three-phase output (U, V, W) on the right through two branches of the Hexverter, achieving direct AC / AC conversion. That is, the industrial frequency 50 Hz grid (input side) and the low-frequency 20 Hz grid (output side) achieve direct AC-AC conversion through the Hexverter.

[0004] Because the submodules and floating capacitors that make up the branches are relatively independent, the Hexverter is susceptible to external factors, leading to additional energy transfer between branches and energy deviations between branches, reducing system reliability. To address this issue, the traditional approach is to inject additional AC components at multiple frequencies into the circulating current and neutral-point voltage to achieve complete control of the energy in each branch. However, in existing methods, the controlled variables (neutral-point voltage or circulating current) always contain components at multiple frequencies simultaneously, making controller design very difficult. Summary of the Invention

[0005] Purpose of the invention: To address the above problems, the present invention proposes a branch energy balance analysis method for a hexagonal modular multi-level AC-AC converter, which can reduce the difficulty of controller design, quickly calculate balance parameters, and achieve branch energy balance of the Hexverter.

[0006] Technical solution: The technical solution adopted by the present invention is a branch energy balance analysis method of a hexagonal modular multi-level AC-AC converter, comprising the following steps:

[0007] Step 1: Based on the circuit topology of the hexagonal modular multi-level AC-AC converter with low-frequency power transmission, a branch power equation is established based on Kirchhoff's law. The branch power equation is:

[0008]

[0009] Where p n is the power of branch n, U1 and U2 represent the phase voltage amplitudes of the power frequency and low frequency sides respectively, ω1 and ω2 represent the angular frequencies of the power frequency and low frequency grids respectively, σ x , σ y They represent the symmetrical phase angles of the three phases at the power frequency and low frequency sides, respectively. I1 and I2 represent the phase current amplitudes at the power frequency and low frequency sides, respectively. Respectively represent the power factor angle of the power frequency and low frequency power grids, n is the branch number, t is the time, V st is the neutral point voltage of the power frequency side relative to the low frequency side, I cir is the circulating current.

[0010] Step 2: Divide every two adjacent branches of the hexagonal modular multilevel AC-AC converter into a group of sub-converters, thereby dividing into sub-converters A, B, C and U, V, W. Then, perform a hierarchical decomposition of the branch power of the hexagonal modular multilevel AC-AC converter to obtain a hierarchical power equation. The decomposition formula of the hierarchical decomposition is:

[0011]

[0012] Where, T p is the hierarchical decomposition matrix of branch power, p0 is the sum of branch power, p xα 、p xβ and p yα 、p yβ Represents the imbalance of power flowing through the sub-converters, where p xα 、p xβ The power of sub-converters A, B, and C is converted by abc / αβ, and p yα 、p yβ The power of sub-converters U, V, and W is converted by abc / αβ, so it represents the imbalance of active power flowing through the three sub-converters, that is, the difference in energy fluctuations between the three sub-converters. d is the power difference between adjacent branches, indicating the power imbalance between adjacent branches, and p1 to p6 are the powers of branches 1 to 6;

[0013] Branch power hierarchical decomposition matrix T p The expression is:

[0014]

[0015] Step 3: Substitute the expression of each power into the hierarchical power equation, and establish a hierarchical model of branch power through coordinate transformation and positive and negative sequence decomposition of the grid current; the model equation of the hierarchical model of branch power is:

[0016]

[0017] Where, I 2pd , I 2pq is the positive sequence active and reactive current amplitude of the low-frequency grid current, I 2nd , I 2nq is the negative sequence active and reactive current amplitude of the low-frequency grid current, I 1nd , I 1nq is the negative sequence active and reactive current amplitude of the power frequency grid current; the transformation matrix T i is a diagonal matrix:

[0018]

[0019] Step 4: Based on the hierarchical model of branch power, a branch energy balance control strategy for the hexagonal modular multilevel AC-AC converter is obtained. Specifically, the strategy includes: first, performing a hierarchical decomposition of the difference between the sum of the squares of the submodule capacitor voltages in each branch and a given value to obtain the branch energy deviation, filtering out the AC component through a low-pass filter, and then generating reference values ​​for the total converter power, the power difference between sub-converters, and the DC component of the power difference between branches within a sub-converter through a proportional-integral controller; then, constructing reference values ​​for the negative-sequence active and reactive current components of the power frequency grid current and the positive- and negative-sequence active and reactive current components of the low-frequency grid current, and constructing the equation using the model equation of the hierarchical model obtained in step 3.

[0020] Beneficial effects: In the existing method, full control of the energy of each branch is achieved by injecting additional AC components of multiple frequencies into the Hexverter circulating current and neutral point voltage. Since the control variable (neutral point voltage or circulating current) always contains components of multiple frequencies at the same time, the controller design is very difficult and the calculation complexity is large. Compared with the existing technology, the balance analysis method proposed in the present invention can reduce the difficulty of controller design. While achieving full control of branch energy, it can quickly calculate the balance parameters and realize the branch energy balance of the Hexverter. The physical concept of the control strategy of this method is clear and definite, and the system control complexity is significantly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1a It is the Hexverter topology;

[0022] Figure 1b This is the structural diagram of Hexverter used for low-frequency power transmission;

[0023] Figure 2 Schematic diagram of two division methods of sub-converters according to the present invention;

[0024] Figure 3 is a schematic diagram of the flow direction of the hierarchical branch power components described in the present invention;

[0025] Figure 4 is the hierarchical power model of the present invention;

[0026] Figure 5 This is a branch energy control block diagram of the present invention;

[0027] Figure 6 is the power difference P0, P in this embodiment xα 、P xβ 、P yα 、P yβ and P d Waveform diagram;

[0028] Figure 7 Detailed waveform diagram of the average voltage of the capacitors in each branch in this embodiment. DETAILED DESCRIPTION

[0029] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0030] The branch energy balance analysis method of the hexagonal modular multi-level AC-AC converter of the present invention comprises the following steps:

[0031] Step 1: According to the circuit topology, establish the branch power equation based on Kirchhoff's law.

[0032] The Hexverter topology is expanded and used for offshore wind power low-frequency transmission. The six branches are named branch n (n = 1, 2 ..., 6) in clockwise order, and the voltage drop of the current-limiting inductor is ignored. u n and i n Indicates the voltage and current of branch n. x and i x (x=A,B,C) represent the phase voltage and phase current on the power frequency side respectively; u y and i y (y=U, V, W) represent the phase voltage and phase current on the low-frequency side respectively.

[0033] The change of branch energy is represented by branch power. Therefore, in order to achieve branch energy stability, it is necessary to first analyze the branch power. The power of branch n is:

[0034] p n =u n i n (1)

[0035] Using Kirchhoff’s voltage and current laws, the branch voltage and current are

[0036]

[0037] Among them, V st is the neutral point voltage of the power frequency side relative to the low frequency side, i BA 、i CB 、i AC 、i UW 、i VU 、i WV They are the phase currents after star-delta transformation on the power frequency side and the frequency division side, I cir is the circulating current.

[0038] In general, when the reactive power of the two grids connected by the Hexverter is unbalanced, it will cause continuous energy transfer between adjacent branches, which will cause the capacitor voltage of the branch submodule to be too high or too low. To solve this problem, the neutral point voltage and circulating current need to satisfy the relationship:

[0039]

[0040] All theoretical and simulation analyses in this paper are carried out on the basis of satisfying formula (4).

[0041] Ideally, the voltages and currents of the two grids connected to the converter are sinusoidal quantities, and their phase voltages and currents can be expressed as:

[0042]

[0043] Where U1 and U2 represent the phase voltage amplitudes at the power frequency and low frequency sides, ω1 and ω2 represent the angular frequencies of the power frequency and low frequency grids, and σ x , σ y They represent the symmetrical phase angles of the three phases at the power frequency and low frequency sides, respectively. I1 and I2 represent the phase current amplitudes at the power frequency and low frequency sides, respectively. Respectively represent the power factor angles of industrial frequency and low frequency power grids.

[0044] Substituting equations (2)-(6) into equation (1), the specific expression of the power of branch n is obtained as shown in equation (7).

[0045]

[0046] Step 2: Divide the sub-converters A, B, C and U, V, W from the perspective of input phase unit and output phase unit, as shown in Figure 2 The energy imbalance of the six branches is represented by the total power, the power deviation between sub-converters, and the power deviation between two branches within a sub-converter, thus achieving hierarchical decomposition of branch power.

[0047] To facilitate branch energy balance analysis, the present invention decomposes the Hexverter into three levels: overall, sub-converter unit, and branch unit, from a global to local approach. Based on this, branch energy stability is decomposed into three dimensions: overall converter energy stability, energy balance between sub-converters, and energy balance between branches within a sub-converter. The degree of imbalance is reflected by the total converter power, the power difference between sub-converters, and the power difference between branches within a sub-converter, respectively.

[0048] The total power of the converter is:

[0049]

[0050] Among them, p0 is the sum of the branch powers, which reflects the magnitude of the overall energy fluctuation of the converter. Its physical meaning is as follows: Figure 3 shown.

[0051] There are two ways to divide the sub-converter: from the perspective of the input phase unit, it is divided into three star-connected sub-converters A, B, and C, which respectively include branches 6 and 1, branches 2 and 3, and branches 4 and 5; from the perspective of the output phase unit, it is divided into three star-connected sub-converters U, V, and W, which respectively include branches 1 and 2, branches 3 and 4, and branches 5 and 6.

[0052] To further simplify the decoupling of sub-converter control and obtain the power difference between sub-converters, Clark transformation is performed on the power of sub-converters A, B, C and U, V, W. The αβ components of the sub-converter power are obtained:

[0053]

[0054] Among them, p A 、p B 、p C are the powers of sub-converters A, B, and C respectively; p U 、p V 、p W are the power of sub-converters U, V, and W respectively. The power of a sub-converter is the sum of the powers of the two branches contained in it. αβ is the Clark transformation matrix:

[0055]

[0056] p xα 、p xβ and p yα 、p yβ are the unbalanced degrees of power flowing through sub-converters A, B, C and U, V, W, respectively, reflecting the energy flow between sub-converters. Figure 3 shown.

[0057] Taking sub-converters U, V, and W as an example, the sum of the power differences between the internal branches of the three sub-converters is:

[0058] p d =p1-p2+p3-p4+p5-p6 (12)

[0059] p d It represents the power imbalance between adjacent branches and reflects the magnitude of energy transfer between adjacent branches in the sub-converter. Its physical meaning is the same as Figure 3 shown.

[0060] Combining equations (8), (9), (10), and (12), we can obtain the matrix of hierarchical decomposition of branch power as follows:

[0061]

[0062] Among them, T p The hierarchical decomposition matrix of branch power is:

[0063]

[0064] Step 3: Perform detailed calculations on the hierarchical power equation obtained in step 2, and establish a hierarchical model of branch power through coordinate transformation and positive and negative sequence decomposition of grid current.

[0065] Step 1 derived the mathematical expression for branch power under ideal conditions. However, in actual operation, energy deviations inevitably exist between branches, which will result in the current of the two connected power grids not being a perfect three-phase positive sequence. To maintain generality, the power frequency and low-frequency three-phase currents are re-expressed as the sum of the fundamental positive and negative sequence components, taking the power frequency side as an example:

[0066]

[0067] Among them, I 1pd , I 1pq is the positive sequence active and reactive current amplitude of the power frequency grid current, I 1nd , I 1nq is the negative sequence active and reactive current amplitude of the power frequency grid current. Transformation matrix T ±dq As shown in formula (16), ω=ω1.

[0068]

[0069] Based on this, we can calculate the p based on the positive and negative sequence dq components of the power frequency grid current xα 、p xβ The specific expression is:

[0070]

[0071] Among them, the DC component of each power term is:

[0072]

[0073] Similarly, the low-frequency grid current is decomposed into positive and negative sequence in the dq coordinate system, and ω = ω2 is taken in formula (14), and p0 and p based on the negative sequence dq component of the low-frequency grid current are obtained. yα 、p yβ 、p d The specific expression is

[0074]

[0075] Its DC component is:

[0076]

[0077] Among them, I 2pd , I 2pq is the positive sequence active and reactive current amplitude of the low-frequency grid current, I 2nd , I 2nq It is the negative sequence active and reactive current amplitude of the low frequency grid current.

[0078] Combining equations (18) and (20), we can get the matrix of the constraint relationship between the current component and the hierarchical power component as follows:

[0079]

[0080] Among them, the transformation matrix T i is a diagonal matrix:

[0081]

[0082] The corresponding hierarchical power model is as follows Figure 4 shown.

[0083] Step 4: Based on the branch power model established in the above steps, the Hexverter branch energy control strategy is proposed as follows: Figure 5As shown in the figure: the overall energy balance of the converter is achieved by constructing the positive-sequence active component of the low-frequency grid current, the energy balance between the sub-converters is achieved by constructing the negative-sequence components of the power frequency and low-frequency grid currents, and the energy balance between the internal branches of the sub-converter is achieved by constructing the negative-sequence reactive component of the low-frequency grid current.

[0084] First, the difference between the sum of the squares of the submodule capacitor voltages in each branch and a given value is hierarchically decomposed to obtain the branch energy deviation. The AC component is filtered out using a low-pass filter. A proportional integral (PI) controller is then used to generate reference values ​​for the total converter power, the power difference between sub-converters, and the DC component of the power difference between branches within a sub-converter:

[0085]

[0086] Among them, k p and k i are the proportional and integral parameters of the PI controller. p is the hierarchical decomposition matrix. c is the DC side capacitor voltage of each submodule in steady state, represents the capacitor voltage in the jth submodule in branch n, j = 1, 2.. N. h(s) is the transfer function of the low-pass filter. From equations (17) and (19), we can see that in addition to the DC component, p0 also contains an AC component with a frequency of 2ω2, p xα 、p xβ 、p yα 、p yβ It also contains AC components with frequencies of ω1, ω2, 2ω1, 2ω2 and ω1+ω2, p d It also contains AC components with frequencies of 2ω2 and ω1+ω2, which need to be filtered out by this filter.

[0087] Finally, the reference values ​​of the negative-sequence active and reactive current components of the power frequency grid current and the reference values ​​of the positive- and negative-sequence active and reactive current components of the low-frequency grid current are constructed according to equations (21) and (22).

[0088] In this example, a Hexverter-based low-frequency transmission model was constructed in Matlab / Simulink to verify the effectiveness of the proposed modeling method and branch energy control strategy. The rated power of the offshore wind farm is set to 100MW, transmitted to the onshore power grid via a 35kV frequency-divided transmission line, and connected to the grid at unity power factor. Considering the highest withstand voltage level of the widely used IGBT modules, the rated voltage of the submodule DC capacitor is set to 3kV. Therefore, each branch requires at least 19 submodules. Considering the dynamic processes and redundancy in the system, the number of submodules in a single branch is set to 24. The main system parameter settings are shown in Table 1.

[0089] During the simulation, the initial capacitor voltage in branch 1 is forced to be 20% higher than that in other branches. This is used as a test scenario to simulate the energy imbalance of branches caused by various factors in actual operation.

[0090] When the branch voltages are not completely equal, power deviations occur between branches, such as Figure 6 P0, P xα 、P xβ 、P yα 、P yβ and P d The control strategy proposed by the present invention realizes the balance and stable control of branch energy, so the power fluctuation will eventually reach a steady-state value. Figure 6 As shown in the figure, in steady state, each power quantity is almost 0. The change of power directly leads to energy transfer between branches, which is manifested as a dynamic change in the average value of the capacitor voltage of each branch. Therefore, corresponding to the change of power, the average value of the capacitor voltage of each branch also tends to be stable. Figure 7 As shown in the figure, although the initial voltages of the branch capacitors are different, they all eventually stabilize around the rated 3kV.

[0091] Table 1 Main parameter settings of the system

[0092]

Claims

1. A branch energy balance analysis method for a hexagonal modular multi-level AC-AC converter, characterized in that: The following steps are involved: Step 1: Based on the circuit topology of the hexagonal modular multi-level AC-AC converter with low-frequency power transmission, a branch power equation is established based on Kirchhoff's law; Step 2: Divide every two adjacent branches of the hexagonal modular multilevel AC-AC converter into a group of sub-converters, thereby dividing the sub-converters into sub-converters A, B, C and U, V, W. Then, perform a hierarchical decomposition of the branch power of the hexagonal modular multilevel AC-AC converter to obtain a hierarchical power equation. Step 3: Substitute the expression of each power into the hierarchical power equation, and establish a hierarchical model of branch power through coordinate transformation and positive and negative sequence decomposition of grid current; Step 4: Based on the hierarchical model of branch power, a branch energy balance control strategy of the hexagonal modular multi-level AC-AC converter is obtained.

2. The branch energy balance analysis method of a hexagonal modular multi-level AC-AC converter according to claim 1, characterized in that: The branch power equation described in step 1 is: Where p n is the power of branch n, U1 and U2 represent the phase voltage amplitudes of the power frequency and low frequency sides respectively, ω1 and ω2 represent the angular frequencies of the power frequency and low frequency grid respectively, σ x , σ y They represent the symmetrical phase angles of the three phases at the power frequency and low frequency sides, respectively. I1 and I2 represent the phase current amplitudes at the power frequency and low frequency sides, respectively. Respectively represent the power factor angle of the power frequency and low frequency power grids, n is the branch number, t is the time, V st is the neutral point voltage of the power frequency side relative to the low frequency side, I cir is the circulating current.

3. The branch energy balance analysis method of a hexagonal modular multi-level AC-AC converter according to claim 1, characterized in that: The branch power of the hexagonal modular multi-level AC-AC converter described in step 2 is decomposed hierarchically, and the decomposition formula is: Where, T p is the hierarchical decomposition matrix of branch power, p0 is the sum of branch power; p xα 、p xβ The power of sub-converters A, B, and C is converted by abc / αβ, and p yα 、p yβ The power of sub-converters U, V, and W is converted by abc / αβ, and p d Represents the power difference between adjacent branches, p1 to p6 are the powers of branches 1 to 6; Branch power hierarchical decomposition matrix T p The expression is:

4. The branch energy balance analysis method of a hexagonal modular multi-level AC-AC converter according to claim 1, characterized in that: The hierarchical model of branch power described in step 3 has the following equation: Where, I 2pd , I 2pq is the positive sequence active and reactive current amplitude of the low-frequency grid current, I 2nd , I 2nq is the negative sequence active and reactive current amplitude of the low-frequency grid current, I 1nd , I 1nq is the amplitude of the negative sequence active and reactive current of the power frequency grid current; p0 is the sum of the branch powers; p xα 、p xβ The power of sub-converters A, B, and C is converted by abc / αβ, and p yα 、p yβ The power of sub-converters U, V, and W is converted by abc / αβ, and p d Represents the power difference between adjacent branches; U1 and U2 represent the phase voltage amplitudes of the power frequency and low frequency sides respectively; I1 and I2 represent the phase current amplitudes of the power frequency and low frequency sides respectively. Respectively represent the power factor angle of the power frequency and low frequency grid; the transformation matrix T i is a diagonal matrix:

5. The branch energy balance analysis method of a hexagonal modular multi-level AC-AC converter according to claim 1, characterized in that: The step 4 includes: first, performing a hierarchical decomposition on the difference between the sum of the squares of the sub-module capacitor voltages in each branch and a given value to obtain a branch energy deviation; filtering out the AC component in the branch energy deviation through a low-pass filter; and then generating reference values ​​of the total power of the converter, the power difference between the sub-converters, and the DC component of the power difference between the branches within the sub-converter through a proportional-integral controller; then constructing reference values ​​of the negative-sequence active and reactive current components of the power frequency grid current and reference values ​​of the positive and negative-sequence active and reactive current components of the low-frequency grid current, and the construction equation adopts the model equation of the hierarchical model obtained in step 3.

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