CN101594045A - A Specific Harmonic Elimination Method for Modular Multilevel Converter - Google Patents

Abstract

The invention proposes a specific harmonic elimination method for a novel modular multilevel converter. The invention applies the specific harmonic elimination method to the three-phase modular multi-level converter, and through reasonable selection of the switching angle of the sub-modules, improves the harmonic characteristics of the output voltage, improves the waveform quality, and achieves smaller harmonic distortion of the output voltage Rate. At the same time, for engineering applications, a narrow pulse optimization strategy is proposed to improve its engineering applicability.

Description

A Specific Harmonic Elimination Method for Modular Multilevel Converter

technical field

The invention belongs to the technical fields of flexible power transmission and distribution of power systems, power electronics, electric drive, motor drive and user electric power, and specifically relates to the field of specific harmonic elimination of a modular multilevel converter.

Background technique

Multilevel converter is a popular high-power electronic converter in recent years, and has been successfully applied in many industrial fields, such as static var compensator, electric drive, FACTS, HVDC transmission and active filter etc. Traditional multilevel converters have many different structures, and the common ones are diode clamped (NPC), flying capacitor (FLC) and cascaded H-bridge (CHC). As a new multilevel converter, Modular Multilevel Converter (MMC) has the advantages of low switching frequency, low switching loss and low high frequency noise of traditional multilevel converters. , The advantage of small voltage change rate. At the same time, compared with the NPC type and FLC type multilevel converter, the degree of modularization is high, the number of switching devices will not increase non-linearly with the increase of the number of levels, and the structural design is simple; compared with the CHC type, the power can be Bi-directional flow, switching devices are also doubled.

There are many modulation strategies that can be used in traditional multilevel converters, such as sinusoidal pulse width modulation (Pulse Width Modulation, PWM for short), space vector pulse width modulation (SVPWM) and specific harmonic elimination pulse width modulation (SHEPWM). And SHEPWM is a more popular one, it can eliminate the specified harmonics and reduce the distortion rate of voltage and current waveforms.

Contents of the invention

In order to make the waveform distortion of MMC output voltage smaller and the waveform quality better, it is necessary to study the method of applying SHEPWM to MMC.

Aiming at the MMC topology of the modular multilevel converter, the present invention proposes a specific harmonic elimination method suitable for the topology. The method can optimize the harmonic characteristics of the MMC output voltage at a lower switching frequency and improve the waveform quality.

In the modular multilevel converter MMC, the upper and lower half bridge arms of each phase are formed by cascading several independent submodules (Submodules), and each submodule can independently control the disconnection. Taking advantage of this advantage, the switching angle of each sub-module is reasonably selected to eliminate specific harmonics in the output voltage, reduce waveform distortion, and improve waveform quality. The specific method is as follows:

By setting a specific harmonic elimination angle in the output ladder wave voltage of the bridge arm, harmonics of a specific order can be eliminated. Since the MMC output voltage has 1/4 cycle symmetry, only the switching angle in 1/4 cycle needs to be considered for solution. If each half-bridge arm uses 2N sub-modules to form the required multi-level ladder wave output voltage, only N sub-modules change the output state, that is to say, only N switching angles within 1/4 cycle need to be solved That's it.

In the three-phase MMC, after the specific harmonic elimination angle of a certain phase is determined, the other two phases are obtained by staggering each other by 120°, so that the output line voltage does not contain triple frequency harmonics, so that more higher harmonics can be eliminated. Specific steps are as follows:

(1) The Fourier series expansion expression of the three-phase MMC output voltage is obtained by theoretical analysis, and the expression includes the switching angle of N submodules;

(2) Let the fundamental wave component in the Fourier series expansion expression be equal to the expected value, and the N-1 specific harmonic components be equal to 0, thereby obtaining N nonlinear transcendental equations;

(3) Determine the fundamental expected value of the MMC output voltage, and calculate the N switching angles corresponding to the half-bridge arms at this time;

(4) With the switching angle in the step (3) as the initial value, solve the nonlinear transcendental equation in the step (2), obtain the initial value of the narrow pulse optimization model;

(5) Perform narrow pulse optimization on the specific harmonic elimination angle obtained in step (4), and finally obtain N switch angles that can be used in engineering.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings.

Fig. 1 is the circuit diagram according to three-phase MMC of the present invention;

Fig. 2 is according to three-phase MMC single bridge arm output voltage waveform schematic diagram of the present invention;

Fig. 3 is according to the calculation method schematic diagram of specific harmonic elimination angle initial value of the present invention;

FIG. 4 is a spectrum diagram of the MMC output voltage when N=5 according to the present invention.

Detailed ways

The following are preferred examples of the present invention, and the technical solutions realized by the present invention will be further described below in conjunction with the accompanying drawings.

As shown in FIG. 1 is a schematic circuit diagram of a three-phase MMC according to the present invention. The modular multilevel converter MMC is composed of six half-bridge arms of three phases, and each half-bridge arm of a phase is formed by cascading 2N sub-modules. The output voltage of each phase is:

v _an ＝N·V _dc -v _au or (1)

v _an ＝-N·V _dc +v _al

The specific harmonic elimination method eliminates harmonics of a specific order by setting a gap at a specific position where the bridge arm outputs a ladder wave voltage. These positions are commonly referred to as specific harmonic elimination angles, and these angles are generally determined by solving nonlinear transcendental equations, usually by numerical methods. Since the MMC output voltage has 1/4 cycle symmetry, only the switching angle in 1/4 cycle needs to be considered for solution. If each half-bridge arm uses 2N sub-modules to form the required multi-level ladder wave output voltage, only N sub-modules change the output state, that is to say, only N switching angles within 1/4 cycle need to be solved That's it.

The output voltage waveform of the modular multilevel converter MMC is shown in Figure 2. The waveform in Figure 2 is expanded into the form of formula (2) by Fourier series, and the fundamental component is equal to the expected value of the fundamental, and the harmonics to be eliminated are equal to 0, thus forming N independent nonlinear equations. Since the switching angles of the bridge arms of the three-phase MMC are staggered by 120°, the triple frequency harmonics in the line voltage cancel each other out.

$\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,3,5</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; dc</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; n\&omega;t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, V _dc is the sub-module capacitor voltage; N is the number of specific harmonic elimination angles in 1/4 cycle; θ _k is the kth specific harmonic elimination angle, and k=1, 2, ..., N; ω is the base frequency angular velocity.

Taking the elimination of N-1 lower harmonics as an example, the highest harmonic elimination can reach 3N-2 harmonics. From the Fourier series, the nonlinear transcendental equations for solving the switching angle can be written as follows:

$\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; dc</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}$

cos(5θ ₁ )+cos(5θ ₂ )+…+cos(5θ _N )＝0

cos(7θ ₁ )+cos(7θ ₂ )+…+cos(7θ _N )＝0 (3)

.

.

.

cos(hθ ₁ )+cos(hθ ₂ )+…+cos(hθ _N )＝0

Among them, V _dc is the sub-module capacitor voltage; V _ref is the expected value of the fundamental wave of the MMC output voltage; θ _k is the kth specific harmonic elimination angle, and k=1, 2, ..., N; h is the specified harmonic to be eliminated times, and h=1, 5, 7, 11, 13, ..., 3N-2.

For three-phase MMC, there are N unknowns in the equations that constitute the switching angle. After determining the expected value of the fundamental wave, you can choose to eliminate N-1 low-order harmonic components. For the case where there are 10 sub-modules in each half-bridge arm, the number of switching angles is 5, and the highest order of eliminated harmonics is 3N-2=13.

So the problem boils down to the solution of five nonlinear transcendental equations. The initial value is chosen arbitrarily, and the iterative calculation shows that the algorithm is not easy to converge. An appropriate initial value must be selected. According to the expected value of the MMC fundamental wave, the reference wave voltage u _ref (ωt) as shown in Figure 3 can be determined. When the output level v(t) of the modular multilevel converter jumps from k to k+1, the areas of shadows 1 and 2 in Figure 3 are equal, and the k+1th specific harmonic elimination can be obtained The initial value of the angle θ _k+1 . The initial value of the iteration can be obtained by performing similar calculations for each level transition moment. Examples prove that the algorithm converges quickly with this initial value for iterative calculation.

Considering that the switching devices in MMC have a certain turn-on and turn-off time, it takes a certain time to turn on and turn off, and the loss of the turn-on and turn-off process will cause the switching device to heat up. When the heat accumulation effect reaches a certain level It will cause the switching device to burn out. Therefore, the minimum pulse width of the MMC, that is, the narrow pulse, is determined according to the turn-on and turn-off times of the switching device. And the following optimization methods are proposed for narrow pulses:

(1) Calculate the narrow pulse = (turn-on time + turn-off time) × 360°/20ms;

(2) If the width of the narrow pulse is not greater than 1/2 of the minimum pulse width, omit the switching angle that constitutes the narrow pulse;

(3) If the width of the narrow pulse is greater than 1/2 of the minimum pulse width, then stretch the narrow pulse to the minimum pulse width.

The switching angle obtained through narrow pulse optimization can be directly used in engineering, and can eliminate harmonics within 3N-2 times and limit them to a very low level.

It can be seen from the spectrum diagram of MMC output voltage when N=5 in Fig. 4 that in the case of 2N=10, the harmonic content of the 13th order and below is very small.

The principle of the invention is simple and easy to implement. When the switching frequency is 100 Hz, the harmonic characteristics of the MMC output voltage are well optimized, and the total harmonic distortion rate of the line voltage is reduced.

The present invention has been described according to preferred examples, it should be understood that the above-mentioned embodiments do not limit the present invention in any form, and all technical solutions obtained in the form of equivalent replacement or equivalent transformation all fall within the protection scope of the present invention.

Claims (3)

1. A specific harmonic elimination method for a three-phase modular multilevel converter, which is characterized in that the method eliminates harmonics of a specific order by setting a specific harmonic elimination angle in the output ladder wave voltage of the bridge arm. The voltage has 1/4 cycle symmetry, only need to consider the switching angle in 1/4 cycle, when there are 2N sub-modules in each half-bridge arm of each phase, only N sub-modules act in 1/4 cycle, that is to say, 1 There are only N switching angles in the /4 cycle, eliminating N-1 specific harmonics except triple frequency harmonics, where N is a natural number; In the three-phase modular multilevel converter, after the specific harmonic elimination angle of a certain phase is determined, the specific harmonic elimination angles of the other two phases are obtained by interchanging 120°, so that the output line voltage does not contain triple frequency harmonics , so that more higher harmonics can be eliminated, the specific steps are as follows: (1) The Fourier series expansion expression of the output voltage of the three-phase modular multilevel converter MMC is obtained by theoretical analysis, and the expression includes the switching angles of N sub-modules: $\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,3,5</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; dc</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; n\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; n\&omega;t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}$ Among them, V _dc is the sub-module capacitor voltage; N is the number of specific harmonic elimination angles in 1/4 cycle; θ _k is the kth specific harmonic elimination angle, and k=1, 2, ..., N; ω is the base frequency angular velocity; (2) Let the fundamental wave component in the Fourier series expansion expression be equal to the fundamental wave expected value, and the N-1 specific harmonic components be equal to 0, thus obtaining N nonlinear transcendental equations: $\frac{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; dc</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ref</span>}}$ cos(5θ ₁ )+cos(5θ ₂ )+…+cos(5θ _N )＝0 cos(7θ ₁ )+cos(7θ ₂ )+…+cos(7θ _N )＝0                                                       cos(hθ ₁ )+cos(hθ ₂ )+…+cos(hθ _N )＝0 Among them, V _dc is the sub-module capacitor voltage; V _ref is the fundamental expected value of the output voltage of the modular multilevel converter MMC; θ _k is the kth specific harmonic elimination angle, and k=1, 2, ..., N ; h is the specified harmonic order to be eliminated; It is worth noting that the N-1 specific harmonics that need to be eliminated can be 5, 7, 11, 13, 17, ..., 3N-2, ... sub-harmonics, that is, the value of h can be one of the above harmonics of N-1; (3) Determine the fundamental expected value of the output voltage of the modular multilevel converter MMC, and calculate the N switching angles corresponding to the half-bridge arm at this time; (4) With the switching angle in the step (3) as the initial value, solve the nonlinear transcendental equation in the step (2), obtain the initial value of the narrow pulse optimization model; (5) Perform narrow pulse optimization on the specific harmonic elimination angle obtained in step (4), and finally obtain N switch angles that can be used in engineering. 2. The method according to claim 1, the following further optimization method is proposed for the narrow pulse in the step (4): (1) Calculate the narrow pulse = (turn-on time + turn-off time) × 360°/20ms; (2) If the width of the narrow pulse is not greater than 1/2 of the minimum pulse width, omit the switching angle that constitutes the narrow pulse; (3) If the width of the narrow pulse is greater than 1/2 of the minimum pulse width, then stretch the narrow pulse to the minimum pulse width. 3. The method according to claim 1-2, expanding the ladder wave voltage output by the bridge arm with Fourier series, and making the fundamental wave component equal to the fundamental wave expected value, and the harmonic component to be eliminated is equal to 0, thus forming N independent nonlinear equations.

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