Inverter for a distributed power generator

Abstract

Provided is a maximum power point (MPP) tracker for a PV cell inverter, and a PV cell inverter. The MPP tracker decouples output power oscillations from the input power generation and extracts maximum available power from the PV cell. The PV cell inverter uses the MPP tracker and generates a sinusoidal output current from the MPP tracker output. The sinusoidal output current may be fed to a power distribution grid. The PV cell inverter may use a pulse width modulation technique to cancel harmonics in the sinusoidal output current. The circuits use a minimum number of components and avoid use of large electrolytic capacitors.

Claims

1. A compensator, comprising: an input that receives a signal corresponding to a voltage source inverter input voltage or a current source inverter input current and generates a compensation signal representing a deviation of the voltage source inverter input voltage or the current source inverter input current from a DC value; an input that receives a pulse width modulation reference signal and modifies the pulse width modulation reference signal according to the compensation signal, and produce a modified pulse width modulation reference signal; and an output that provides the modified pulse width modulation reference signal to a pulse width modulator; wherein the modified pulse width modulation reference signal controls the pulse width modulator such that a harmonic in a voltage source inverter output current or a current source inverter output current is substantially reduced; wherein the harmonic arises from voltage source inverter input voltage oscillation or current source inverter input current oscillation.

2. The compensator of claim 1, wherein the pulse width modulation reference signal is modified in proportion to the compensation signal; wherein the compensation signal is a ratio of average and instantaneous values of the voltage source inverter input voltage or the current source inverter input current.

3. The compensator of claim 1, wherein: the voltage source inverter output current or the current source inverter output current is connected to a power distribution grid having a grid frequency; and wherein at least one harmonic that is substantially reduced is at a frequency that is twice the grid frequency.

4. The compensator of claim 1, wherein the compensator is connected to a circuit comprising: a high side input point and a low side input point for connection to a distributed power generator; a parallel input capacitor connected across the high side input point and the low side input point; and a first regulating circuit connected in parallel with the parallel input capacitor, the first regulating circuit having a high side output point connected to the voltage source inverter input so as to provide the voltage source inverter input voltage; wherein the parallel input capacitor has a small value such that voltage source inverter input voltage oscillation is not substantially reduced.

5. The compensator of claim 4, wherein the first regulating circuit comprises: a switch connected between the high side input point and a node; an output inductor connected between the node and the high side output point; and a diode connected between the node and a low side output point.

6. The compensator of claim 4, wherein the first regulating circuit regulates voltage across the parallel input capacitor between a lower limit and an upper limit; wherein the upper limit is a reference voltage and the lower limit is selected so that a switching frequency of the switch and voltage oscillation across the parallel input capacitor do not exceed selected values.

7. The compensator of claim 6, Wherein the reference voltage is obtained from a maximum power point tracking (MPPT) algorithm.

8. The compensator of claim 1, wherein the compensator is connected to a circuit comprising: a high side input point and a low side input point for connection to a distributed power generator; a series input inductor having a first terminal and a second terminal, the first terminal connected to one of the high side input point and the low side input point; and a second regulating circuit connected between the second terminal of the series input inductor and the other of the high side input point and the low side input point, the second regulating circuit having a high side output point connected to the current source inverter input so as to provide the current source inverter input current; wherein the series input inductor has a small value such that current source inverter input current oscillation is not substantially reduced.

9. The compensator of claim 8, wherein the second regulating circuit comprises: a switch connected between the second terminal of the series input inductor and the other of the high side input point and the low side input point; and a diode connected in series between the second terminal of the series input inductor and a corresponding high side output point or low side output point.

10. The compensator of claim 8, wherein the second regulating circuit regulates current through the series input inductor between a lower limit and an upper limit; wherein the upper limit is a reference current and the lower limit is selected so that a switching frequency of the switch and current oscillation through the series input inductor do not exceed selected values.

11. The compensator of claim 10, wherein the reference current is obtained from a maximum power point tracking (MPPT) algorithm.

12. The compensator of claim 4, wherein the distributed power generator comprises a photovoltaic cell.

13. The compensator of claim 8, Wherein the distributed power generator comprises a photovoltaic cell.

14. A method for controlling a voltage source inverter or a current source inverter, comprising: receiving a signal corresponding to an input voltage of the voltage source inverter or an input current of the current source inverter and generating a compensation signal representing a deviation of the voltage source inverter input voltage or the current source inverter input current from a DC value; modifying a pulse width modulation reference signal according to the compensation signal; and outputting the modified pulse width modulation reference signal to a pulse width modulator; wherein the pulse width modulator controls a voltage source inverter or a current source inverter such that a harmonic in the voltage source inverter output current or current source inverter output current is substantially reduced; wherein the harmonic arises from voltage source inverter input voltage oscillation or current source inverter input current oscillation.

15. The method of claim 14, comprising modifying the pulse width modulation reference signal in proportion to the compensation signal, wherein the compensation signal is a ratio of average and instantaneous values of the voltage source inverter input voltage or the current source inverter input current.

16. The method of claim 14, comprising: connecting the voltage source inverter output current or the current source inverter output current to a power distribution grid having a grid frequency; and substantially reducing at least one harmonic at a frequency that is twice the grid frequency.

17. The method of claim 14, further comprising: using a first regulating circuit to provide the voltage source inverter input voltage, the first regulating circuit including: a high side input point and a low side input point for connection to a distributed power generator; and a parallel input capacitor connected across the high side input point and the low side input point; and selecting a small value of the parallel input capacitor such that voltage source inverter input voltage oscillation is not substantially reduced.

18. The method of claim 17, comprising: operating the first regulating circuit to regulate voltage across the parallel input capacitor between a lower limit and an upper limit; wherein the upper limit is a reference voltage; and selecting the lower limit so that a switching frequency of a switch of the first regulating circuit and voltage oscillation across the parallel input capacitor do not exceed selected values.

19. The method of claim 18, comprising obtaining the reference voltage from a maximum power point tracking (MPPT) algorithm.

20. The method of claim 14, further comprising: using a second regulating circuit to provide the current source inverter input current, the second regulating circuit including: a high side input point and a low side input point for connection to a distributed power generator; and a series input inductor connected in series with the high side input point or the low side input point; and selecting a small value of the series input inductor such that current source inverter input current oscillation is not substantially reduced.

21. The method of claim 20, comprising: operating the second regulating circuit to regulate current through the series input inductor between a lower limit and an upper limit; wherein the upper limit is a reference current; and selecting the lower limit so that a switching frequency of a switch of the second regulating circuit and current oscillation through the series input inductor do not exceed selected values.

22. The method of claim 21, comprising obtaining the reference current from a maximum power point tracking (MPPT) algorithm.

23. The method of claim 17, wherein the distributed power generator comprises a photovoltaic cell.

24. The method of claim 20, wherein the distributed power generator comprises a photovoltaic cell.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) For a better understanding of the invention, and to show more clearly how it may be carried into effect, embodiments will now be described, by way of example, with reference to the accompanying drawings, wherein:

(2) FIG. 1A shows a block diagram of PV cell systems categorized by different PV cell configurations and inverter types, according to the prior art.

(3) FIG. 1B shows a block diagram of a multi-string PV cell inverter configuration, according to the prior art.

(4) FIG. 2 is a generalized block diagram of a PV cell inverter according to an aspect of the invention.

(5) FIG. 3A is a schematic diagram of a maximum power point tracker circuit and a controller according to one embodiment. The inset plot of V.sub.pv as a function of time shows operation of the main switch S.sub.B according to one embodiment.

(6) FIG. 3B is a schematic diagram of a maximum power point tracker circuit and a controller according to another embodiment. The inset plot of I.sub.pv as a function of time shows operation of the main switch S.sub.B according to the embodiment.

(7) FIG. 3C shows only the ripple of the PV cell voltage, power, and current waveforms during three switching cycles of the embodiment of FIG. 3A.

(8) FIGS. 4A and 4B show voltage and current waveforms for the inductor L.sub.B in the embodiment of FIG. 3A.

(9) FIG. 5A is a schematic diagram of a single-string grid-connected PV cell inverter according to one embodiment.

(10) FIG. 5B is a schematic diagram of a multi-string grid-connected PV cell inverter based on the single-string embodiment of FIG. 5A.

(11) FIG. 6 shows an embodiment of a modified pulse width modulation technique used in the controller for the current source inverter of the embodiment shown in FIG. 5A or 5B.

(12) FIG. 7 is a block diagram of a control scheme for a single-string inverter according to one embodiment, showing control of the modified pulse width modulation technique of FIG. 6.

(13) FIG. 8 is a block diagram of a control scheme for a multi-string inverter based on the embodiment of FIG. 7.

(14) FIG. 9 is a plot showing output grid current with no harmonic cancellation and a 120 Hz harmonic, then harmonic cancellation, and finally with a low inductor current reference.

(15) FIG. 10 is a plot showing results of a simulation of the embodiments shown in FIGS. 5B and 8, under various conditions of irradiance level, input voltage, and partial shading of the PV cells.

DETAILED DESCRIPTION OF EMBODIMENTS

(16) Described herein are systems, circuits, and methods for obtaining power from a distributed power generator, the obtained power being suitable for injection into a power distribution grid. A distributed power generator may be, for example, a wind turbine or a photovoltaic cell. Whereas embodiments of the systems, circuits, and methods are described herein primarily with respect to photovoltaic cells, it will be appreciated that the systems, circuits, and methods are not limited thereto.

(17) For example, described herein is an inverter for obtaining power from one or more photovoltaic cells. In one embodiment, the inverter is for interfacing one or more PV cells to a power distribution grid. Such an embodiment is shown in FIG. 2. This embodiment includes an input capacitor C.sub.1 connected across the PV cell(s) 10, a first stage including an MPP tracker circuit 20 connected across the input capacitor, and a series inductor L.sub.B connected to the MPP tracker output, and a second stage including an output inverter, and an output capacitor C.sub.AC. The first stage also includes a controller 50 for the MPP tracker circuit 20, and a circuit 40 to generate a reference voltage. With the controller 20, the MPP tracker circuit 20 controls the voltage across the input capacitor C.sub.1. The second stage also includes a controller 60 for the inverter 30.

(18) Features of the PV inverter embodiments described herein include: a low PV cell voltage is accepted, which improves efficiency at partial shading conditions of the PV cells; a wide range of input voltage is accepted; adaptive control of the inductor L.sub.B current DC level optimizes the modulation index for the inverter over a wide range of input power levels; input and output power decoupling are provided with only a small input capacitor C.sub.1; a fast MPP tracker; and integration of the MPP tracker into a PV cell array is possible because no passive component is required for the input of the MPP tracker stage. These features will be described in detail below.

(19) As used herein, the terms maximum power point tracking (MPPT) and maximum power point tracker (MPP tracker) are distinct. MPPT refers to an algorithm and MPP tracker refers to hardware (i.e., a circuit). The MPPT calculates the optimum operating point for a distributed power generator such as a photovoltaic cell, and provides a reference point for MPP tracker to steer the system toward the optimum operating point.

(20) As used herein, the term photovoltaic cell refers to any cell having a light absorbing material to absorb photons and generate electrons via a photoelectric effect. A non-limiting example of a photovoltaic cell is a solar cell. The light absorbing material may absorb light in any wavelength or combination of wavelengths, including, for example, wavelengths of solar light that reach the earth's surface, and/or wavelengths of solar light beyond the earth's atmosphere. Two or more light absorbing materials having specific wavelengths of light absorption may be used in combination to take advantage of different light absorption and charge separation mechanisms. The light absorbing material may be configured as, for example, bulk material, thin-film (e.g., inorganic layers, organic dyes, and organic polymers), and/or nanocrystals. The photovoltaic cells may be combined into arrays, strings, or panels.

(21) As used herein, the term photovoltaic cell string refers to a plurality of photovoltaic cells connected together in a series, parallel, series-parallel, or other configuration.

(22) Power Decoupling

(23) The instantaneous output power oscillates at twice the grid frequency in single-phase grid-connected systems. In PV systems, the input power generation is dc and thus the oscillation of the instantaneous output power, if reflected in the input, causes the input operating point to deviate from dc. If there is power oscillation on the PV side, maximum power is only achievable at the peak of oscillation, which translates into less average power extraction than the available maximum power. This is a power loss that reduces the efficiency of the PV system. Substantially the same problem exists in systems with wind turbines or fuel cells at the input for single phase systems or unbalanced three phase systems. Therefore, power oscillation is a key problem in such systems and the converter should decouple the output power oscillation from the input dc power generation to maximize efficiency. Power decoupling is conventionally performed by using large electrolytic capacitors in the design to minimize the effect of the output power oscillation on the input operating point. However, use of large capacitors lowers the reliability of the hardware, resulting in high maintenance expenses.

(24) Conventional approaches use a control system to regulate the average of the input voltage or current to achieve maximum power point tracking and to reach sufficient amplification gain. In such approaches decoupling is accomplished by either passive elements or auxiliary power circuits.

(25) In contrast, the maximum power point tracker described herein forces the input voltage or current to track a reference signal very tightly. As a result, the double frequency oscillation is displaced and the input power generation is at or very close to the optimum dc level.

(26) Power decoupling as described herein may be implemented using a closed loop control system with high bandwidth, such as, for example, a hysteresis controller, or an open loop control system having high gain at the frequency of the oscillatory harmonic. That is, although the operating point of the converter oscillates at twice the grid frequency, the converter should respond with sufficient speed to reject the effect of this distortion from the power generation (e.g., PV) side.

(27) The high open loop gain or closed loop bandwidth of the system will eventually cause very low or zero steady state error with fast tracking of the input reference point. As a result, input power decoupling is accomplished only by means of the control strategy and/or the high switching frequency, rather than methods that use bulky passive elements or auxiliary circuits. For example, a high switching frequency converter at the PV side as described herein can remove the oscillatory harmonics at the input. Power decoupling may also be accomplished using a resonant controller tuned at the oscillatory harmonic to generate high open loop gain at the PV side converter.

(28) MPP Tracker

(29) FIG. 3A is a schematic diagram of an MPP tracker circuit 20, and its controller 50 and reference voltage circuit 40, according to one embodiment. The inset plot of V.sub.pv as a function of time shows an embodiment of a control strategy for this circuit. Other control strategies may also be used. In the embodiment shown in FIG. 3A, the MPP tracker circuit includes a series switch S.sub.B connected to the high side input terminal and a unidirectional conducting device such as a diode D.sub.B connected between the switch output and the low side input terminal. In operation, the main switch S.sub.B is used to regulate the input capacitor C.sub.1 voltage. Regulating the input voltage enables the inverter to displace output power oscillation from the input terminal, substantially removing PV cell voltage oscillation and avoiding the need for large input capacitors at the PV terminals. Removal of the input voltage oscillation stabilizes the input operating point, resulting in high efficiency conversion with much smaller capacitors.

(30) FIG. 3B is a schematic diagram of an MPP tracker circuit 20, and its controller 50 and reference voltage circuit 40, according to another embodiment. The inset plot of I.sub.pv as a function of time shows an embodiment of a control strategy for this circuit. Other control strategies may also be used. In the embodiment shown in FIG. 3B, the MPP tracker circuit includes a series input inductor L.sub.pv, a switch S.sub.B, and a unidirectional conducting device such as a diode D connected in series with the high side output terminal. In operation, the main switch S.sub.B is used to regulate the current through the inductor L.sub.pv. Regulating the inductor current enables the inverter to displace output power oscillation from the input terminal, substantially removing PV cell voltage oscillation and avoiding the need for large input capacitors at the PV terminals. Removal of the input current oscillation stabilizes the input operating point, resulting in high efficiency conversion with much smaller capacitors.

(31) FIG. 3C shows the ripple of the input voltage, power, and current waveforms from the PV cells, for the embodiment of FIG. 3A. A typical PV cell i-v characteristic curve includes three operating conditions: 1) operation at a voltage lower than the optimum point where the PV cell voltage is increased and the power is increased; 2) operation at a voltage higher than the optimum point where the PV cell voltage is increased and the power is decreased; and 3) operation around the optimum point where the PV voltage is increased and the power is maximum, where the MPP is tracked. It is clear from FIG. 3B that the MPP is tracked since during the rise time of the PV cell voltage, the output power reaches its maximum. The control strategy of the above MPP tracker embodiment may accept a reference voltage from any MPP tracking algorithm (such as, for example, a perturb/observe algorithm), to obtain the maximum power available from the PV cells independent of the output voltage and current. The power is delivered to the inverter stage 30 and, as described below, the output current and voltage of the MPP tracker are controlled and induced by the inverter stage. This topology may provide power to any load or inverter configuration (e.g., voltage source inverter, current source inverter) at the next stage.

(32) As shown in FIG. 4A, the output of the switch S.sub.B is a high frequency oscillating voltage V.sub.D. However, the input of the inverter 30 is a low frequency (e.g., twice the grid frequency, 120 Hz) oscillating voltage V.sub.inv. The current in the inductor L.sub.B includes dc, an oscillating current at twice the grid frequency, and high frequency harmonics. Therefore, as shown in FIG. 4B, the inductor current includes a double grid frequency harmonic that should not be injected to the output grid current. in one embodiment, described below, the double grid frequency harmonic is removed using a modified pulse width modulation (PWM) strategy.

(33) Control Strategy for MPP Tracker

(34) An embodiment of the input capacitor C.sub.1 voltage control may be briefly described as follows. The capacitor voltage V.sub.pv is maintained between two upper and lower levels. This is done by the hysteresis control strategy as shown in FIG. 3A. The controller may be implemented with two comparators and two comparison levels. The upper level, V.sub.pv.sup.ref, may be obtained from an MPPT algorithm. The lower level, V.sub.pv.sup.refV.sub.pv, is not constant and is calculated in such a way that for all conditions, the switching frequency and the voltage ripple do not exceed selected values. This will be shown below. When the input capacitor voltage V.sub.pv exceeds the upper level, the output of the upper comparator becomes high, the flip-flop is set, which turns the main switch S.sub.B on, and discharges the capacitor. The switch remains on until the flip-flop is reset when the capacitor voltage hits the lower limit.

(35) In summary, the controller maintains the PV cell voltage very close to the optimum reference point provided by the MPPT algorithm. Since the level of the input voltage is proportional to the power generation, by controlling the input voltage the power fed to the circuit is controlled and this stage becomes a controllable power source. For example, if the output of this stage was connected to a heater (e.g., a resistor), the heat transfer would be linearly controlled by the input reference voltage.

(36) The capacitor value and V.sub.pv may be selected such that the operating frequency of the circuit is always less than a certain limit and the voltage ripple is less than %8.5V.sub.pv.sup.MPP in order to reach a utilization ratio higher than %98. Any ripple at the PV cell voltage decreases the efficiency (or utilization ratio), because the maximum power is extracted when the voltage is equal to V.sub.pv.sup.MPP, and any deviation due to the voltage ripple decreases the output power.

(37) During the time that the switch S.sub.B is off the following relationship is valid:

(38) $\begin{array}{cc}Q=C{V}_{\mathrm{pv}}=i_{\mathrm{pv}}{t}_{\mathrm{off}}.Math.V_{\mathrm{pv}}=\frac{i_{\mathrm{pv}}}{C_{1}f},f=\frac{1}{t_{\mathrm{off}}}& \left(1\right)\end{array}$

(39) To limit the switching frequency, f is restricted because

(40) $f_{S=\frac{1}{t_{\mathrm{off}}+t_{\mathrm{on}}}}<f.$
The equation above shows that

(41) $f=\frac{i_{\mathrm{pv}}}{C_1{V}_{\mathrm{pv}}}.$
By substitution it can be shown that if V.sub.pv is chosen as

(42) $\frac{i_{\mathrm{pv}}}{C_1{f}^m},$
for all conditions the time off will be almost constant because

(43) $\frac{1}{t_{\mathrm{off}}}=f=f^m,$
where f.sup.m is the maximum frequency.

(44) The voltage of the PV cells is minimized, i.e., V.sub.min.sup.MPP, at the lowest operating temperature. As mentioned above, it is desired that V.sub.pv<%8.5V.sub.pv.sup.MPP. Therefore, this inequality holds true for all conditions if V.sub.pv<%8.5V.sub.min.sup.MPP.

(45) From (1) and the above inequality it can be shown that

(46) $\frac{i_{\mathrm{pv}}}{C_1{f}^d}<\%8.5V_{\min }^{MPP}.$
For this inequality to be true for all conditions, the left hand side is maximized to calculate the capacitor value. The maximum value of the PV cells i.sub.max.sup.MPP is known and occurs at irradiation. As a result, the input capacitor C.sub.1 value may be determined as:

(47) $C_1=\frac{i_{\max }^{MPP}}{\%8.5V_{\min }^{MPP}{f}^m}$

(48) It is clear from the above equation for C.sub.1 that in obtaining a desired PV voltage variation, there is a trade-off between the switching frequency and the capacitor value. If the parameters are chosen in this way, this control scheme provides that for all irradiation and temperature levels the circuit operates below the selected desired frequency and the above %98 utilization ratio. For example, if i.sub.pv.sup.max=4 A, V.sub.min.sup.MPP=100 V, and f.sup.m=20 KHz, the capacitor will be C.sub.1=20 F, where the PV cell voltage variation is selected to be V.sub.pv=5V.

(49) Current Source PV Cell Inverter

(50) FIG. 5A is a circuit diagram of a single-string PV cell inverter according to one embodiment. Shown is the PV cell string 10, the MPP tracker 20, a current source inverter 30, and a low pass filter 70 including Cf and Lf to eliminate output current high frequency components. The low pass filter 70 may be replaced by higher order filters for a further reduction in the size of the passive components.

(51) FIG. 5B shows a circuit diagram of a multi-string PV cell inverter according to another embodiment. This embodiment is based on the circuit of FIG. 5A, but includes two MPP tracker power circuits, and two strings of PV cell modules. However, any number of power circuits and PV cell strings may be used. In the first stage the MPP trackers are connected in parallel, and each MPP tracker is connected to a PV cell string. The second stage includes a current source inverter, which is connected to the distribution grid. With this embodiment of the control algorithm a voltage source inverter may be used instead of the current source inverter, if a small capacitor is used at the input of the voltage source inverter.

(52) In one embodiment, the controller for the current source inverter uses a PWM scheme. To understand the principle of operation, first assume that the current source inverter is fed by a dc current source and the PWM scheme modulates a sinusoidal reference waveform to generate a sinusoidal output current, as shown in FIG. 6. As a result of the PWM strategy the voltage induced at the input of the current source inverter is the modulated grid voltage, full-wave rectified, V.sub.inv, as shown in FIG. 4A. However, the input of the current source inverter stage is connected to the MPP tracker output, which is not a constant current source. Thus, the input current of the current source inverter changes according to the induced voltage as discussed above. Oscillation induced in the inductor current is inevitable because the input power generation is kept constant by the MPP tracker circuit, but the output power oscillates at twice the grid frequency and thus, the power oscillation has to be supplied from an energy storage component, such as the inductors of the MPP tracker circuits. Therefore, the PWM technique may be modified to generate a pure sinusoidal waveform based on the oscillatory input current source. In one embodiment, shown in FIG. 6, this is accomplished by formulating the inductor current, and then modifying the reference signal to the PWM modulator so that it regulates and controls the dc component of the inductor current i.sub.L, and prevents the double frequency harmonic component of i.sub.L from appearing in the output ac current.

(53) Inductor DC Current Regulation

(54) Inductor current regulation will now be described with respect to PV string #1 of FIG. 5B. Assume that the converter is lossless (P.sub.in=P.sub.avgo) and the output filter energy storage is negligible. Also, assume that there is only one PV cell string (string #1) connected to the circuit. Therefore, the only energy storage component is L.sub.A. As discussed above, the MPP tracker circuit extracts constant power from the PV cells. Assuming that the current source inverter generates a current in-phase with the grid voltage, the output power may be derived as follows:

(55) $\begin{array}{cc}{i}_o\left(t\right)=I_o\sin \left(t\right),v_o\left(t\right)=V_o\sin \left(t\right).Math.p_o\left(t\right)=\frac{1}{2}{V}_o{I}_o\left(1-\cos \left(2t\right)\right).Math.P_{\mathrm{in}}=P_o^{\mathrm{avg}}=\frac{1}{2}{}_0^{\frac{2}{}}{p}_o\left(t\right)t=\frac{1}{2}{V}_o{I}_o& \left(2\right)\end{array}$
At

(56) $t=\frac{}{4},$
we have po(t)=P.sub.in, and if

(57) 0$t\underset{\_}{\left(-\frac{}{4},\frac{}{4}\right),}$
the input power will be greater than the output power. Therefore, for this time period the inductor L.sub.A will be charged from IL.sub.Amin to IL.sub.Amax:

(58) $\begin{array}{cc}\frac{1}{2}{L}_A{I_L^2}_{{}_A\max }-\frac{1}{2}{L}_A{I}_{L_A\min }^2={}_{\frac{-}{4}}^{\frac{}{4}}\left(P_{\mathrm{in}}-p_o\left(t\right)\right)t=\frac{P_{\mathrm{in}}}{}.Math.& \left(3\right)\\ I_{L}A=\frac{P_{\mathrm{in}}}{2L_A{\stackrel{\_}{I}}_{L_A}},{\stackrel{\_}{I}}_{L_A}=\frac{I_{L_A\min }+I_{L_A\max }}{2}& \left(4\right)\end{array}$

(59) Since the inductor current is equal to its dc value at t=0, using a similar procedure as described above the inductor current as a function oft may be derived as follows:

(60) $\begin{array}{cc}{i}_{L_A}\left(t\right)=\sqrt{{\stackrel{\_}{I}}_{L_A}^2+\frac{1}{2L_A}{V}_o{I}_o\sin 2t}& \left(5\right)\end{array}$

(61) With reference to FIG. 6, control of the inductor dc component using the modulation index of the PWM may be explained as follows. By reducing the modulation index the output current is reduced temporarily. Consequently, the output power decreases and the difference energy is stored in the inductor which in turn increases its dc value. As a result, the output current increases up to the point where the average power injected into the grid equals the input power.

(62) To reduce the conduction losses and to obtain a flatter efficiency curve, the inductor dc current may be minimized by the modulation index for different input power levels. Equations (4) and (5) show that oscillation of the inductor current depends on the input power, the inductor value, and the inductor dc current. Thus, as the inductor dc current decreases, I.sub.L increases, which eventually results in a discontinuous mode of operation where the output current becomes distorted.

(63) To avoid this mode of operation, the minimum of the inductor current should be higher than the maximum output current when the second stage is, for example, a voltage boost inverter or a step down current source inverter. If a voltage source inverter is utilized at the second stage the oscillations will occur at the voltage of the inverter input capacitor. To avoid a discontinuous mode of operation the capacitor voltage should be larger than the grid voltage, and a similar approach may be used to derive equations for this mode of operation. Thus, the following inequality has to be satisfied:

(64) $\begin{array}{cc}{I}_{L\mathrm{dc}}-I_L{I}_o=\frac{2P_{\mathrm{in}}}{V_o}.Math.& \left(6\right)\\ I_{L\mathrm{dc}}\frac{P_{\mathrm{in}}}{V_o}+\sqrt{\frac{P_{\mathrm{in}}^2}{V_o^2}+\frac{P_{\mathrm{in}}}{2L}}& \left(7\right)\end{array}$

(65) The right hand side of the inequality forms the reference inductor current. FIG. 7 shows an example of the case when the reference current is too low and the grid current is distorted (see FIG. 9; low inductor current reference). Since the minimum possible inductor current is desired, the equality may be used in the controller system to generate a reference signal for the inductor dc current, as shown in FIG. 7, time interval (t.sub.1t.sub.2).

(66) FIG. 7 shows a block diagram of an embodiment of the current source inverter control system, which consists of two parts: a proportional integral (PI) controller 100 to stabilize the inductor dc current level and prevent discontinuous modes of operation; and a compensator 200 that modifies the PWM reference signal to cancel harmonics at the grid current. To form the feedback loop, first the dc inductor value is measured and then the error signal is fed into the PI controller. The output of the PI controller adjusts the amplitude of the output current reference signal. When the error signal is positive, the inductor dc current is higher than the reference and has to be reduced. In this case the PI controller increases the reference PWM signal and consequently the output current and power increase. This, in turn, decreases the inductor current until the error signal is zero where the output of the PI controller remains constant. The case where the error signal is positive is similar. Since a PI controller is used, the steady state error will be zero and as a result, according to equation (7), the inductor current is always minimized to optimize conduction losses and also to ensure that the output current will not become discontinuous. When there is more than one PV cell string connected to the circuit, the output power equals the sum of the input powers. Thus, the output current may be decomposed into components corresponding to each string, for example, i.sub.o(t)=i.sub.o1(t)+i.sub.o2(t). However, the charging and discharging of each inductor depends on the difference between the power generated by a string and the power injected to the system from that string. Therefore, equations (2), (4), and (5) hold true for any number of PV cell strings j, if i.sub.o, p.sub.o, P.sub.in and L.sub.A are substituted by i.sub.oj, p.sub.oj, P.sub.inj and L.sub.X. If the inequality (6) is satisfied for each string for any condition, the sum of the inductors' currents will be larger than the maximum output current. The reference current for each string is calculated and added together to form one reference inductor current and as a result, the control strategy shown in FIG. 7 regulates the dc inductor current of all strings. An embodiment for a multi string inverter is shown in FIG. 8.

(67) A feature of this multi-string topology embodiment is that the output power oscillation is not supplied only by one inductor. Rather, all strings contribute to the power oscillation. As a result, with more strings, the current oscillation on each inductor is reduced and smaller inductors may be used. Moreover, because of the smaller oscillations, equation (5) results in a smaller dc reference for the inductor currents, which in turn reduces the conduction losses.

(68) Harmonic Cancelation Method Using Modified PWM Technique

(69) The embodiment described in the following section is based on a current source inverter (CSI). However, the method may be used to cancel an oscillation at the input of other converters, and in another embodiment a voltage source inverter (VSI) is used. The below description also applies to a voltage source inverter, the only difference being that the input source is voltage, the inductors are replaced by capacitors, and currents are replaced with voltages, and vice versa.

(70) As shown in equation (5), the inductor current oscillates around a dc value at twice the grid frequency. Conventional sine PWM techniques assume a constant dc input current, and thus any harmonic of the input source will be reflected to the modulated output current. This problem may be avoided by introducing a compensation factor as shown in FIG. 7. When the oscillatory current source inverter input dc current increases, the compensator decreases the modulation index proportionally, which is done by the multiplication of the signal labeled comp (t) and the sine PWM reference signal as shown in FIG. 7. As a result, an increase in the dc current value is compensated by a reduction in the modulation pulse width, and vice versa. This type of compensation prevents oscillatory harmonics from appearing at the output current because the PWM modulator creates the new sine PWM reference signal at the output of the inverter and thus the energy transfer to the output is equivalent to the case where the inductor current is a constant dc current with no oscillation. The modulation signals and compensation method are shown in detail in FIG. 6. In FIG. 6(a) two cases when the inductor current is dc or oscillatory are demonstrated. FIG. 6(b) shows PWM reference and carrier signals for the above mentioned cases. As shown, the reference is modified by a factor which shows how much the inductor current has deviated from the dc level. The effect of this modification is shown in FIGS. 6(b), (c) for the interval when the inductor current is higher than the dc level. It can be observed from waveform (d) that since the current is higher, the pulse width is lower than the dc current and both waveforms transfer the same amount of energy to the output. As a result, with this modification, the case where the inductor current is oscillatory, the harmonics at the output are similar to the case where the inductor current is pure dc. As explained above this modification may also be applied to the case where the second stage is a voltage source inverter and the input voltage is oscillatory.

(71) The following non-limiting example is provided to further illustrate the invention.

(72) Example

(73) To demonstrate the impact of the irradiance level, input voltage level, and partial shading on the performance of a two-string PV cell inverter as shown in FIGS. 5B and 8, a simulation was carried out using PSIM 7.0 software and the values set forth in Table I, and the results are shown in FIG. 10, The system was started with string #2 partially shaded (40% of the full irradiation level) and string #1 at full power. At t=0.2 (s) both strings were partially shaded at 15% of the full irradiation level and the system response was obtained. At t=0.3 (s) the temperature of the PV cells was increased so that the output voltage of the PV cells decreased from 150V to 80V, which is less than the grid voltage. At t=0.4 (s) both strings were exposed to full irradiance. It can be seen from FIG. 10 that after each change, the controller quickly stabilized the output current. In addition, the maximum input power extraction was almost instantaneous, confirming the fast dynamic response of the MPP tracker circuit. Overall, the simulation results show that the converter is robust, and provides excellent decoupling performance for medium-power systems (such as residential applications).

(74) TABLE-US-00001 TABLE I SIMULATION PARAMETERS Parameters Values C.sub.PV1, C.sub.PV2 20 F C.sub.f 2 F L.sub.A, L.sub.B 2000 H L.sub.f 1000 H CSI f.sub.s 10 KHz First stage f.sub.s.sup.max 20 KHz Grid voltage 110 V Grid frequency 60 Hz PV String MPP 1.1 KW

(75) The contents of all references, pending patent applications, and published patents cited throughout this application are hereby expressly incorporated by reference.

(76) Equivalents

(77) Those skilled in the art will recognize or be able to ascertain variants of the embodiments described herein. Such variants are within the scope of the invention and are covered by the appended claims.

REFERENCES

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