Harmonic injection parameter determination method for half-bridge MMC capacitor voltage fluctuation suppression

Abstract

The invention discloses a hybrid harmonic injection parameter determination method suitable for capacitor voltage fluctuation suppression of a half-bridge modular multilevel converter (MMC), and belongs to the technical field of power systems and power electronics. The method comprises the following steps: firstly, constructing a time domain expression of a bridge arm current and a bridge arm switching function of the half-bridge MMC, and calculating a fundamental component amplitude and a double frequency component amplitude of an average capacitor voltage of a sub-module; secondly, setting the amplitude and phase of the third harmonic voltage, improving the value range of the modulation ratio, and calculating the optimal value of the modulation ratio; and finally, optimizing the amplitude and the phase of the double-frequency circulating current by adopting a particle swarm algorithm. The invention provides a novel and simple parameter determination method for hybrid harmonic injection.

Description

Technical Field

[0001] This invention relates to the fields of power system technology and power electronics technology, specifically to a method for determining hybrid harmonic injection parameters suitable for voltage fluctuation suppression in half-bridge MMC capacitors. Background Technology

[0002] Modular multilevel converters (MMCs) are widely used in high-voltage direct current (HVDC) transmission systems due to their advantages such as high modularity, strong scalability, low harmonic content, low switching frequency, and four-quadrant operation. Currently, several MMC-HVDC projects based on half-bridge submodules have been put into operation globally for renewable energy grid connection. However, in high-voltage, high-capacity HVDC projects, the large number of power devices and distributed capacitors within the MMC leads to significant issues related to weight, size, and cost.

[0003] Since the sub-modules inside the MMC are in a suspended state, the sub-module capacitor voltage will inevitably fluctuate to some extent. Excessive capacitor voltage fluctuation will lead to increased stress on power devices, increased interphase circulating current, and increased harmonics in the output voltage and current. Increasing the capacitance value of the sub-module capacitor can reduce the voltage fluctuation. However, currently, the sub-module capacitor accounts for more than half of the volume and weight of the MMC converter valve, and its manufacturing cost accounts for more than one-third. In addition, the increased interphase circulating current increases the effective value of the bridge arm current, resulting in higher converter losses, while the capacitor voltage fluctuation raises the peak value of the capacitor voltage, which is detrimental to the stable operation of the MMC. Therefore, it is necessary to study methods to suppress the voltage fluctuation of the sub-module capacitor to reduce capacitor requirements and achieve a lightweight MMC. Currently, various capacitor voltage fluctuation suppression strategies have been proposed, among which the control strategy based on harmonic hybrid injection has the most advantageous effect. However, since harmonic hybrid injection involves multiple parameters that need to be designed, and the strong coupling characteristics between the parameters make optimization design difficult. Therefore, it is necessary to propose a hybrid harmonic injection parameter determination method suitable for suppressing capacitor voltage fluctuation in half-bridge MMCs to solve the parameter design problem. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining hybrid harmonic injection parameters suitable for suppressing voltage fluctuations in half-bridge MMC capacitors, so as to reduce the voltage fluctuation amplitude of capacitors as much as possible while reducing the complexity of parameter design, thereby achieving lightweight design of submodule capacitors.

[0005] The above-mentioned objectives of the present invention can be achieved through the following technical solutions:

[0006] A method for determining harmonic injection parameters to suppress voltage fluctuations in a half-bridge MMC capacitor, wherein harmonic injection refers to injecting a second-harmonic circulating current into the bridge arm of the half-bridge MMC and injecting a third harmonic voltage into the voltage modulation wave; the method includes the following:

[0007] Construct time-domain expressions for the arm current and arm switching function of a half-bridge MMC, and calculate the fundamental frequency component amplitude and second harmonic component amplitude of the average capacitor voltage of the submodule.

[0008] The amplitude U3 of the third harmonic voltage is set to mU. dc / 12, Phase To set the value to 0, the range of values ​​for the modulation ratio m is increased, where m is the modulation ratio after the third harmonic voltage is injected into the half-bridge MMC, U dc Here is the DC-side voltage of the half-bridge MMC; the optimal value for the modulation ratio m is set to the minimum of 1.155m0 and m1, where m0 is the modulation ratio of the half-bridge MMC without third harmonic voltage injection, and the formula for calculating m1 is as follows:

[0009]

[0010] In the formula, k2 = 3I2 / I dc I dc This refers to the DC-side current of the half-bridge MMC. The power factor angle for a half-bridge MMC; The phase of the second harmonic circulation;

[0011] The objective function is set as the sum of the amplitudes of the fundamental frequency component and the second harmonic component. A particle swarm optimization method for optimizing the second harmonic circulation injection parameters is employed to solve for the second harmonic circulation injection parameters k2 and k2, which minimize the objective function.

[0012] Preferably, the average capacitor voltage of the submodule is the average value of the capacitor voltages of all half-bridge submodules in the selected bridge arm, and the calculation method of the fundamental frequency component amplitude and the second harmonic component amplitude includes the following steps:

[0013] Step A1: Multiply the arm current by the time-domain expression of the arm switching function to obtain the first value;

[0014] Step A2: Perform indefinite integration on the first value to obtain the second value;

[0015] Step A3: Remove the DC component that does not change with time from the second value to obtain the third value;

[0016] Step A4: Divide the third value by the capacitance value of the half-bridge MMC submodule capacitor to obtain the fourth value;

[0017] Step A5: Separate all components with the fundamental frequency in the fourth value, calculate the amplitude of these components, and obtain the amplitude of the fundamental frequency component;

[0018] Step A6: Separate all components with a frequency of second harmonic from the fourth value, calculate the amplitude of these components, and obtain the amplitude of the second harmonic component.

[0019] Preferably, the second-harmonic circulation injection parameter optimization method based on particle swarm optimization includes the following steps:

[0020] Step B1: Initialize particle swarm parameters, including particle swarm size, particle dimension, maximum number of iterations, inertia weight, learning factor, and velocity range;

[0021] Step B2: Input the system parameters of the half-bridge MMC, including the number of bridge arm sub-modules, sub-module capacitance value, bridge arm reactance value, initial modulation ratio, power factor angle, and system angular frequency;

[0022] Step B3: Settings The range of values ​​for is [-π, π], and the range of values ​​for k2 is set to [0, k]. 2,max ], where k 2,max The expression is as follows:

[0023]

[0024] In the formula, ω is the angular frequency of the AC-side grid voltage of the half-bridge MMC; C sm The capacitance value of the submodule capacitor in a half-bridge MMC; L arm N represents the inductance value of the bridge arm in a half-bridge MMC; N is the number of bridge arm sub-modules.

[0025] Step B4: Calculate the sum of the amplitudes of the fundamental frequency component and the second harmonic component, and set it as the objective function of the particle swarm algorithm;

[0026] Step B5: Perform iterative optimization using the particle swarm optimization algorithm, and output the optimal solution of the objective function and the corresponding k2 and k2.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] This invention aims to suppress the sum of the fundamental and second harmonic components of the capacitor voltage fluctuation in the submodule, prioritizing the determination of the third harmonic voltage injection amplitude k3 and phase. Based on this, a method for determining the modulation ratio m was established, and the second harmonic circulating current injection parameters were optimized using a particle swarm optimization algorithm, thereby reducing the voltage fluctuation of the submodule capacitor. This method can significantly reduce the voltage fluctuation of the submodule capacitor while reducing optimization complexity, thus achieving lightweighting of the submodule capacitor. This has important guiding significance for reducing the size, weight, and cost of the MMC engineering platform. Attached Figure Description

[0029] The invention will be further described with reference to the following figures:

[0030] Figure 1 This is a flowchart of the method for determining harmonic injection parameters to suppress voltage fluctuations in a half-bridge MMC capacitor proposed in this invention;

[0031] Figure 2 This is a schematic diagram of the topology of the half-bridge MMC proposed in Embodiment 1 of the present invention;

[0032] Figure 3 The flowchart for optimizing the second harmonic circulation injection parameters based on the particle swarm optimization algorithm proposed in Embodiment 1 of this invention is shown below.

[0033] Figure 4 This is a block diagram of the receiving-end half-bridge MMC control system with harmonic hybrid injection proposed in Embodiment 1 of the present invention;

[0034] Figure 5 This is the result of the optimization of the second harmonic circulation injection parameters based on the particle swarm optimization algorithm proposed in Embodiment 1 of the present invention;

[0035] Figure 6 The waveforms of the sending-end MMC without the strategy, the injected third harmonic voltage, and the submodule capacitor voltage fluctuation after adopting the present invention are shown in Embodiment 1 of the present invention.

[0036] Figure 7 The waveforms of the submodule capacitor voltage fluctuations are shown in Embodiment 1 of the present invention, in the order of no strategy, second harmonic circulating current suppression, and submodule capacitor voltage fluctuations after adopting the present invention. Detailed Implementation

[0037] To facilitate a better understanding of the present invention by those skilled in the art, the technical solutions of the present invention will be described in more detail, clearly, and accurately below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] Example 1:

[0039] This invention integrates second harmonic circulating current and third harmonic voltage injection, and proposes a hybrid harmonic injection parameter determination method suitable for suppressing voltage fluctuations in half-bridge MMC capacitors. By conducting theoretical analysis and parameter optimization design of the injected harmonics, the voltage fluctuations of submodule capacitors are significantly reduced while reducing the complexity of the optimization process.

[0040] Please see Figure 2 The topology of a half-bridge MMC is as follows: Figure 1 As shown, it consists of a three-phase, six-arm bridge. Each arm has N half-bridge submodules and one smoothing reactor L. arm They are connected in series. Each bridge arm has N half-bridge sub-modules and a smoothing reactor L. arm It is connected in series. U dc with I dc These represent the DC-side voltage and current, respectively. j with i j These refer to the AC side voltage and current, respectively. ju with i jd Let j represent the current in the upper arm and the current in the lower arm, respectively, where j = a, b, c. sm This refers to the capacitance value of the submodule.

[0041] The flowchart of the method for determining hybrid harmonic injection parameters applicable to voltage fluctuation suppression of half-bridge MMC capacitors proposed in this invention is as follows: Figure 1 As shown, it includes the following steps:

[0042] First, construct the time-domain expressions for the arm current and arm switching function of the half-bridge MMC, and calculate the fundamental frequency component amplitude and second harmonic component amplitude of the average capacitor voltage of the submodule.

[0043] Secondly, the amplitude U3 of the third harmonic voltage is set to mU. dc / 12, Phase To set the value to 0, the range of values ​​for the modulation ratio m is increased, where m is the modulation ratio after the third harmonic voltage is injected into the half-bridge MMC, U dc This represents the DC-side voltage of the half-bridge MMC. The optimal value for the modulation ratio m is set to the minimum of 1.155m0 and m1, where m0 is the modulation ratio of the half-bridge MMC without third harmonic voltage injection, and m1 is calculated using the following formula:

[0044]

[0045] Where, k2 = 3I2 / I dc I dc This refers to the DC-side current of the half-bridge MMC. The power factor angle for a half-bridge MMC. This represents the phase of the second harmonic circulation.

[0046] Finally, the sum of the fundamental frequency component amplitude and the second harmonic component amplitude is set as the objective function. A second harmonic circulation injection parameter optimization method based on particle swarm optimization is used to solve for the second harmonic circulation injection parameters k2 and k2, which minimize the objective function.

[0047] In the above steps, it is necessary to analyze the frequency components of the arm current and arm voltage. Taking the upper arm of phase A of a half-bridge MMC as an example, the expressions for its arm current and arm voltage are as follows:

[0048]

[0049] Where k3 = 2U3 / U dc .

[0050] The switching function of the upper bridge arm of phase A, obtained from the bridge arm voltage, is as follows:

[0051]

[0052] The average capacitor voltage of a submodule is the average value of the capacitor voltages of all half-bridge submodules in a selected bridge arm. The calculation method for the amplitude of the fundamental frequency component and the amplitude of the second harmonic component includes the following steps:

[0053] Step A1: Multiply the arm current by the time-domain expression of the arm switching function to obtain the first value;

[0054] Step A2: Perform indefinite integration on the first value to obtain the second value;

[0055] Step A3: Remove the DC component that does not change with time from the second value to obtain the third value;

[0056] Step A4: Divide the third value by the capacitance value of the half-bridge MMC submodule capacitor to obtain the fourth value;

[0057] Step A5: Separate all components with the fundamental frequency in the fourth value, calculate the amplitude of these components, and obtain the amplitude of the fundamental frequency component;

[0058] Step A6: Separate all components with a frequency of second harmonic from the fourth value, calculate the amplitude of these components, and obtain the amplitude of the second harmonic component.

[0059] Assuming the submodule capacitor voltages are approximately balanced, the average capacitor voltage u of all submodules in the upper arm of phase A is... au,ave It can be represented as:

[0060]

[0061] Among them, u au,α For u au,aveThe expression for the αth harmonic component is as follows:

[0062]

[0063] Injecting the third harmonic voltage with an amplitude of mU dc Substituting / 6 and phase 0 into the submodule's average capacitor voltage u au,ave From the expression, we can obtain u au,ave The fundamental frequency component amplitude U au,1 With the amplitude of the second harmonic component U au,2 They are as follows:

[0064]

[0065] The flowchart for optimizing second-harmonic circulation injection parameters based on particle swarm optimization is as follows: Figure 3 As shown, it includes the following steps:

[0066] Step B1: Initialize particle swarm parameters: particle swarm size, particle dimension, maximum number of iterations, inertia weight, learning factor, velocity range;

[0067] Step B2: Input the system parameters of the half-bridge MMC: number of bridge arm sub-modules, sub-module capacitance value, bridge arm reactance value, initial modulation ratio, power factor angle, and system angular frequency;

[0068] Step B3: Settings The range of values ​​for is [-π, π], and the range of values ​​for k2 is set to [0, k]. 2,max ], where k 2,max The expression is:

[0069]

[0070] Where ω is the angular frequency of the AC-side grid voltage of the half-bridge MMC, and C sm L is the capacitance value of the submodule capacitor in a half-bridge MMC. arm This represents the bridge arm inductance value of a half-bridge MMC.

[0071] Step B4: Calculate the sum U of the fundamental frequency component amplitude and the second harmonic component amplitude. au,1 +U au,2 Set it as the objective function of the particle swarm algorithm;

[0072] Step B5: Perform iterative optimization using the particle swarm optimization algorithm, and output the optimal solution of the objective function and the corresponding k2 and k2.

[0073] This invention is applied to a receiving-end half-bridge MMC of a high-voltage direct current transmission system, wherein the AC side voltage is 230kV; the initial modulation ratio m0 is 0.9, the transmission power is 550MW, the rectifier side power factor angle is 0°, the DC voltage is 400kV; the bridge arm inductance is set to 66.7mH, the number of sub-modules N on each bridge arm is 200, the capacitance of each sub-module is 9mF, the rated voltage of each sub-module is 2kV, and the system angular frequency is 100π. Figure 4 The control block diagram of the receiver-end half-bridge MMC with harmonic hybrid injection is shown. The amplitude of the second harmonic circulating current reference value, I2 = k2I, is determined based on the optimization results of the particle swarm optimization algorithm. dc / 3 and phase And through decoupling control, a voltage modulation signal u2 is generated, and simultaneously according to the set U3 and The third harmonic voltage modulation signal u3 is obtained. Finally, u2 and u3 are superimposed on the bridge arm voltage modulation signal obtained by conventional dual closed-loop control for control, thereby suppressing the voltage fluctuation of the capacitor in the half-bridge MMC submodule.

[0074] Figure 5 The results of parameter optimization for second-harmonic circulation injection based on particle swarm optimization (PSO) algorithm are shown. The particle swarm size is set to 5, and the particle dimension is 2 (i.e., k2 and k2). Two variables), the maximum number of iterations is set to 30, and the objective function is the sum of the amplitude of the fundamental frequency component and the amplitude of the second harmonic component (i.e., U). au,1 +U au,2 The velocity range is [-2, 2], the learning factor is 2, and the inertia weight decreases from 0.8 to 0.2 with the number of iterations. The final optimal solution is: k2 = 0.68 and

[0075] Figure 6 The waveforms are shown in three stages: the MMC at the sending end without the strategy, the injected third harmonic voltage, and the submodule capacitor voltage fluctuation after adopting the present invention.

[0076] Phase 1: 1.2-1.4s, without any circulating control strategy or harmonic injection strategy.

[0077] Phase 2: 1.4-2.0s, inject the third harmonic voltage, where k3 = 1.04 / 6 = 0.173. And increase the modulation ratio to 0.9 × 1.155 = 1.04.

[0078] Phase 3: 2.0-2.6s, based on the third harmonic voltage injection, the second harmonic circulating current is controlled with parameter k2 = 0.68. Note that the proposed control strategy is implemented in stage 3. It can be seen that in stage 2, after the third harmonic voltage injection, the voltage fluctuation of the submodule capacitor slightly decreased, with its peak-to-peak value dropping from 340V to 290V. After the proposed control strategy is implemented in stage 3, the voltage fluctuation of the submodule capacitor is significantly suppressed, with its peak-to-peak value decreasing to 130V. In other words, the voltage fluctuation is reduced by 61.7%, significantly reducing the voltage fluctuation of the submodule capacitor.

[0079] Figure 7 The waveforms of the submodule capacitor voltage fluctuations after the MMC at the sending end were obtained without the strategy, after second harmonic circulating current suppression, and after the application of this invention. These waveforms also include three stages, with stages 1 and 3... Figure 5 Stages 1 and 3 are the same. In stage 2 (1.4-2.0s), circulating current suppression is implemented. It can be seen that in stage 2, the voltage fluctuation of the submodule capacitor is also reduced, with its peak-to-peak value decreasing from 340V to 260V. It is noteworthy that although the second harmonic circulating current is completely suppressed, the voltage fluctuation of the submodule capacitor is still greater than that under the proposed control strategy.

[0080] Through the detailed description of the above embodiments, those skilled in the art can clearly understand that the present invention can be implemented using either a pure software solution or by combining a hardware platform with supporting software. Based on this technical feature, the core solution of the present invention can be presented in the form of a computer program product. This program product can be stored on various non-volatile storage media (including but not limited to optical discs, solid-state storage devices, and portable hard drives), and its included programming instructions can drive electronic devices with data processing capabilities (including personal terminals, cloud servers, and IoT devices) to accurately execute the technical processes defined in the various embodiments of the present invention. This flexibility of implementation ensures the adaptability and scalability of the technical solution in different application scenarios, while providing a standardized interface for subsequent functional expansion and maintenance.

Claims

1. A method for determining harmonic injection parameters to suppress voltage fluctuations in a half-bridge MMC capacitor, characterized in that, The harmonic injection refers to injecting a second-harmonic circulating current into the bridge arm of a half-bridge MMC and injecting a third harmonic voltage into the voltage modulation waveform; the method includes the following: Construct time-domain expressions for the arm current and arm switching function of a half-bridge MMC, and calculate the fundamental frequency component amplitude and second harmonic component amplitude of the average capacitor voltage of the submodule. The amplitude U3 of the third harmonic voltage is set to mU dc / 12, Phase To set the value to 0, the range of values ​​for the modulation ratio m is increased, where m is the modulation ratio after the third harmonic voltage is injected into the half-bridge MMC, U dc This is the DC-side voltage of the half-bridge MMC; The objective function is set as the sum of the amplitudes of the fundamental frequency component and the second harmonic component. A particle swarm optimization method for optimizing the second harmonic circulation injection parameters is employed to solve for the second harmonic circulation injection parameters k2 and k2, which minimize the objective function.

2. The method according to claim 1, characterized in that, The average capacitor voltage of the submodule is the average value of the capacitor voltages of all half-bridge submodules in the selected bridge arm. The calculation method for the fundamental frequency component amplitude and the second harmonic component amplitude includes the following steps: Step A1: Multiply the arm current by the time-domain expression of the arm switching function to obtain the first value; Step A2: Perform indefinite integration on the first value to obtain the second value; Step A3: Remove the DC component that does not change with time from the second value to obtain the third value; Step A4: Divide the third value by the capacitance value of the half-bridge MMC submodule capacitor to obtain the fourth value; Step A5: Separate all components with the fundamental frequency in the fourth value, calculate the amplitude of these components, and obtain the amplitude of the fundamental frequency component; Step A6: Separate all components with a frequency of second harmonic from the fourth value, calculate the amplitude of these components, and obtain the amplitude of the second harmonic component.

3. The method according to claim 1, characterized in that, The optimal value for the modulation ratio m is set to the minimum of 1.155m0 and m1, where m0 is the modulation ratio of the half-bridge MMC without third harmonic voltage injection, and m1 is calculated as follows: In the formula, k2 = 3I2 / I dc I dc This refers to the DC-side current of the half-bridge MMC. The power factor angle for a half-bridge MMC; This represents the phase of the second harmonic circulation.

4. The method according to claim 1, characterized in that, The second-harmonic circulation injection parameter optimization method based on particle swarm optimization includes the following steps: Step B1: Initialize particle swarm parameters, including particle swarm size, particle dimension, maximum number of iterations, inertia weight, learning factor, and velocity range; Step B2: Input the system parameters of the half-bridge MMC, including the number of bridge arm sub-modules, sub-module capacitance value, bridge arm reactance value, initial modulation ratio, power factor angle, and system angular frequency; Step B3: Settings The range of values ​​for is [-π, π], and the range of values ​​for k2 is set to [0, k]. 2,max ] Step B4: Calculate the sum of the amplitudes of the fundamental frequency component and the second harmonic component, and set it as the objective function of the particle swarm algorithm; Step B5: Perform iterative optimization using the particle swarm optimization algorithm, and output the optimal solution of the objective function and the corresponding k2 and k2.

5. The method according to claim 1, characterized in that, k in step B3 2,max The expression is as follows: In the formula, ω is the angular frequency of the AC-side grid voltage of the half-bridge MMC; C sm The capacitance value of the submodule capacitor in a half-bridge MMC; L arm is the inductance value of the bridge arm of the half-bridge MMC; N is the number of bridge arm sub-modules.

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