CN103078479A - Control method for canceling specified harmonics of three-level midpoint clamp photovoltaic inverter - Google Patents

Abstract

The invention discloses a control method for canceling specified harmonics of a three-level midpoint clamp photovoltaic inverter. The control method comprises the following steps of: firstly, establishing a mathematical model of the control method for the specified harmonics of the three-level midpoint clamp photovoltaic inverter and solving the following nonlinear transcendental equations; secondly, establishing a midpoint current mathematical model of the three-level midpoint clamp photovoltaic inverter; and thirdly, solving by adopting a continuous space ant colony algorithm. According to the control method disclosed by the invention, the control method for canceling the specified harmonics of the three-level midpoint clamp photovoltaic inverter is combined with midpoint voltage balance; the midpoint voltage balance can be effectively controlled while the specified low-order harmonics are canceled, so that an output waveform is greatly improved and the total harmonic distorsion is reduced.

Description

Three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic are eliminated control method

Technical field

The present invention relates to a kind of three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic and eliminate control method.

Background technology

The particular harmonic of three level neutral-point-clamped photovoltaic DC-to-AC converters is eliminated control method and is selected by the optimization of switching time, and the pwm voltage waveform of control inverter rightly makes not have in the voltage of inverter output that some is specific for low order) harmonic wave.

The where the shoe pinches that particular harmonic is eliminated control method mainly is to find the solution one group of non-linear transcendental equation group, traditional method is to adopt Newton iteration method, the method is found the solution Nonlinear System of Equations needs one group of initial value, whether the whether suitable algorithm that directly determined that initial value is selected restrains, thus initial value choose will be as far as possible near the solution of equation.Choosing of initial value do not have system, effective method, the method that the researcher generally adopts examination to gather, and efficient is very low.And traditional particular harmonic is eliminated control method only from eliminating the angle of specific low-order harmonic, does not consider the overall performance of photovoltaic DC-to-AC converter.Be directed to three level neutral-point-clamped photovoltaic DC-to-AC converters, then when eliminating particular harmonic, do not consider key technical problem---the neutral point voltage balance problem of three level neutral-point-clamped inverters.

Summary of the invention

The purpose of this invention is to provide a kind ofly find the solution easily and fast, three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic are eliminated control method accurately.

The technical scheme that realizes the object of the invention is that a kind of three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic are eliminated control method, may further comprise the steps:

1. set up three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic and eliminate the control method Mathematical Modeling, find the solution following non-linear transcendental equation group:

$\left\{\begin{array}{c}{f}_1\left(\mathrm{\α}\right)=\frac{U_{\mathrm{sm}\left(1\right)}}{U_{d/2}}=\frac{4}{\mathrm{\π}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(-1)}^{i+1}\cos \left({\mathrm{\α}}_i\right)=m\\ f_2\left(\mathrm{\α}\right)=\frac{U_{\mathrm{sm}\left(5\right)}}{U_{d/2}}=\frac{4}{5\mathrm{\π}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(-1)}^{i+1}\cos \left(5{\mathrm{\α}}_i\right)=0\\ M\\ f_N\left(\mathrm{\α}\right)=\frac{U_{\mathrm{sm}\left(M\right)}}{U_{d/2}}=\frac{4}{\mathrm{M\π}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(-1)}^{i+1}\cos \left(M{\mathrm{\α}}_i\right)=0\end{array}\right.;$

U in the formula _dBe the DC side supply voltage, N is closed the half-convergency number by taking away in 1/4 cycle, and switching angle should satisfy condition: $D:0<{\mathrm{\&alpha;}}_1<{\mathrm{\&alpha;}}_2<\mathrm{\&Lambda;}<{\mathrm{\&alpha;}}_{n-1}<{\mathrm{\&alpha;}}_N<\frac{\mathrm{\&pi;}}{2};$

2. set up three level neutral-point-clamped photovoltaic DC-to-AC converter mid point electric current Mathematical Modelings: at a sampling period T _SInterior current in middle wire can be expressed as:

$i_{\mathrm{NP}}=i_{\mathrm{NP}\_\mathrm{Medium}}+i_{\mathrm{NP}\_\mathrm{Small}}$

$=T_M\&CenterDot;\left[\begin{array}{ccc}{M}_a& M_b& M_c\end{array}\right]\&CenterDot;\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{cc}{k}_0& k_1\end{array}\right]\&CenterDot;\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="0"\; label="T\; S"\; filenames="HDA0000101802980000011.png"\; state="\{\{state\}\}">T</figure-callout>}}_S& 0\\ 0& T_{S1}\end{array}\right]\&CenterDot;\left[\begin{array}{ccc}{S0}_a& S{0}_b& {S0}_c\\ {S1}_a& {S1}_b& {S1}_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]$

Work as i _NP=0 or i _NPThe mid-point voltage of → 0 o'clock three level neutral-point-clamped photovoltaic DC-to-AC converter reaches balance;

3. adopt the continuous space ant colony optimization for solving:

1. 2. can get following equation with step by step: $\left\{\begin{array}{c}{g}_1\left(\mathrm{\&alpha;}\right)=4/\mathrm{\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left({\mathrm{\&alpha;}}_i\right)-m=0\\ g_2\left(\mathrm{\&alpha;}\right)=4/5\mathrm{\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(5{\mathrm{\&alpha;}}_i\right)=0\\ M\\ g_{n-1}\left(\mathrm{\&alpha;}\right)=4/\mathrm{N\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(N{\mathrm{\&alpha;}}_i\right)=0\\ g_n\left(\mathrm{\&alpha;}\right)=i_{\mathrm{NP}}=0\end{array}\right.$

This equation group is interpreted as the optimization problem of asking n target, that is:

$\mathrm{Min}:\left\{\begin{array}{c}{y}_1={\left(g_1\left(\mathrm{\&alpha;}\right)\right)}^2\\ y_2={\left(g_2\left(\mathrm{\&alpha;}\right)\right)}^2\\ M\\ y_{n-1}={\left(g_N\left(\mathrm{\&alpha;}\right)\right)}^2\\ y_n={\left(i_{\mathrm{NP}}\right)}^2\end{array}\right.$

According to the Objective Programming principle, be a target with above n target unification, that is:

$\mathrm{Min}:y=-\frac{1}{1+{y_1}^2+{y_2}^2+K{y_n}^2}.$

Step 2. in, the switch function M that middle vector is corresponding _aM _bM _cBe defined as:

Middle vector	M a	M b	M c
				pon	0	1	0
opn	1	0	0
				npo	0	0	1
nop	0	1	0
				onp	1	0	0
pno	0	0	1

The switch function S0 that small vector is corresponding _aS0 _bS0 _cAnd S1 _aS1 _bS1 _cBe defined as:

Small vector	S0 a	S0 b	S0 c	Small vector	S1 a	S1 b	S1 c
								poo/onn	1	0	0	ppo/oon	0	0	1
opo/non	0	1	0	opp/noo	1	0	0
								pop/nno	0	0	1	pop/ono	0	1	0

After having adopted technique scheme, the present invention has following positive effect: (1) control method of the present invention is combined the particular harmonic elimination control method of three level neutral-point-clamped photovoltaic DC-to-AC converters with neutral point voltage balance, eliminating specific low-order harmonic simultaneously, can effectively control neutral point voltage balance, can effectively eliminate low-order harmonic, improve greatly output waveform, reduced total harmonic distortion.

(2) the present invention uses ant colony optimization algorithm in the finding the solution of inverter particular harmonic elimination control method, ant colony optimization algorithm when finding the solution Nonlinear System of Equations unlike traditional Newton iteration method, it does not need the initial value of solving equation and the variation tendency that prediction is separated, its initial population produces at random, can accelerate the computational speed of algorithm, be easy to realize On-line Control.

Description of drawings

Summary of the invention is easier to be expressly understood in order to make, and the below is described in further detail invention, wherein according to specific embodiment also by reference to the accompanying drawings

Fig. 1 is the solution trajectory diagram of three level photovoltaic inverter switch angles.

Fig. 2 is three level photovoltaic inverter output line voltage waveforms, dc capacitor voltage waveform and line voltage frequency spectrum.

Embodiment

Three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic are eliminated control method, may further comprise the steps:

1. set up three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic and eliminate the control method Mathematical Modeling:

The single-phase voltage waveform of three level neutral-point-clamped photovoltaic DC-to-AC converters satisfies 1/4 periodic symmetry, and by Diric hlet theorem, waveform can resolve into following fourier series:

$U_{\mathrm{AN}}\left(\mathrm{\&omega;t}\right)=\frac{A_0}{2}+\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[A_n\sin \left(\mathrm{n\&omega;t}\right)+B_n\cos \left(\mathrm{n\&omega;t}\right)]---\left(1\right)$

In the formula

$A_n=\frac{2}{\mathrm{\&pi;}}{\&Integral;}_0^{\frac{\mathrm{\&pi;}}{2}}\frac{U_d}{2}\cos \left(\mathrm{n\&omega;t}\right)d\left(\mathrm{\&omega;t}\right)---\left(2\right)$

$B_n=\frac{2}{\mathrm{\&pi;}}{\&Integral;}_0^{\frac{\mathrm{\&pi;}}{2}}\frac{U_d}{2}\sin \left(\mathrm{n\&omega;t}\right)d\left(\mathrm{\&omega;t}\right)---\left(3\right)$

Because symmetry (the waveform odd symmetry and right of phase voltage waveform

Axial symmetry), therefore only contain the odd sine term harmonic wave, so

$\left\{\begin{array}{c}{A}_n=0\\ B_n=\left\{\begin{array}{cc}0,& n=\mathrm{even}\\ =U_{\mathrm{sm}\left(n\right)}=\frac{{2U}_d}{\mathrm{n\&pi;}}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{k+1}\cos \left(n{\mathrm{\&alpha;}}_k\right),& n=\mathrm{odd}\end{array}\right.---\left(4\right)\end{array}\right.$

In the following formula: U _dBe the DC side supply voltage, N is closed the half-convergency number by taking away in 1/4 cycle, and switching angle should satisfy condition

$D:0<{\mathrm{\&alpha;}}_1<{\mathrm{\&alpha;}}_2<\mathrm{\&Lambda;}<{\mathrm{\&alpha;}}_{n-1}<{\mathrm{\&alpha;}}_N<\frac{\mathrm{\&pi;}}{2}.$

Consider in the three-phase photovoltaic DC-to-AC converter, Zero-pharse harmonic can be eliminated according to three-phase three-wire system output, so emphasis harmonic carcellation number of times is 5,7,11,13 in the three-phase tri-level photovoltaic DC-to-AC converter application system ..., 6i-1,6i+1 (i=1,2,3 ...).

By (4) formula as can be known, the amplitude of each harmonic is switching angle α _iFunction, as long as suitably select α ₁, α ₂..., α _NValue, just can make U _{Sm (i)}=0, namely having eliminated angular frequency is the harmonic wave of i ω.

If first-harmonic modulation degree

Eliminate 5,7,11 ..., 6i-1,6i+1, Λ M subharmonic (M be eliminable high order harmonic component number of times) obtains equation as shown in the formula (5).

$\left\{\begin{array}{c}{f}_1\left(\mathrm{\&alpha;}\right)=\frac{U_{\mathrm{sm}\left(1\right)}}{U_{d/2}}=\frac{4}{\mathrm{\&pi;}}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left({\mathrm{\&alpha;}}_i\right)=m\\ f_2\left(\mathrm{\&alpha;}\right)=\frac{U_{\mathrm{sm}\left(5\right)}}{U_{d/2}}=\frac{4}{5\mathrm{\&pi;}}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(5{\mathrm{\&alpha;}}_i\right)=0\\ M\\ f_N\left(\mathrm{\&alpha;}\right)=\frac{U_{\mathrm{sm}\left(M\right)}}{U_{d/2}}=\frac{4}{\mathrm{M\&pi;}}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(M{\mathrm{\&alpha;}}_i\right)=0\end{array}\right.---\left(5\right)$

Obviously, formula (5) is a non-linear transcendental equation group.

2. set up three level neutral-point-clamped photovoltaic DC-to-AC converter mid point electric current Mathematical Modelings:

At a sampling period T _SInterior current in middle wire can be expressed as formula (6):

$i_{\mathrm{NP}}=i_{\mathrm{NP}\_\mathrm{Medium}}+i_{\mathrm{NP}\_\mathrm{Small}}$

$=T_M\&CenterDot;\left[\begin{array}{ccc}{M}_a& M_b& M_c\end{array}\right]\&CenterDot;\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{cc}{k}_0& k_1\end{array}\right]\&CenterDot;\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="0"\; label="T\; S"\; filenames="HDA0000101802980000011.png"\; state="\{\{state\}\}">T</figure-callout>}}_S& 0\\ 0& T_{S1}\end{array}\right]\&CenterDot;\left[\begin{array}{ccc}{S0}_a& S{0}_b& {S0}_c\\ {S1}_a& {S1}_b& {S1}_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]$

(6)

In the formula: the switch function M that middle vector is corresponding _aM _bM _cDefine as shown in table 1:

Vector switch function table in the table 1

Middle vector	M a	M b	M c
				pon	0	1	0
opn	1	0	0
				npo	0	0	1
nop	0	1	0
				onp	1	0	0
pno	0	0	1

The switch function S0 that small vector is corresponding _aS0 _bS0 _cAnd S1 _aS1 _bS1 _cDefine as shown in table 2.

Table 2 small vector switch function table

Small vector	S0 a	S0 b	S0 c	Small vector	S1 a	S1 b	S1 c
								poo/onn	1	0	0	ppo/oon	0	0	1
opo/non	0	1	0	opp/noo	1	0	0
								pop/nno	0	0	1	pop/ono	0	1	0

Work as i _NP=0 or i _NPThe mid-point voltage of → 0 o'clock three level neutral-point-clamped photovoltaic DC-to-AC converter reaches balance.

3. adopt the continuous space ant colony optimization for solving:

Ant group algorithm (Ant Colony Algorithm) is according to the research to Food Recruiment In Ants behavior under the nature, and Italian scholar Dorigo M proposed first in 1991.It is the intelligence system of a complexity in essence, has stronger robustness, and good Distributed Calculation mechanism such as is easy to be combined with additive method at the characteristics.With the immediate a kind of continuous space ant group algorithm of Basic Ant Group of Algorithm be the TACO (touring ant colony optimization) that was proposed by people such as Hiroyasu in 2000.Practice shows, the continuous optimization ant group algorithm that use is similar to discrete optimization ant group algorithm structure can be tried to achieve with speed faster the optimal solution of function, and a lot of aspects such as the convergence of this type method, convergence rate can be used existing theory very easily.The present invention is applied to the continuous space ant group algorithm to consider that the particular harmonic of three level neutral-point-clamped photovoltaic DC-to-AC converters of neutral point voltage balance eliminates finding the solution of model, ask for the switch angle that particular harmonic is eliminated, ant group algorithm when finding the solution Nonlinear System of Equations unlike traditional Newton iteration method, it does not need the initial value of solving equation and the variation tendency that prediction is separated, and has therefore accelerated computational speed.

Can get following equation (7) by (5) formula and (6) formula: $\left\{\begin{array}{c}{g}_1\left(\mathrm{\&alpha;}\right)=4/\mathrm{\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left({\mathrm{\&alpha;}}_i\right)-m=0\\ g_2\left(\mathrm{\&alpha;}\right)=4/5\mathrm{\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(5{\mathrm{\&alpha;}}_i\right)=0\\ M\\ g_{n-1}\left(\mathrm{\&alpha;}\right)=4/\mathrm{N\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(N{\mathrm{\&alpha;}}_i\right)=0\\ g_n\left(\mathrm{\&alpha;}\right)=i_{\mathrm{NP}}=0\end{array}\right.---\left(7\right)$

This equation group can be interpreted as the optimization problem of asking n target, that is:

$\mathrm{Min}:\left\{\begin{array}{c}{y}_1={\left(g_1\left(\mathrm{\&alpha;}\right)\right)}^2\\ y_2={\left(g_2\left(\mathrm{\&alpha;}\right)\right)}^2\\ M\\ y_{n-1}={\left(g_N\left(\mathrm{\&alpha;}\right)\right)}^2\\ y_n={\left(i_{\mathrm{NP}}\right)}^2\end{array}\right.---\left(8\right)$

According to the Objective Programming relative theory, be a target with above n target unification, that is:

$\mathrm{Min}:y=-\frac{1}{1+{y_1}^2+{y_2}^2+K{y_n}^2}---\left(9\right)$

By formula (9) as can be known: satisfying under the certain error condition, when n target function all got or near minimum value 0 time, it is minimum that y also just can reach.As fitness function, utilize TACO just can obtain the approximate solution (collection) of equation with this, obtain mid point electric current particular harmonic and eliminate control angle.

Be example with cancellation 5,7,11 subharmonic, utilize the continuous space ant group algorithm to solve an equation and calculate α ₁, α ₂, α ₃, α ₄Under the prerequisite that guarantees neutral point voltage balance, the solution track of the switch angle that obtains as shown in Figure 1, output line voltage waveform, dc capacitor voltage waveform and line voltage frequency spectrum are as shown in Figure 2 when modulation degree m=0.8, as seen when eliminating specific low-order harmonic, mid-point voltage obtains good balance.

Above-described specific embodiment; purpose of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the above only is specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. a level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic is eliminated control method, it is characterized in that may further comprise the steps:

1. set up three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic and eliminate the control method Mathematical Modeling, find the solution following non-linear transcendental equation group:

$\left\{\begin{array}{c}{f}_1\left(\mathrm{\&alpha;}\right)=\frac{U_{\mathrm{sm}\left(1\right)}}{U_{d/2}}=\frac{4}{\mathrm{\&pi;}}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left({\mathrm{\&alpha;}}_i\right)=m\\ f_2\left(\mathrm{\&alpha;}\right)=\frac{U_{\mathrm{sm}\left(5\right)}}{U_{d/2}}=\frac{4}{5\mathrm{\&pi;}}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(5{\mathrm{\&alpha;}}_i\right)=0\\ M\\ f_N\left(\mathrm{\&alpha;}\right)=\frac{U_{\mathrm{sm}\left(M\right)}}{U_{d/2}}=\frac{4}{\mathrm{M\&pi;}}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(M{\mathrm{\&alpha;}}_i\right)=0\end{array}\right.;$

U in the formula _dBe the DC side supply voltage, N is closed the half-convergency number by taking away in 1/4 cycle, and switching angle should satisfy condition: $D:0<{\mathrm{\&alpha;}}_1<{\mathrm{\&alpha;}}_2<\mathrm{\&Lambda;}<{\mathrm{\&alpha;}}_{n-1}<{\mathrm{\&alpha;}}_N<\frac{\mathrm{\&pi;}}{2};$

2. set up three level neutral-point-clamped photovoltaic DC-to-AC converter mid point electric current Mathematical Modelings: at a sampling period T _SInterior current in middle wire can be expressed as:

$i_{\mathrm{NP}}=i_{\mathrm{NP}\_\mathrm{Medium}}+i_{\mathrm{NP}\_\mathrm{Small}}$

$=T_M\&CenterDot;\left[\begin{array}{ccc}{M}_a& M_b& M_c\end{array}\right]\&CenterDot;\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{cc}{k}_0& k_1\end{array}\right]\&CenterDot;\left[\begin{array}{cc}{T}_{S0}& 0\\ 0& T_{S1}\end{array}\right]\&CenterDot;\left[\begin{array}{ccc}{S0}_a& S{0}_b& {S0}_c\\ {S1}_a& {S1}_b& {S1}_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]$

Work as i _NP=0 or i _NPThe mid-point voltage of → 0 o'clock three level neutral-point-clamped photovoltaic DC-to-AC converter reaches balance;

3. adopt the continuous space ant colony optimization for solving:

1. 2. can get following equation with step by step: $\left\{\begin{array}{c}{g}_1\left(\mathrm{\&alpha;}\right)=4/\mathrm{\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left({\mathrm{\&alpha;}}_i\right)-m=0\\ g_2\left(\mathrm{\&alpha;}\right)=4/5\mathrm{\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(5{\mathrm{\&alpha;}}_i\right)=0\\ M\\ g_{n-1}\left(\mathrm{\&alpha;}\right)=4/\mathrm{N\&pi;}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(-1)}^{i+1}\cos \left(N{\mathrm{\&alpha;}}_i\right)=0\\ g_n\left(\mathrm{\&alpha;}\right)=i_{\mathrm{NP}}=0\end{array}\right.$

This equation group is interpreted as the optimization problem of asking n target, that is:

$\mathrm{Min}:\left\{\begin{array}{c}{y}_1={\left(g_1\left(\mathrm{\&alpha;}\right)\right)}^2\\ y_2={\left(g_2\left(\mathrm{\&alpha;}\right)\right)}^2\\ M\\ y_{n-1}={\left(g_N\left(\mathrm{\&alpha;}\right)\right)}^2\\ y_n={\left(i_{\mathrm{NP}}\right)}^2\end{array}\right.$

According to the Objective Programming principle, be a target with above n target unification, that is:

$\mathrm{Min}:y=-\frac{1}{1+{y_1}^2+{y_2}^2+K{y_n}^2}.$

2. three level neutral-point-clamped photovoltaic DC-to-AC converter particular harmonic according to claim 1 are eliminated control method, it is characterized in that:

Step 2. in, the switch function M that middle vector is corresponding _aM _bM _cBe defined as:

Middle vector M _a M _b M _c pon 0 1 0 opn 1 0 0 npo 0 0 1 nop 0 1 0 onp 1 0 0 pno 0 0 1

The switch function S0 that small vector is corresponding _aS0 _bS0 _cAnd S1 _aS1 _bS1 _cBe defined as:

Small vector S0 _a S0 _b S0 _c Small vector S1 _a S1 _b Sl _c poo/onn 1 0 0 ppo/oon 0 0 1 opo/non 0 1 0 opp/noo 1 0 0 pop/nno 0 0 1 pop/ono 0 1 0

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