CN104820124A - Three-phase harmonic wave current detection method based on synchronization rotation mean value theory - Google Patents

Abstract

The invention discloses a three-phase harmonic wave current detection method based on a synchronization rotation mean value theory. The current detection process of the synchronization rotation mean value theory is as follows: three-phase power network voltages u<a>, u<b> and u<c> and three-phase load currents i<la>, i<lb> and i<lc> are converted into u<alpha> and u<beta>, and i<alpha> and i<beta>, and i<alpha'> and i<beta'> on alpha beta coordinates through alpha beta coordinate transformation. According to the invention, the detection method, through simultaneously carrying out synchronization rotation coordinate transformation on the three-phase voltages and the currents, solves the phase problem of a phase-locked loop, and by use of differences between the load currents and fundamental wave positive sequence currents and negative sequence currents, obtains accurate harmonic wave currents.

Description

A kind of three phase harmonic electric current testing based on synchronous rotary mean value theory

Technical field

The present invention relates to a kind of electric power to detect, specifically a kind of three phase harmonic electric current testing based on synchronous rotary mean value theory.

Background technology

Along with the development of Power Electronic Technique, and the application of power electronic equipment in electric system is equal to a harmonic source relative to electrical network, and this will cause the harmonic pollution problems of system day by day serious.So, harmonic wave control just becomes the problem of extensive concern.In order to the safe operation of electrical network and the continuation development of Power Electronic Technique, need to take effective braking measure to mains by harmonics.The power electronic equipments such as APF, STATCOM become the important device of administering mains by harmonics, compensating reactive power, one of its gordian technique be fundamental positive sequence reactive current and harmonic current real-time, detect accurately.

Since the red wooden Thai language (H.Akagi) of Japanese scholars proposed after based on the instantaneous reactive power theory of three-phase circuit in nineteen eighty-three, this theory, through constantly perfect, defines the theoretical system of system.Meanwhile, many scholars have done many fruitful research work in current detecting.Some scholar eliminates phaselocked loop, introduces feedback, compensate for the time delay of low-pass filter.Some scholar is then separated with harmonic component fundametal compoment in the rotated coordinate system.

Summary of the invention

The object of the present invention is to provide the three phase harmonic electric current testing based on synchronous rotary mean value theory of a kind of correctness and validity, to solve the problem proposed in above-mentioned background technology.

For achieving the above object, the invention provides following technical scheme:

Based on a three phase harmonic electric current testing for synchronous rotary mean value theory, the current detecting process of described synchronous rotary mean value theory is: three-phase power grid voltage u _a, u _b, u _cwith threephase load current i _la, i _lb, i _lcu under α β coordinate transform transforms to them on α β coordinate _α, u _βand i _α, i _βand i _{α ＇}, i _{β ＇}, its relational expression is as follows:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right]=C_{23}\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right],\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=C_{23}\left[\begin{array}{c}{i}_{\mathrm{la}}\\ i_{\mathrm{lb}}\\ i_{\mathrm{lc}}\end{array}\right],\left[\begin{array}{c}{i}_{{\mathrm{\&alpha;}}^{\&prime;}}\\ i_{{\mathrm{\&beta;}}^{\&prime;}}\end{array}\right]=C_{{23}^{\&prime;}}\left[\begin{array}{c}{i}_{1a}\\ i_{1b}\\ i_{1c}\end{array}\right]---\left(1\right)$

Its transition matrix is:

$C_{23}=\sqrt{\frac{2}{3}}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}\end{array}\right],$

$C_{{23}^{\&prime;}}=\sqrt{\frac{2}{3}}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]---\left(2\right)$

Meanwhile, A phase line voltage, through phaselocked loop and cosine and sine signal circuit for generating, obtains and the synchronous cosine and sine signal of A phase line voltage, if phase place is its relational expression is as follows:

$\left[\begin{array}{c}{u}_p\\ u_q\end{array}\right]=C\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right],\left[\begin{array}{c}{i}_p\\ i_q\end{array}\right]=C\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right],$

$\left[\begin{array}{c}{i}_{p^{\&prime;}}\\ i_{q^{\&prime;}}\end{array}\right]=C\left[\begin{array}{c}{i}_{{\mathrm{\&alpha;}}^{\&prime;}}\\ i_{{\mathrm{\&beta;}}^{\&prime;}}\end{array}\right]---\left(3\right)$

Wherein Matrix C is:

As the further scheme of the present invention: obtain u through mean value theory _p, u _q, i _p, i _qand i _{p ＇}, i _{q ＇}dC component u _p, u _q, i _p, i _qand i _{p ＇}, i _{q ＇}, then obtain fundamental positive sequence voltage u respectively through inverse transformation _af, u _bf, u _cf, fundamental positive sequence current i _af1, i _bf1, i _cf1, fundamental negative sequence current i _{af ＇}, i _{bf ＇}, i _{cf ＇}, then, load current and fundamental positive sequence electric current and fundamental negative sequence current are subtracted each other the harmonic component i obtaining load current _ah, i _bh, i _ch;

$\left[\begin{array}{c}{i}_{\mathrm{af}1}\\ i_{\mathrm{bf}1}\\ i_{\mathrm{cf}1}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_p\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right],\left[\begin{array}{c}{i}_{a{f}^{\&prime;}}\\ i_{b{f}^{\&prime;}}\\ i_{c{f}^{\&prime;}}\end{array}\right]=C_{{32}^{\&prime;}}{C}^{-}\left[\begin{array}{c}{{\stackrel{\&OverBar;}{i}}_p}^{\&prime;}\\ {{\stackrel{\&OverBar;}{i}}_q}^{\&prime;}\end{array}\right],$

$\left[\begin{array}{c}{u}_{\mathrm{af}}\\ u_{\mathrm{bf}}\\ u_{\mathrm{cf}}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{u}}_p\\ {\stackrel{\&OverBar;}{u}}_q\end{array}\right]---\left(5\right)$

$C_{32}=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right],$

$C_{{32}^{\&prime;}}=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}\end{array}\right],$

In addition, u _p, u _qand i _p, i _qi can be obtained through synchronous rotary _{p ＇}, i _{q ＇}, then fundamental positive sequence active current under inverse transformation can obtain imperfect voltage or fundamental positive sequence reactive current i ⁺ _af, i ⁺ _bf, i ⁺ _cf;

$\left[\begin{array}{c}{i}_{\mathrm{af}}^{+}\\ i_{\mathrm{bf}}^{+}\\ i_{\mathrm{cf}}^{+}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{i_p}^{\&prime;}\\ {i_q}^{\&prime;}\end{array}\right]---\left(7\right)$

$\left\{\begin{array}{c}{i}_{\mathrm{la}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-})]\\ i_{\mathrm{lb}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+}-\frac{2\mathrm{\&pi;}}{3})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-}+\frac{2\mathrm{\&pi;}}{3})]\\ i_{\mathrm{lc}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+}+\frac{2\mathrm{\&pi;}}{3})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-}-\frac{2\mathrm{\&pi;}}{3})]\end{array}\right.---\left(8\right)$

$\left\{\begin{array}{c}{u}_a=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[U_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{+})+U_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{-})+U_n^0\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^0)]\\ u_b=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[U_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{+}-\frac{2\mathrm{\&pi;}}{3})+U_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{-}+\frac{2\mathrm{\&pi;}}{3})+U_n^0\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^0)]\\ u_c=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[U_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{+}+\frac{2\mathrm{\&pi;}}{3})+U_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{-}-\frac{2\mathrm{\&pi;}}{3})+U_n^0\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^0)]\end{array}\right.---\left(9\right)$

θ in formula ⁺ _inand θ ⁺ _unfor the initial phase angle of each primary current of positive sequence and voltage; θ ^- _inand θ ^- _unfor the initial phase angle of each primary current of negative phase-sequence and voltage; θ ⁰ _unfor the initial phase angle of zero sequence each voltage.

As the present invention's further scheme: through Fourier decomposition, calculate according to above-mentioned relation expression formula simultaneously, have:

Therefrom i can be seen _p, i _qin except DC component, the cycle of AC compounent is 1/6 of power cycle, and namely AC compounent mean value in 1/6 power cycle is 0.I can be obtained by this average algorithm _pand i _qdC component i _pand i _q:

That is:

As the present invention's further scheme: under pq coordinate, electric current resultant vector i is projected as instantaneous positive sequence active current vector on voltage resultant vector u; Electric current resultant vector i is projected as instantaneous positive sequence reactive current vector in voltage resultant vector u normal direction.

As the present invention's further scheme: there is distortion and asymmetric situation for line voltage, carry out emulation experiment at Matlab7.1/Simulink environment simultaneously.

As the present invention's further scheme: adopt the i that mean value theory and low-pass filter detect _pwaveform, detects under its desirable grid conditions, and it is shorter than adopting the time of low-pass filter detection method to adopt the time of mean value theory detection method.

As the present invention's further scheme: when only compensation harmonic electric current, the described three phase harmonic electric current testing based on synchronous rotary mean value theory is more accurate.

As the present invention's further scheme: the three phase harmonic electric current testing of described synchronous rotary mean value theory solves the phase problem of phaselocked loop.

Compared with prior art, the invention has the beneficial effects as follows: this detection method, by carrying out to three-phase voltage and electric current the phase problem that synchronous rotating angle solves phaselocked loop simultaneously, utilizes the difference of load current and fundamental positive sequence electric current and negative-sequence current to obtain accurate harmonic current.

Accompanying drawing explanation

Fig. 1 is current detecting block diagram;

Fig. 2 is mean value theory method schematic diagram;

Fig. 3 is synchronous rotary instantaneous positive sequence reactive current vector;

Fig. 4 is the i that mean value theory and low-pass filter detect _pwaveform;

Fig. 5 is threephase load current waveform;

Fig. 6 is harmonic current waveforms;

Fig. 7 is i _p-i _qthe harmonic current waveforms of algorithm;

Fig. 8 is i _p-i _qalgorithm disconnects i _qafter, the waveform of A phase fundamental positive sequence electric current and voltage;

Fig. 9 is the three phase harmonic electric current testing A phase fundamental positive sequence electric current of synchronous rotary mean value theory and the waveform of voltage.

Embodiment

Be described in more detail below in conjunction with the technical scheme of embodiment to this patent.

Based on a three phase harmonic electric current testing for synchronous rotary mean value theory, the theory diagram of the electric current detecting method of described synchronous rotary mean value theory refers to Fig. 1, and its detailed current detecting process is as described below:

Three-phase power grid voltage u _a, u _b, u _cwith threephase load current i _la, i _lb, i _lcu under α β coordinate transform transforms to them on α β coordinate _α, u _βand i _α, i _βand i _{α ＇}, i _{β ＇}, its relational expression is as follows:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right]=C_{23}\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right],\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=C_{23}\left[\begin{array}{c}{i}_{\mathrm{la}}\\ i_{\mathrm{lb}}\\ i_{\mathrm{lc}}\end{array}\right],\left[\begin{array}{c}{i}_{{\mathrm{\&alpha;}}^{\&prime;}}\\ i_{{\mathrm{\&beta;}}^{\&prime;}}\end{array}\right]=C_{{23}^{\&prime;}}\left[\begin{array}{c}{i}_{1a}\\ i_{1b}\\ i_{1c}\end{array}\right]---\left(1\right)$

Its transition matrix is:

$C_{23}=\sqrt{\frac{2}{3}}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}\end{array}\right],$

$C_{{23}^{\&prime;}}=\sqrt{\frac{2}{3}}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]---\left(2\right)$

Meanwhile, A phase line voltage, through phaselocked loop and cosine and sine signal circuit for generating, obtains and the synchronous cosine and sine signal of A phase line voltage, if phase place is its relational expression is as follows:

$\left[\begin{array}{c}{u}_p\\ u_q\end{array}\right]=C\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right],\left[\begin{array}{c}{i}_p\\ i_q\end{array}\right]=C\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right],$

$\left[\begin{array}{c}{i}_{p^{\&prime;}}\\ i_{q^{\&prime;}}\end{array}\right]=C\left[\begin{array}{c}{i}_{{\mathrm{\&alpha;}}^{\&prime;}}\\ i_{{\mathrm{\&beta;}}^{\&prime;}}\end{array}\right]---\left(3\right)$

Wherein Matrix C is:

Then, u is obtained through mean value theory _p, u _q, i _p, i _qand i _{p ＇}, i _{q ＇}dC component Jian u _p, u _q, i _p, i _qand i _{p ＇}, i _{q ＇}, then obtain fundamental positive sequence voltage u respectively through inverse transformation _af, u _bf, u _cf, fundamental positive sequence current i _af1, i _bf1, i _cf1, fundamental negative sequence current i _{af ＇}, i _{bf ＇}, i _{cf ＇}, then, load current and fundamental positive sequence electric current and fundamental negative sequence current are subtracted each other the harmonic component i obtaining load current _ah, i _bh, i _ch.

$\left[\begin{array}{c}{i}_{\mathrm{af}1}\\ i_{\mathrm{bf}1}\\ i_{\mathrm{cf}1}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_p\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right],\left[\begin{array}{c}{i}_{a{f}^{\&prime;}}\\ i_{b{f}^{\&prime;}}\\ i_{c{f}^{\&prime;}}\end{array}\right]=C_{{32}^{\&prime;}}{C}^{-}\left[\begin{array}{c}{{\stackrel{\&OverBar;}{i}}_p}^{\&prime;}\\ {{\stackrel{\&OverBar;}{i}}_q}^{\&prime;}\end{array}\right],$

$\left[\begin{array}{c}{u}_{\mathrm{af}}\\ u_{\mathrm{bf}}\\ u_{\mathrm{cf}}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{u}}_p\\ {\stackrel{\&OverBar;}{u}}_q\end{array}\right]---\left(5\right)$

$C_{32}=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right],$

$C_{{32}^{\&prime;}}=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}\end{array}\right],$

In addition, u _p, u _qand i _p, i _qi can be obtained through synchronous rotary _{p ＇}, i _{q ＇}, then fundamental positive sequence active current under inverse transformation can obtain imperfect voltage or fundamental positive sequence reactive current i ⁺ _af, i ⁺ _bf, i ⁺ _cf.

$\left[\begin{array}{c}{i}_{\mathrm{af}}^{+}\\ i_{\mathrm{bf}}^{+}\\ i_{\mathrm{cf}}^{+}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{i_p}^{\&prime;}\\ {i_q}^{\&prime;}\end{array}\right]---\left(7\right)$

$\left\{\begin{array}{c}{i}_{\mathrm{la}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-})]\\ i_{\mathrm{lb}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+}-\frac{2\mathrm{\&pi;}}{3})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-}+\frac{2\mathrm{\&pi;}}{3})]\\ i_{\mathrm{lc}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+}+\frac{2\mathrm{\&pi;}}{3})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-}-\frac{2\mathrm{\&pi;}}{3})]\end{array}\right.---\left(8\right)$

$\left\{\begin{array}{c}{u}_a=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[U_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{+})+U_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{-})+U_n^0\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^0)]\\ u_b=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[U_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{+}-\frac{2\mathrm{\&pi;}}{3})+U_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{-}+\frac{2\mathrm{\&pi;}}{3})+U_n^0\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^0)]\\ u_c=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[U_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{+}+\frac{2\mathrm{\&pi;}}{3})+U_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^{-}-\frac{2\mathrm{\&pi;}}{3})+U_n^0\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{un}}^0)]\end{array}\right.---\left(9\right)$

θ in formula ⁺ _inand θ ⁺ _unfor the initial phase angle of each primary current of positive sequence and voltage; θ ^- _inand θ ^- _unfor the initial phase angle of each primary current of negative phase-sequence and voltage; θ ⁰ _unfor the initial phase angle of zero sequence each voltage.

Through Fourier decomposition, calculate according to above-mentioned relation expression formula simultaneously, have:

Therefrom i can be seen _p, i _qin except DC component, the cycle of AC compounent is 1/6 of power cycle, and namely AC compounent mean value in 1/6 power cycle is 0.I can be obtained by this average algorithm _pand i _qdC component i _pand i _q:

That is:

The schematic diagram of its mean value theory method, refers to Fig. 2.

In like manner can obtain:

But this algorithm adopts and cuts off i _por i _qafter passage, accurately can not ask for fundamental positive sequence active current or fundamental positive sequence reactive current.To cut off i _pfor example:

$\left[\begin{array}{c}{i}_{\mathrm{af}}\\ i_{\mathrm{bf}}\\ i_{\mathrm{cf}}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_p\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right]=\left[\begin{array}{c}\sqrt{2}{I}_1^{+}\sin (\mathrm{\&omega;t}+{\mathrm{\&theta;}}_{i1}^{+})\\ \sqrt{2}{I}_1^{+}\sin (\mathrm{\&omega;t}+{\mathrm{\&theta;}}_{i1}^{+}-\frac{2\mathrm{\&pi;}}{3})\\ \sqrt{2}{I}_1^{+}\sin (\mathrm{\&omega;t}+{\mathrm{\&theta;}}_{i1}^{+}+\frac{2\mathrm{\&pi;}}{3})\end{array}\right]---\left(14\right)$

Under imperfect voltage conditions, phase angle be not equal to the phase angle theta of A phase fundamental positive sequence voltage ⁺ _u1, the phase place of the A phase line voltage detected due to phaselocked loop is not the phase place of fundamental positive sequence voltage, therefore, and i ⁺ _af, i ⁺ _bf, i ⁺ _cfit not fundamental positive sequence active current.In like manner can show that fundamental positive sequence reactive current also has same problem to exist.

Propose the method for synchronous rotary to solve the problem, its method is as follows: under pq coordinate, and electric current resultant vector i is projected as instantaneous positive sequence active current vector on voltage resultant vector u; Electric current resultant vector i is projected as instantaneous positive sequence reactive current vector in voltage resultant vector u normal direction.For positive sequence reactive current vector instantaneous under synchronous rotary, refer to Fig. 3.

$\begin{array}{c}\left[\begin{array}{c}{i}_{\mathrm{af}}^{+}\\ i_{\mathrm{bf}}^{+}\\ i_{\mathrm{cf}}^{+}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{i_p}^{\&prime;}\\ {i_q}^{\&prime;}\end{array}\right]=\\ \left[\begin{array}{c}\sqrt{2}{I}_1^{+}\sin ({\mathrm{\&theta;}}_{u1}^{+}-{\mathrm{\&theta;}}_{i1}^{+})\sin (\mathrm{\&omega;t}+{\mathrm{\&theta;}}_{u1}^{+})\\ \sqrt{2}{I}_1^{+}\sin ({\mathrm{\&theta;}}_{u1}^{+}-{\mathrm{\&theta;}}_{i1}^{+})\sin (\mathrm{\&omega;t}+{\mathrm{\&theta;}}_{u1}^{+}-\frac{2\mathrm{\&pi;}}{3})\\ \sqrt{2}{I}_1^{+}\sin ({\mathrm{\&theta;}}_{u1}^{+}-{\mathrm{\&theta;}}_{i1}^{+})\sin (\mathrm{\&omega;t}+{\mathrm{\&theta;}}_{u1}^{+}+\frac{2\mathrm{\&pi;}}{3})\end{array}\right]\end{array}---\left(17\right)$

There is distortion and asymmetric situation for line voltage simultaneously, carry out emulation experiment at Matlab7.1/Simulink environment.Nonlinear load selects three-phase bridge rectifier circuit, inductance L=2mH, resistance R=5 Ω; Under desirable electrical network voltage conditions, suppose supply voltage symmetry and undistorted phase voltage effective value is

220V, A phase voltage initial phase angle is 0 °.Under line voltage non-ideal condition, suppose that positive sequence phase voltage effective value is that 220V, ABC three-phase voltage initial phase is respectively 25 ° ,-125 ° 120 °, negative phase-sequence phase voltage effective value is 30V, increases by the quintuple harmonics of 10% on this basis respectively again.

Refer to Fig. 4, adopt the i that mean value theory and low-pass filter detect _pwaveform, under its desirable grid conditions.It is shorter than adopting the time of low-pass filter detection method to adopt the time of mean value theory detection method, therefore, adopts the real-time of mean value theory detection method better.

Fig. 5 is the current waveform of threephase load; Fig. 6 is the harmonic current of electric current testing detection herein; Fig. 7 is i _p-i _qthe harmonic current of algorithm, is actually harmonic wave and fundamental negative sequence current sum.Therefore, as can be seen from Fig. 6 and Fig. 7 relatively, if only compensation harmonic electric current, electric current testing is more accurate herein.

Fig. 8 is i _p-i _qalgorithm disconnects i _qafter, the waveform of A phase fundamental positive sequence electric current and A phase fundamental positive sequence voltage; Fig. 9 is the A phase fundamental positive sequence electric current of electric current testing detection herein and the waveform of A phase fundamental positive sequence voltage.Therefore, as can be seen from Fig. 8 and Fig. 9 relatively, electric current testing solves the phase problem of phaselocked loop herein.

Above the better embodiment of this patent is explained in detail, but this patent is not limited to above-mentioned embodiment, in the ken that one skilled in the relevant art possesses, can also makes a variety of changes under the prerequisite not departing from this patent aim.

Claims (8)

1. based on a three phase harmonic electric current testing for synchronous rotary mean value theory, it is characterized in that, the current detecting process of described synchronous rotary mean value theory is: three-phase power grid voltage u _a, u _b, u _cwith threephase load current i _la, i _lb, i _lcu under α β coordinate transform transforms to them on α β coordinate _α, u _βand i _α, i _βand i _{α ＇}, i _{β ＇}, its relational expression is as follows:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right]=C_{23}\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right],\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=C_{23}\left[\begin{array}{c}{i}_{\mathrm{la}}\\ i_{\mathrm{lb}}\\ i_{\mathrm{lc}}\end{array}\right],\left[\begin{array}{c}{i}_{{\mathrm{\&alpha;}}^{\&prime;}}\\ i_{{\mathrm{\&beta;}}^{\&prime;}}\end{array}\right]=C_{{23}^{\&prime;}}\left[\begin{array}{c}{i}_{1a}\\ i_{1b}\\ i_{1c}\end{array}\right]---\left(1\right)$

Its transition matrix is:

$C_{23}=\sqrt{\frac{2}{3}}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}\end{array}\right],$

$C_{{23}^{\&prime;}}=\sqrt{\frac{2}{3}}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]---\left(2\right)$

Meanwhile, A phase line voltage, through phaselocked loop and cosine and sine signal circuit for generating, obtains and the synchronous cosine and sine signal of A phase line voltage, if phase place is its relational expression is as follows:

$\left[\begin{array}{c}{u}_p\\ u_q\end{array}\right]=C\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}}\\ u_{\mathrm{\&beta;}}\end{array}\right],\left[\begin{array}{c}{i}_p\\ i_q\end{array}\right]=C\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right],$

$\left[\begin{array}{c}{i}_{p^{\&prime;}}\\ i_{q^{\&prime;}}\end{array}\right]=C\left[\begin{array}{c}{i}_{{\mathrm{\&alpha;}}^{\&prime;}}\\ i_{{\mathrm{\&beta;}}^{\&prime;}}\end{array}\right]---\left(3\right)$

Wherein Matrix C is:

2. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 1, is characterized in that, obtain u through mean value theory _p, u _q, i _p, i _qand i _{p ＇}, i _{q ＇}dC component u _p, u _q, i _p, i _qand i _{p ＇}, i _{q ＇}, then obtain fundamental positive sequence voltage u respectively through inverse transformation _af, u _bf, u _cf, fundamental positive sequence current i _af1, i _bf1, i _cf1, fundamental negative sequence current i _{af ＇}, i _{bf ＇}, i _{cf ＇}, then, load current and fundamental positive sequence electric current and fundamental negative sequence current are subtracted each other the harmonic component i obtaining load current _ah, i _bh, i _ch;

$\left[\begin{array}{c}{i}_{\mathrm{af}1}\\ i_{\mathrm{bf}1}\\ i_{\mathrm{cf}1}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_p\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right],\left[\begin{array}{c}{i}_{{\mathrm{af}}^{\&prime;}}\\ i_{{\mathrm{bf}}^{\&prime;}}\\ i_{{\mathrm{cf}}^{\&prime;}}\end{array}\right]=C_{{32}^{\&prime;}}{C}^{-}\left[\begin{array}{c}{{\stackrel{\&OverBar;}{i}}_p}^{\&prime;}\\ {{\stackrel{\&OverBar;}{i}}_q}^{\&prime;}\end{array}\right],$

$\left[\begin{array}{c}{u}_{\mathrm{af}}\\ u_{\mathrm{bf}}\\ u_{\mathrm{cf}}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{\stackrel{\&OverBar;}{u}}_p\\ {\stackrel{\&OverBar;}{u}}_q\end{array}\right]---\left(5\right)$

$C_{32}=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right],$

$C_{{32}^{\&prime;}}=\sqrt{\frac{2}{3}}\left[\begin{array}{cc}1& 0\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}\end{array}\right],$

In addition, u _p, u _qand i _p, i _qi can be obtained through synchronous rotary _{p ＇}, i _{q ＇}, then fundamental positive sequence active current under inverse transformation can obtain imperfect voltage or fundamental positive sequence reactive current i ⁺ _af, i ⁺ _bf, i ⁺ _cf;

$\left[\begin{array}{c}{i}_{\mathrm{af}}^{+}\\ i_{\mathrm{bf}}^{+}\\ i_{\mathrm{cf}}^{+}\end{array}\right]=C_{32}{C}^{-}\left[\begin{array}{c}{i_p}^{\&prime;}\\ {i_q}^{\&prime;}\end{array}\right]---\left(7\right)$

$\left\{\begin{array}{c}{i}_{\mathrm{la}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-})]\\ i_{\mathrm{lb}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+}-\frac{2\mathrm{\&pi;}}{3})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-}+\frac{2\mathrm{\&pi;}}{3})]\\ i_{\mathrm{lc}}=\sqrt{2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[I_n^{+}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{+}+\frac{2\mathrm{\&pi;}}{3})+I_n^{-}\sin (\mathrm{n\&omega;t}+{\mathrm{\&theta;}}_{\mathrm{in}}^{-}-\frac{2\mathrm{\&pi;}}{3})]\end{array}\right.---\left(8\right)$

θ in formula ⁺ _inand θ ⁺ _unfor the initial phase angle of each primary current of positive sequence and voltage; θ ^- _inand θ ^- _unfor the initial phase angle of each primary current of negative phase-sequence and voltage; θ ⁰ _unfor the initial phase angle of zero sequence each voltage.

3. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 2, is characterized in that, through Fourier decomposition, calculates simultaneously, have according to above-mentioned relation expression formula:

Therefrom i can be seen _p, i _qin except DC component, the cycle of AC compounent is 1/6 of power cycle, and namely AC compounent mean value in 1/6 power cycle is 0; I can be obtained by this average algorithm _pand i _qdC component i _pand i _q:

${\stackrel{\&OverBar;}{i}}_p=\frac{6}{T}_t{\&Integral;}^{t+6/T}{i}_p\mathrm{dt},{\stackrel{\&OverBar;}{i}}_q=\frac{6}{T}{\&Integral;}^{t+\frac{6}{T}}{i}_q\mathrm{dt}---\left(11\right)_t$

That is:

4. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 2, is characterized in that, under pq coordinate, electric current resultant vector i is projected as instantaneous positive sequence active current vector on voltage resultant vector u; Electric current resultant vector i is projected as instantaneous positive sequence reactive current vector in voltage resultant vector u normal direction.

5. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 2, is characterized in that, there is distortion and asymmetric situation simultaneously, carry out emulation experiment at Matlab7.1/Simulink environment for line voltage.

6. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 2, is characterized in that, adopts the i that mean value theory and low-pass filter detect _pwaveform, detects under its desirable grid conditions, and it is shorter than adopting the time of low-pass filter detection method to adopt the time of mean value theory detection method.

7. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 2, is characterized in that, when only compensation harmonic electric current, the described three phase harmonic electric current testing based on synchronous rotary mean value theory is more accurate.

8. the three phase harmonic electric current testing based on synchronous rotary mean value theory according to claim 2, is characterized in that, the three phase harmonic electric current testing of described synchronous rotary mean value theory solves the phase problem of phaselocked loop.