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PEDS2009

A New control strategy for Single Phase Series Connected PV Module Inverter for Grid Voltage Compensation

S. Dasgupta, Graduate Student Member, IEEE, S. K. Sahoo, Member, IEEE, *S. K. Panda, Senior Member, IEEE

*Department of Electrical and Computer Engineering National University of Singapore Singapore 117576 Telephone: (65) 6516-6484 Email: eleskp@nus.edu.sg

Abstract—In this paper, a new control strategy for a low cost series connected single phase PV module inverter is introduced that delivers full PV power (at MPPT) to the load together with voltage compensation. The inverter operates during the day time as an active power compensator as well as load voltage regulator under grid voltage sag, swell or even under normal condition. The compensating voltage provided by the inverter is always added vectorially in series with the grid voltage in such a way that it maintains the load voltage magnitude constant. This eliminates the need for battery or any other energy storage device at the DC link. This reduces the investment cost of the system. Moreover, the proposed control strategy works in such a way that even in the presence of lagging power factor load, it is possible to supply reactive power back to grid that can be utilized in some other lagging power factor load connected directly to grid. An adaptive proportional resonant controller is used to track the required load voltage magnitude as well as phase angle. This control strategy is simple to implement and provides improved performance as compared to a conventional PI controller. Detailed simulation studies and experiments have been carried out and results demonstrate the ef?cacy of the proposed control strategy. Index Terms—Series PV inverter, day time control, system without active energy storage device, proportional resonant controller application

DC-DC converter followed by the inverter. If the DC-DC converter is operating with the MPPT of the PV panel and the full energy can not be transferred to the load, so the extra energy has to be stored in a battery between the DCDC converter and the inverter. When there is a voltage swell in the grid during day time, it compensates the load voltage to nominal level and the inverter operates as recti?er and transfers extra power from grid to the battery and PV panel is disconnected. If there is no change in grid voltage magnitude, the inverter becomes inactive and the PV power is either lost or stored in a battery. In the proposed paper, a new ”day time control strategy” is proposed for this series PV inverter. The control is to transfer, the full MPP power of the PV panel to the load, under grid voltage sag, swell and even if no change in grid voltage magnitude condition, along with maintaining the nominal voltage level across the load. This eliminates the need of the battery or any other storage device between the DC-DC converter and the inverter. II. D ESCRIPTION OF THE I NVERTER C ONFIGURATION

AND ITS CONTROL

A. Description of the inverter I. I NTRODUCTION The series con?guration of PV inverter with bidirectional switches is proposed in [1]. The basic work of this series inverter is two fold. During day time if there is voltage sag or swell in the grid voltage, the inverter would add or subtract a compensating voltage component to the grid voltage to maintain the load voltage constant. During night time, when there is a voltage swell, the same inverter would operate like a voltage regulator by taping the grid voltage itself [2]. But, these bi-directional switches are costly. So, a low cost series PV inverter with improved control strategy and with the uni-directional switch is proposed in [3]. This inverter provides rated voltage across the load irrespective of the voltage condition in the grid. Now, during day time, the inverter supplies PV power to load during grid voltage sag to maintain nominal load voltage. But, if the full con?guration of PV system is concerned, PV panel is followed by a Figure 1 showing the schematic of the power circuit of the series connected PV inverter assembly. The DC to DC converter of the system operates in such a way that the PV panel operates at maximum Power Point(MPP). During building up of the DC link voltage of the Inverter, vdc is controlled by controlling amount of active power ?ow through the inverter as shown in Figure 2. Typically, the DC to DC converter is a Flyback converter operating in Discontinuous Conduction Mode (DCM)[4]. So, the duty cycle of the Flyback converter is controlled to match the transfer output resistance of PV panel [5], so that PV panel operates in MPPT and the output DC voltage of this Flyback converter, vdc , is controlled depending of the DC link requirement of the inverter. The -ve gain, ?k [6]is used to take care of the condition that, if inverter power ?ow reduces, the PV power is stored in the DC link capacitor, resulting to an increase of DC link voltage. To be speci?c, if the error between the DC link

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voltage reference and actual DC link voltage increases in positive direction, the power input to the inverter from the DC link side needs to be reduced, so that, more PV power can ?ow through the DC link capacitor to increase DC link voltage. The control of the inverter is such that, it can control the load voltage to its nominal value as well as the active power ?ow through the inverter as discussed in the following sections.

Fig. 4.

Proposed control phasor diagram of the PV inverter

Fig. 1.

Schematic diagram of the series Inverter assembly

shown in Figure 4. So, the power needed from the grid, Pg can be calculated as shown in eqn (1). Pg = PL ? Pinv (1)

Fig. 2.

DC link voltage control structure

where, total load power, PL = |VL | × |IL | × cos(θ), where θ is the power factor angle of the load. The load current at steady state with voltage regulated at nominal rms value |VL |, |IL | = |VL | , where |Z| is the impedance of the load at line |Z| frequency. Thus, eqn (1) can be rewritten in the following form: |VL |2 cos(θ) ? Pinv (2) Pg = |Z| From grid point of view, the active power drawn from grid can be written as shown in eqn (3). Pg = |Vg | × |VL | cos(γ) |Z| (3)

B. Control of the inverter For the sake of analysis of the control strategy of the inverter, it is assumed that, the PV string is operating under a steady insolation level. So, the DC link voltage Vdc is at the steady level and the inverter output power Pinv is same as the MPP power of the panel, Pmpp . So, the DC link (i.e. the PV string along with the isolated DC/DC converter) can be modeled as a battery with a series diode. The series diode ensures that there is no power feedback to the PV panel. The load is assumed to be a linear R ? L load. The approximate power circuit along with its control phasor diagram is shown in Figure 3 and 4. As, the inverter operates to transfer total

From eqn (2) and (3), the angle between grid voltage and load current, γ can be found out as shown in equation 4. cos(γ) =

|VL |2 |Z|

cos(θ) ? Pinv |Vg |. |VL | |Z|

(4)

It can be noted that, if the grid voltage is vg (t) = √ |Vg | 2 cos(β), where β = ( ω dt) + δ, ω is the grid frequency and by estimating the requirement of γ using equation 4, the load voltage can be forced to be vL (t) = √ |VL | 2 cos(β +γ +θ). The grid voltage angle β is estimated by using PLL. By this process, not only the load voltage is regulated at nominal rms value |VL |, but the total mpp PV power is transferred to the load also at steady state. The operation is possible irrespective of the voltage condition in the grid. So, the maximum power of the PV panel is utilized under all condition in grid voltage along with the proper regulation of the load voltage, without any use of battery or any other active energy storage element. C. Constraint on the PV inverter system It can also be noted from eqn (4) that for an acceptable value of power angle γ, eqn (5) and (6) have to be satis?ed as shown below. 0 ≤ cos(γ) ≤ 1 (5)

Fig. 3.

Simpli?ed Power Circuit of the PV inverter

PV power to load and rest of the load power comes from grid along with the voltage regulation of the load. So, at steady state different phasors are marked in the the phasor diagram

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|Vg | ≥

|VL |2 |Z|

cos(θ) ? Pmpp

|VL | |Z|

(6)

given by eqn (10). Vdc |min = 2 × [|Vg |2 + 2|Vg ||VL | sin(θ) + |VL |2 ] (10)

Eqn (6) is true at steady state, where Pinv = Pmpp . Then for a speci?c solar insolation level, the maximum dip in the grid voltage, i.e. the minimum rms value of grid voltage can be calculated from eqn (6). It is assumed that, the inverter, operates with sine PWM. So, to maintain the SPWM in the linear range, there should be certain level of minimum DC link voltage. In the worst condition, it can be assumed that, no power is taken from the grid, i.e. γ = 900 . The phasor diagram of this condition is shown in Figure 5.

So, if the mpp power of the panel Pmpp and the maximum dc link voltage that can be developed, Vdc , are known, then from eqn (6), the minimum possible grid voltage dip and from eqn (10), maximum possible grid voltage swell, that can be regulated by this inverter system can be estimated. Accordingly, the inverter operating conditions, like DC link voltage, maximum grid sag as swell that can be compensated, are to be designed. D. Controller structure for the Inverter assembly From the above discussions, it can be found that, there is a need to maintain load voltage having a speci?ed nominal magnitude and a particular phase relation with the grid voltage as found from eqn (4) and Figure 4. So, the control is all about to track a sinusoidal load voltage in its phase and magnitude. So, an Adaptive Proportional Resonant controller [7], [8] is used. The over all control structure is shown in Figure 6. The mathematical structure of the adaptive PR controller is given in eqn (11).

Fig. 5.

Phasors diagram of the inverter quantities when Pg = 0

Gc (s) = Kp +

s2

2sKi 2 + ωr

(11)

Kp and Ki are the parameters of the controller and ωr is the frequency of the reference sinusoid to be tracked, found from the PLL. So, the control action of the system will not be hampered due to the change in the grid frequency. III. D ESIGNING A TYPICAL PROTOTYPE SYSTEM The parameters of the system used are, Load Resistance, R = 150 ?, Load Inductance, L = 0.1 H, the nominal rms load voltage requirement, |VL | = 110 V , the Maximum Power Point, Pmpp = 50 W . The load impedance is |Z| = R2 + (2πf L)2 = 153.25 ?. 110 So, |IL | = 153.25 = 0.718 A and the power factor angle ?1 2πf L θ = tan = 11.830 . Minimum grid voltage that can R be regulated by this system is calculated using eqn (6) and the value is |Vg |min = 38 V , which is equivalent to 38% sag in grid voltage. If it is considered to have maximum 18% swell in grid voltage, i.e. |Vg |max = 130 V , the minimum level DC link voltage needed for this prototype can be calculated using eqn (10). So, the minimum DC link voltage needed is: Vdc ≥ 264.06V . So, for prototype experiment, DC link voltage level is set at Vdc = 270 V . Using eqn (4), different values of power angle γ are calculated, as shown in table (I), under different condition of grid voltage to facilitate Pinv = Pmpp = 50 W . These power angle values are used in simulation as well in experiment. IV. S IMULATION R ESULTS The series inverter system is simulated in MATLAB/SIMULINK environment. The grid voltage is considered to have sag and swell and the simulation results are shown in Figures 7 and 8. It can be noted from Figure 7 that, during 0 < t ≤ 0.125 sec, there is no change in grid voltage magnitude, during 0.125sec < t ≤ 0.255sec, there is a dip of 18% of the nominal rms value of the grid voltage and

Fig. 6.

The general control diagram of the proposed inverter

So, from Figure 5, the phasor equation of the inverter voltage can be written as shown in eqn (7). → ? ? ? → → → ? Vi = VL ? Vg =? Vi = [?|Vg |?|VL | sin(θ)]+j|VL | cos(θ) (7) Eqn (7) gives the inverter voltage having the maximum rms magnitude. Beyond this point, the operation of the inverter is restricted. So, the maximum rms value of the inverter voltage is written in eqn (8). |Vi |max = |Vg |2 + 2|Vg ||VL | sin(θ) + |VL |2 (8)

If the DC link voltage is maintained at the level Vdc , the maximum rms value of the output voltage of the constant triangular voltage SPWM inverter [4] in linear range is given in eqn (9). Vdc |Vi |max = √ (9) 2 So, from eqn (9) and (8) the minimum value of the DC link voltage needed for this sort of application can found out as

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TABLE I D IFFERENT VALUES OF P OWER A NGLE Grid Voltage, |Vg | (Volts) 110 90 130 Comment Normal condition at grid 18% sag at grid 18% swell at grid value of Power Angle, γ 69.7880 65.0220 730

during 0.255 sec < t ≤ 4 sec there is a swell of 18% of the nominal rms value of the grid voltage. But, the control action is acting in a way, so that during full 0 < t < 4 sec, the load voltage magnitude is maintained at the rated rms level, 110V , as can be seen from Figure 7. If Figure 9, is noted carefully, it can be seen that, when there is a grid voltage sag, the grid power factor, cos γ, is increasing and when there is a voltage swell the grid power factor, cos γ, is reducing dynamically in accordance to eqn (4) to maintain grid power output to be maintained at constant level (Pg = 27.5 W ). From Figure

Fig. 8. Simulation diagram of Grid Voltage, Vg , Grid Current, IL and Inverter Output Power, Pinv

Fig. 7.

Simulation diagram of Load Voltage, VL , and Grid Voltage, Vg

Fig. 9. Simulation diagram of Grid Voltage, Vg , Grid Power, Pg and Grid Power factor, cos(γ)

8 it can be seen that during grid voltage sag, swell as well as nominal grid voltage condition, the fundamental active power output of the inverter is equal to the maximum power point power of the PV string, Pmpp = 50 W . So, the DC link voltage at steady state is stabilized as well as there is no need of any active power storage element. During transient period, it can be seen, that there is a dynamics power output. During this dynamics, Pinv = Pmpp , so there is a possibility of DC voltage, Vdc to increase dynamically. But, if the DC link voltage control loop, shown in Figure 2, is made 10 times slower than the AC voltage control loop, as shown in Figure 6, then the dynamics of the DC link voltage will not affect the operation of the PV inverter. If Figure 8, is further noted, it can be seen that for all grid voltage condition (sag, swell or normal condition), the grid current leads the grid voltage. This means, the PV inverter is supplying power at leading power factor and both grid and load is sharing that positive reactive power supplied by the

PV inverter. If any other lagging load is connected directly to grid, this extra positive reactive power, that is coming to grid, can serve the reactive power requirement of that extra stand alone load. So, utility power bill savings is more in this control strategy as compared to that of the systems proposed earlier[1], [3]. V. E XPERIMENTAL R ESULTS In order to verify the feasibility of the proposed scheme, experiments are carried out under normal grid condition, grid sag condition as well as grid swell condition. The control system as shown in Figure 6 is implemented in a dSPACE platform (DS1104) with Matlab/Simulink Real Time Interface (RTI) toolbox. Both of the inverter sine pwm switching frequency as well as the control system sampling frequency are kept at 10KHz. Inside the control program, a single phase PLL is used to

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sense the absolute phase of the grid voltage and the relative phase lead of the load voltage under different operating conditions (grid sag, swell or normal condition) are given externally from control panel to test the feasibility of the control scheme. The steady state experimental results are shown in Figure 10, 11 and 12. Figure 10 shows the steady state experimental waveform of

Fig. 12. Experimental results under 18% grid voltage swell condition, of grid voltage vg , load voltage vL , load current iL and inverter voltage vi

leading from grid voltage, Vg by the required amount of angle (γ = 630 ) as calculated in Table I. Figure 12 shows the steady state experimental waveform of inverter voltage (Vi ), load current (IL ), load voltage (VL ) and grid voltage (Vg ) under the under 18% swell in grid voltage. It can be seen that the load voltage is maintained at nominal value and to ensure the required power ?ow through the inverter, the load current, IL is forced to be leading from grid voltage, Vg by the required amount of angle (γ = 720 ) as calculated in Table I. The following remarks can be drawn from the experimental waveforms. ? Under all the conditions of the grid (normal condition, grid voltage sag as well as grid voltage swell condition), the load voltage (VL ) is maintained at nominal level 110 V . ? If the experimental phase angle between load voltage VL and load current IL (Power factor angle θ) as well as phase angle between load current IL and grid voltage Vg (Power angle γ) are concerned, it can be remarked that the control system is successful in maintaining the corresponding power angle requirements (γ) for different conditions of grid ( as the power angle requirement given in Table I). The slight mismatch between the theoretical and experimental values can be justi?ed by considering the experimental restriction. As mentioned before, in the control desk, the load voltage reference, ? VL is given with magnitude reference 110 V and phase angle reference as γ + θ. As can be seen from the experimental results, the actual power factor angle (at f = 50Hz, the calculated value of power factor angle is θth = 11.830 and the experimental value of power factor angle is θex = 180 ) is slightly different from the theoretical value due to slight uncertainty of load parameters as well as grid frequency. Moreover the experimental power factor is slightly more that the theoretical value, so in all the conditions of grid, the experimental value of power angle γ is slightly less than

Fig. 10. Experimental results at normal grid condition, of grid voltage vg , load voltage vL , load current iL and inverter voltage vi

Fig. 11. Experimental results under 18% grid voltage sag condition, of grid voltage vg , load voltage vL , load current iL and inverter voltage vi

inverter voltage (Vi ), load current (IL ), load voltage (VL ) and grid voltage (Vg ) under the normal condition of grid voltage. It can be seen that the load voltage is maintained at nominal value and to ensure the required power ?ow through the inverter, the load current, IL is forced to be leading from grid voltage, Vg by the required amount of angle (γ = 67.50 ) as calculated in Table I. Figure 11 shows the steady state experimental waveform of inverter voltage (Vi ), load current (IL ), load voltage (VL ) and grid voltage (Vg ) under the under 18% sag in grid voltage. It can be seen that the load voltage is maintained at nominal value and to ensure the required power ?ow through the inverter, the load current, IL is forced to be

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the corresponding theoretical value. If the power provided by the inverter is calculated as Pinv = |VL ||IL | cos(θ) ? |Vg ||IL | cos(γ) and all the experimental values are used to ?nd out the result of the expression, it can be seen that Pinv = 45.74 W , 45.08 W , 46.28 W respectively for normal grid condition, grid voltage sag condition and grid voltage swell condition respectively. The inverter power is slightly lower than the reference power 50W because of the slightly lower value of power angle, γ (power angle lower causes more power drawn from grid and less power drawn from the inverter). In spite of this slight mismatch, it can be remarked that, the phase shifting of VL with respect to Vg (as explained in Figure 4) is successful. It can also be noted that, under all the conditions of grid, the power angle, γ is a leading angle. This is forced to create leading power factor operation from grid side even at lagging power factor load. VI.

CONCLUSION [7] R. Teodorescu, F. Blaabjerg, M. Liserre, P.C. Loh, ”Proportional resonant controllers and ?lters for grid - connected voltage - source converters”, IEE Proc. - Electr. Power Appl, Vol. 153, pp 750-762, September 2006 [8] Adrian V. Timbus, Mihai Ciobotaru, Remus Teodorescu, Frede Blaabjerg, ”Adaptive Resonant Controller for Grid-Connected Converters in Distributed power generation Systems”, Applied Power Electronics Conference and Exposition, 2006. APEC ’06. Twenty-First Annual IEEE, pp 1601-1606, 19-23 March 2006.

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A new day time control strategy of the low cost series connected single phase PV inverter is proposed. The control strategy in day time works satisfactorily to stabilize the load voltage irrespective of the grid voltage magnitude as well as transfers full MPP power of the PV string to the load. Besides these, the inverter is forced to operate in such a way that, grid always sees a leading power factor load even at the presence of lagging power factor load. So, the utilization factor of the inverter as well as the PV string is increased as compared to earlier proposed schemes in [1], [3]. This eliminates the need of any active power storage device say, battery. Now, if the series PV inverter assembly can be run in daytime by this control strategy, there will be some decrease in the investment cost of such system as compared to the process found in [1], [3]. As during daytime, it is supplying full PV mpp power to load as well as it is supplying some positive reactive power to grid, so there will be more utility power bill cut as compared to the case found in [1], [3]. As this type of PV system is useful in underdeveloped countries, where economy is a problem, the above mentioned advantages will add more usability of this system. R EFERENCES

[1] Fei Kong, Rodriguez Cuauhtemoc, Amaratunga Gehan, Panda Sanjib Kumar, ”Series Connected Photovoltaic Power Inverter”, IEEE international conference on sustainable energy technology, 2008, ICSET 2008, pp595-600, Nov 24 -27. [2] Ming Tsung Tsai, ”Design of a Compact Series-connected AC Voltage Regulator with an Improved Control Algorithm”, IEEE transactions on industrial electronics, Vol 51. No. 4, pp 933-936, August 2004. [3] Fei Kong, Gehan Amaratunga, Sanjib Kumar Panda, ”Series connected Photovoltaic Power Inverter Using High Frequency Isolation Transformer”, submitted for review in PEDS 2009, Taiwan. [4] Ned Mohan, T M Undeland, W P Robbins ”Power Electronics, converters, applications and design”, John Willey and Sons, Inc., Third edition, 2003. [5] Hardik P Desai and H. K. Patel , ”maximum Power Point Algorithm in PV Generation: An Overview”, PEDS 2007, pp624-630. [6] Cuauhtemoc .Rodriguez, GA.J Amaratunga ”Long-Lifetime Power Inverter for Photovoltaic AC Modules”, IEEE transcactions on industrial electronics, Vol.55, No. 7, pp. 2593-2601, JULY 2008.

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