Photovoltaic Array Based Multilevel Inverter for Power Conditioning Rajasekar.S, Student Member IEEE and Rajesh Gupta, Senior Member IEEE
Abstract— This paper proposes a photovoltaic (PV) array supported five-level cascaded H-bridge multilevel inverter (CHBMLI) based shunt active power filter (SAPF). The combined system is used for power conditioning application to improve power quality in the distribution network. The photovoltaic supported CHBMLI makes attractive solution because this inverter need isolated dc source in the dc side of the each H-bridge. The SAPF is used to compensate both reactive and harmonic components of the current drawn by the non linear load. Additionally, it also balances the supply current for unbalanced load. In this paper it is shown that the PV based multilevel inverter configured SAPF not only compensates the harmonic current, reactive power and unbalancing but also injects real power whenever it is demanded in the distribution system. The compensation and power flow control in this paper is developed based on the instantaneous power theory. The simulation results presented in this paper evidently proves the compensation capabilities and real power injection. The simulation studies are carried out under power system computer aided design PSCAD/EMTDC 4.2 environment. Index Terms— Cascaded H-bridge multilevel inverter (CHBMLI), harmonic compensation, nonlinear load, photovoltaic (PV array), reactive power
I. INTRODUCTION Recently the power electronics based non linear loads are increased tremendously in the distribution network. These include, switched mode power supplies, variable speed drives, uninterrupted power supplies etc. These non linear loads create harmonics or current distortion problem in the supply side of the distribution system [1]. The harmonic induce malfunctions of sensitive equipments, over voltage by resonance and harmonic voltage drop across the network impedance, and these significantly deteriorate the power quality in the distribution system. Traditionally, passive filters are used to eliminate harmonics and improve power quality of the distribution system. But it fails to work because of certain limitation like fixed compensation, resonance problem and bulky in nature. In order to overcome the above mentioned limitations, a new set of compensators based on power electronics technology has been introduced in the market [2]. One of the important set of such compensators is called active power filters. Basic principle of active power filter is proposed by Gyugyi and Strycula in the year 1976 [3], [4]. In 1984, Hirofumi Akgai introduced a new concept of instantaneous Authors are with the Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad-211004, India (e-mail:
[email protected],
[email protected])
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reactive power (p-q) theory in [5]. It deals in three-phase, three-wire system and later extended for three-phase four-wire system by Watanabe and Aredes in [6]. The generalized instantaneous reactive power theory which is valid for sinusoidal or non-sinusoidal, balanced or unbalanced threephase power systems and with or without zero-sequence currents, was later proposed by Peng and Lai in [7]-[8]. The active filter can be connected in series or in parallel with the supply network. The series active power filter is suitable for voltage harmonic compensation. Most of the industrial applications need current harmonic compensation, so the shunt active filter is more popular than the series active filter [9]. Currently, remarkable progress in the capacity and switching speed of power semiconductor devices such as insulated-gate bipolar transistors (IGBTs) has spurred interest in APFs. The shunt active power filter compensation process based on the instantaneous real-power theory provides good compensation characteristics in steady state as well as in transient states. The instantaneous real-power theory generates the reference current required to compensate the distorted line current harmonics and reactive power. It also tries to maintain the constant dc-bus voltage across the capacitor. Another important characteristic of this real-power theory is the simplicity of the calculations, which involves only algebraic calculations. In recent years, need of clean energy makes more interest towards renewable energy resources such as solar, wind, geothermal, tidal etc. Among these solar energy paid much more attention due to its environmental friendly nature and its abundant availability [10]. Light energy is directly converted into DC power by photovoltaic array. These DC power from photovoltaic array is transformed into more convenient AC power through inverter system. The photovoltaic array coupled with CHBMLI can supply real power from photovoltaic array to the load and can also compensate harmonic and reactive components of the current in the distribution system. This paper present an instantaneous power theory based photovoltaic (PV) array supported five level cascaded inverter used for the shunt active power filter. The filter is used for harmonics and reactive power compensation and also able to inject real power whenever it is demanded in the distribution system. The cascaded H-bridge multilevel VSI has been applied for active filter applications due to increased number of voltage levels, low switching losses and higher order of harmonic compensation. The cascade M-level inverter consists of (M–1)/2 H-bridges and each bridge has its own separate dc source, whereas in proposed topology dc source is replaced by photovoltaic array.
II. PHOVOLTAIC MODEL AND ITS CHARACTERISTICS The electrical equivalent circuit of solar cell is shown in the Fig. 1. Solar cell can be modeled as current source in parallel with a diode. Rs is the intrinsic series resistance of the solar cell whose value is very low. Rsh is the equivalent shunt resistance whose value is very high. A solar cell is a basic unit of a photovoltaic module. The cell generates current carriers when sunlight falls on it. A solar module is a combination of number of solar cells that are connected in series and/or parallel to increase the output power of a PV module. A PV array is the group of modules that are connected in series and or in parallel to increase output power of the PV array.
current source into voltage source. In case of an H-bridge voltage source inverter the DC capacitor is connected across the input. Hence PV module is coupled with H-bridge through a DC link capacitor in order to get constant DC voltage source.
Fig. 3. Current versus voltage at constant solar insolation G = 1000 W/m2.
III. PROPOSED TOPOLOGY
⎡
⎛ q(V + IRs ) ⎞ ⎤ V + IRs ⎟ − 1⎥ − Rsh ⎝ α KT ⎠ ⎦
I = I pv − I o ⎢exp ⎜
⎣
(1)
where, Ipv is photocurrent; Io is diode saturation current; q is coulomb constant (1.602×10-19C); K is Boltzman’s constant (1.381×10-23 J/K); T is cell temperature in ºC; α is P-N junction ideality factor; Rs and Rsh are the intrinsic series and shunt resistances of the cell, respectively. The characteristics of PV module are shown in Fig. 2 and Fig. 3 with different solar insolation and cell temperature.
Vsa Vsb Vsc
AC
AC
AC
PCC Rsa Lsa
Isa
ILa
Rsb Lsb
Isb
ILb
Rsc Lsc
Isc
ILc
Lsha
Isha
Fig..2. Current versus voltage at constant cell temperature T = 25 ºC.
It can be seen from Fig. 2 and 3 that the PV module has non-linear voltage and current characteristics. From these characteristics we can observe that as the solar insolation decreases the PV module output current decreases, whereas increase in cell temperature will cause marginal decrease in PV module voltage. Generally PV array output act like a current source. Whereas H-bridge inverters are voltage source inverter, it needs input as a voltage source. Using high value of DC capacitor across the PV module it is possible to convert
Swa11 Swa13
Vdca1
Ishc
Swb11 Swb13
Vdcb1 Swa14 Swa12
Swa21 Swa23
Vdca2
Swc11 Swc13
Vdcc1 Swb14 Swb12
PV Panel
PV Panel
Swc14 Swc12
PV Panel
Swc21 Swc23
Swb21 Swb23
Vdcc2
Vdcb2
Swc24 Swc22
Swb24 Swb22
Swa24 Swa22
PV Panel
Ishb
PV Panel
Non Linear Load
Lshc
The characteristics equation of the PV model is given by [11]
Proposed five-level cascaded active filter for power line conditioning system is connected in the distribution network at the point of common coupling through filter inductances and operates in a closed loop. The three-phase active power filter comprises of 24 number of power switches with freewheeling diodes. Each phase consists of two-H-bridges in cascaded connection and every H-bridge has an isolated dc supplies in the conventional arrangement. The proposed topology in this paper uses isolated PV modules of the PV array in place of the dc supplies across the H-bridges as shown in Fig. 4. It is shown that this arrangement can improve power quality in the distribution system by compensating current harmonics in the source side, reactive power compensation, and can also injects real power whenever it is demanded in the distribution system. Each H-bridge can produce three different voltage levels –Vdc, 0 and +Vdc. The ac-output of each H-bridge is connected in series such that the synthesized output voltage waveform is the sum of all the individual H-bridges and produces five-level output.
Lshb
Fig.1. Electrical equivalent circuit of PV cell.
PV Panel
Fig. 4 Photovoltaic array supported five-level inverter based shunt active power filter.
As shown in Fig. 4, the three-phase supply is connected to the nonlinear load. The instantaneous source current is defined as iS (t ) = iL (t ) - iC (t ) and the instantaneous source voltage is defined as vs (t ) = vm sin ωt . The nonlinear load current will have a fundamental component and harmonic current components, which can be represented as below. ∞ iL (t ) = ∑ I n sin( nωt + Φ n ) n =1
(2)
360
o
( m -1)
The instantaneous reactive power theory [4] is based on the transformation of three phase quantities to two phase quantities in α –β frame. The instantaneous active and reactive powers are calculated in this frame. Fig. 3 shows the block diagram of the implementation strategy. The mathematical derivation is explained below. Consider the system voltages as va = vm sin(ωt ); vb = vm sin(ωt -120); vc = vm sin(ωt - 240) and respective load currents are given below
If the active power filter provides the total reactive and harmonic power, then the source current will be sinusoidal and in-phase with the utility voltage. The active filter will provide compensation current iC (t ) = iL (t ) - iS (t ) . The SAPF injects equal and opposite current at the point of common coupling. The IGBT switches used in H-bridges of each phase are switched using phase-shifted multicarrier modulation []. Multiple triangular carriers used in this modulation technique has same frequency and same peak to peak amplitude but there is phase shift between any two adjacent carrier waves of magnitude given by Φ cr =
IV. REFERENCE CURRENT GENERATION
(3)
Where, m is the number of voltage levels of the multilevel inverter. Gate drive signals are generated by comparing the modulating signal with the carrier signal. The two triangular carriers used in the five-level inverter are 90º phase shifted and shown in Fig. 5. The intersection of these carriers with the modulating signal generates gating signal for the switches of the two H-bridges. In this PWM method the equivalent switching frequency of the converter output is (m–1) times as that of the frequency of each power device. This means the carrier phase shifted PWM can achieve a high equivalent switching frequency effect at very low real device switching frequency which is mostly useful in high power applications.
iLa = ∑ I Lan sin{n (ωt ) - θ an }
(4)
iLb = ∑ I Lbn sin{n (ωt -120) - θ bn }
(5)
iLc = ∑ I Lcn sin{n(ω t - 240) - θ cn }
(6)
In abc coordinates, a, b and c-axes are fixed on the same plane and are phase displaced by 120º. The instantaneous space vectors, va and iLa are set on the a-axis and their amplitude varies in positive and negative directions with the time. This is true for other phases also. These phasors can easily be transformed into α-β coordinates as follows.
⎡vα ⎤ 2 ⎛1 -1/2 ⎢v ⎥ = ⎜ 3 ⎝ 0 3/2 ⎣ β⎦
⎡ va ⎤ -1/2 ⎞ ⎢ ⎥ ⎟ vb - 3/2 ⎠ ⎢ ⎥ ⎣⎢vc ⎦⎥
(7)
⎡iα ⎤ 2 ⎛ 1 -1/2 ⎢i ⎥ = ⎜ 3 ⎝ 0 3/2 ⎣β⎦
⎡ia ⎤ -1/2 ⎞ ⎢ ⎥ ⎟ ib - 3/2 ⎠ ⎢ ⎥ ⎣⎢ic ⎦⎥
(8)
where, α and β axes are the orthogonal coordinates. The instantaneous power p for the three phase circuit can be defined as p = vα iα + vβ iβ
(9)
Similarly, the instantaneous reactive power q is defined as below. q = −vβ iα + vα iβ
(10)
Therefore in the matrix form the instantaneous real and reactive power are given as
⎡ p ⎤ ⎡vα ⎢q ⎥ = ⎢ − v ⎣ ⎦ ⎣ β
vβ ⎤ ⎡iα ⎤
⎥⎢ ⎥
vα ⎦ ⎣iβ ⎦
(11)
The α–β currents can be obtained as
⎡iα ⎤ 1 ⎡vα ⎢i ⎥ = ⎢ ⎣ β ⎦ Δ ⎣v β 2
− vβ ⎤ ⎡ p ⎤
⎥
vα ⎦ ⎢⎣q ⎥⎦
(12)
2
where, Δ = vα + vβ Fig. 5 Generation of gating signal using phase shifted PWM technique
The instantaneous active and reactive power p and q can be decomposed into the average and an oscillatory component.
p = p + p q = q + q
(13)
where, p and q are the average parts and p and q are the oscillatory parts of the real and reactive instantaneous powers, respectively. The compensating currents can now be calculated to compensate the instantaneous reactive power and the oscillatory component of the instantaneous active power. In this case the source transmits only the non-oscillating component of active power. Therefore the reference source * * current isα and isβ in α–β co ordinate are expressed as
⎡i* ⎤ 1 ⎡v ⎢ sα ⎥ = ⎢ α ⎢⎣i*sβ ⎥⎦ Δ ⎣ − vβ
vβ ⎤ ⎡ p ⎤ vα
⎥⎢ ⎥ ⎦ ⎣0 ⎦
filter. Each H-bridge is connected to a separate photovoltaic module that serves as a energy storage elements to supply real power difference between the demaded load and available source real power. The switching pulses are generated using carrier phase shifted pulse width modulation technique. The harmonic compensation is achieved by injecting equal but opposite current harmonic components at the point of common coupling. The system parameters considered in the simulation are given in Table I. Table I System Parameters
(14)
These currents can be transformed in abc quantities to find the reference current in a-b-b coordinate
⎡i*sa ⎤ ⎛1 / 2 1 0 ⎞ ⎡i0 ⎤ ⎢*⎥ 2⎜ ⎟⎢ ⎥ 3 / 2 ⎟ iα ⎢isb ⎥ = ⎜1 / 2 −1 / 2 ⎢ ⎥ 3 ⎢*⎥ ⎜ ⎟ 1 / 2 1 / 2 3 / 2 − − ⎝ ⎠ ⎢⎣iβ ⎥⎦ ⎢⎣isc ⎥⎦
(15)
Where, i0 is the zero sequence components which is zero in three-phase three-wire system.
Parameters
Numerical Value
Source Voltage VS per phase Number of solar cell connected in series Number of solar cell connected in parallel Number of modules connected in series Number of modules connected in parallel System Frequency Source Impedance: Source Resistor (RS) Source Inductor (LS) Non-Linear Load: Diode Rectifier Load Resistor (RL) Load Inductor (LL)
70 V 108 2 2 1 50 Hz 1Ω 0.5 mH 6-diode 10 Ω 100 mH
Filter: Inductor (LF) Resistor (RF) DC-side Capacitance (CDC) Reference Voltage (VDCref)
2 mH 1Ω 1000 µF 160 V
The diode rectifier load is connected at the junction of the acgrid and the photovoltaic based cascaded shunt active power filter is coupled at the shunt part, i.e., at the point of common coupling (PCC) to inject the current harmonics and compensate the reactive power. The non-linear load consists of six-diode with RL impedance. It will generate six-pulse rectifier waveform. The rectifier load current that is also same as the source current before compensation is shown in Fig. 7. Therefore the source current contains all the load harmonics and carry reactive component of the load current.
. Fig. 6 Block diagram of the reference current extraction through p-q theory.
V. SIMULATION RESULTS A. Simulation of PV based five-level Cascaded Multilevel Inverter for Power Conditioning The performance of the photovoltaic based cascaded active power filter is evaluated through extensive simulation studies using PSCAD/EMTDC 4.2 in order to model and test the system performance. A five-level cascaded H-bridge inverter is used as a voltage source inverter for the shunt active power
Fig..7. Load current for uncompensated distribution system of phase-a.
The PV based cascaded multilevel inverter shunt active filter is providing a compensating current iC ( t ) = i L ( t ) - i S ( t ) . The compensated source current is shown in Fig.8. It can be seen from the figure that the source current is closed to sinusoidal waveshape and free from harmonics. This proves the proposed PV based five-level cascaded multilevel inverter makes source current sinusoidal. The compensating shunt current is shown in Fig. 9. In addition, the supply power factor is close to the unity as seen in the Fig.10, i.e., the source
voltage and source current are in-phase. The shunt current tracking performance is shown in the Fig. 11. The actual shunt current is accurately tracked by the shunt reference current. The shunt reference current is generated by reference current extraction through p-q theory using equation (15).
The harmonic spectrum of the source current is shown in Fig. 12. After compensation the total harmonic distortion is greatly reduced to 2.24 % which is acceptable to IEEE 519 standard. The harmonic spectrum of the compensated source current is shown in Fig. 13. This shows that the proposed topology compensates reactive and harmonic component of the load current and makes the source current close to sinusoidal.
Fig..8 Source current for compensated distribution system of phase-a.
Fig.12. Harmonic spectrum of source current before compensation.
Fig. 9. Compensating shunt current for phase-a.
Fig. 13. Harmonic Spectrum of Source current after compensation
Table II indicates the individual harmonic distortion of three level and five level photovoltaic based shunt active filter. It is clearly visible from the below table that the proposed topology of five level cascaded multilevel shunt active power filter effectively compensates the current harmonics. Table II Individual harmonic distortion Fig. 10. Source current in-phase with source voltage for phase –a.
Topology PV based 3-Level Cascaded MLI PV based 5-Level Cascaded MLI
Harmonic distortion in % Before compensation After compensation Before compensation After compensation
1
5
100
18.68
100
7
11
13
2.47
6.52
4.72
5.51
4.72
4.01
2.99
100
18.68
12.47
6.52
4.72
100
3.91
2.7
0.20
0.19
B. Real Power Injection of PV based five-level Cascaded Multilevel Inverter for Power Conditioning.
Fig.11. Shunt current tracking for phase-a.
The total harmonic distortion (THD) is the most powerful tool used to determine the quality of AC waveforms using Fast Fourier Transformation (FFT) analysis. The total harmonic distortion of source current before compensation is 24.24 %.
In order to validate and test the real power injection of photovoltaic system based shunt active power filter. In this section we are considering two cases, in first case each Hbridge inverter is connected to DC capacitor whereas in second case each H-bridge inverter is supported by photovoltaic array.
Consider under steady state condition where sudden real power demand occurs in the system. Fig.14 represents capacitor voltage, shunt current tracking and source voltage and source current for the DC capacitor based cascaded multilevel shunt active power filter. It fails to compensate the real power demand and the capacitor voltage collapsed and it leads to poor tracking of shunt current and harmonic contamination in the source current. Fig.15 represents capacitor voltage, shunt current tracking, source voltage and source current for the PV based cascaded multilevel shunt active power filter. It is clearly depicted that the proposed photovoltaic based multilevel inverter shunt active filter is able to compensate real power demand and additionally it gives unity power factor correction, harmonic and reactive power compensation.
power theory is found to be an effective solution for power line conditioning. The proposed topology reduces harmonics and provides reactive power compensation due to non-linear load current. As a result source current become sinusoidal and unity power factor is also achieved. It is also able to inject real power whenever real power demand occurs in the system. As evident from the simulation studies that photovoltaic based five-level cascaded multilevel inverter shunt active filter is the better choice for power conditioning applications. The THD of the source current after compensation is 2.242 % which is less than 5 % requirement of the harmonic limit imposed by the IEEE-519 standards. VII. REFERENCES [1] [2] [3] [4] [5] [6]
[7] [8] Fig. 14. Capacitor Voltage, Shunt current tracking, Source Voltage and Source Current using Capacitor based SAPF.
[9] [10] [11] [12] [13] [14] [15] [16] [17]
Fig. 15. Capacitor Voltage, Shunt current tracking, Source Voltage and Source Current using PV based SAPF.
VI. CONCLUSION In this paper, photovoltaic based five-level cascaded multilevel inverter shunt active filter using instantaneous
B. Singh, K. Al-Haddad and A. Chandra, “A new control approach to 3phase active filter for harmonics and reactive power compensation”,IEEE Trans. on Power Systems, vol. 46, no. 5, pp.133 – 138, Oct. 1999. W.M.Grady, M.J.Samotyj, A.H.Noyola “Survey of active power line conditioning methodologies”, IEEE Trans on Power Delivery, vol.5, no.3, pp.1536-1542, July.1990 H. Akagi, “Trends in active power line conditioners”, IEEE Trans on Power Electronics, vol.9, no.3,pp.263-268, May.1994 L.Gyugyi, E. C. Strycula, “Active ac power filters”, in Proc. IEEE/IAS Annu. Meeting, vol.19, pp 529-535, 1976 H. Akagi, Y. Kanazawa, A. Nabae “Instantaneous reactive power compensators comprising switching devices without energy storage components”, IEEE Trans on Industry Appl, vol.3, pp.625-630, 1984. E. H. Watanabe, R. M. Stephan, M. Aredes, “New concepts of instantaneous active and reactive powers in electrical systems with generic loads”, IEEE Trans. Power Delivery, vol.8, no.2, pp.697-703, April.1993 F. Z. Peng and J.S Lai, “Generalized Instantaneous reactive power theory for three-phase power systems”, IEEE Trans. on Inst. and Meast, vol.45, no.1, pp.293-297,February .1996 J.Afonso, C.Couto, J Martins “Active filters with control based on the pq theory”, IEEE Industrial Elec letter,vol.47,no.3,pp.September.2000 L G. Leslie, “Design and analysis of a grid connected photovoltaic generation system with active filtering function” Master of Science in Electrical Engineering Blacksburg, Virginia March 14, 2003. M Malinowkski, K.Gopakumar, J Rodriguez and M A.Perez “A survey on cascaded multilevel inverters”, IEEE Trans on Indus. Electronics, Vol.57, No7, pp.2197-2205, July-2010. R. Gupta, A. Ghosh and A. Joshi, “Cascaded multilevel control of DSTATCOM using multiband hysteresis modulation”, IEEE Power Eng. Soc. General Meeting, pp.18–22, Jun. 2006. G. Vachtsevanos and K. Kalaitzakis, “A hybrid photovoltaic simulator for utility interactive studies,” IEEE Trans. Energy Conv., vol. EC-2, pp. 227–231, June 1987. P.Karuppanan, S.Rajasekar, Mahapatra, K.K, “Five-Level Cascaded Active Filter for Power Line Conditioners”, in Proc.IEEE, International Conference on Power, Control and Embedded Systems,pp. 1-6,Dec M. G. Jaboori, M. M. Saied, and A. A. Hanafy, “A contribution to the simulation and design optimization of photovoltaic systems,” IEEE Trans. Energy Conv., vol. 6, pp. 401–406, Sept. 1991 R. Gupta, A. Ghosh and A. Joshi, “Control of 3-level shunt active power filter using harmonic selective controller”, Proc. IEEE Power India Conference, pp. 10-15. April 2006. R.Gupta, G.Gupta, D.Kastwar, A.Hussain, H. Ranjan, “ Modeling and Design of MPPT Controller for a PV Module using PSCAD/EMTDC” in IEEE Power Energy Society conference, pp. 1-6, Oct. 2010. R. Gupta, A. Ghosh and A. Joshi, “Multi-band hysteresis modulation and switching characterization for sliding mode controlled cascaded multilevel inverter”, IEEE Trans. Ind. Electron., vol. 57, no.7, July 2010.
