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A grid-connected photovoltaic power conversion system with single-phase multilevel inverter
Available online at www.sciencedirect.com
Solar Energy 84 (2010) 2056–2067 www.elsevier.com/locate/solener
A grid-connected photovoltaic power conversion system with single-phase multilevel inverter Ersoy Beser, Birol Arifoglu, Sabri Camur, Esra Kandemir Beser ⇑ Department of Electrical Engineering, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, Turkey Received 7 May 2010; received in revised form 26 September 2010; accepted 28 September 2010 Available online 20 October 2010 Communicated by: Associate Editor Nicola Romeo
Abstract This paper presents a grid-connected photovoltaic (PV) power conversion system based on a single-phase multilevel inverter. The proposed system fundamentally consists of PV arrays and a single-phase multilevel inverter structure. First, configuration and structural parts of the PV assisted inverter system are introduced in detail. To produce reference output voltage waves, a simple switching strategy based on calculating switching angles is improved. By calculated switching angles, the reference signal is produced as a multilevel shaped output voltage wave. The control algorithm and operational principles of the proposed system are explained. Operating PV arrays in the same load condition is a considerable point; therefore a simulation study is performed to arrange the PV arrays. After determining the number and connection types of the PV arrays, the system is configured through the arrangement of the PV arrays. The validity of the proposed system is verified through simulations and experimental study. The results demonstrate that the system can achieve lower total harmonic distortion (THD) on the output voltage and load current, and it is capable of operating synchronous and transferring power values having different characteristic to the grid. Hence, it is suitable to use the proposed configuration as a PV power conversion system in various applications. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic; Photovoltaic power conversion; Grid-connected; Single-phase multilevel inverter
1. Introduction Recently, renewable energy resources have been becoming popular due to the decrease of fuel sources and their damages to the environment. As a result of the negative effects of global warming and climate changes, the interest of renewable resources has been increased gradually. Solar energy is one of these alternative energy resources. It is converted to the electrical energy by photovoltaic (PV) arrays. PV arrays do not generate any toxic or harmful substances that pollute the environment (Kang et al., 2005a,b). Another considerable feature of them is the ⇑ Corresponding author. Tel.: +90 2623033466; fax: +90 2623033003.
E-mail addresses: [email protected] (E. Beser), barif@kocaeli. edu.tr (B. Arifoglu), [email protected] (S. Camur), esrakandemir@ kocaeli.edu.tr (E.K. Beser). 0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.09.011
requirement of low maintenance. Depending on the development in photovoltaic technologies, the efficiency of the PV arrays has been improved. Therefore, studies on PV systems have increased gradually. PV systems are occasionally operated in stand-alone mode and they feed fixed loads by stand-alone PV inverters (Myrzik, 2001; Kang et al., 2005a,b; Daher et al., 2008; Lalouni et al. 2009; Saravana Ilango et al., 2010). PV systems are also interconnected to the grid. Interconnecting a PV system to the grid has been the popular design trend and grid-connection types of PV inverters have been proposed (Calais et al., 1999; Myrzik, 2001; Kuo et al., 2001; Alonso et al., 2003; Yu et al., 2005; Wu et al., 2005; Patcharaprakiti et al., 2005; Lee et al., 2008; Hassaine et al., 2009; Rahim et al., 2010). Therefore various power electronics technologies are improved to convert the dc to ac power for PV applications.
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Nomenclature Ck f I IPM Ls m n PLMk Pref P0 Qk(t) Qref Rs S t tmax tsample Vb Vbus
capacity of the kth capacitor group (lF) grid frequency (Hz) inverter current (A) maximum power current value (A) inductance of the self inductor (H) number of the level modules output level number power of the kth level module (W) reference real power (W) system output power (W) the kth switching signal reference reactive power (VAr) resistance of the self inductor (X) sum of the energy ratios instantaneous time value (s) maximum value of the sample time (s) value of the sample time (s) voltage of the base level module (V) bus voltage (V)
In addition, it is important to operate PV energy conversion systems near the maximum power point to increase the output efficiency of PV arrays (Kuo et al., 2001; Alonso et al., 2003; Yuvarajan et al., 2004; Yu et al., 2005; Patcharaprakiti et al., 2005; Lee et al., 2008). Thus, power electronics inverters are required for maximum power point tracking (MPPT) algorithm, which provides maximum PV power. They are also needed for transferring the PV power to a load or to the grid. Multilevel inverters are suitable choices for realizing this objective. Various multilevel inverter topologies have been introduced and studied in the literature. The most considerable of these types are the diode clamped, the flying capacitor, the cascaded H-Bridge, the magnetic coupled and the full bridge with cascaded transformers inverters. The remarkable feature of these inverters is generating less harmonic components on both output voltage and load current. By increasing the number of output levels, the quality of the output voltage and load current is increased step by step (Calais et al., 1999; Rodriguez et al., 2002; Kang et al., 2005a,b; Daher et al., 2008; Rahim et al., 2010; Beser et al., 2010). Due to the production of less harmonic components, the PV power is transferred to the load or to the grid in a high-quality form by multilevel inverter structures. Related to these developments, this study presents a PV assisted multilevel inverter system for the conversion of PV power to the electrical power. The proposed structure of the inverter system is quite suitable for the use of PV arrays. Owing to the use of a multilevel inverter structure, more sinusoidal shaped output voltage waves are obtained. Therefore, the THD of the output voltage is considerably reduced. Placement of the PV arrays in the system is the
Vbusref VCk Vg Vmax VPM Vref Vz V0 WCk WLMk XLs Zs Dt d dref h u x
the reference bus voltage (V) voltage of the kth capacitor group (V) grid voltage (V) maximum value of the required voltage (V) maximum power voltage value (V) reference voltage (V) voltage of the self inductor (V) output voltage (V) energy of the kth capacitor group (J) energy of the kth level module (J) reactance of the self inductor (X) impedance of the self inductor (X) time between ti and ti+1 (s) angle between V0 and Vg (°) reference angle between Vref and Vg (°) the angle between Rs and XLs (°) power angle (°) angular speed (rad s1)
significant point of the study because of loading the arrays in the same condition. To accomplish this, a simulation study is performed and the number and connection types of the PV arrays in the system are determined. According to the order of the PV arrays a configuration is formed for the PV assisted inverter system. The system is simulated while operating synchronous and transferring various power values having different characteristics to the grid. The validity of the proposed system is also verified through an experimental study. The measured THD values of the output voltage and current are quite low. The system provides good performance as a PV energy conversion system. 2. Proposed PV assisted single-phase multilevel inverter system 2.1. Configuration and structural parts of the proposed system Fig. 1 shows the base configuration of the proposed PV assisted multilevel inverter. It consists of PV modules, level modules (LM) and a conventional H-Bridge module. The base configuration of the multilevel inverter generates a 7-level shaped output voltage wave. However, the proposed system can be easily expanded and the number of output voltage levels is increased by adding level modules to the system (Beser et al., 2010). The proposed inverter structure provides an advantage in point of switching element number compared to some inverter types in the literature. A switch number comparison related to output level number (n) is made between different inverter types in Table 1.
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Fig. 1. Configuration of the proposed PV assisted single-phase multilevel inverter system.
Table 1 Switch number comparison related to output level number (n). Inverter type
Switch number
Diode clamped Flying capacitor Cascaded H-Bridge Magnetic coupled Full-bridge with cascaded transformer Proposed
2(n 1) 2(n 1) 2(n 1) 4 log3(n) 4 log3(n 2) + 4 2 log2(n + 1) + 2
It can be seen from Table 1 that 60 switches are used in diode clamped, flying capacitor and cascaded H-Bridge inverters to obtain 31-level output voltage. The magnetic coupled inverter type uses 12 switches and shapes 27-level voltage wave. The full bridge with cascaded transformer inverter type uses 16 switches and forms 29-level shaped output voltage. However, the proposed inverter achieves 31-level output voltage by using only 12 switches. Another considerable feature of the proposed inverter is that the system configuration allows operating regenerative. So this feature provides to transfer both active and reactive power to the grid.
Depending on the increase of the output level number, PV arrays are suitably connected serially and PV module is expanded according to the number of level modules. The configuration of the expanded PV module is shown in Fig. 3. The voltage between the points Pk and Nk is the voltage of serially connected PV arrays. Therefore the voltage of the capacitor group should be chosen in respect of the PV module voltage. The voltage of the capacitor group VCk is expressed as V Ck ¼ 2ðk1Þ V b
ð1Þ
k ¼ 1; 2; 3; . . . ; m
ð2Þ
2.1.2. Level module Level module (LM) consists of two switching devices and a dc source input. The points Pk and Nk in the dc source input are connected to output of the PV module.
2.1.1. PV module Fig. 2 shows the configuration of the PV module. It can be seen from Fig. 2 that it consists of PV arrays and a capacitor group.
Fig. 2. Configuration of the PV module.
Fig. 3. Configuration of the serially connected PV arrays in the PV module.
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The first level module (LM1) is named as the base level module. The configuration of the level module is illustrated in Fig. 4. 2.1.3. H-Bridge module Conventional H-Bridge structure is used in the proposed system. The numbers of output voltage levels can be increased by varying the number of PV and level modules. However, no modification is made in the structure of the H-Bridge module. Therefore, H-Bridge module is defined as the stable part of the proposed system (Beser et al., 2010). The configuration of the H-Bridge module is shown in Fig. 5. It can be seen from Fig. 5 that the grid connection can be made between the points A and B. A load can also be connected to the points A and B, and thus the system is operated in stand-alone mode. 2.2. Switching strategy Switching strategy in the PV assisted inverter structure is to generate gate signals by calculating switching angles. In order to calculate switching angles, first, the reference output voltage Vref is determined as follows:
V ref ¼ V max sinðxt þ dref Þ
ð3Þ
A sample reference output voltage wave is illustrated in Fig. 6. Dt seen in Fig. 6 gives the sample time of the switching signals. The maximum value of the sample time is related to the frequency of the reference output voltage and the level module number. In Eq. (4) the maximum value of sample time (tmax) is given 1 tmax ¼ sin1 ðmþ1Þ ð4Þ ð2pf Þ1 2 2 tsample ¼ Dt ¼ tiþ1 ti
ð5Þ
tsample tmax
ð6Þ
During operation, the sample time (tsample) should be chosen smaller than tmax. The smaller tsample is chosen, the better results are obtained for the output voltage. Thus, the output voltage more closely resembles the reference signal. But the speed of the microcontroller in the system can make a lower limitation for tsample. According to the microcontroller speed, tsample is chosen as tmax/10 in this study. Vref value at any time is taken from the curve and used in the switching equations. The switching equations are expressed as Q1 ðtÞ ¼ V ref ðtÞ mod 2 mod 2 V ref ðtÞ V ref ðtÞ Q2 ðtÞ ¼ 2
Fig. 4. Configuration of the level module.
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ð7Þ mod 2
ð8Þ
By using the equations, the switching signals are obtained. Switching equations can be generalized and the general switching function related to the level module number is defined as follows: V ref ðtÞ V ref ðtÞ mod 2ðk1Þ Qk ðtÞ ¼ ð9Þ mod 2 2ðk1Þ By using Eq. (9), the switching signals are obtained for the proposed multilevel inverter structure including four level modules. Therefore, the reference output voltage wave in Fig. 6 is configured as a 31-level shaped output voltage wave. The switching signals and the simulated output voltage wave are given in Figs. 7 and 8, respectively. Switching strategy changes related to PV module and level module number in the system. In order to obtain more
Fig. 5. Configuration of the H-Bridge module.
Fig. 6. A sample reference output voltage wave.
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Fig. 7. Switching signals in the proposed multilevel inverter including four level modules.
Fig. 10. Output voltage waves for various amplitudes and frequencies in the multilevel inverter.
3. Control algorithm and operational principles of the proposed system A control algorithm is improved for generating the reference signals at the inverter output and transferring PV power to the grid. A simplified electrical circuit of the PV assisted system can be drawn as in Fig. 11. A self inductor is used between the multilevel inverter output and the grid. The impedance of the inductor can be defined as Fig. 8. 31-Level shaped output voltage of the proposed multilevel inverter including four level modules.
quality output voltage, module number is increased. So, the PV arrays are suitably connected serially in a PV module to obtain suitable dc voltage values. In this case the switching strategy changes. However, if the system power is required to increase, PV arrays are connected parallel in the PV module. The switching strategy does not change at this time. The proposed system is able to produce output voltage waves having different amplitude. The amplitude of the output voltage is easily regulated without modifying the number of level modules. So, the system can easily tolerate the changes on the load. The multilevel inverter structure is also capable of producing output voltage waves having different frequency. Experimental output voltage waves for various amplitudes and frequencies are shown in Figs. 9 and 10, respectively.
Z s ¼ Rs þ jX Ls ¼ jZ s j\h
ð10Þ
Beside the determination of the reference signals, the algorithm achieves MPPT feature, which provides maximum utility from the PV power. Fig. 12 shows the control block diagram of the proposed PV assisted inverter system. For determining the reference real power Pref, DC bus voltage Vbus is first subtracted from the reference voltage Vbusref, and then, the error is evaluated by the controller and Pref is generated. To operate the system for the required power factor, the reactive power Qref is entered to the control system by the user. Therefore, energy transferring is realized for the required power factor. The current I and the power angle u are derived from the Eq. (11) and Eq. (12) as follows: Qref u ¼ a tan ð11Þ P ref I¼
P ref V g cos u
ð12Þ
Then, voltage of the self inductor Vz is calculated as V z ¼ I\u Z s \h ¼ jV z j\ðu þ hÞ
Fig. 9. Output voltage waves for various amplitudes in the multilevel inverter.
Fig. 11. Simplified electrical circuit of the PV assisted system.
ð13Þ
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Fig. 12. Control block diagram of the proposed PV assisted inverter system.
and the reference output voltage Vref and the reference angle dref comments can be determined by adding Vz to the grid voltage Vg as V ref \dref ¼ V g \0 þ V z \ðu þ hÞ
ð14Þ
The calculated Vref and dref values are used in Eq. (9) and switching signals are obtained as it has been mentioned in Section 2. Control algorithm is easily provided by a PIC18F452 microcontroller in the digital control unit. A principle scheme of the digital control unit is shown in Fig. 13. Owing to zero crossing sensing (ZCS) circuit, zero crossing points of the Vg are determined. The points are sensed and a timer is operated by the microcontroller. By the data taken from the timer output, a sinus shaped output voltage which is synchronous to the grid is obtained. The output voltage can be shifted forward or backward by the angle dref. Vg, Vbus and I are sampled by the analogue inputs of the microcontroller. By these data, Vref and dref are calculated and switching signals are obtained for the switching devices. Thus, the multilevel inverter structure generates the output voltage based on the switching signals. By means of the proposed control algorithm, PV arrays are operated at the maximum power transfer point. This feature is provided by the embedded MPPT algorithm in the system. The MPPT procedure does not require any extra equipment, it consists of an algorithm. The algorithm
Fig. 14. I–V and P–V characteristic of the PV arrays.
Table 2 Specifications of PV arrays. Rated power (PM) Maximum power voltage (VPM) Maximum power current (IPM) Open-circuit power (VOC) Short-circuit current (ISC)
5W 17.1 V 0.30 A 21.7 V 0.31 A
tracks the maximum power transfer voltage (VPM). Vbusref in the control algorithm represents the maximum power transfer voltage (VPM).
Fig. 13. Principle scheme of the digital control unit.
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Fig. 15. Calculation of the level module energy.
Fig. 17. Simulation results of the transferred output power in the proposed system including four level modules where P1 = 960 W, Q1 = 290 VAr and P2 = 540 W, Q2 = 180 VAr.
Fig. 16. Calculation of the load energy.
4. Arrangement of the PV arrays in the system In the proposed system, setting only the voltage of the dc sources is not sufficient for operating the system. When the system is arranged only according to the voltage values, PV arrays are not loaded in the equal load conditions. Some of them are forced to operate over capacity and the others are forced to operate under capacity. Over loaded PV arrays can not transfer the power and output voltage of the PV arrays decreases. On the other hand, under loaded PV arrays can not generate the rated power
value and output voltage of the arrays increases. This situation can be seen from the I–V and P–V characteristic of the PV arrays in Fig. 14. As a result, required voltage levels are not provided for the multilevel inverter and a sinusoidal shaped voltage wave can not be generated. To prevent this problem, the required energy transferred by each level module and the connection types of the PV arrays should be determined. To determine the number and arrangement of the PV arrays in the PV modules, a simulation study is first implemented. The specifications of each PV array are given in Table 2. System output power (P0) is determined as 1 kW and PV arrays are placed into the PV modules with respect to the output power. In order to determine the amount of the transferred energy to the load by each dc source in level modules, the multilevel inverter system is simulated for var-
Table 3 Transferred energy to the load and energy ratios of the level modules for various load conditions in the proposed system including four level modules. PV array side WLM1 (J)
0.488 0.975 1.946 0.299 0.847
WLM2 (J)
1.116 2.230 4.457 0.686 1.938
Load side WLM3 (J)
2.549 5.097 10.190 1.568 4.430
WLM4 (J)
5.897 11.790 23.572 3.629 10.248
WLMT (J)
10.049 20.092 40.165 6.182 17.463
WLM2/ WLM1
2.288 2.288 2.291 2.292 2.289
WLM3/ WLM1
5.228 5.230 5.237 5.241 5.231
WLM4/ WLM1
12.093 12.099 12.115 12.129 12.100
WL (J)
10.048 20.089 40.157 6.180 17.460
PL (W)
502 1004 2008 309 873
QL (VAr)
0 0 0 464 338
Series load R (W)
XL (W)
XC (W)
65.76 32.88 16.44 32.88 32.88
– – – 49.32 –
– – – – 12.73
Table 4 Arrangement of PV arrays and calculated capacity values in the PV modules for the proposed inverter system including four level modules. LM
Level module capacity
PV connection type
Label
Capacity (mF)
Voltage (V)
Series
Parallel
LM1 LM2 LM3 LM4
C1 C2 C3 C4
30,000 17,000 10,000 6000
25 50 100 200
1 2 4 8
10 12 13 15
Total PV number
Total PV number (W)
LM voltage (V)
10 24 52 120
50 120 260 600
17.1 34.2 68.4 136.8
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ious loads which have a different value and characteristic (resistive, inductive and capacitive). To determine the powers obtained from the level modules, dc sources are used instead of the PV arrays in the simulation study. It is seen that the transferred energy of each level module (WLMk) to the load is different from one another (WLM1 – WLM2 – WLM3 – WLM4). The calculation of the level module and load energy is shown in Figs. 15 and 16, respectively. In addition, to determine the energy ratio of the level 2 W LM3 W LM4 modules ðWW LM ; ; Þ, the energy of each level module LM 1 W LM1 W LM1 is divided by the energy of the base level module (LM1) and a ratio is obtained for the dc source in each level module. It is determined that the ratio between LM1 and the other level modules does not change related to characteristic and value of the load, each ratio is calculated as a different constant value for a specific level module number. Table 3 shows the transferred energy to the load and energy ratios of the level modules for various load conditions. In order to determine the PV power in the level modules, the sum of the energy ratios of the level modules are first obtained as S ¼1þ
W LM2 W LM3 W LM4 þ þ W LM1 W LM1 W LM1
ð15Þ
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occurring during the charging and discharging (V1 V2) are directly related to the transferred energy from the capacitors. The transferred energy by the capacitor group is defined as 1 W ck ¼ C k V 21 V 22 2
ð18Þ
The required energy is considered for a period of time in the simulation study and the required capacity values are calculated by Eq. (18). Table 4 shows the arrangement of PV arrays and calculated capacity values in the PV modules for the proposed inverter system including four level modules. 5. Simulated and experimental results and discussion After determining the situation of PV arrays, the proposed PV power conversion system was simulated and implemented. It was first operated synchronous to the grid (110Vac, 50 Hz) and two different states were performed in the simulation study. First, approximately all of the generated power was transferred, and then, less than the generated power was transferred to the grid. The parameters
and then power values of the base level module and the other level modules are calculated as follows P LM1 ¼
P0 S
P LMk ¼ P LM1
ð16Þ W LMk W LM1
ð17Þ
In this study, PLM1 is calculated as 48 W for the output power 1 kW and accepted as 50 W. PLM2, PLM3 and PLM4 are obtained as 114 W, 260 W and 604 W, respectively and they are accepted as 120 W, 260 W and 600 W. According to the calculated values, PV number and connection types are determined and PV arrays are placed into the level modules. Therefore, each PV array is operated in the same load condition and the required voltage levels are achieved for the inverter structure. The current value transferred from the PV arrays varies in relation to the instantaneous magnitude of the sinus shaped current and on/off conditions of the PV arrays. On/off conditions of the PV modules are given in Fig. 7 for a period of time. Due to their characteristic, PV arrays can not realize power transfer in case of exceeding the maximum power current (IPM) value. When the PV arrays are first connected to the system, a current value higher than IPM is occurred and PV arrays can not realize power transfer at this duration. This problem can be solved by using proper capacitors in the PV module. The capacitors compensate the instantaneous over currents and prevent the PV array from the short-circuit situation. The capacitors are charged from the PV arrays in case the PV arrays do not feed the system. However, they are discharged, when the PV arrays are connected to the system. Voltage ripples
Fig. 18. Simulation results of the inverter output voltage and inverter current in the proposed PV assisted multilevel inverter: (a) P1 = 960 W, Q1 = 290 VAr and (b) P2 = 540 W, Q2 = 180 VAr.
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Rs = 0.39 X and Ls = 4 mH are used for the self inductor in the simulation and experimental study. Fig. 17 shows simulation result of the transferred real power and reactive power values for two different states (P1, Q1; P2, Q2). The simulation results of the voltage and current waveforms at the power values P1, Q1 and P2, Q2 is shown in Fig. 18a and b. If the power is not transferred as much as the generation of the PV arrays, voltages of the capacitors approach the open circuit voltage of the PV arrays and the system can not be operated at the maximum power transfer point. In case of transferring the power to the grid as much as the PV arrays generate, output voltage of the PV arrays decreases to the maximum power voltage (VPM). Simulation results of the voltages of the capacitors are shown in Fig. 19 for transferring approximately all of the generated power and less power than generated. It can be seen from Fig. 19 that when the less power (P2) than generated is transferred, the capacitor voltages reach higher values than the maximum power voltage and the system diverges from the maximum power transferring point. In case of transferring approximately all of the generated power (P1) by the PV arrays, the capacitor voltages reach to maximum power voltage value. As it can be seen from Fig. 19, the voltage of base level module is obtained as 17.4 V. It can be also seen from Table 2 that the real
maximum power voltage value (VPM) of the PV arrays is 17.1 V. The simulated and real values are so close to each other. Therefore, the base level module operates at the maximum power transfer point. The voltages of the other modules are calculated as 35.8 V, 70 V and 140 V in the simulation study. These values are approximately equal to 2VPM, 4VPM and 8VPM. Thus, it is observed that the other level modules operate at the maximum power transfer point. After the simulation study, experimental tests were realized by multilevel inverter structure. The proposed inverter system includes four level modules, an H-Bridge module, a digital control unit and zero crossing sensing circuit. PIC18F452 microcontroller is preferred in the digital control unit. A maximum of 31-level output voltage waveform can be obtained by six level modules. IRFP460 mosfets (500 V, 20 A) are used in level and H-Bridge modules. The proposed system was tested in the laboratory conditions. Similar to the simulation study, the system was connected to the grid (110Vac, 50 Hz) in synchronous mode and power transfer is realized. The THD values of the output voltages and currents are also measured by a harmonic analyzer. Experimental wave forms are shown in Figs. 20 and 21 for different operation points, respectively. Measured THD values are given in Table 5.
Fig. 19. Simulation results of the capacitor voltages in the PV modules while transferring the powers P1, Q1 and P2, Q2.
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Fig. 20. Experimental results of inverter output voltage and grid voltage while operating synchronous to the grid for different operation points: (a) Vg = 114 V, P = 405 W, Q = 68 VAr, d = 0; (b) Vg = 113 V, P = 415 W, Q = 806 VAr, d = 10; (c) Vg = 113 V, P = 105 W, Q = 525 VAr, d = 10; and (d) Vg = 76 V, P = 295 W, Q = 185 VAr, d = 0.
Grid voltage (Vg) and inverter output voltage (V0) waves are given in Fig. 20. The curves are so close to each other. This shows that the proposed system operates synchronous to the grid. It can be seen from the experimental results that the required real power and reactive power values are transferred to the grid in sinusoidal form as mentioned in the
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Fig. 21. Experimental results of inverter output voltage and current while operating synchronous to the grid for different operation points: (a) Vg = 114 V, P = 405 W, Q = 68 VAr, d = 0; (b) Vg = 113 V, P = 415 W, Q = 806 VAr, d = 10; (c) Vg = 113 V, P = 105 W, Q = 525 VAr, d = 10; and (d) Vg = 76 V, P = 295 W, Q = 185 VAr, d = 0.
proposed control algorithm. In addition Figs. 20d and 21d show that the system can operate for the different grid voltage values. Hence, the system is flexible and capable of operating for different points. According to the IEEE 519-1992 standard, THD value of the voltages under 69 kV should not be over 5%. Table 5 shows that THD value of the output voltage is acceptable for the IEEE standard in each operation point.
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Table 5 Measured THD values for different operation points. P (W)
Q (VAr)
Delta (°)
Grid
Multilevel inverter
Voltage (V)
THD (%)
Voltage (V)
THD (%)
Current (A)
THD (%)
Efficiency (%)
405 415 105 295 458 452
68 806 525 185 1090 565
0 10 10 0 10 10
114 113 113 76 131 141
1.87 1.71 1.28 2.01 1.81 1.39
114 112 117 80 119 143
1.86 3.36 2.4 3.28 3.37 1.83
3.66 8.25 4.69 4.55 9.08 5.07
5.03 4.94 6.34 3.36 6.45 5.07
97.79 97.87 97.67 92.57 98.75 99.00
6. Conclusions A PV power conversion system based on a single-phase multilevel inverter was proposed in this paper. The configuration of the proposed system was designed first, and then, the system was simulated and implemented. The simulated and experimental results are presented and explained. Presentable results of the proposed system are summarized as follows: (1) The inverter structure in the proposed system produces multilevel shaped output voltage waveforms. Therefore, it reduces dv/dt stresses imposed on the switching devices and generates less harmonic components on the output voltage and current. (2) The inverter can be easily expanded by increasing level modules. Thus, number of the output levels is increased and the inverter generates higher-quality output voltage waveforms. (3) The switching strategy is considerably simple. By only using Vref and dref, switching signals are easily determined. (4) A control algorithm is improved for generating the reference signals at the inverter output and transferring PV power to the grid. A considerable advantage of the control algorithm is being realized by a simple microprocessor structure. By means of the algorithm, the proposed system operates near the maximum power point. Thus, the system does not require any MPPT unit as the algorithm achieves MPPT feature. (5) To include PV arrays into the system suitably, a simulation study was made and PV arrays were arranged for the inverter system. Owing to this configuration, each PV arrays are loaded in equal conditions. As a result, the required voltage levels are achieved for the inverter structure. (6) The proposed system was verified through simulations and experimental study. The system was operated in synchronous mode and the PV power was transferred to the grid. It is seen that the results are considerably similar to the reference signals. (7) It is seen from the experimental results that the THD values of the output voltage and current are quite low. Thus, it can be said that the transferred power to the grid is in good quality.
(8) These results show that the proposed system can suitably achieve the transfer of the PV power to the grid. Consequently, this study provides an efficient employment of PV energy since there is a shortage of the energy resources and an increasing importance of renewable energy resources in these days.
References Alonso, O., Sanchis, P., Gubia E., Marroyo, L., 2003. Cascaded H-bridge multilevel converter for grid connected photovoltaic generators with independent maximum power point tracking of each solar array. In: Proc. IEEE Power Electronics Specialist Conf., pp. 731–735. Beser, E., Arifoglu, B., Camur, S., Kandemir Beser, E., 2010. Design and application of a single phase multilevel inverter suitable for using as a voltage harmonic source. Journal of Power Electronics 10 (2), 138–145. Calais, M., Agelidis, V.G., Meinhardt, M., 1999. Multilevel converters for single-phase grid connected photovoltaic systems: an overview. Solar Energy 66 (5), 325–335. Daher, S., Schmid, J., Antunes, F.L.M., 2008. Multilevel inverter topologies for stand-alone PV systems. IEEE Transactions on Industrial Electronics 55 (7), 2703–2712. Hassaine, L., Olias, E., Quintero, J., Haddadi, M., 2009. Digital power factor control and reactive power regulation for grid-connected photovoltaic inverter. Renewable Energy 34 (1), 315–321. Kang, F.-S., Park, S.-J., Cho, S.E., Kim, C.-U., Ise, T., 2005a. Multilevel PWM inverters suitable for the use of stand-alone photovoltaic power systems. IEEE Transactions on Energy Conversion 20 (4), 906–915. Kang, F.-S., Cho, S.E., Park, S.-J., Kim, C.-U., Ise, T., 2005b. A new control scheme of a cascaded transformer type multilevel PWM inverter for a residential photovoltaic power conditioning system. Solar Energy 78 (6), 727–738. Kuo, Y.-C., Liang, T.-J., Chen, J.-F., 2001. Novel maximum-power-pointtracking controller for photovoltaic energy conversion system. IEEE Transactions on Industrial Electronics 48 (3), 594–601. Lalouni, S., Rekioua, D., Rekioua, T., Matagne, E., 2009. Fuzzy logic control of stand-alone photovoltaic system with battery storage. Journal of Power Sources 193 (2), 899–907. Lee, S.-H., Song, S.-G., Park, S.-J., Moon, C.-J., Lee, M.-H., 2008. Gridconnected photovoltaic system using current-source inverter. Solar Energy 82 (5), 411–419. Myrzik, J.M.A., 2001. Novel inverter topologies for single-phase standalone or grid connected photovoltaic systems. In: Proc. IEEE Power Electronics Drive Systems Conf., pp. 103–108. Patcharaprakiti, N., Premrudeepreechacharn, S., Sriuthaisiriwong, Y., 2005. Maximum power point tracking using adaptive fuzzy logic control for grid-connected photovoltaic system. Renewable Energy 30 (11), 1771–1788. Rahim, N.A., Selvaraj, J., Krismadinata, C., 2010. Five-level inverter with dual reference modulation technique for grid-connected PV system. Renewable Energy 35 (3), 712–720.
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nonlinear inductor consideration. IEEE Transactions on Industry Applications 41 (4), 1075–1083. Yu, H., Pan, J., Xiang, A., 2005. A multi-function grid-connected PV system with reactive power compensation for the grid. Solar Energy 79 (1), 101–106. Yuvarajan, S., Yu, D., Xu, S., 2004. A novel power converter for photovoltaic applications. Journal of Power Sources 135 (1–2), 327– 331.
Solar Energy 84 (2010) 2056–2067 www.elsevier.com/locate/solener
A grid-connected photovoltaic power conversion system with single-phase multilevel inverter Ersoy Beser, Birol Arifoglu, Sabri Camur, Esra Kandemir Beser ⇑ Department of Electrical Engineering, Kocaeli University, Umuttepe Campus, 41380 Kocaeli, Turkey Received 7 May 2010; received in revised form 26 September 2010; accepted 28 September 2010 Available online 20 October 2010 Communicated by: Associate Editor Nicola Romeo
Abstract This paper presents a grid-connected photovoltaic (PV) power conversion system based on a single-phase multilevel inverter. The proposed system fundamentally consists of PV arrays and a single-phase multilevel inverter structure. First, configuration and structural parts of the PV assisted inverter system are introduced in detail. To produce reference output voltage waves, a simple switching strategy based on calculating switching angles is improved. By calculated switching angles, the reference signal is produced as a multilevel shaped output voltage wave. The control algorithm and operational principles of the proposed system are explained. Operating PV arrays in the same load condition is a considerable point; therefore a simulation study is performed to arrange the PV arrays. After determining the number and connection types of the PV arrays, the system is configured through the arrangement of the PV arrays. The validity of the proposed system is verified through simulations and experimental study. The results demonstrate that the system can achieve lower total harmonic distortion (THD) on the output voltage and load current, and it is capable of operating synchronous and transferring power values having different characteristic to the grid. Hence, it is suitable to use the proposed configuration as a PV power conversion system in various applications. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic; Photovoltaic power conversion; Grid-connected; Single-phase multilevel inverter
1. Introduction Recently, renewable energy resources have been becoming popular due to the decrease of fuel sources and their damages to the environment. As a result of the negative effects of global warming and climate changes, the interest of renewable resources has been increased gradually. Solar energy is one of these alternative energy resources. It is converted to the electrical energy by photovoltaic (PV) arrays. PV arrays do not generate any toxic or harmful substances that pollute the environment (Kang et al., 2005a,b). Another considerable feature of them is the ⇑ Corresponding author. Tel.: +90 2623033466; fax: +90 2623033003.
E-mail addresses: [email protected] (E. Beser), barif@kocaeli. edu.tr (B. Arifoglu), [email protected] (S. Camur), esrakandemir@ kocaeli.edu.tr (E.K. Beser). 0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.09.011
requirement of low maintenance. Depending on the development in photovoltaic technologies, the efficiency of the PV arrays has been improved. Therefore, studies on PV systems have increased gradually. PV systems are occasionally operated in stand-alone mode and they feed fixed loads by stand-alone PV inverters (Myrzik, 2001; Kang et al., 2005a,b; Daher et al., 2008; Lalouni et al. 2009; Saravana Ilango et al., 2010). PV systems are also interconnected to the grid. Interconnecting a PV system to the grid has been the popular design trend and grid-connection types of PV inverters have been proposed (Calais et al., 1999; Myrzik, 2001; Kuo et al., 2001; Alonso et al., 2003; Yu et al., 2005; Wu et al., 2005; Patcharaprakiti et al., 2005; Lee et al., 2008; Hassaine et al., 2009; Rahim et al., 2010). Therefore various power electronics technologies are improved to convert the dc to ac power for PV applications.
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Nomenclature Ck f I IPM Ls m n PLMk Pref P0 Qk(t) Qref Rs S t tmax tsample Vb Vbus
capacity of the kth capacitor group (lF) grid frequency (Hz) inverter current (A) maximum power current value (A) inductance of the self inductor (H) number of the level modules output level number power of the kth level module (W) reference real power (W) system output power (W) the kth switching signal reference reactive power (VAr) resistance of the self inductor (X) sum of the energy ratios instantaneous time value (s) maximum value of the sample time (s) value of the sample time (s) voltage of the base level module (V) bus voltage (V)
In addition, it is important to operate PV energy conversion systems near the maximum power point to increase the output efficiency of PV arrays (Kuo et al., 2001; Alonso et al., 2003; Yuvarajan et al., 2004; Yu et al., 2005; Patcharaprakiti et al., 2005; Lee et al., 2008). Thus, power electronics inverters are required for maximum power point tracking (MPPT) algorithm, which provides maximum PV power. They are also needed for transferring the PV power to a load or to the grid. Multilevel inverters are suitable choices for realizing this objective. Various multilevel inverter topologies have been introduced and studied in the literature. The most considerable of these types are the diode clamped, the flying capacitor, the cascaded H-Bridge, the magnetic coupled and the full bridge with cascaded transformers inverters. The remarkable feature of these inverters is generating less harmonic components on both output voltage and load current. By increasing the number of output levels, the quality of the output voltage and load current is increased step by step (Calais et al., 1999; Rodriguez et al., 2002; Kang et al., 2005a,b; Daher et al., 2008; Rahim et al., 2010; Beser et al., 2010). Due to the production of less harmonic components, the PV power is transferred to the load or to the grid in a high-quality form by multilevel inverter structures. Related to these developments, this study presents a PV assisted multilevel inverter system for the conversion of PV power to the electrical power. The proposed structure of the inverter system is quite suitable for the use of PV arrays. Owing to the use of a multilevel inverter structure, more sinusoidal shaped output voltage waves are obtained. Therefore, the THD of the output voltage is considerably reduced. Placement of the PV arrays in the system is the
Vbusref VCk Vg Vmax VPM Vref Vz V0 WCk WLMk XLs Zs Dt d dref h u x
the reference bus voltage (V) voltage of the kth capacitor group (V) grid voltage (V) maximum value of the required voltage (V) maximum power voltage value (V) reference voltage (V) voltage of the self inductor (V) output voltage (V) energy of the kth capacitor group (J) energy of the kth level module (J) reactance of the self inductor (X) impedance of the self inductor (X) time between ti and ti+1 (s) angle between V0 and Vg (°) reference angle between Vref and Vg (°) the angle between Rs and XLs (°) power angle (°) angular speed (rad s1)
significant point of the study because of loading the arrays in the same condition. To accomplish this, a simulation study is performed and the number and connection types of the PV arrays in the system are determined. According to the order of the PV arrays a configuration is formed for the PV assisted inverter system. The system is simulated while operating synchronous and transferring various power values having different characteristics to the grid. The validity of the proposed system is also verified through an experimental study. The measured THD values of the output voltage and current are quite low. The system provides good performance as a PV energy conversion system. 2. Proposed PV assisted single-phase multilevel inverter system 2.1. Configuration and structural parts of the proposed system Fig. 1 shows the base configuration of the proposed PV assisted multilevel inverter. It consists of PV modules, level modules (LM) and a conventional H-Bridge module. The base configuration of the multilevel inverter generates a 7-level shaped output voltage wave. However, the proposed system can be easily expanded and the number of output voltage levels is increased by adding level modules to the system (Beser et al., 2010). The proposed inverter structure provides an advantage in point of switching element number compared to some inverter types in the literature. A switch number comparison related to output level number (n) is made between different inverter types in Table 1.
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Fig. 1. Configuration of the proposed PV assisted single-phase multilevel inverter system.
Table 1 Switch number comparison related to output level number (n). Inverter type
Switch number
Diode clamped Flying capacitor Cascaded H-Bridge Magnetic coupled Full-bridge with cascaded transformer Proposed
2(n 1) 2(n 1) 2(n 1) 4 log3(n) 4 log3(n 2) + 4 2 log2(n + 1) + 2
It can be seen from Table 1 that 60 switches are used in diode clamped, flying capacitor and cascaded H-Bridge inverters to obtain 31-level output voltage. The magnetic coupled inverter type uses 12 switches and shapes 27-level voltage wave. The full bridge with cascaded transformer inverter type uses 16 switches and forms 29-level shaped output voltage. However, the proposed inverter achieves 31-level output voltage by using only 12 switches. Another considerable feature of the proposed inverter is that the system configuration allows operating regenerative. So this feature provides to transfer both active and reactive power to the grid.
Depending on the increase of the output level number, PV arrays are suitably connected serially and PV module is expanded according to the number of level modules. The configuration of the expanded PV module is shown in Fig. 3. The voltage between the points Pk and Nk is the voltage of serially connected PV arrays. Therefore the voltage of the capacitor group should be chosen in respect of the PV module voltage. The voltage of the capacitor group VCk is expressed as V Ck ¼ 2ðk1Þ V b
ð1Þ
k ¼ 1; 2; 3; . . . ; m
ð2Þ
2.1.2. Level module Level module (LM) consists of two switching devices and a dc source input. The points Pk and Nk in the dc source input are connected to output of the PV module.
2.1.1. PV module Fig. 2 shows the configuration of the PV module. It can be seen from Fig. 2 that it consists of PV arrays and a capacitor group.
Fig. 2. Configuration of the PV module.
Fig. 3. Configuration of the serially connected PV arrays in the PV module.
E. Beser et al. / Solar Energy 84 (2010) 2056–2067
The first level module (LM1) is named as the base level module. The configuration of the level module is illustrated in Fig. 4. 2.1.3. H-Bridge module Conventional H-Bridge structure is used in the proposed system. The numbers of output voltage levels can be increased by varying the number of PV and level modules. However, no modification is made in the structure of the H-Bridge module. Therefore, H-Bridge module is defined as the stable part of the proposed system (Beser et al., 2010). The configuration of the H-Bridge module is shown in Fig. 5. It can be seen from Fig. 5 that the grid connection can be made between the points A and B. A load can also be connected to the points A and B, and thus the system is operated in stand-alone mode. 2.2. Switching strategy Switching strategy in the PV assisted inverter structure is to generate gate signals by calculating switching angles. In order to calculate switching angles, first, the reference output voltage Vref is determined as follows:
V ref ¼ V max sinðxt þ dref Þ
ð3Þ
A sample reference output voltage wave is illustrated in Fig. 6. Dt seen in Fig. 6 gives the sample time of the switching signals. The maximum value of the sample time is related to the frequency of the reference output voltage and the level module number. In Eq. (4) the maximum value of sample time (tmax) is given 1 tmax ¼ sin1 ðmþ1Þ ð4Þ ð2pf Þ1 2 2 tsample ¼ Dt ¼ tiþ1 ti
ð5Þ
tsample tmax
ð6Þ
During operation, the sample time (tsample) should be chosen smaller than tmax. The smaller tsample is chosen, the better results are obtained for the output voltage. Thus, the output voltage more closely resembles the reference signal. But the speed of the microcontroller in the system can make a lower limitation for tsample. According to the microcontroller speed, tsample is chosen as tmax/10 in this study. Vref value at any time is taken from the curve and used in the switching equations. The switching equations are expressed as Q1 ðtÞ ¼ V ref ðtÞ mod 2 mod 2 V ref ðtÞ V ref ðtÞ Q2 ðtÞ ¼ 2
Fig. 4. Configuration of the level module.
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ð7Þ mod 2
ð8Þ
By using the equations, the switching signals are obtained. Switching equations can be generalized and the general switching function related to the level module number is defined as follows: V ref ðtÞ V ref ðtÞ mod 2ðk1Þ Qk ðtÞ ¼ ð9Þ mod 2 2ðk1Þ By using Eq. (9), the switching signals are obtained for the proposed multilevel inverter structure including four level modules. Therefore, the reference output voltage wave in Fig. 6 is configured as a 31-level shaped output voltage wave. The switching signals and the simulated output voltage wave are given in Figs. 7 and 8, respectively. Switching strategy changes related to PV module and level module number in the system. In order to obtain more
Fig. 5. Configuration of the H-Bridge module.
Fig. 6. A sample reference output voltage wave.
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Fig. 7. Switching signals in the proposed multilevel inverter including four level modules.
Fig. 10. Output voltage waves for various amplitudes and frequencies in the multilevel inverter.
3. Control algorithm and operational principles of the proposed system A control algorithm is improved for generating the reference signals at the inverter output and transferring PV power to the grid. A simplified electrical circuit of the PV assisted system can be drawn as in Fig. 11. A self inductor is used between the multilevel inverter output and the grid. The impedance of the inductor can be defined as Fig. 8. 31-Level shaped output voltage of the proposed multilevel inverter including four level modules.
quality output voltage, module number is increased. So, the PV arrays are suitably connected serially in a PV module to obtain suitable dc voltage values. In this case the switching strategy changes. However, if the system power is required to increase, PV arrays are connected parallel in the PV module. The switching strategy does not change at this time. The proposed system is able to produce output voltage waves having different amplitude. The amplitude of the output voltage is easily regulated without modifying the number of level modules. So, the system can easily tolerate the changes on the load. The multilevel inverter structure is also capable of producing output voltage waves having different frequency. Experimental output voltage waves for various amplitudes and frequencies are shown in Figs. 9 and 10, respectively.
Z s ¼ Rs þ jX Ls ¼ jZ s j\h
ð10Þ
Beside the determination of the reference signals, the algorithm achieves MPPT feature, which provides maximum utility from the PV power. Fig. 12 shows the control block diagram of the proposed PV assisted inverter system. For determining the reference real power Pref, DC bus voltage Vbus is first subtracted from the reference voltage Vbusref, and then, the error is evaluated by the controller and Pref is generated. To operate the system for the required power factor, the reactive power Qref is entered to the control system by the user. Therefore, energy transferring is realized for the required power factor. The current I and the power angle u are derived from the Eq. (11) and Eq. (12) as follows: Qref u ¼ a tan ð11Þ P ref I¼
P ref V g cos u
ð12Þ
Then, voltage of the self inductor Vz is calculated as V z ¼ I\u Z s \h ¼ jV z j\ðu þ hÞ
Fig. 9. Output voltage waves for various amplitudes in the multilevel inverter.
Fig. 11. Simplified electrical circuit of the PV assisted system.
ð13Þ
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Fig. 12. Control block diagram of the proposed PV assisted inverter system.
and the reference output voltage Vref and the reference angle dref comments can be determined by adding Vz to the grid voltage Vg as V ref \dref ¼ V g \0 þ V z \ðu þ hÞ
ð14Þ
The calculated Vref and dref values are used in Eq. (9) and switching signals are obtained as it has been mentioned in Section 2. Control algorithm is easily provided by a PIC18F452 microcontroller in the digital control unit. A principle scheme of the digital control unit is shown in Fig. 13. Owing to zero crossing sensing (ZCS) circuit, zero crossing points of the Vg are determined. The points are sensed and a timer is operated by the microcontroller. By the data taken from the timer output, a sinus shaped output voltage which is synchronous to the grid is obtained. The output voltage can be shifted forward or backward by the angle dref. Vg, Vbus and I are sampled by the analogue inputs of the microcontroller. By these data, Vref and dref are calculated and switching signals are obtained for the switching devices. Thus, the multilevel inverter structure generates the output voltage based on the switching signals. By means of the proposed control algorithm, PV arrays are operated at the maximum power transfer point. This feature is provided by the embedded MPPT algorithm in the system. The MPPT procedure does not require any extra equipment, it consists of an algorithm. The algorithm
Fig. 14. I–V and P–V characteristic of the PV arrays.
Table 2 Specifications of PV arrays. Rated power (PM) Maximum power voltage (VPM) Maximum power current (IPM) Open-circuit power (VOC) Short-circuit current (ISC)
5W 17.1 V 0.30 A 21.7 V 0.31 A
tracks the maximum power transfer voltage (VPM). Vbusref in the control algorithm represents the maximum power transfer voltage (VPM).
Fig. 13. Principle scheme of the digital control unit.
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Fig. 15. Calculation of the level module energy.
Fig. 17. Simulation results of the transferred output power in the proposed system including four level modules where P1 = 960 W, Q1 = 290 VAr and P2 = 540 W, Q2 = 180 VAr.
Fig. 16. Calculation of the load energy.
4. Arrangement of the PV arrays in the system In the proposed system, setting only the voltage of the dc sources is not sufficient for operating the system. When the system is arranged only according to the voltage values, PV arrays are not loaded in the equal load conditions. Some of them are forced to operate over capacity and the others are forced to operate under capacity. Over loaded PV arrays can not transfer the power and output voltage of the PV arrays decreases. On the other hand, under loaded PV arrays can not generate the rated power
value and output voltage of the arrays increases. This situation can be seen from the I–V and P–V characteristic of the PV arrays in Fig. 14. As a result, required voltage levels are not provided for the multilevel inverter and a sinusoidal shaped voltage wave can not be generated. To prevent this problem, the required energy transferred by each level module and the connection types of the PV arrays should be determined. To determine the number and arrangement of the PV arrays in the PV modules, a simulation study is first implemented. The specifications of each PV array are given in Table 2. System output power (P0) is determined as 1 kW and PV arrays are placed into the PV modules with respect to the output power. In order to determine the amount of the transferred energy to the load by each dc source in level modules, the multilevel inverter system is simulated for var-
Table 3 Transferred energy to the load and energy ratios of the level modules for various load conditions in the proposed system including four level modules. PV array side WLM1 (J)
0.488 0.975 1.946 0.299 0.847
WLM2 (J)
1.116 2.230 4.457 0.686 1.938
Load side WLM3 (J)
2.549 5.097 10.190 1.568 4.430
WLM4 (J)
5.897 11.790 23.572 3.629 10.248
WLMT (J)
10.049 20.092 40.165 6.182 17.463
WLM2/ WLM1
2.288 2.288 2.291 2.292 2.289
WLM3/ WLM1
5.228 5.230 5.237 5.241 5.231
WLM4/ WLM1
12.093 12.099 12.115 12.129 12.100
WL (J)
10.048 20.089 40.157 6.180 17.460
PL (W)
502 1004 2008 309 873
QL (VAr)
0 0 0 464 338
Series load R (W)
XL (W)
XC (W)
65.76 32.88 16.44 32.88 32.88
– – – 49.32 –
– – – – 12.73
Table 4 Arrangement of PV arrays and calculated capacity values in the PV modules for the proposed inverter system including four level modules. LM
Level module capacity
PV connection type
Label
Capacity (mF)
Voltage (V)
Series
Parallel
LM1 LM2 LM3 LM4
C1 C2 C3 C4
30,000 17,000 10,000 6000
25 50 100 200
1 2 4 8
10 12 13 15
Total PV number
Total PV number (W)
LM voltage (V)
10 24 52 120
50 120 260 600
17.1 34.2 68.4 136.8
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ious loads which have a different value and characteristic (resistive, inductive and capacitive). To determine the powers obtained from the level modules, dc sources are used instead of the PV arrays in the simulation study. It is seen that the transferred energy of each level module (WLMk) to the load is different from one another (WLM1 – WLM2 – WLM3 – WLM4). The calculation of the level module and load energy is shown in Figs. 15 and 16, respectively. In addition, to determine the energy ratio of the level 2 W LM3 W LM4 modules ðWW LM ; ; Þ, the energy of each level module LM 1 W LM1 W LM1 is divided by the energy of the base level module (LM1) and a ratio is obtained for the dc source in each level module. It is determined that the ratio between LM1 and the other level modules does not change related to characteristic and value of the load, each ratio is calculated as a different constant value for a specific level module number. Table 3 shows the transferred energy to the load and energy ratios of the level modules for various load conditions. In order to determine the PV power in the level modules, the sum of the energy ratios of the level modules are first obtained as S ¼1þ
W LM2 W LM3 W LM4 þ þ W LM1 W LM1 W LM1
ð15Þ
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occurring during the charging and discharging (V1 V2) are directly related to the transferred energy from the capacitors. The transferred energy by the capacitor group is defined as 1 W ck ¼ C k V 21 V 22 2
ð18Þ
The required energy is considered for a period of time in the simulation study and the required capacity values are calculated by Eq. (18). Table 4 shows the arrangement of PV arrays and calculated capacity values in the PV modules for the proposed inverter system including four level modules. 5. Simulated and experimental results and discussion After determining the situation of PV arrays, the proposed PV power conversion system was simulated and implemented. It was first operated synchronous to the grid (110Vac, 50 Hz) and two different states were performed in the simulation study. First, approximately all of the generated power was transferred, and then, less than the generated power was transferred to the grid. The parameters
and then power values of the base level module and the other level modules are calculated as follows P LM1 ¼
P0 S
P LMk ¼ P LM1
ð16Þ W LMk W LM1
ð17Þ
In this study, PLM1 is calculated as 48 W for the output power 1 kW and accepted as 50 W. PLM2, PLM3 and PLM4 are obtained as 114 W, 260 W and 604 W, respectively and they are accepted as 120 W, 260 W and 600 W. According to the calculated values, PV number and connection types are determined and PV arrays are placed into the level modules. Therefore, each PV array is operated in the same load condition and the required voltage levels are achieved for the inverter structure. The current value transferred from the PV arrays varies in relation to the instantaneous magnitude of the sinus shaped current and on/off conditions of the PV arrays. On/off conditions of the PV modules are given in Fig. 7 for a period of time. Due to their characteristic, PV arrays can not realize power transfer in case of exceeding the maximum power current (IPM) value. When the PV arrays are first connected to the system, a current value higher than IPM is occurred and PV arrays can not realize power transfer at this duration. This problem can be solved by using proper capacitors in the PV module. The capacitors compensate the instantaneous over currents and prevent the PV array from the short-circuit situation. The capacitors are charged from the PV arrays in case the PV arrays do not feed the system. However, they are discharged, when the PV arrays are connected to the system. Voltage ripples
Fig. 18. Simulation results of the inverter output voltage and inverter current in the proposed PV assisted multilevel inverter: (a) P1 = 960 W, Q1 = 290 VAr and (b) P2 = 540 W, Q2 = 180 VAr.
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Rs = 0.39 X and Ls = 4 mH are used for the self inductor in the simulation and experimental study. Fig. 17 shows simulation result of the transferred real power and reactive power values for two different states (P1, Q1; P2, Q2). The simulation results of the voltage and current waveforms at the power values P1, Q1 and P2, Q2 is shown in Fig. 18a and b. If the power is not transferred as much as the generation of the PV arrays, voltages of the capacitors approach the open circuit voltage of the PV arrays and the system can not be operated at the maximum power transfer point. In case of transferring the power to the grid as much as the PV arrays generate, output voltage of the PV arrays decreases to the maximum power voltage (VPM). Simulation results of the voltages of the capacitors are shown in Fig. 19 for transferring approximately all of the generated power and less power than generated. It can be seen from Fig. 19 that when the less power (P2) than generated is transferred, the capacitor voltages reach higher values than the maximum power voltage and the system diverges from the maximum power transferring point. In case of transferring approximately all of the generated power (P1) by the PV arrays, the capacitor voltages reach to maximum power voltage value. As it can be seen from Fig. 19, the voltage of base level module is obtained as 17.4 V. It can be also seen from Table 2 that the real
maximum power voltage value (VPM) of the PV arrays is 17.1 V. The simulated and real values are so close to each other. Therefore, the base level module operates at the maximum power transfer point. The voltages of the other modules are calculated as 35.8 V, 70 V and 140 V in the simulation study. These values are approximately equal to 2VPM, 4VPM and 8VPM. Thus, it is observed that the other level modules operate at the maximum power transfer point. After the simulation study, experimental tests were realized by multilevel inverter structure. The proposed inverter system includes four level modules, an H-Bridge module, a digital control unit and zero crossing sensing circuit. PIC18F452 microcontroller is preferred in the digital control unit. A maximum of 31-level output voltage waveform can be obtained by six level modules. IRFP460 mosfets (500 V, 20 A) are used in level and H-Bridge modules. The proposed system was tested in the laboratory conditions. Similar to the simulation study, the system was connected to the grid (110Vac, 50 Hz) in synchronous mode and power transfer is realized. The THD values of the output voltages and currents are also measured by a harmonic analyzer. Experimental wave forms are shown in Figs. 20 and 21 for different operation points, respectively. Measured THD values are given in Table 5.
Fig. 19. Simulation results of the capacitor voltages in the PV modules while transferring the powers P1, Q1 and P2, Q2.
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Fig. 20. Experimental results of inverter output voltage and grid voltage while operating synchronous to the grid for different operation points: (a) Vg = 114 V, P = 405 W, Q = 68 VAr, d = 0; (b) Vg = 113 V, P = 415 W, Q = 806 VAr, d = 10; (c) Vg = 113 V, P = 105 W, Q = 525 VAr, d = 10; and (d) Vg = 76 V, P = 295 W, Q = 185 VAr, d = 0.
Grid voltage (Vg) and inverter output voltage (V0) waves are given in Fig. 20. The curves are so close to each other. This shows that the proposed system operates synchronous to the grid. It can be seen from the experimental results that the required real power and reactive power values are transferred to the grid in sinusoidal form as mentioned in the
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Fig. 21. Experimental results of inverter output voltage and current while operating synchronous to the grid for different operation points: (a) Vg = 114 V, P = 405 W, Q = 68 VAr, d = 0; (b) Vg = 113 V, P = 415 W, Q = 806 VAr, d = 10; (c) Vg = 113 V, P = 105 W, Q = 525 VAr, d = 10; and (d) Vg = 76 V, P = 295 W, Q = 185 VAr, d = 0.
proposed control algorithm. In addition Figs. 20d and 21d show that the system can operate for the different grid voltage values. Hence, the system is flexible and capable of operating for different points. According to the IEEE 519-1992 standard, THD value of the voltages under 69 kV should not be over 5%. Table 5 shows that THD value of the output voltage is acceptable for the IEEE standard in each operation point.
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Table 5 Measured THD values for different operation points. P (W)
Q (VAr)
Delta (°)
Grid
Multilevel inverter
Voltage (V)
THD (%)
Voltage (V)
THD (%)
Current (A)
THD (%)
Efficiency (%)
405 415 105 295 458 452
68 806 525 185 1090 565
0 10 10 0 10 10
114 113 113 76 131 141
1.87 1.71 1.28 2.01 1.81 1.39
114 112 117 80 119 143
1.86 3.36 2.4 3.28 3.37 1.83
3.66 8.25 4.69 4.55 9.08 5.07
5.03 4.94 6.34 3.36 6.45 5.07
97.79 97.87 97.67 92.57 98.75 99.00
6. Conclusions A PV power conversion system based on a single-phase multilevel inverter was proposed in this paper. The configuration of the proposed system was designed first, and then, the system was simulated and implemented. The simulated and experimental results are presented and explained. Presentable results of the proposed system are summarized as follows: (1) The inverter structure in the proposed system produces multilevel shaped output voltage waveforms. Therefore, it reduces dv/dt stresses imposed on the switching devices and generates less harmonic components on the output voltage and current. (2) The inverter can be easily expanded by increasing level modules. Thus, number of the output levels is increased and the inverter generates higher-quality output voltage waveforms. (3) The switching strategy is considerably simple. By only using Vref and dref, switching signals are easily determined. (4) A control algorithm is improved for generating the reference signals at the inverter output and transferring PV power to the grid. A considerable advantage of the control algorithm is being realized by a simple microprocessor structure. By means of the algorithm, the proposed system operates near the maximum power point. Thus, the system does not require any MPPT unit as the algorithm achieves MPPT feature. (5) To include PV arrays into the system suitably, a simulation study was made and PV arrays were arranged for the inverter system. Owing to this configuration, each PV arrays are loaded in equal conditions. As a result, the required voltage levels are achieved for the inverter structure. (6) The proposed system was verified through simulations and experimental study. The system was operated in synchronous mode and the PV power was transferred to the grid. It is seen that the results are considerably similar to the reference signals. (7) It is seen from the experimental results that the THD values of the output voltage and current are quite low. Thus, it can be said that the transferred power to the grid is in good quality.
(8) These results show that the proposed system can suitably achieve the transfer of the PV power to the grid. Consequently, this study provides an efficient employment of PV energy since there is a shortage of the energy resources and an increasing importance of renewable energy resources in these days.
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