CN112688543A - Method for eliminating specific harmonic of three-level NPC converter - Google Patents
Method for eliminating specific harmonic of three-level NPC converter Download PDFInfo
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Abstract
The invention discloses a method for eliminating specific harmonics of a three-level NPC converter, which comprises the steps of constructing a nonlinear transcendental equation set for solving a switching angle according to input and output signals of the three-level NPC converter, realizing equalisation of inequality constraint conditions in the nonlinear transcendental equation set by utilizing coordinate transformation, solving the switching angle according to the obtained equalisation nonlinear transcendental equation set, converting the solved switching angle into a pulse signal, and driving a switching tube in the three-level NPC converter to be switched on and off by utilizing the pulse signal, namely eliminating the specific harmonics of the three-level NPC converter. The method for eliminating the specific harmonic of the three-level NPC converter simplifies multivariable constraint conditions into single-variable judgment conditions through the idea of geometric planning, improves the calculation speed and precision, further improves the accuracy of eliminating the specific harmonic of the three-level NPC converter, and has good application value.
Description
Technical Field
The invention belongs to the technical field of flexible power transmission and distribution of a power system, and relates to a method for eliminating specific harmonics of a three-level NPC converter.
Background
In some high voltage high power applications, self-heating of the devices in the power converter is a serious problem, and therefore, the switching frequency of the converter is not designed to be very high. During the operation of the converter, in order to ensure the quality of the output waveform, a cumbersome filter system needs to be designed, which undoubtedly increases the overall system loss and economic cost. For this purpose, a specific Harmonic cancellation Pulse Width Modulation (SHEPWM) strategy is proposed. The SHEPWM can eliminate selected low-order harmonic waves and realize accurate control of the harmonic waves by predetermining the switching angle at the switching-on and switching-off time. However, in solving for the switching angle, SHEPWM needs to write out a nonlinear transcendental system of equations for the switching angle, and the complexity of the system of equations increases as the number of switching angles to be solved increases.
A large number of researches show that the solving method of the nonlinear transcendental equation system is generally divided into a mathematical iterative algorithm and an intelligent algorithm. The initial value needs to be set in advance in the process of using the iterative algorithm to solve, but the calculation process of the initial value is complicated, and the accuracy of the calculation result is greatly influenced by the given range. The intelligent algorithm is used for solving the problem that initial values do not need to be given, but the non-sequence of the optimization results of the intelligent algorithm can cause that the solved results cannot meet the inherent relation between the switch angles, and in addition, the traditional intelligent algorithm also has the defect of long solving time. An expert proposes an idea of performing element replacement by using a trigonometric function relation of sum-difference products according to a constraint condition between SHEPWM switching angles, but the method causes the times of equations after element replacement to be too high, also brings great burden to calculation, causes the accuracy of a calculation result to be lower, and further causes the elimination accuracy of specific harmonics of the converter to be lower.
The three-level NPC converter can realize higher voltage output under the condition of lower input voltage, and is widely applied to the fields of flexible power transmission systems, high-power motor driving and the like. SHEPWM is widely applied to the three-level field as a modulation strategy aiming at optimizing output harmonic waves, but the problems can also occur in the practical application process. Therefore, a fast SHEPWM strategy applied to a three-level NPC converter needs to be provided, so that the speed and the precision in the calculation process are improved.
Disclosure of Invention
The invention aims to provide a method for eliminating specific harmonics of a three-level NPC converter, and solves the problems that the existing method for eliminating specific harmonics is complex in calculation process and low in accuracy of eliminating the specific harmonics of the converter.
The invention adopts the technical scheme that a method for eliminating specific harmonics of a three-level NPC converter comprises the following steps:
step 1, constructing a nonlinear transcendental equation system for solving a switching angle according to input and output signals of a three-level NPC converter:
in the formula, n represents the harmonic order, betaiRepresenting the switching angle of the ith switching angle, m representing the modulation ratio, and N representing the number of the switching angles;
step 2, realizing equalisation of inequality constraint conditions in the nonlinear transcendental equation set by utilizing coordinate transformation;
step 3, solving a switch angle according to the equalisation nonlinear transcendental equation set obtained in the step 2;
and 4, converting the solved switching angle into a pulse signal, and driving the on-off of a switching tube in the three-level NPC converter by using the pulse signal, namely eliminating the specific harmonic of the three-level NPC converter.
The present invention is also technically characterized in that,
the specific process of step 1 is as follows:
step 1.1, collecting input and output signals of a three-level NPC converter, and utilizing three currentsOutput phase reference voltage U of flat NPC converterrefAnd converter input side DC voltage UdcSolving the modulation ratio m:
step 1.2, collecting output phase voltage waveforms of the three-level NPC converter, and writing the amplitude a of each subharmonic according to waveform symmetryn，bnDetermines the number of switching angles N according to the number of harmonics N to be eliminated:
step 1.3, making the fundamental wave amplitude a1Equal to the reference voltage, and the amplitude of the eliminated subharmonic is selected to be equal to zero, so that a nonlinear transcendental equation set for solving the switching angle is constructed.
The specific process of step 2 is as follows:
introducing variable alphai，αi∈[0,R]N, R ≧ 1,2,3, establishes αiAnd betaiThe established equation is as follows:
the solution of the switching angle beta can be derived from equation (4)NThe equation of (a) is as follows:
in which B is a variable alphaiThe relational expression (c) of (c).
The specific process of step 3 is as follows:
step 3.1, establishing a model objective function F:
in the formula (f)nRepresenting a set error function, n being an odd number;
step 3.2, establishing a constraint condition of a model objective function F:
step 3.3, solving an objective function F through the formula (6) and the formula (7);
step 3.4, setting an optimal expected value P, returning to the step 3.3 to solve the objective function F again if the objective function F is not more than P, and otherwise, carrying out the next step;
step 3.5, satisfy variable alpha under the optimum expectation value PiConverted into a switching angle β in equation (5)iJudging whether the angle of each switch satisfies
If yes, the next step is carried out, and if not, the step 3.3 is returned to solve the target function F again.
And 4, acquiring the solved switching angle by adopting a digital signal acquisition device and converting the switching angle into a pulse signal.
The method has the advantages that a nonlinear transcendental equation set for solving the switching angle is constructed according to input and output signals of the three-level NPC converter, inequality constraint condition equalisation in the nonlinear transcendental equation set is realized by utilizing coordinate transformation, the switching angle is solved, the solved switching angle is converted into a pulse signal, the pulse signal is utilized to drive a switching tube in the three-level NPC converter to be switched on and off, and specific harmonics of the three-level NPC converter are eliminated. According to the method, multivariate constraint conditions are simplified into single variable judgment conditions through the idea of coordinate transformation, high-performance hardware equipment is not needed to provide calculation support for a complex nonlinear equation set, the calculation speed and precision are improved through the idea of nonlinear programming, the specific harmonic elimination accuracy of the three-level NPC converter is further improved, and the method has a good application value.
Drawings
FIG. 1 is a flow chart of a three-level NPC converter specific harmonic cancellation method of the present invention;
FIG. 2 is a topology block diagram of an application in an embodiment of the present invention;
FIG. 3 is the A-phase voltage U of FIG. 2AOA waveform diagram of (a);
FIG. 4 is a waveform of a line voltage calculated directly using an intelligent algorithm in an embodiment of the present invention;
FIG. 5 is a graph of an FFT analysis of line voltage calculated directly using an intelligent algorithm in an embodiment of the present invention;
FIG. 6 is a waveform diagram of a phase voltage calculated directly using an intelligent algorithm in an embodiment of the present invention;
FIG. 7 is a graph of an FFT analysis of phase voltages calculated directly using an intelligent algorithm according to an embodiment of the present invention;
FIG. 8 is a waveform of line voltage obtained using the particular harmonic cancellation method of the present application in an embodiment of the present invention;
FIG. 9 is a graph of an FFT analysis of line voltage obtained using the particular harmonic cancellation method of the present application in an embodiment of the present invention;
FIG. 10 is a waveform diagram of a phase voltage obtained using the particular harmonic cancellation method of the present application in an embodiment of the present invention;
FIG. 11 is a plot of an FFT analysis of phase voltages obtained using the particular harmonic cancellation method of the present application in accordance with an embodiment of the present invention;
FIG. 12 is a graph of the iterative effect of directly using an intelligent algorithm to compute the optimal expected value in the practice of the present invention;
fig. 13 is a graph of the iterative effect of achieving the optimal desired value using the specific harmonic cancellation method of the present application in the embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a method for eliminating specific harmonics of a three-level NPC converter, which comprises the following steps of:
step 1, constructing a nonlinear transcendental equation set for solving a switching angle according to input and output signals of a three-level NPC converter;
step 1.1, collecting input and output signals of a three-level NPC converter, and utilizing an output reference voltage U of the three-level NPC converterrefAnd converter input side DC voltage UdcSolving the modulation ratio m:
step 1.2, collecting output phase voltage waveforms of the three-level NPC converter, and writing the amplitude a of each subharmonic according to waveform symmetryn，bn：
In the formula, n represents the harmonic order, betaiThe number of switching angles N is determined according to the number of harmonics to be eliminated, and in the present embodiment, the number of switching angles N is 5, and the number of specific harmonics that can be eliminated is N-1 — 4.
Referring to fig. 2 and 3, in the three-phase neutral ungrounded system, the harmonic quantity of 3 times is self-eliminated, and thus equation (2) becomes
Step 1.3, making the fundamental wave amplitude a1Equal to the magnitude of the reference voltage, selecting the subharmonic amplitude equal to zero, and constructing a nonlinear transcendental equation system for solving the switching angle:
thus, in the embodiment where m is 0.6 and N is 5, the nonlinear transcendental system of switching angles is solved as follows:
step 2, coordinate transformation is utilized to realize equalisation of inequality constraint conditions in the nonlinear transcendental equation set, and the specific process is as follows:
introducing variable alphai，αi∈[0,R]N, R ≧ 1,2,3, establishes αiAnd betaiThe established equation is as follows:
the solution of the switching angle beta can be derived from equation (4)NThe equation of (a) is as follows:
in which B is a variable alphaiThe relationship (c) of (a) to (b),
variables of
Step 3, solving a switch angle according to the equalisation nonlinear transcendental equation set obtained in the step 2;
step 3.1, establishing a model objective function F:
in the formula (f)nRepresenting a set error function, n being an odd number;
step 3.2, establishing a constraint condition of a model objective function F:
step 3.3, solving the model by adopting a group intelligent algorithm, wherein the variable alpha is introduced in the step 2iThe value can be randomly taken according to the upper and lower boundaries, and an objective function F is solved through the formula (8) and the formula (9);
step 3.4, setting the optimal expected value P to be 0.99 according to the requirement, returning to the step 3.3 to solve the objective function F again if the objective function F is not more than P, and otherwise, carrying out the next step;
step 3.5, satisfy variable alpha under the optimum expectation value PiConverted into a switching angle β in equation (7)iJudging whether the angle of each switch satisfies
If yes, the next step is carried out, and if not, the step 3.3 is returned to solve the target function F again.
And 4, converting the solved switching angle into a pulse signal by adopting a digital signal collector, and driving the on-off of a switching tube in the three-level NPC converter by using the pulse signal, namely eliminating the specific harmonic of the three-level NPC converter.
Fig. 4 and 5 are a waveform diagram and an FFT analysis diagram of a line voltage calculated directly using an intelligent algorithm, respectively, in which the abscissa of fig. 5 is the harmonic order n and the ordinate is the content of each harmonic, and it can be seen from the diagrams that the THD content of the line voltage calculated directly using the intelligent algorithm is 65.72%.
Fig. 6 and 7 are a waveform diagram and an FFT analysis diagram of a phase voltage calculated directly by an intelligent algorithm, respectively, in which the abscissa of fig. 7 is the number n of harmonics and the ordinate is the content of each harmonic, and it can be seen from the diagrams that the THD content of the line voltage calculated directly by the intelligent algorithm is 91.91%.
Fig. 8 and 9 are a waveform diagram and an FFT analysis diagram of the line voltage calculated by using the method for eliminating the specific harmonic of the three-level NPC converter of the present application, respectively, where the abscissa of fig. 9 is the harmonic number n and the ordinate is the content of each harmonic, and it can be seen from comparison with fig. 5 that the line voltage THD content is reduced from 65.72% to 61.58% by using the method of the present application, which achieves a better elimination effect.
Fig. 10 and 11 are a waveform diagram and an FFT analysis diagram, respectively, of phase voltages obtained using the three-level NPC converter specific harmonic cancellation method of the present application. The abscissa of fig. 11 is the number of harmonics, and the ordinate is the content of each harmonic, and it can be seen from comparison with fig. 7 that, by using the method of the present application, the content of the phase voltage THD is reduced from 91.91% to 89.76%, so as to achieve a better cancellation effect.
Fig. 12 and 13 are graphs of iterative effects calculated by directly using the intelligent algorithm and the optimal expected value achieved by using the method of the present application, respectively, in which the abscissa represents the number of iterations and the ordinate represents the objective function value of each generation, and it can be seen from a comparison between fig. 12 and 13 that, compared with the case of directly using the intelligent algorithm, the number of iterations required to achieve the set optimal expected value in the present application is reduced from 664 to 454, the convergence rate is increased, and the calculation rate is greatly increased.
The method for eliminating the specific harmonic of the three-level NPC converter is a method for judging that a thought multivariable constraint condition of geometric programming is a single variable aiming at the situation that an intelligent algorithm optimizing result does not meet an angle constraint condition in a disordered way, can quickly realize the solution of a SHEPWM nonlinear transcendental equation set without improving a circuit structure and additional equipment, and improves the calculation speed and the calculation accuracy, thereby improving the accuracy of the specific harmonic elimination of the three-level NPC converter.
Claims (5)
1. A method for cancellation of specific harmonics in a three-level NPC converter, comprising the steps of:
step 1, constructing a nonlinear transcendental equation system for solving a switching angle according to input and output signals of a three-level NPC converter:
in the formula, n represents the harmonic order, betaiRepresenting the switching angle of the ith switching angle, m representing the modulation ratio, and N representing the number of the switching angles;
step 2, realizing equalisation of inequality constraint conditions in the nonlinear transcendental equation set by utilizing coordinate transformation;
step 3, solving a switch angle according to the equalisation nonlinear transcendental equation set obtained in the step 2;
and 4, converting the solved switching angle into a pulse signal, and driving the on-off of a switching tube in the three-level NPC converter by using the pulse signal, namely eliminating the specific harmonic of the three-level NPC converter.
2. The modulation method for the specific harmonic elimination pulse width of the three-level NPC converter as claimed in claim 1, wherein the specific process of step 1 is as follows:
step 1.1, collecting input and output signals of a three-level NPC converter, and utilizing an output reference voltage U of the three-level NPC converterrefAnd converter input side DC voltage UdcSolving the modulation ratio m:
step 1.2, collecting output phase voltage waveforms of the three-level NPC converter, and writing the amplitude a of each subharmonic according to waveform symmetryn，bnThe number of switching angles N is determined according to the number N of harmonics to be eliminated:
step 1.3, making the fundamental wave amplitude a1And (3) the amplitude of the selected subharmonic is equal to zero, and a nonlinear transcendental equation set for solving the switching angle is constructed.
3. The modulation method for the specific harmonic elimination pulse width of the three-level NPC converter as claimed in claim 1, wherein the specific process of step 2 is as follows:
introducing variable alphai，αi∈[0,R]N, R ≧ 1,2,3, establishes αiAnd betaiThe established equation is as follows:
the solution of the switching angle beta can be derived from equation (4)NThe equation of (a) is as follows:
in which B is a variable alphaiThe relational expression (c) of (c).
4. The modulation method for the specific harmonic elimination pulse width of the three-level NPC converter as claimed in claim 3, wherein the specific process of step 3 is as follows:
step 3.1, establishing a model objective function F:
in the formula (f)nRepresenting a set error function, n being an odd number;
step 3.2, establishing a constraint condition of a model objective function F:
step 3.3, solving an objective function F through the formula (6) and the formula (7);
step 3.4, setting an optimal expected value P, returning to the step 3.3 to solve the objective function F again if the objective function F is not more than P, and otherwise, carrying out the next step;
step 3.5, satisfy variable alpha under the optimum expectation value PiConverted into a switching angle β in equation (5)iJudging whether the angle of each switch satisfies
If yes, the next step is carried out, and if not, the step 3.3 is returned to solve the target function F again.
5. The method as claimed in claim 1, wherein in step 4, the digital signal collector is used to collect the solved switching angle and convert the switching angle into a pulse signal.
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