Implementation of Genetic Algorithm-Based SHE for a ...

Implementation of Genetic Algorithm-Based SHE for a Cascaded Half-Bridge Multilevel Inverter Fed from PV Modules Kotb M. Kotb 1, Abd El-Wahab Hassan 2 and Essam M. Rashad 3 1

Department of Electrical Power and Machines Engineering, University of Tanta, Egypt [email protected], 2 [email protected] and 3 [email protected]

Abstract--This paper presents both analysis and experimental verification of applying Selective Harmonic Elimination (SHE) technique for cascaded half-bridge multilevel inverters. The inverter units are fed from PV modules throughout step-down dc-to-dc converters to regulate the inverter input voltage. The inverter has to be asymmetric which allows more possibility to connect PV modules to get maximum possible number of voltage levels. Genetic Algorithm (GA) optimization technique based on SHE theory has been used to compute the optimum switching angles in order to eliminate the low order harmonics and minimize the total harmonic distortion. This can be achieved throughout utilizing a proper fitness function. A complete laboratory system fed from PV modules has been established based upon a DAQ controller. Results of both static and dynamic loads are obtained for single-phase 7-levels and 11-levels fed from 12 PV modules. Index Terms—Cascaded Half-Bridge Inverter, Genetic Algorithm, Photovoltaic Modules and Selective Harmonic Elimination

I. INTRODUCTION In the last decades, inverters became very important for a lot of applications such as controlling electric motors, power systems, and recently for supplying residential appliances [1]- [3]. Multilevel inverters (MLIs) are strongly recommended due to drawbacks associated with the conventional inverters [4]. One of the most attractive features of MLIs is that it can be easily interfaced with renewable energy sources e.g. through the photovoltaic modules. It also reduces stresses on the switches and gives better harmonic profile. Other advantages are given in [5]. MLIs can be supplied from separated dc sources such as the cascaded h-bridge inverter and also form a common dc bus like the flying capacitor and clamping diode inverters [6]- [7]. The main problem associated with MLIs is the great number of the used switches. Each switch requires its gate drive circuit so that inverter becomes bulky, very expensive and complex to control. New topologies of MLI have been developed recently which has the ability to produce higher number of levels using less number of switches compared to the traditional MLIs [4]. Multilevel inverters can be classified as shown in Fig.1. Among the recent topologies of reduced devices count, the cascaded halfbridge multilevel inverter is selected. Selection of this topology has been carried out depending on different comparisons. The major selection factors were the ability

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to produce higher number of levels using less number of switches and the ability to be interfaced throughout separated dc sources not a single dc bus. Different control techniques can be used to control MLIs. These techniques can be classified according to the switching frequency into fundamental switching frequency modulation (FSFM) and high switching frequency modulation (HSFM) [8]. Modulation techniques based on FSFM are preferred since it reduce the switching losses. Multilevel Inverter Topologies

Conventional Topologies

Recent Topologies

Neutral Point Inverters Flying Capacitors Inverters

Cascaded H-bridge Inverters

With H-Bridge

Without H-Bridge

Cascaded Half-bridge Based Multilevel DC link inverter

Packed U-cell MLI Cascaded Bi-polar switched Cells Based Multilevel

Reversing Voltage Topology Switches Series Parallel Sources Based MLI T-Type Inverter Series Connected Switched Sources Based MLI

Fig. 1. Classification of MLIs [4]

Solar energy is characterized by the great quantity, availability and easy collecting around the earth. Egypt is one of the sun-belt countries [9]. Therefore, energy collecting from the sunlight is considered one of the main solutions for the increasing demands specially in summer times. Due to these abilities of the solar energy and the features provided by the MLIs, integration between them is useful. Fig. 2 shows a block diagram of a stand-alone PV system fed single-phase MLI.

+ PV Modules

+

-

+

-

Charger

DC-to-DC converter

+ -

MLI

Induction Motor L o a d

Controller

Battery Fig. 2. Block diagram of a stand-alone PV system fed MLI

In this paper, a single-phase 7-levels and 11-levels inverter fed from PV modules has been implemented. Fundamental switching frequency is used to control the inverter once by the staircase with fixed time step modulation method (SFTS) and once by the SHE technique using genetic algorithm (GA) to eliminate the lowest order harmonics and minimize the total harmonic distortion (THD). II. OPERATION OF THE CASCADED HALF-BRIDGE MLI The cascaded half-bridge MLI consists of two stages as shown in Fig. 3. The level-generation stage creates a stepped dc voltage while the polarity-generation stage converts it to a stepped ac voltage. The level-generation consists of cascaded units; each unit has its own dc source and two series switches. Both switches of each unit are operated in opposite way to avoid short circuiting the dc supply as illustrated in Table I while the level-generation switching state are listed in Table II. S1 S2

V1

+

+

Vo1

Sa

Sc

S2n

Sd

+

Sb

Von -

Level-generation stage

T time

T/2

(a) Level-generation stage output voltage Vo Vmax V1+V2 V2 V1 0

T

T/2

time

-Vmax

(b) Polarity-generation stage output voltage Fig. 4. Resultant voltage waveforms of the inverter

There are different fashions used to choose magnitudes of the dc sources [10]. However, the most commonly used methods are the “binary” and “trinary” fashions which proposed in [11]. In these fashions, magnitudes are suggested to be chosen like a geometric progression with a factor of 2 for binary or 3 for trinary as follows: or Vj=3j-1 Vdc

and j=1, 2,…n

(1)

Unfortunately, the trinary fashion cannot be applied to the selected inverter since several combinations of dc sources cannot be obtained. Another fashion can be named “twice fashion” keeps a dc source magnitude equal to a certain value while the rest of dc sources magnitudes are twice this value [12]. Table III compares between the binary fashion and the twice fashion.

Vo

S2n-1 Vn

V1+V2 V2 V1 0

Vj=2j-1 Vdc

-

Vdc

Vo Vmax

-

Polarity-generation stage

Fig. 3. Schematic diagram of the cascaded half-bridge MLI

State 1 2

TABLE I BASIC UNIT SWITCHING STATES Switches states S1 S2 1 0 0 1

Vo1 V1 0

TABLE II POSSIBLE SWITCHING STATES OF THE LEVEL-GENERATION STAGE S1 S2 S2n-1 S2n Vdc 0 1 0 1 0 1 0 0 1 V1 0 1 1 0 Vn 1 0 1 0 V1+Vn

If both switches Sa and Sb are switched ON, the polarity-generation stage produces the output voltage in positive polarity. If Sc and Sd are switched ON, the polarity-generation stage produces the output voltage in negative polarity as shown in Fig. 4. If (n) number of cascaded units are supplied by dc sources equal in magnitudes, the possible number of levels (m) is 2n+1 e.g. for n=3, m=7. If the level-generation stage is supplied from dc sources have different magnitudes, number of levels can be increased without cascading more units. Different number of levels can be obtained from the inverter depending on the voltage magnitude of each of the level-generation stage units.

TABLE III COMPARISON BETWEEN THE BINARY AND TWICE FASHIONS Sources Fashion m Vomax for n=3 magnitudes j- 1 m=15 Vj= (2 ) Vdc Binary 2n+1 -1 (2n-1) Vdc Vomax=7Vdc j=1,2,…n V1=Vdc m=11 Twice 4n-1 (2n-1) Vdc Vj=2Vdc Vomax=5Vdc j=2,3,4…n

It can be noticed that the binary fashion is better than the twice fashion since it enables the inverter to produce higher number of levels and higher maximum voltage in the output. III. CONTROL USING GA BASED-SHE TECHNIQUE In order to show the effect of SHE technique, a SFTS modulation is firstly used. In this method, the waveform is divided into m-equal time intervals (ts) so that the equivalent switching instants can be found. Fig. 5 shows a half cycle of an 11-levels waveform using the SFTS method. The waveform is divided into an 11-interval, the conduction intervals (ts) can be found by ts=1/(2m*f) where f is the fundamental switching frequency. One advantage of this technique is the simplicity. However, the voltage spectrum contains low order harmonics (LOH) which increase the THD.

cos( )  cos( )  cos( )  ...  cos( )  m   0  f cos(3 )  cos(3 )  cos(3 )  ...  cos(3 )  0  f

Vo

1

5Vdc

1

3

2

s

3

a

1

s

2

(5)

.

4Vdc

cos(n )  cos(n )  cos(n )  ...  cos(n )  0  f 1

3Vdc 2Vdc

2

2

3

s

s

where, ma defines the modulation index M since M=ma /s. ts/2

ts/2

The previous set of equations listed in (5) can be solved by iterative methods but these methods require a good initial guess of switching angles to insure convergence. In addition, it become more complex for higher levels [15].

Vdc

ts ts ts ts ts ts ts ts ts ts

t

( 1/ 2*f ) Fig. 5. Half cycle of the output voltage using the SFTS method

It should be noticed that the time step is dependent on the number of levels and cannot be varied for the same number of levels. So, making a smaller equal time step requires higher number of levels. In the FSFM, in addition to the LOH, the most dominant harmonics exist around (2m) and its multiples. In the SHE technique, the switching angles are precalculated forming the fundamental output voltage waveform and eliminate the LOH [13]- [14]. As a result, the THD can be minimized. Moreover, the size of output filter can be reduced. Since the switching angles are precalculated off-line, it is considered an open loop control technique. Fig. 6 shows a typical m-levels inverter output voltage using the FSFM. Vo

Genetic Algorithm is considered a probabilistic intelligent search algorithm which apply the biological evolution in the optimization process [16]. It is considered a simple and easy implemented technique. Also, it does not require mathematical modelling. Hence, it can be easily applied to solve the SHE problem. There are many optimization techniques, but GA searches a population of points in parallel rather than individual points search. It also uses probabilistic rules not deterministic ones. Fig. 7 shows the flow chart of the GA optimization technique. For the presented problem, the main target of using GA is finding the optimum switching angles that ensures that harmonics are eliminated and THD is minimum. Start Initialize chromosome population

Calculate the cost of each member including the penalty function

sVdc Evaluate fitness of each individual and perform fitness scaling

(s-1)Vdc

Parent chromosomes selections 2Vdc

Create a new offspring (Crossover & Mutation)

Vdc

α2s

α(2s-1)

α(s+2)

α(2s-2)

π/2

α(s+1)

αs

α(s-1)

α3

α2

α1

0

Evaluate offspring and insert the best replacing worst parents

π ωt

No

Fig. 6. Half cycle of an m-level inverter output voltage waveform

The general Fourier’s expansion of the waveform is: 

vo (t )  a0   (an cos(nwt )  bn sin(nwt )) n1

(2)

Due to nature of the waveform that makes a0=an=0, its Fourier’s expansion is reduced to: 

vo (t )   bn sin( nwt )

Yes

Stop

Fig. 7. Flow chart of GA optimization technique [17]

The non-linear equations given in (5) have been solved using a GA code using the Matlab environment in order to satisfy the following objective function: s

(3)

OF   f i  THD

n 1

(6)

i 1

where, 4V bn  dc cosn1   ...  cosn s  n

Max. number of generation reached

where, α1< α2< α3< α4…. αs< π/2 and THD equals to: (4)

It is noted that number of terms between square brackets equals number of dc sources s which defines number of levels m by the relation s=(m-1)/2. In a singlephase system, applying the SHE technique eliminates the (m-3)/2 or (s-1) lowest order odd harmonics. Equations of the fundamental component and harmonics that can be eliminated are listed as follows:

1  n3,5,..  n cos(n1 )  ...  cos(n s )    THD  cos(1 )  ... cos( s )

2



(7)

Genetic algorithm finds one solution for each value of modulation index M. Therefore, it has to be run many times to cover the whole range of M. Fig. 8 shows the variation of switching angles versus modulation index for the 11-levels.

obtained at a solar irradiation of 550 w/m2 and a working temperature of 30o C. The measured results are close to the simulation ones that obtained using the following relation of the general PV module representation [18]:

I  N p I ph

(a) Variation of switching angles

IRs Np  V   q( N  N )  V ( N )  IRs s p s  N p I o exp   1  kATC Rsh      

(8)

where, Iph is the light generated current Io is the reverse saturation current Rsh is the shunt resistance q is the electron charge Np is the no. of PV cells in parallel

Tc is the working temperature A is the cell ideality factor Rs is the series resistance k is a constant Ns is the no. of PV cells in series

(b) Variation of THD Fig. 8. 11-levels results obtained using GA

Genetic Algorithm is strongly recommended for the industrial field as an online controller. However, this requires large amount of pre-calculated switching angles at the different values of modulation index. These calculated values can be saved in a look-up table and implemented in the control system depends on the controller type. IV. SYSTEM DESCRIPTION AND RESULTS The inverter units are supplied from the PV modules throughout buck converter units which used to regulate the inverter input voltage. A data acquisition (DAQ) controller is used to provide the system with the required control processing. Both static load and a single-phase induction motor (SPIM) are fed from the inverter. The overall system setup is shown in Fig. 9.

Fig. 10. The used PV modules (Inventux X3-125)

(a) V-I characteristics of one module

Fig. 9. System setup (1-PV connection terminals, 2- Voltage reduction stage, 3- the inverter, 4- Loading unit, 5- The host PC and 6- Scope)

The used PV modules are a Micro-morph (a-Si/µc-Si) type (Inventux X3-125 model), as shown in Fig. 10, each has the characteristics shown in Fig. 11 and its datasheet is available in the Appendix. The measured results were

(b) V-P characteristics of one module Fig. 11. Measured and simulated characteristics of the used PV modules

The inverter input voltage was adjusted so that rms value of the fundamental component of output voltage is 220 V. Results were obtained at a solar irradiation of 550 w/m2 and temperature of 30 oC during the mid-day of August and September of 2016. Fig. 12 and Fig.13 show a comparison between the obtained results using both SFTS method and GA-based SHE for both 7-level and 11-level respectively. It should be noted that the SPIM current is multiplied by a gain of 10 by the scope.

are not possible. Both Fig. 14 and Fig. 15 show the obtained results for 11-level inverter of different resistive loads and inductive loads respectively.

(a) SFTS

(b) GA based SHE Output voltage THD=10.1%

THD=14.2%

(a) SFTS

(b) GA based SHE Output voltage

(c) SFTS

(d) GA based SHE Output voltage spectrum

Fig. 13. Comparison between the 11-level results by SFTS and SHE THD%=17.4%

1

2

(c) Output voltage spectrum using the SFTS method

1

THD=12.8%

2

(a) The stepped dc voltage (d) Output voltage spectrum using GA based SHE voltage

current

(e) Steady-state no-load current of SPIM using the SFTS method

3

4

3

4

voltage current (b) Output voltage

5 (f) Steady-state no-load current of SPIM using the GA based SHE

5

Fig. 12. Comparison between the 7-level results

Due to the current capability of the used PV modules and its limited number (only 12-modules available), results of 11-level fed the single-phase induction motor

(c) Resistive load current Fig. 14. 11-level results of resistive load changing

References

6

6

(a) Output voltage

7

7

(b) Inductive load current Fig. 15. 11-levels results of inductive load changing

V. CONCLUSION From both analytically and experimentally work, it was verified that the genetic algorithm based on the SHE technique can be successfully applied to eliminate previously-specified LOH of cascaded half-bridge multilevel inverters output voltage. It was found that the total harmonic distortion has been minimized to 10.1% for 11- level inverter with elimination up to the 9th harmonic order so that the load current of dynamic loads becomes more sinusoidal. APPENDIX The used PV modules have the following parameters according to the manufacturer datasheet: Data Maximum electrical output power (-0/+5) Voltage at maximum power Open circuit voltage Voc Short circuit current Isc Temperature coefficient of Voc Temperature coefficient of Isc Temperature coefficient of Pmax

Value 125 W 124 V 165 V 1.17 A -0.4 V/oC +0.07 A/oC -0.3 W/ oC

[1] Sireesha, A. and et al., “Generalized Cascaded Multi Level Inverter Using Reduced Number of Components with PV Systems,” IEEE Biennial Int. conf. on Power and Energy Systems, Jan. 2016. [2] Tae-Jin Kim and et al., “The analysis of conduction and switching losses in multi-level inverter system,” In Proc. IEEE Power Electron. Specialist conf., vol. 3, pp. 13631368,2001. [3] L. M. Tolbert and F. Hall, “Multilevel Converters as a Utility Interface for Renewable Energy Systems,” In the IEEE Power Engineering Society Summer Meeting, 2009. [4] K. K. Gupta and et al., "Multilevel Inverter Topologies with Reduced Device Count: A Review," IEEE Trans. Power Electron., vol. 31, no. 1, pp. 135-151, 2016. [5] S. Kouro and et al., “Recent Advances and Industrial Applications of Multilevel Converters,” IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2553–2580, 2010. [6] C. Young and et al., "A Single-Phase Multilevel Inverter with Battery Balancing," IEEE Trans. on Ind. Electron., vol. 60, no. 5, pp. 1972-1978, May 2013. [7] T. Abdelhamid and N. Abbasy; ''A New Topology of Three phase five Level Inverter Applied to Static VAR Generation Schemes,'' Int. Review of electrical Engineering, vol. 2, pp. 359-368, 2007. [8] Kotb M. Kotb and et al., “Simplified Sinusoidal Pulse Width Modulation for Cascaded Half-Bridge Multilevel Inverter,” In Proc. of the 18th Int. Middle-East Power Systems Conf. (MEPCON 2016), Cairo (Egypt), Dec. 2016. [9] http://www.solargis.info [10] S. Daher, and et al., “Multilevel Inverter Topologies for Stand-Alone PV Systems,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2703–2712, 2008. [11] A. Rufer, and et al., “Asymmetric Multilevel Converter for High Resolution Voltage Phasor Generation,” In European Conf. of Power Electron. and Applications, 1998. [12] E. Babaei, S. Hosseini; ''New cascaded multilevel inverter topology with minimum number of switches,” Energy Conversion and Management, vol. 50, no. 11, pp. 2761– 276, 2009. [13] M. Rai and R. K. Tripathi, “A Novel Multilevel Inverter Topology with Selective Harmonic Elimination Technique,” In Int. Conf. on Power, Control and Embedded Systems (ICPCES), 2014. [14] B. Alamri and et al., “Optimum SHE for Cascaded HBridge Multilevel Inverters Using: NR-GA-PSO, Comparative Study,” In the 11th IET Int. Conf. on AC and DC Power Transmission, 2015. [15] J. Kumar, B. Das, and P. Agarwal, “Selective Harmonic Elimination Technique for a Multilevel Inverter,” In the 15th National Power Systems Conf. (NPSC), 2008. [16] Prashanth L Gopal and F.T Josh, “Elimination of Lower Order Harmonics in Multilevel Inverters Using Genetic Algorithm,” International Journal of Engineering and Advanced Technology (IJEAT), vol. 2, no. 3, Feb. 2013. [17] K. Hasannen and H. A. Mansour, “Selective Harmonic Elimination PWM Voltage Source Inverter Based on Genetic Algorithm,” In Recent Trends in Energy System Conf. (RTES), 2015. [18] H. Tsai, C. Tu, and Y. Su, “Development of Generalized Photovoltaic Model Using MATLAB / SIMULINK,” In the World Congress on Engineering and Computer ScienceWCECS, 2008.