Enhanced control method for three-vector prediction optimization based on extended active power theory
阅读说明:本技术 一种基于扩展有功理论的三矢量预测优化的增强控制方法 (Enhanced control method for three-vector prediction optimization based on extended active power theory ) 是由 冉晓洪 徐波 冷仕鹏 刘开培 于 2019-09-23 设计创作,主要内容包括:本发明提出一种基于扩展有功理论的三矢量预测优化的增强控制方法。本发明采集网侧三相电压、网侧三相电流以及直流侧电容电压,得到两相静止坐标系下的电压与电流;根据网侧两相静止坐标系的电压与电流,基于扩展瞬时有功功率理论建立其新型有功功率与无功功率的数学模型,分别求导并进行离散化;分析不平衡电网条件下AC/DC变换器的平均功率与二倍频分量的构成;建立新型有功与无功功率偏差平方和最小成本函数模型;确定第一作用非零电压矢量、第二作用非零电压矢量以及零电压矢量;进一步计算第一作用非零电压矢量、第二作用非零电压矢量以及零电压矢量的最优作用时间。本发明优点在于无需额外功率补偿计算,功率脉动小且网侧电流谐波含量小。(The invention provides an enhancement control method of three-vector prediction optimization based on an extended active power theory. The method comprises the steps of collecting network side three-phase voltage, network side three-phase current and direct current side capacitor voltage to obtain voltage and current under a two-phase static coordinate system; establishing a novel mathematical model of active power and reactive power of the grid-side two-phase static coordinate system based on an extended instantaneous active power theory according to the voltage and the current of the grid-side two-phase static coordinate system, and respectively deriving and discretizing; analyzing the composition of the average power and the frequency doubling component of the AC/DC converter under the unbalanced power grid condition; establishing a novel active and reactive power deviation square sum minimum cost function model; determining a first acting non-zero voltage vector, a second acting non-zero voltage vector and a zero voltage vector; further, the optimal acting time of the first acting non-zero voltage vector, the second acting non-zero voltage vector and the zero voltage vector is calculated. The method has the advantages of no need of extra power compensation calculation, small power pulsation and small harmonic content of the current on the network side.)
1. An enhancement control method of three-vector prediction optimization based on an extended active power theory is characterized by comprising the following steps:
step 1: collecting network side three-phase voltage, network side three-phase current and direct current side capacitor voltage, and respectively converting abc coordinate systems of the network side three-phase voltage and the network side three-phase current into an alpha beta coordinate system by using Clarke transformation so as to obtain voltage and current under a two-phase static coordinate system;
step 2: establishing a novel mathematical model of active power and reactive power of the grid-side two-phase static coordinate system based on an extended instantaneous active power theory according to the voltage and the current of the grid-side two-phase static coordinate system, and respectively deriving and discretizing;
and step 3: analyzing the composition of the average power and the second harmonic component of the AC/DC converter under the unbalanced power grid condition based on a novel mathematical model of active power and reactive power;
and 4, step 4: based on the power analysis of a converter under the condition of an unbalanced power grid, a novel active power deviation and reactive power deviation square sum minimum cost function model is established by taking the elimination of double-frequency fluctuation of active power and the guarantee of the sine of current on the grid side as control targets;
and 5: determining a first action nonzero voltage vector, a second action nonzero voltage vector and a zero voltage vector by utilizing a defined novel active power deviation and reactive power deviation square sum minimum cost function model;
step 6: respectively solving the partial derivatives of the defined novel active power deviation, reactive power deviation square and minimum cost function model to obtain a first action nonzero voltage vector, a second action nonzero voltage vector and the optimal action time of the zero voltage vector;
and 7: by utilizing a space vector modulation method, a switching signal is sent out to inhibit the second harmonic component of the novel active power of the AC/DC converter under the condition of unbalanced network voltage and reduce the harmonic content of network side current.
2. The enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: in the step 1, the three-phase voltage at the network side is as follows:
acquiring the three-phase voltage of the grid side through the three-phase voltage sensor;
the A-phase grid voltage is eaThe B-phase grid voltage is ebThe C-phase grid voltage is ec;
Collecting the three-phase current of the grid side through the three-phase current sensor;
in the step 1, the three-phase current at the network side is as follows:
the A-phase grid current is iaThe B-phase grid current is ibThe C-phase grid current is ic;
In the step 1, the voltage of the direct current side capacitor is as follows:
collecting the direct current side capacitance voltage through the direct current voltage sensor;
the voltage of the DC side capacitor is udc;
Transmitting the network side three-phase voltage, the network side three-phase current and the direct current side capacitor voltage to the main controller;
respectively converting an abc coordinate system of the three-phase voltage on the grid side into an alpha beta coordinate system by Clarke transformation, wherein the method comprises the following steps:
wherein e isαCorresponding three-phase voltage on grid side to grid voltage value on alpha axis, eβCorresponding the three-phase voltage on the network side to the voltage value of the power grid on the beta axis;
respectively converting an abc coordinate system of the three-phase current on the grid side into an alpha beta coordinate system by Clarke transformation, wherein the method comprises the following steps:
wherein iαThe grid side three-phase current corresponds to the grid current value i on the alpha axisβThe three-phase current at the network side corresponds to the current value of the power grid on a beta axis;
the grid-side three-phase voltage vector e can be expressed as:
e=eα+jeβ
the grid-side three-phase current vector i can be expressed as:
i=iα+jiβ
in addition, the amplitude and the phase angle of the three-phase voltage vector on the grid side are respectively as follows:
wherein E is the amplitude of the three-phase voltage vector on the network side, theta1Is the phase angle of the three-phase voltage vector on the network side.
3. The enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: step 2, establishing a novel mathematical model of active power and reactive power based on an extended instantaneous active power theory, wherein the expression is as follows:
wherein i*Is the conjugate of the grid-side three-phase current vector i, and e' represents the voltage vector obtained after the grid-side three-phase voltage vector e is delayed by 1/4 grid periods, PnewThe method comprises the steps of representing novel active power based on an extended instantaneous active power theory, Q representing reactive power based on the extended instantaneous active power theory, and Im representing the imaginary part of a vector; e.g. of the typeαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβFor the three-phase network voltage to correspond to the network voltage value on the beta axis, iαIs the power grid current value i of the three-phase power grid current corresponding to the alpha axisβThe current value of the power grid corresponding to the three-phase power grid current on the beta axis is obtained; e'αIs the value of the grid voltage on the delayed alpha axis, e'βThe value is the power grid voltage value on the beta axis after time delay;
in step 2, the new active power and reactive power derivation is respectively:
wherein e is a three-phase voltage vector on the network side, e*Is a three-phase power on the side of the networkThe conjugate of a voltage vector e, e' represents a voltage vector obtained after the delay of the three-phase voltage vector e at the grid side for 1/4 grid periods, v is an output voltage vector of the converter, v*For the conjugate of the converter output voltage vector v, R is the parasitic resistance value of the grid-side filter, L is the inductance value of the grid-side filter, and ω is the grid angular frequency;
discretizing the derivative of the novel active power and the reactive power into:
wherein k ispiRepresenting a voltage vector of vi(i-0, 1,2, …,7) new active power variation size, kqiRepresenting a voltage vector of vi(i is 0,1,2, …,7) and e is the amount of change in reactive power*kIs a three-phase voltage vector e on the network sidekIn kTsMagnitude of time, e'kRepresenting three-phase voltage vector e on network sidekVoltage vector obtained after 1/4 power grid cycles are delayed in kTsSize of the moment, ekFor grid side three-phase voltage vector at kTsMagnitude of time, vi *kFor converter output voltage vector vi kIn kTsSize of the moment, Pnew,kShowing the novel active power based on the theory of expanding the active power in kTsMagnitude of time, QkExpressing reactive power at kT based on the theory of expanding active powersThe magnitude of the time, R is the parasitic resistance value of the net-side filter, L is the inductance value of the net-side filter, and ω is the grid angular frequency.
4. The enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: the analysis of the average power and the second harmonic component of the AC/DC converter under the unbalanced power grid condition in the step 3 specifically comprises the following steps:
the novel active power and reactive power under the unbalanced grid voltage condition can be expressed as:
the average power and the second harmonic component of the novel instantaneous active power are as follows:
wherein e isdq +Is the positive sequence component of the grid voltage under the positive sequence rotating coordinate system idq +Is the positive sequence component of the grid current in a positive sequence rotating coordinate system, edq -Is the negative sequence component of the grid voltage under the negative sequence rotating coordinate system idq -Is the negative sequence component of the power grid current under the negative sequence rotating coordinate system,
the average power and the second harmonic component of the instantaneous reactive power are:
wherein e isdq +Is the positive sequence component of the grid voltage under the positive sequence rotating coordinate system idq +Is the positive sequence component of the grid current in a positive sequence rotating coordinate system, edq -Is the negative sequence component of the grid voltage under the negative sequence rotating coordinate system idq -Is the negative sequence component, Q, of the grid current in a negative sequence rotating coordinate system0Being a direct component of reactive power, Qc2Coefficient of the cosine term of the double frequency component of the reactive power, Qs2The coefficient is a sine term of a frequency doubling component of the reactive power;
by comparison, it can be seen that,
5. The enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: in step 4, in order to eliminate active power pulsation and obtain a unit power factor and ensure the sine of the current of the power grid, the equation can be described as follows:
wherein the content of the first and second substances,eαfor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβMapping the three-phase mains voltage to the mains voltage value, e 'on the β -axis'αIs the value of the grid voltage on the delayed alpha axis, e'βThe value is the power grid voltage value on the beta axis after time delay; i.e. iαIs the power grid current value i of the three-phase power grid current corresponding to the alpha axisβIs the grid current value i 'of the three-phase grid current corresponding to the beta axis'αIs the value of the grid voltage i 'on the delayed alpha axis'βThe value is the power grid voltage value on the beta axis after time delay;
solving the corresponding reference current as follows:
wherein e isαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβMapping the three-phase mains voltage to the mains voltage value, e 'on the β -axis'αIs the value of the grid voltage on the delayed alpha axis, e'βFor the value of the grid voltage on the beta axis after the delay,
obtaining a current reference value according to calculation, eliminating active power pulsation based on an extended instantaneous active power theory, obtaining a unit power factor, and ensuring the sine of the current of the power grid, wherein the power compensation size is as follows:
wherein the content of the first and second substances,
the step 4 of establishing a novel active power deviation and reactive power deviation square sum minimum cost function model specifically comprises the following steps:
in each control period, two adjacent non-zero voltage vectors and a zero voltage vector are used for synthesizing an expected vector, and by using the slope magnitude of the novel active power and reactive power, the magnitude of the novel active power and reactive power at the end of each control period can be expressed as:
wherein, Pnew(k +1) is novel active power at (k +1) TsSize of (D), Pnew(k) For new active power in kTsSize of the time, kp1For the first acting non-zero voltage vector to the new active power variation, kp2For the second-acting non-zero voltage vector to the new active power variation, kp0The variation of the zero vector to the novel active power; q (k +1) is reactive power at (k +1) TsThe magnitude of the time, Q (k), is the reactive power in kTsSize of the time, kq1For the variation of the first acting non-zero voltage vector on the reactive power, kq2Is of the second actionAmount of change of zero voltage vector to reactive power, kq0The variation of the zero vector to the reactive power; t is t1Is the magnitude of the first acting non-zero voltage vector2Is the magnitude of the second acting non-zero voltage vector0The action time size of the zero vector;
after each control cycle is finished, the error amounts of the novel active power and the novel reactive power are respectively
Wherein, Δ PnewThe error magnitude of the novel active power is shown, the delta Q is the error magnitude of the reactive power,
therefore, the cost function of the square sum of the active power deviation and the reactive power deviation established in step 4 is:
J(t1,t2)=(ΔPnew)2+(ΔQ)2。
6. the enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: in step 5, the determination of the first acting non-zero voltage vector, the second acting non-zero voltage vector and the zero vector is specifically as follows:
firstly, through the defined cost function, the minimum value of the cost function determined by traversing six non-zero voltage vectors is marked as JrAnd records the corresponding voltage vector VrI.e. a first acting non-zero voltage vector;
determining the second acting non-zero voltage vector taking into account VtMust be and VrTwo adjacent non-zero voltage vectors Vr-1And Vr+1Then calculate V separatelyr-1,Vr+1Value of cost function Jr-1And Jr+1If the voltage vector V is non-zeror-1Corresponding cost function value Jr-1Greater than a non-zero voltage vector Vr+1Corresponding cost function value Jr+1Then V ist=Vr+1Otherwise, Vt=Vr-1;
Wherein the zero vector is selected based on the minimum switching principle, and when the determined second acting non-zero voltage vector is V2,V4And V6At that time, t is the very beginning0T 4 and last t0The voltage vector of/4 is V0At t0/4+t1/2+t2/2+t0The zero voltage vector at the time point/2 is V7(ii) a When the determined second applied non-zero voltage vector is V1,V3And V5Then t is the beginning0T 4 and last t0The voltage vector of/4 is V0At t0/4+t1/2+t2/2+t0The zero voltage vector at the time point/2 is V0;
The determined voltage vectors in step 5 have 8 voltage vectors, wherein six non-zero voltage vectors are:
V1=(1,0,0),V2=(1,1,0),V3=(0,1,0),V4=(0,1,1),V5=(0,0,1),V6=(1,0,1);
the two zero voltage vectors in step 5 are:
V0=(0,0,0),V7=(1,1,1)。
7. the enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: in step 6, the optimal action time of the first action non-zero voltage vector, the second action non-zero voltage vector and the zero voltage vector is as follows:
wherein the content of the first and second substances,
and is provided with
Θ=kq0kp2-kq1kp2-kq2kp0+kq1kp0-kq0kp1+kq2kp1
Wherein k isp1For the first acting non-zero voltage vector to the new active power variation, kp2For the second acting non-zero voltage vector, kp0The variation of the zero vector to the novel active power; k is a radical ofq1For the variation of the first acting non-zero voltage vector on the reactive power, kq2For the variation of the second acting non-zero voltage vector to the reactive power, kq0The variation of the zero vector to the reactive power; t is t1Is the magnitude of the first acting non-zero voltage vector2Is the magnitude of the second acting non-zero voltage vector0The action time size of the zero vector;
suppose t1+t2>TsThen, the correction formula is:
thus, the action time of the zero voltage vector is:
t0=Ts-t1-t2。
8. the enhancement control method based on the extended active theory three-vector prediction optimization of claim 1, wherein: and 7, after determining the action time of the first action non-zero voltage vector, the second action non-zero voltage vector and the zero voltage vector, sending a switching signal to inhibit a second harmonic component of the novel active power of the AC/DC converter under the condition of unbalanced grid voltage and reduce the harmonic content of the current on the grid side by using a space vector modulation method.
9. A three-vector prediction optimization enhancement control system based on an extended active theory is characterized by comprising the following components: the system comprises a three-phase alternating current power grid, a three-phase filter inductor, a three-phase voltage sensor, a three-phase current sensor, a direct current voltage sensor, a main controller, a three-phase AC/DC converter, a direct current side capacitor and a direct current side load;
the three-phase alternating current power grid is connected with the three-phase voltage sensor through a wire; the three-phase power grid is connected with the three-phase current sensor through a wire; the direct current side capacitor is connected with the direct current voltage sensor through a lead; the main controller is respectively connected with the three-phase voltage sensor, the three-phase current sensor and the direct current voltage sensor in sequence through leads; the main controller is connected with the three-phase AC/DC converter through a lead; the three-phase alternating current power grid, the three-phase filter inductor, the three-phase AC/DC converter, the direct current side capacitor and the direct current side load are sequentially connected in series through a lead.
Technical Field
The invention belongs to the technical field of operation and control of a converter of a flexible direct current transmission system, and particularly relates to an enhanced control method of three-vector prediction optimization based on an extended active power theory.
Technical Field
The AC micro-grid and the DC micro-grid become main components of a power distribution network in China gradually and respectively consist of a distributed power supply, an energy conversion device, an energy storage device and an AC/DC load, wherein an AC/DC converter connecting the AC micro-grid and the DC micro-grid becomes an important support of the whole micro-grid, and the stable operation capability of the AC/DC converter under the complex power grid operation condition has important influence on the safe and reliable operation of the micro-grid. Therefore, the research on the stable control of the AC/DC converter under the complex grid operation condition, particularly under the unbalanced grid condition, has important practical significance.
At present, as the rapid development of model predictive control technology has become one of the important control methods of power electronic converters, the method has wide application in AC/DC converters, mainly including: the method comprises the following steps of single-vector/multi-vector model predictive control of a converter under a normal operation condition and single-vector/multi-vector model predictive control with power compensation under an unbalanced power grid condition, but the control method needs to calculate extra power compensation in each control period and is large in calculation amount. Therefore, scholars propose single-vector and multi-vector model predictive control methods under unbalanced power grid conditions based on the extended instantaneous power theory, the control methods do not need sequence component decomposition and extra power compensation calculation, the single-vector model predictive control method is developed to the multi-vector model predictive control technology, and the control precision is higher and higher. In order to further enrich the diversity and control precision of model prediction technology, the invention defines a calculation method for expanding instantaneous active power, introduces the method into the design of a controller of an AC/DC converter under the condition of an unbalanced power grid, and provides an enhanced control method based on three-vector prediction optimization of an expanded active theory. The control method does not need sequence component decomposition, a phase-locked loop, extra power compensation calculation and the like, and has the characteristics of high control precision and good control performance.
Disclosure of Invention
The technical scheme of the system is a three-vector prediction optimization enhancement control method based on an extended active power theory, and is characterized by comprising the following steps: the system comprises a three-phase alternating current power grid, a three-phase filter inductor, a three-phase voltage sensor, a three-phase current sensor, a direct current voltage sensor, a main controller, a three-phase AC/DC converter, a direct current side capacitor and a direct current side load;
the three-phase alternating current power grid is connected with the three-phase voltage sensor through a wire; the three-phase power grid is connected with the three-phase current sensor through a wire; the direct current side capacitor is connected with the direct current voltage sensor through a lead; the main controller is respectively connected with the three-phase voltage sensor, the three-phase current sensor and the direct current voltage sensor in sequence through leads; the main controller is connected with the three-phase AC/DC converter through a lead; the three-phase alternating current power grid, the three-phase filter inductor, the three-phase AC/DC converter, the direct current side capacitor and the direct current side load are sequentially connected in series through a lead.
The invention provides an enhancement control method of three-vector prediction optimization based on an extended active power theory, which mainly comprises the following steps:
step 1: collecting network side three-phase voltage, network side three-phase current and direct current side capacitor voltage, and respectively converting abc coordinate systems of the network side three-phase voltage and the network side three-phase current into an alpha beta coordinate system by using Clarke transformation so as to obtain voltage and current under a two-phase static coordinate system;
step 2: establishing a novel mathematical model of active power and reactive power of the grid-side two-phase static coordinate system based on an extended instantaneous active power theory according to the voltage and the current of the grid-side two-phase static coordinate system, and respectively deriving and discretizing;
and step 3: analyzing the composition of the average power and the second harmonic component of the AC/DC converter under the unbalanced power grid condition based on a novel mathematical model of active power and reactive power;
and 4, step 4: based on the power analysis of a converter under the condition of an unbalanced power grid, a novel active power deviation and reactive power deviation square sum minimum cost function model is established by taking the elimination of double-frequency fluctuation of active power and the guarantee of the sine of current on the grid side as control targets;
and 5: determining a first action nonzero voltage vector, a second action nonzero voltage vector and a zero voltage vector by utilizing a defined novel active power deviation and reactive power deviation square sum minimum cost function model;
step 6: respectively solving the partial derivatives of the defined novel active power deviation, reactive power deviation square and minimum cost function model to obtain a first action nonzero voltage vector, a second action nonzero voltage vector and the optimal action time of the zero voltage vector;
and 7: a switching signal is sent out by utilizing a space vector modulation method to inhibit a second harmonic component of novel active power of the AC/DC converter under the condition of unbalanced grid voltage and reduce the harmonic content of current on the grid side;
preferably, in step 1, the grid-side three-phase voltage is:
acquiring the three-phase voltage of the grid side through the three-phase voltage sensor;
the A-phase grid voltage is eaThe B-phase grid voltage is ebThe C-phase grid voltage is ec;
Collecting the three-phase current of the grid side through the three-phase current sensor;
in the step 1, the three-phase current at the network side is as follows:
the A-phase grid current is iaThe B-phase grid current is ibThe C-phase grid current is ic;
In the step 1, the voltage of the direct current side capacitor is as follows:
collecting the direct current side capacitance voltage through the direct current voltage sensor;
the voltage of the DC side capacitor is udc;
Transmitting the network side three-phase voltage, the network side three-phase current and the direct current side capacitor voltage to the main controller;
respectively converting an abc coordinate system of the three-phase voltage on the grid side into an alpha beta coordinate system by Clarke transformation, wherein the method comprises the following steps:
wherein e isαCorresponding three-phase voltage on grid side to grid voltage value on alpha axis, eβCorresponding the three-phase voltage on the network side to the voltage value of the power grid on the beta axis;
respectively converting an abc coordinate system of the three-phase current on the grid side into an alpha beta coordinate system by Clarke transformation, wherein the method comprises the following steps:
wherein iαThe grid side three-phase current corresponds to the grid current value i on the alpha axisβThe three-phase current at the network side corresponds to the current value of the power grid on a beta axis;
the grid-side three-phase voltage vector e can be expressed as:
e=eα+jeβ
the grid-side three-phase current vector i can be expressed as:
i=iα+jiβ
in addition, the amplitude and the phase angle of the three-phase voltage vector on the grid side are respectively as follows:
wherein E is the amplitude of the three-phase voltage vector on the network side, theta1Is the phase angle of the three-phase voltage vector at the network side;
preferably, in
wherein i*Is the conjugate of the grid-side three-phase current vector i, and e' represents the voltage vector obtained after the grid-side three-phase voltage vector e is delayed by 1/4 grid periods, PnewThe method comprises the steps of representing novel active power based on an extended instantaneous active power theory, Q representing reactive power based on the extended instantaneous active power theory, and Im representing the imaginary part of a vector; e.g. of the typeαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβFor the three-phase network voltage to correspond to the network voltage value on the beta axis, iαIs the power grid current value i of the three-phase power grid current corresponding to the alpha axisβThe current value of the power grid corresponding to the three-phase power grid current on the beta axis is obtained; e'αIs the value of the grid voltage on the delayed alpha axis, e'βThe value is the power grid voltage value on the beta axis after time delay;
in
wherein e is a three-phase voltage vector on the network side, e*Is the conjugate of a grid-side three-phase voltage vector e, e' represents a voltage vector obtained after the grid-side three-phase voltage vector e is delayed by 1/4 power grid periods, v is a converter output voltage vector, v*For the conjugate of the converter output voltage vector v, R is the parasitic resistance value of the grid-side filter, L is the inductance value of the grid-side filter, and ω is the grid angular frequency;
discretizing the derivative of the novel active power and the reactive power into:
wherein k ispiRepresenting a voltage vector of vi(i-0, 1,2, …,7) new active power variation size, kqiRepresenting a voltage vector of vi(i is 0,1,2, …,7) and e is the amount of change in reactive power*kIs a three-phase voltage vector e on the network sidekIn kTsMagnitude of time, e'kRepresenting three-phase voltage vector e on network sidekVoltage vector obtained after 1/4 power grid cycles are delayed in kTsSize of the moment, ekFor grid side three-phase voltage vector at kTsMagnitude of time, vi *kFor converter output voltage vector vi kIn kTsSize of the moment, Pnew,kShowing the novel active power based on the theory of expanding the active power in kTsMagnitude of time, QkExpressing reactive power at kT based on the theory of expanding active powersThe magnitude of the moment, R is the parasitic resistance value of the grid-side filter, L is the inductance value of the grid-side filter, and omega is the grid angular frequency;
preferably, the analyzing the average power and the second harmonic component of the AC/DC converter under the unbalanced grid condition in step 3 specifically includes:
the novel active power and reactive power under the unbalanced grid voltage condition can be expressed as:
the average power and the second harmonic component of the novel instantaneous active power are as follows:
wherein e isdq +Is the positive sequence component of the grid voltage under the positive sequence rotating coordinate system idq +For positive sequence of the grid current under the positive sequence rotating coordinate systemComponent edq -Is the negative sequence component of the grid voltage under the negative sequence rotating coordinate system idq -Is the negative sequence component of the power grid current under the negative sequence rotating coordinate system,
is a direct current component of the novel active power,the cosine coefficient of the double frequency component of the active power,the sine term coefficient is a frequency doubling component of the novel active power;
the average power and the second harmonic component of the instantaneous reactive power are:
wherein e isdq +Is the positive sequence component of the grid voltage under the positive sequence rotating coordinate system idq +Is the positive sequence component of the grid current in a positive sequence rotating coordinate system, edq -Is the negative sequence component of the grid voltage under the negative sequence rotating coordinate system idq -Is the negative sequence component, Q, of the grid current in a negative sequence rotating coordinate system0Being a direct component of reactive power, Qc2Coefficient of the cosine term of the double frequency component of the reactive power, Qs2Being coefficients of a second harmonic component sine term of reactive power;
By comparison, it can be seen that,
andthat is, under the condition of an unbalanced power grid, the novel 2-frequency multiplication fluctuation of active power is eliminated, and simultaneously the 2-frequency multiplication fluctuation of reactive power is also eliminated;preferably, in
wherein e isαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβMapping the three-phase mains voltage to the mains voltage value, e 'on the β -axis'αIs the value of the grid voltage on the delayed alpha axis, e'βThe value is the power grid voltage value on the beta axis after time delay; i.e. iαIs the power grid current value i of the three-phase power grid current corresponding to the alpha axisβIs the grid current value i 'of the three-phase grid current corresponding to the beta axis'αIs the value of the grid voltage i 'on the delayed alpha axis'βThe value is the power grid voltage value on the beta axis after time delay;the reference value of the novel active power is obtained;
solving the corresponding reference current as follows:
wherein e isαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβMapping the three-phase mains voltage to the mains voltage value, e 'on the β -axis'αIs the value of the grid voltage on the delayed alpha axis, e'βFor time-delayed beta axisThe value of the grid voltage of (a),
is a reference value of the novel active power,for the reference value of the three-phase grid current corresponding to the grid current on the alpha axis,corresponding the three-phase grid current to the reference value of the grid current on the beta axis;obtaining a current reference value according to calculation, eliminating active power pulsation based on an extended instantaneous active power theory, obtaining a unit power factor, and ensuring the sine of the current of the power grid, wherein the power compensation size is as follows:
wherein the content of the first and second substances,
reference value, Q, for new active powerrefIs a reference value of reactive power, PcompMagnitude of compensation for new active power, QcompThe compensation quantity is the reactive power; by comparison, the control target of eliminating active power pulsation, obtaining unit power factor and ensuring power grid current sine is realized on the basis of an expansion instantaneous active power theory under the condition of an unbalanced power grid, and extra power compensation is not needed.The
in each control period, two adjacent non-zero voltage vectors and a zero voltage vector are used for synthesizing an expected vector, and by using the slope magnitude of the novel active power and reactive power, the magnitude of the novel active power and reactive power at the end of each control period can be expressed as:
wherein, Pnew(k +1) is novel active power at (k +1) TsSize of (D), Pnew(k) For new active power in kTsSize of the time, kp1For the first acting non-zero voltage vector to the new active power variation, kp2For the second-acting non-zero voltage vector to the new active power variation, kp0The variation of the zero vector to the novel active power; q (k +1) is reactive power at (k +1) TsThe magnitude of the time, Q (k), is the reactive power in kTsSize of the time, kq1For the variation of the first acting non-zero voltage vector on the reactive power, kq2For the variation of the second acting non-zero voltage vector to the reactive power, kq0The variation of the zero vector to the reactive power; t is t1Is the magnitude of the first acting non-zero voltage vector2Is the magnitude of the second acting non-zero voltage vector0The action time size of the zero vector;
after each control cycle is finished, the error amounts of the novel active power and the novel reactive power are respectively
Wherein, Δ PnewThe error magnitude of the novel active power is shown, the delta Q is the error magnitude of the reactive power,
reference value, Q, for new active powerrefIs a reference value of reactive power;therefore, the cost function of the square sum of the active power deviation and the reactive power deviation established in
J(t1,t2)=(ΔPnew)2+(ΔQ)2
preferably, the determining of the first acting non-zero voltage vector, the second acting non-zero voltage vector and the zero vector in step 5 is specifically as follows:
firstly, through the defined cost function, the minimum value of the cost function determined by traversing six non-zero voltage vectors is marked as JrAnd records the corresponding voltage vector VrI.e. a first acting non-zero voltage vector;
determining the second acting non-zero voltage vector taking into account VtMust be and VrTwo adjacent non-zero voltage vectors Vr-1And Vr+1Then calculate V separatelyr-1,Vr+1Value of cost function Jr-1And Jr+1If the voltage vector V is non-zeror-1Corresponding cost function value Jr-1Greater than a non-zero voltage vector Vr+1Corresponding cost function value Jr+1Then V ist=Vr+1Otherwise, Vt=Vr-1;
Wherein the zero vector is selected based on the minimum switching principle, and when the determined second acting non-zero voltage vector is V2,V4And V6At that time, t is the very beginning0T 4 and last t0The voltage vector of/4 is V0At t0/4+t1/2+t2/2+t0The zero voltage vector at the time point/2 is V7(ii) a When the determined second applied non-zero voltage vector is V1,V3And V5Then t is the beginning0T 4 and last t0The voltage vector of/4 is V0At t0/4+t1/2+t2/2+t0The zero voltage vector at the time point/2 is V0;
The determined voltage vectors in step 5 have 8 voltage vectors, wherein six non-zero voltage vectors are:
V1=(1,0,0),V2=(1,1,0),V3=(0,1,0),V4=(0,1,1),V5=(0,0,1),V6=(1,0,1);
the two zero voltage vectors in step 5 are:
V0=(0,0,0),V7=(1,1,1);
preferably, in
wherein the content of the first and second substances,
and is provided with
Θ=kq0kp2-kq1kp2-kq2kp0+kq1kp0-kq0kp1+kq2kp1
Wherein k isp1For the first acting non-zero voltage vector to the new active power variation, kp2For the second acting non-zero voltage vector, kp0The variation of the zero vector to the novel active power; k is a radical ofq1For the variation of the first acting non-zero voltage vector on the reactive power, kq2For the variation of the second acting non-zero voltage vector to the reactive power, kq0The variation of the zero vector to the reactive power; t is t1Is the magnitude of the first acting non-zero voltage vector2Is the magnitude of the second acting non-zero voltage vector0The action time size of the zero vector;reference value, Q, for new active powerrefIs a reference value of reactive power, TsRepresents a control period; pnew(k) To new active power kTsThe magnitude of the time, Q (k), is the reactive power kTsThe size of the moment;
suppose t1+t2>TsThen, the correction formula is:
thus, the action time of the zero voltage vector is:
t0=Ts-t1-t2
step 7, after determining the action time of the first action nonzero voltage vector, the second action nonzero voltage vector and the zero voltage vector, sending a switching signal to suppress a second harmonic component of the novel active power of the AC/DC converter under the unbalanced grid voltage condition and reduce the harmonic content of the current on the grid side by using a space vector modulation method;
the method has the advantages that the control method does not need extra power compensation calculation, realizes unbalanced control under a static coordinate system, and has small power pulsation, small harmonic content of network side current and high precision.
Drawings
FIG. 1: optimizing and enhancing a control flow chart for three-vector prediction based on an extended active theory;
FIG. 2: the active power and reactive power results of the enhanced control based on the extended active theory;
FIG. 3: the three-phase voltage and three-phase current result of the enhanced control based on the extended active theory;
FIG. 4: the simulation result of the A-phase voltage and the A-phase current based on the extended active theory is obtained;
FIG. 5: phase current spectrum diagram.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical solution of the present invention is further specifically described by embodiments with reference to fig. 1 to 5. In the embodiment of the invention, in order to verify the effectiveness of the three-vector prediction optimization enhancement control algorithm based on the extended active power theory, a model of a three-phase two-level AC/DC converter is built for simulation verification.
In the embodiment of the present invention, an AC/DC converter system is constructed, including: the system comprises a three-phase alternating current power grid, a three-phase filter inductor, a three-phase voltage sensor, a three-phase current sensor, a direct current voltage sensor, a main controller, a three-phase AC/DC converter, a direct current side capacitor and a direct current side load;
the three-phase alternating current power grid is connected with the three-phase voltage sensor through a wire; the three-phase power grid is connected with the three-phase current sensor through a wire; the direct current side capacitor is connected with the direct current voltage sensor through a lead; the main controller is respectively connected with the three-phase voltage sensor, the three-phase current sensor and the direct current voltage sensor in sequence through leads; the main controller is connected with the three-phase AC/DC converter through a lead; the three-phase alternating current power grid, the three-phase filter inductor, the three-phase AC/DC converter, the direct current side capacitor and the direct current side load are sequentially connected in series through a lead.
The three-phase alternating current grid model is TSGC-9 kVA; the three-phase filter inductor is selected as GT-LOR-0012; the model of the three-phase voltage sensor is ZMPT 107; the three-phase current sensor is selected to be ZMCT 101B; the direct-current voltage sensor is selected from HCPL 7840; the master controller is TMS320F28069 in type selection; the three-phase AC/DC converter consists of six IGBTs, and the selection type of the IGBT is 2MBI200U 4H-170-50; the direct current side capacitor is selected to be an electrolytic capacitor of 2200 mu F; the DC side load is selected to be a 31 ohm resistor.
The flow chart of the three-vector prediction optimization enhancement control method based on the extended active power theory is shown in fig. 1. The unbalance degree of the power grid voltage is set to be 10%, the sampling frequency is 12.8kHz, the reference value of novel active power is 3000W, the reference value of reactive power is 0Var, the direct-current side capacitor is 2200 muF, the load resistor is 31 omega, and the positive sequence voltage amplitude V of the power grid is V+Set to 122.45V, negative sequence voltage magnitude V-Set to 12.245V. Further, the DC voltage is set to 300V, and it is assumed that the DC voltage is performed by an inverter at the opposite endAnd (5) controlling.
The following describes the embodiments of the present invention with reference to fig. 1 to 5:
step 1: collecting network side three-phase voltage, network side three-phase current and direct current side capacitor voltage, and respectively converting abc coordinate systems of the network side three-phase voltage and the network side three-phase current into an alpha beta coordinate system by using Clarke transformation so as to obtain voltage and current under a two-phase static coordinate system; wherein, the positive sequence voltage amplitude V+122.45V, negative sequence voltage amplitude V—12.245V;
in the step 1, the three-phase voltage at the network side is as follows:
acquiring the three-phase voltage of the grid side through the three-phase voltage sensor;
the A-phase grid voltage is eaThe B-phase grid voltage is ebThe C-phase grid voltage is ec;
Collecting the three-phase current of the grid side through the three-phase current sensor;
in the step 1, the three-phase current at the network side is as follows:
the A-phase grid current is iaThe B-phase grid current is ibThe C-phase grid current is ic;
In the step 1, the voltage of the direct current side capacitor is as follows:
collecting the direct current side capacitance voltage through the direct current voltage sensor;
the voltage of the DC side capacitor is udc;
Transmitting the network side three-phase voltage, the network side three-phase current and the direct current side capacitor voltage to the main controller;
respectively converting an abc coordinate system of the three-phase voltage on the grid side into an alpha beta coordinate system by Clarke transformation, wherein the method comprises the following steps:
wherein e isαCorresponding three-phase voltage on grid side to grid voltage value on alpha axis, eβCorresponding the three-phase voltage on the network side to the voltage value of the power grid on the beta axis;
respectively converting an abc coordinate system of the three-phase current on the grid side into an alpha beta coordinate system by Clarke transformation, wherein the method comprises the following steps:
wherein iαThe grid side three-phase current corresponds to the grid current value i on the alpha axisβThe three-phase current at the network side corresponds to the current value of the power grid on a beta axis;
the grid-side three-phase voltage vector e can be expressed as:
e=eα+jeβ
the grid-side three-phase current vector i can be expressed as:
i=iα+jiβ
in addition, the amplitude and the phase angle of the three-phase voltage vector on the grid side are respectively as follows:
wherein E is the amplitude of the three-phase voltage vector on the network side, theta1Is the phase angle of the three-phase voltage vector at the network side;
wherein i*Is the conjugate of the grid-side three-phase current vector i, and e' represents the voltage vector obtained after the grid-side three-phase voltage vector e is delayed by 1/4 grid periods, PnewThe method comprises the steps of representing novel active power based on an extended instantaneous active power theory, Q representing reactive power based on the extended instantaneous active power theory, and Im representing the imaginary part of a vector; e.g. of the typeαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβFor the three-phase network voltage to correspond to the network voltage value on the beta axis, iαIs the power grid current value i of the three-phase power grid current corresponding to the alpha axisβThe current value of the power grid corresponding to the three-phase power grid current on the beta axis is obtained; e'αIs the value of the grid voltage on the delayed alpha axis, e'βThe value is the power grid voltage value on the beta axis after time delay;
in
wherein e is a three-phase voltage vector on the network side, e*Is the conjugate of a grid-side three-phase voltage vector e, e' represents a voltage vector obtained after the grid-side three-phase voltage vector e is delayed by 1/4 power grid periods, v is a converter output voltage vector, v*For the conjugate of the converter output voltage vector v, R is the parasitic resistance value of the grid-side filter, L is the inductance value of the grid-side filter, and ω is the grid angular frequency; in the invention, R is 0.3 omega, L is 10mH, and omega is 314 rad/s;
discretizing the derivative of the novel active power and the reactive power into:
wherein k ispiRepresenting a voltage vector of vi(i-0, 1,2, …,7) new active power variation size, kqiRepresenting a voltage vector of vi(i is 0,1,2, …,7) and e is the amount of change in reactive power*kIs a three-phase voltage vector e on the network sidekIn kTsMagnitude of time, e'kRepresenting three-phase voltage vector e on network sidekVoltage vector obtained after 1/4 power grid cycles are delayed in kTsSize of the moment, ekFor grid side three-phase voltage vector at kTsMagnitude of time, vi *kFor converter output voltage vector vi kIn kTsSize of the moment, Pnew,kShowing the novel active power based on the theory of expanding the active power in kTsMagnitude of time, QkExpressing reactive power at kT based on the theory of expanding active powersThe magnitude of the moment, R is the parasitic resistance value of the grid-side filter, L is the inductance value of the grid-side filter, and omega is the grid angular frequency; in the invention, R is 0.3 omega, L is 10mH, and omega is 314 rad/s;
and step 3: analyzing the composition of the average power and the second harmonic component of the AC/DC converter under the unbalanced power grid condition based on a novel mathematical model of active power and reactive power;
the analysis of the average power and the second harmonic component of the AC/DC converter under the unbalanced power grid condition in the step 3 specifically comprises the following steps:
the novel active power and reactive power under the unbalanced grid voltage condition can be expressed as:
the average power and the second harmonic component of the novel instantaneous active power are as follows:
wherein e isdq +Is the positive sequence component of the grid voltage under the positive sequence rotating coordinate system idq +Is the positive sequence component of the grid current in a positive sequence rotating coordinate system, edq -Is the negative sequence component of the grid voltage under the negative sequence rotating coordinate system idq -Is the negative sequence component of the power grid current under the negative sequence rotating coordinate system,
is a direct current component of the novel active power,the cosine coefficient of the double frequency component of the active power,the sine term coefficient is a frequency doubling component of the novel active power;
the average power and the second harmonic component of the instantaneous reactive power are:
wherein e isdq +Is the positive sequence component of the grid voltage under the positive sequence rotating coordinate system idq +Is the positive sequence component of the grid current in a positive sequence rotating coordinate system, edq -Is the negative sequence component of the grid voltage under the negative sequence rotating coordinate system idq -Is the negative sequence component, Q, of the grid current in a negative sequence rotating coordinate system0Being a direct component of reactive power, Qc2Systems of cosine terms of the double frequency component of reactive powerNumber, Qs2The coefficient is a sine term of a frequency doubling component of the reactive power;
by comparison, it can be seen that,
andthat is, under the condition of an unbalanced power grid, the novel 2-frequency multiplication fluctuation of active power is eliminated, and simultaneously the 2-frequency multiplication fluctuation of reactive power is also eliminated;and 4, step 4: based on the power analysis of a converter under the condition of an unbalanced power grid, a novel active power deviation and reactive power deviation square sum minimum cost function model is established by taking the elimination of double-frequency fluctuation of active power and the guarantee of the sine of current on the grid side as control targets;
in
wherein e isαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβMapping the three-phase mains voltage to the mains voltage value, e 'on the β -axis'αIs the value of the grid voltage on the delayed alpha axis, e'βThe value is the power grid voltage value on the beta axis after time delay; i.e. iαIs the power grid current value i of the three-phase power grid current corresponding to the alpha axisβIs the grid current value i 'of the three-phase grid current corresponding to the beta axis'αIs the value of the grid voltage i 'on the delayed alpha axis'βThe value is the power grid voltage value on the beta axis after time delay;
the reference value of the novel active power is obtained;solving the corresponding reference current as follows:
wherein e isαFor the three-phase network voltage to correspond to the network voltage value on the alpha axis, eβMapping the three-phase mains voltage to the mains voltage value, e 'on the β -axis'αIs the value of the grid voltage on the delayed alpha axis, e'βFor the value of the grid voltage on the beta axis after the delay,
is a reference value of the novel active power,for the reference value of the three-phase grid current corresponding to the grid current on the alpha axis,corresponding the three-phase grid current to the reference value of the grid current on the beta axis;obtaining a current reference value according to calculation, eliminating active power pulsation based on an extended instantaneous active power theory, obtaining a unit power factor, and ensuring the sine of the current of the power grid, wherein the power compensation size is as follows:
wherein the content of the first and second substances,
reference value, Q, for new active powerrefIs a reference value of reactive power, PcompMagnitude of compensation for new active power, QcompThe compensation quantity is the reactive power; by comparison, the control target of eliminating active power pulsation, obtaining unit power factor and ensuring power grid current sine is realized on the basis of an expansion instantaneous active power theory under the condition of an unbalanced power grid, and extra power compensation is not needed.The
in each control period, two adjacent non-zero voltage vectors and a zero voltage vector are used for synthesizing an expected vector, and by using the slope magnitude of the novel active power and reactive power, the magnitude of the novel active power and reactive power at the end of each control period can be expressed as:
wherein, Pnew(k +1) is novel active power at (k +1) TsSize of (D), Pnew(k) For new active power in kTsSize of the time, kp1For the first acting non-zero voltage vector to the new active power variation, kp2For the second-acting non-zero voltage vector to the new active power variation, kp0The variation of the zero vector to the novel active power; q (k +1) is reactive power at (k +1) TsThe magnitude of the time, Q (k), is the reactive power in kTsSize of the time, kq1For the variation of the first acting non-zero voltage vector on the reactive power, kq2For the variation of the second acting non-zero voltage vector to the reactive power, kq0The variation of the zero vector to the reactive power; t is t1Is the magnitude of the first acting non-zero voltage vector2Is the magnitude of the second acting non-zero voltage vector0The action time size of the zero vector;
after each control cycle is finished, the error amounts of the novel active power and the novel reactive power are respectively
Wherein, Δ PnewThe error magnitude of the novel active power is shown, the delta Q is the error magnitude of the reactive power,
reference value, Q, for new active powerrefIs a reference value of reactive power;therefore, the cost function of the square sum of the active power deviation and the reactive power deviation established in
J(t1,t2)=(ΔPnew)2+(ΔQ)2
and 5: determining a first action nonzero voltage vector, a second action nonzero voltage vector and a zero voltage vector by utilizing a defined novel active power deviation and reactive power deviation square sum minimum cost function model;
in step 5, the determination of the first acting non-zero voltage vector, the second acting non-zero voltage vector and the zero vector is specifically as follows:
firstly, through the defined cost function, the minimum value of the cost function determined by traversing six non-zero voltage vectors is marked as JrAnd records the corresponding voltage vector VrI.e. a first acting non-zero voltage vector;
determining the second acting non-zero voltage vector taking into account VtMust be and VrTwo adjacent non-zero voltage vectors Vr-1And Vr+1Then calculate V separatelyr-1,Vr+1Value of cost function Jr-1And Jr+1If the voltage vector V is non-zeror-1Corresponding cost function value Jr-1 is greater than the non-zero voltage vector Vr+1Corresponding cost function value Jr+1Then V ist=Vr+1Otherwise, Vt=Vr-1;
Wherein the zero vector is selected based on the minimum switching principle, and when the determined second acting non-zero voltage vector is V2,V4And V6At that time, t is the very beginning0T 4 and last t0The voltage vector of/4 is V0At t0/4+t1/2+t2/2+t0The zero voltage vector at the time point/2 is V7(ii) a When the determined second applied non-zero voltage vector is V1,V3And V5Then t is the beginning0T 4 and last t0The voltage vector of/4 is V0At t0/4+t1/2+t2/2+t0The zero voltage vector at the time point/2 is V0;
The determined voltage vectors in step 5 have 8 voltage vectors, wherein six non-zero voltage vectors are:
V1=(1,0,0),V2=(1,1,0),V3=(0,1,0),V4=(0,1,1),V5=(0,0,1),V6=(1,0,1);
the two zero voltage vectors in step 5 are:
V0=(0,0,0),V7=(1,1,1);
step 6: respectively solving the partial derivatives of the defined novel active power deviation, reactive power deviation square and minimum cost function model to obtain a first action nonzero voltage vector, a second action nonzero voltage vector and the optimal action time of the zero voltage vector;
in
wherein the content of the first and second substances,
and is provided with
Θ=kq0kp2-kq1kp2-kq2kp0+kq1kp0-kq0kp1+kq2kp1
Wherein k isp1For the first acting non-zero voltage vector to the new active power variation, kp2For the second acting non-zero voltage vector, kp0The variation of the zero vector to the novel active power; k is a radical ofq1For the variation of the first acting non-zero voltage vector on the reactive power, kq2For the variation of the second acting non-zero voltage vector to the reactive power, kq0For zero vector to reactive powerA variation amount; t is t1Is the magnitude of the first acting non-zero voltage vector2Is the magnitude of the second acting non-zero voltage vector0The action time size of the zero vector;reference value, Q, for new active powerrefIs a reference value of reactive power, TsRepresents a control period; pnew(k) To new active power kTsThe magnitude of the time, Q (k), is the reactive power kTsThe size of the moment;
suppose t1+t2>TsThen, the correction formula is:
thus, the action time of the zero voltage vector is:
t0=Ts-t1-t2
and 7: a switching signal is sent out by utilizing a space vector modulation method to inhibit a second harmonic component of novel active power of the AC/DC converter under the condition of unbalanced grid voltage and reduce the harmonic content of current on the grid side;
step 7, after determining the action time of the first action nonzero voltage vector, the second action nonzero voltage vector and the zero voltage vector, sending a switching signal to suppress a second harmonic component of the novel active power of the AC/DC converter under the unbalanced grid voltage condition and reduce the harmonic content of the current on the grid side by using a space vector modulation method;
the simulation results of the three-vector prediction optimization enhancement control method based on the extended active theory are shown in fig. 2 to 5. Fig. 2 shows results of novel active power, conventional active power and reactive power under an unbalanced grid condition, fig. 3 shows simulation results of voltage and current of a three-phase grid under the unbalanced grid condition, fig. 4 is a phase diagram of voltage and current of an a-phase grid side, and fig. 5 is a frequency spectrum diagram of current under the unbalanced grid condition. As shown in fig. 2 and fig. 3, the new active power and reactive power of the three-vector prediction optimization enhanced control strategy based on the extended active theory can be controlled to be constant and effectively track their reference values, and the power ripple is small, the net side current is sinusoidal, and the control precision is high, but at this time, the traditional active power has larger power ripple. As can be seen from fig. 4, the grid-side voltage and the grid-side current are in phase, so the proposed control method can realize the unit power operation of the AC/DC converter. Under the condition of unbalanced grid voltage, the harmonic content of the grid-side current is higher due to the action of the negative sequence component, but the enhanced control strategy provided by the invention can not only make the grid-side current sinusoidal, but also make the harmonic content very low, which is only 0.54%, as shown in fig. 5.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
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