single phase low thd optimized inverter for pv voltage regulation

Int. J. Process Systems Engineering, Vol. 3, Nos. 1/2/3, 2015 3

Copyright © 2015 Inderscience Enterprises Ltd.

Single phase low THD optimised inverter for PV voltage regulation

Antonio Valderrabano-Gonzalez* Universidad Panamericana Campus Guadalajara, Prol. Calzada Circunvalación Pte. No. 49, Col. Ciudad Granja. Zapopan, Jal., 45010, México Fax: +52-33-1368-2201 Email: [email protected] *Corresponding author

Francisco Beltran-Carbajal Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Departamento de Energía, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, C.P. 02200 México, D.F., México Email: [email protected]

Ruben Tapia-Olvera Universidad Politécnica de Tulancingo, Ingenierías No. 100, Huapalcalco, Hgo., 43629, México Email: [email protected]

Julio Cesar Rosas-Caro Universidad Panamericana Campus Guadalajara, Prol. Calzada Circunvalación Pte. No. 49, Col. Ciudad Granja. Zapopan, Jal., 45010, México Email: [email protected]

Hossam A. Gabbar University of Ontario Institute of Technology, UOIT, 2000 Simcoe Street North Oshawa, ON L1H 7K4, Canada Email: [email protected]

4 A. Valderrabano-Gonzalez et al.

Adel M. Sharaf Sharaf Energy Systems, Inc., 147 Berkley Drive, Fredericton E3C 2P2, New Brunswick, Canada Email: [email protected]

Abstract: This paper illustrates a way to verify optimised angles for five and seven level single-phase inverters. The ability to follow strict angles for switching times is due to a simple synchronising scheme used along with the arctangent method. Power stage is focused to attain the lowest number of switches and DC sources, and can be used in a cascade multilevel strategy. Comparison of harmonic contents and total harmonic distortion is presented for several optimisation strategies carried out on the literature, and a compensation scheme for regulation with two degree of freedom that brings the inverter to have 11 or 15 level and be within the standard is proposed.

Keywords: facts; inverter; optimisation power quality; total harmonic distortion; THD.

Reference to this paper should be made as follows: Valderrabano-Gonzalez, A., Beltran-Carbajal, F., Tapia-Olvera, R., Rosas-Caro, J.C., Gabbar, H.A. and Sharaf, A.M. (2015) ‘Single phase low THD optimised inverter for PV voltage regulation’, Int. J. Process Systems Engineering, Vol. 3, Nos. 1/2/3, pp.3–19.

Biographical notes: Antonio Valderrabano-Gonzalez received his BS in Industrial Electronics from the Instituto Tecnológico de Puebla (México), his MSc in Electronics from the Instituto Nacional de Astrofísica, Óptica y Electrónica (México), and his PhD in Electrical Engineering from Cinvestav Guadalajara (México) in 2010. He is working as a Professor at Universidad Panamericana Campus Guadalajara México. His research interests are power electronics, control of power electronic converters, FACTS devices, and power quality.

Francisco Beltran-Carbajal received his BS in Electromechanical Engineering from the Instituto Tecnológico de Zacatepec (México) and his PhD in Electrical Engineering (Mechatronics) from the Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV-IPN) in Mexico City. He is currently Titular Professor in the Energy Department in the Universidad Autónoma Metropolitana (UAM), Unidad Azcapotzalco in Mexico City. His main research interests are vibration control, rotating machinery, mechatronics, and automatic control of electromechanical and electronic systems.

Rubén Tapia-Olvera obtained his BS in Electrical Engineering from Instituto Tecnológico de Pachuca, México in 1999, his MSc and PhD in Electrical Engineering from CINVESTAV Guadalajara, México in 2002 and 2006, respectively. He is currently a Professor at Universidad Politécnica de Tulancingo. His primary area of interest is in modeling and control of FACTS devices with computational intelligence techniques, including its operation in electrical power systems.

Single phase low THD optimised inverter for PV voltage regulation 5

Julio Cesar Rosas-Caro received his BS in Electronics and his MS in Sciences in Electrical Engineering from the Madero City Institute of Technology, Mexico, in 2004 and 2005, respectively, and his PhD in Sciences in Electrical Engineering from the Guadalajara campus of CINVESTAV, Mexico in 2009. He is currently with the Universidad Panamericana Campus Guadalajara, Mexico. He has been a visiting scholar at Michigan State University in 2007 and at the University of Colorado at Denver in 2012 and 2014. His research interest is power electronics including dc-dc converters, FACTS devices and power converter topologies.

Hossam A.Gabbar is a Professor in the Faculty of Energy Systems and Nuclear Science, and cross appointed in the Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT). He obtained his PhD from Okayama University (Japan), while his undergrad degree (BSc, with First Class of Honor) is in the area of automatic control from Alexandria University, Egypt. He is specialised in smart energy grid engineering with focus on safety and control systems. He worked in energy process control in national and international research and industrial projects in Japan, UAE, Kuwait, Qatar, Egypt, and Canada.

Adel M. Sharaf received his BSc in Electrical Engineering from Cairo University, Cairo, Egypt (Electric Power Systems and Machines Section), his MSc, and PhD in Electrical Engineering, University of Manitoba, Winnipeg, MB, Canada. He is the President of Sharaf Energy Systems, and Intelligent Environmental Energy Systems, Inc. His research areas include electric utility planning and operation, power quality-PQ, sustainable green power-renewable energy, FACTS technology, power electronics, energy conservation, power system control, protection, security and stability and sustainable green power NUG-generation. He has authored and co-authored over 820 scholarly technical journals, conference papers and engineering reports, and four book chapters.

1 Introduction

Solar panels generate the most electricity on clear days with abundant sunshine, and they have a ‘maximum power rating’, which is the measurement of how much power the panels produce under ideal conditions. That is calculated in labs by using the equivalent light of a sunny day, at noon, at the equator; however, the solar panel should be able to be located at residential roofs, where the amount of sunlight varies throughout the day, and throughout the year, and the weather conditions can be very different of the lab. Typical solar panels can produce 10–25% of their rated capacity in a foggy day, but the exact amount will vary depending upon the density of the clouds, the type of solar panel, etc., but even with a standard solar panel on a cloudy day, you will be able to generate some power when it’s daylight. Utility-interconnected photovoltaic (PV) systems are not used normally for voltage regulation. Therefore, the voltage operating ranges for PV inverters are selected as a protection function that responds to abnormal utility conditions, not as a voltage regulation function. For residential applications, the PV systems should be capable of operating within the limits normally experienced on utility distribution lines. The operating window for these small PV systems is 106–132 V on a 120 V base, that is, 88–110% of nominal voltage. This range results in trip points at 105 V and at 133 V. (ANSI/IEEE Std 929-1988, 1987). A great deal of research has been made for procuring


a maximum power point tracking on the PV panels for three phase and single phase systems, but a high restriction to solve for spreading its use is the total harmonic distortion (THD). There have been many works trying to establish the limits on the THD; the description of the maximum allowable values for harmonic distortion for single phase inverters is provided in Ward and Ward (2002), but a long discussion for low voltage systems was presented in IEEE P519.1/D12 (2012), giving the result of a maximum THD of 8%, with maximum individual harmonic of 5%, but according to IEEE P519.1/D12 (2012), residential loads are indeed harmonic producers whose limits are not covered IEEE STD 519 (IEEE Std 519-2014, 2014), the harmonic voltage levels will be a function of the harmonics on the overall distribution system, and the combined effect of harmonic currents injected from each of the residences supplied from a common distribution transformer. It results obvious that whenever there is a confusion on the parameters the strongest requirement should be followed in order to fulfil all the others; that is the reason for a lot of work in micro inverters and middle power inverters to have low THD. Several studies point to the use of cascaded H-Bridge and look for an optimisation on the firing angle of the switches. On this context, Ismail et al. (2014) bring a selective harmonic elimination method for five-level inverter using particle swarm optimisation, while Mansoor et al. (2008), illustrate the modelling for a five-level inverter and optimised angles using Newton-Rapson approximation, and Diong et al. (2013) bring a frequency-weighted THD of the staircase-modulated output voltage of single-phase multilevel inverters, with or without elimination of the lowest order harmonic. Seven level inverters have also gained popularity due to their ability to be combined with a 12 pulses, resulting in an 84 pulses configuration (Valderrábano-González et al., 2012; Valderrabano and Ramirez, 2010a, 2010b), the spice model for a seven level inverter and optimised angles using Newton-Raphson approximation is presented in Iero et al. (2014), while the obtaining of optimised angles for it, using SHE-OHESW equations is offered in Krismadinata et al. (2013). The addition of one more degree of freedom in the optimisation for harmonic minimisation is introduced in Jiang and Lipo (2000), and the optimised switching angles for an 11 level inverter using SHE method are granted in Kumar et al. (2010). Voltage harmonic distortion limits in low-voltage networks. New topologies arise to drop down the amount of switches on single-phase inverters. The cascaded seven level inverter with capacitors for splitting the voltage using the charging or discharging time of the capacitors as part of the optimising method for obtaining the firing angles of the switches is illustrated in Zhong et al. (2009), and the use of two bidirectional switches and a H-bridge for seven level generation in Rahim et al. (2010). Very important is to connect these inverters to the grid for islanding and non-islanding loads, and strong efforts have been made to track the single-phase signal as presented in da Silva et al. (2011, 2008), Crowhurst et al. (2010), Tan Kheng and Masri (2010), Qi et al. (2010), Ciobotaru et al. (2006), Dong et al. (2011) and Zhibing et al. (2010), and three-phase arctangent method has been validated in Valderrabano-Gonzalez et al. (2013) to have a saw tooth on the limits 0 – 2π and use standard pulse width modulation technique for gating the switches. This paper presents an alternate solution that employs a simple RC array to generate quadrature signals for a 60 Hz single phase grid, and exploit the arctangent method to track the angle. Our proposal brings the idea of using a single PV panel connected in series for regulation of the voltage using bilinear relationship for the firing angles. The opportunities to connect this inverter and lower the THD are evident when we evaluate the gating signals at angles that provide an optimised signal. Simulations are included to verify the viability of the proposal.


2 Quadrature signal generation

Figure 1 illustrates the circuit used for generating the quadrature signals used on the synchronising scheme. Here a VPP10–250 transformer is used to monitor a 127 V/60 Hz

grid. This transformer has a turn ratio of 23115 : ,2

so we have 11.043 V peak on the

secondary winding. This sinusoidal signal is used to feed an RC circuit with impedances of 2,652.58Ω, and –j2,652.58Ω, which lead to values C = 1e-6 and R = 2,652.58. The current on this circuit will generate two voltage signals in quadrature: VR = 7.808∠45°; VC = 7.808∠–45°, and we can associate the voltage on the capacitor to Alpha (α), and the voltage on the resistor to Beta (β). It is important to notice that these two signals are lagged 45° from the stationary reference frame. These two signals are passed through an INA159 with REF2930 to be multiplied by 1/5 and added an offset of 1.5 V, in order to be fed to a microcontroller or DSP.

Figure 1 Circuit for quadrature signal generation

3 Synchronising signal

By using the signals Alpha (α) and Beta (β), defined previously, we can apply the strategy presented in equation (1), to obtain the tracking of the signal Alpha (α), which is denoted as ωt and depicted on Figure 2. The model for obtaining this ωt signal is presented in Figure 3.

12 2

2 tan2πωt −

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟= − +

⎜ ⎟⎢ ⎥+ −⎝ ⎠⎣ ⎦

αα β β

(1)

hp user

Resaltado

hp user

Resaltado

hp user

Resaltado

hp user

Resaltado


Figure 2 Synchronising signal along with alpha, beta, and transformer output

Figure 3 Single-phase synchronising strategy model

wt1

sqrt(alpha *alpha +beta *beta )

MATLABFunction

TrigonometricFunction 2

atan

Kp2

2

Kp1

-1

Divide

pi/2

ALPHA2

BETA1

The use of this synchronising scheme allows a very precise pulse width modulation angle control for gating signals, using ωt as the carrier signal. The first step is to convert the signal ωt to degrees and then lead it 45° for compensation of the quadrature circuit as presented in (2).

180* 45 mod (360 )angle ωtπ

°⎛ ⎞= + ° °⎜ ⎟⎝ ⎠

(2)

4 Power electronics stage

A big number of configurations has been studied in order to connect PV-panels to grid, and obtain the lowest THD possible. Most of these configurations use the cascaded single-phase bridge due to its modularity as illustrated on Figure 4(a). Five and seven levels are the most popular in order to apply optimisation techniques, and they are dependent of two values of single DC sources used for providing the inverted AC signal


as schematised on Figure 4(b). These DC sources should have independent references in order to apply the standard cascaded gating techniques. If these two values are equal, the resultant signal will have five levels, on the other hand, if one is twice the amplitude of the other, the resultant signal will have seven levels. This means we need eight switches and two different VDC sources in order to have five or seven levels of voltage on the output. The strategy followed on this proposal uses a single-phase bridge connected to a bidirectional switch (Shalchi Alishah et al., 2014) to obtain a five-level inverter as presented in Figure 5, so the amount of switches is reduced to five. The switching combination needed to produce the five-level output is presented in Table 1. This structure uses two VDC sources that are connected with a neutral point joined to the bidirectional switch. In order to get these two DC sources, several strategies using capacitors for splitting (Zhong et al., 2009), multilevel boosting (Rosas-Caro et al., 2010), or simply by a series connection of renewable sources with a central tap has been used. On this paper, and due to this inverter will be used for active power sent to the grid, a traditional continuous conduction mode buck converter for half of the input voltage is used, obeying to the equations presented in (3), (4), and (5).

0 SV V k= (3)

0Δ (1 )SVI k kLf

= − (4)

0 2

(1 )Δ8SV k kV

LCf−

= (5)

On these equations, Vs is the input of the buck converter, V0 the output voltage, k the duty cycle, f the switching frequency, ΔV0 and ΔI0 the maximum allowed variations in output voltage and output current respectively, and L and C the values of the inductance and capacitance. With this array, we can either use a PV string voltage, a battery bank, or the resulting voltage of a boost converter to have the duty cycle of the boost as one degree of freedom for controlling the amplitude of the converter output, and obeying to equations (6), (7), and (8). The strategy followed on this paper uses a boost converter to ensure the input to the buck is of the same values for different luminance values on the PV string. The resulting converter is presented on Figure 6.

0 1SVVk

=−

(6)

0Δ SVI kLf

= (7)

0Δ(1 )

SV kVk fRC

=−

(8)


Figure 4 (a) Cascaded inverter circuit (b) Five and seven level configuration (see online version for colours)

Figure 5 Five level inverted structure followed on this strategy (see online version for colours)

Table 1 Swiching combination for five level output

s1 s2 s3 s4 s5 Output

1 0 0 1 0 2 VDC

0 0 0 1 1 VDC

0 0 1 1 0 0

0 1 0 0 1 –VDC

0 1 1 0 0 –2 VDC


Figure 6 Boost and buck converters used to split the PV string voltage for five level inverter

Table 2 Optimised five and seven level switching angles

Reference Author Technique Number of levels α1 α2 α3 THD

5 Ismail et al PSO 5 31.8 70.88 37.76 6 Mansoor et al Newton-Raphson 5 16.23 51.56 18.9 7 Diong et al WTHD 5 13.4 41.9 16.44 11 Iero et al Newton-Raphson 7 11.7 26.9 56.06 12.53 12 Krismandinata et al SHE-OHESW 7 9.06 28.52 55.05 11.92 13 Jiang et al +1 degree of

freedom 7 7.94 25.04 42.47 12.91

Equispaced 7 14.28 40 65.7 16.82

Figure 7 Five level output comparison in (a) shape and (b) harmonic content

(a)


Figure 7 Five level output comparison in (a) shape and (b) harmonic content (continued)

(b)

Figure 8 Seven level output comparison in (a) shape and (b) harmonic content

(a)


Figure 8 Seven level output comparison in (a) shape and (b) harmonic content (continued)

(b)

Figure 9 (a) Eleven level output and (b) harmonic content (see online version for colours)

(a)


Figure 9 (a) Eleven level output and (b) harmonic content (continued) (see online version for colours)

(b)

Figure 10 (a) Fifteen level output and (b) harmonic content (see online version for colours)

(a)


Figure 10 (a) Fifteen level output and (b) harmonic content (continued) (see online version for colours)

(b)

5 Gating optimisation

Once the problem of synchronisation is solved, and the power electronics configuration is defined, the following stage is to set a gating scheme that produces the lowest THD on the inverter output. Optimised angles for the lowest THD for five and seven levels are provided on Table 2, using α1, α2, and α3 as the starting point for level change. The output is presented in Figure 7(a) for five levels. Important is to verify that regardless the technique used for power stage on these converters, the THD gotten using Piece-wise Linear Electrical Circuit Simulation for Simulink (PLECS), and 100 harmonics is out of the IEEE standard 519. The ability of using precise firing angles is due to the synchronising scheme followed on this strategy. The 50 initial harmonic values are illustrated in Figure 7(b) for five levels. Most traditional seven level inverters commuted at fundamental frequency use an strategy of equal duration of the levels, which brings a THD of 16.82%, but again, with a precise system to synchronise the firing signals it is possible to get a lower THD. The corresponding values for seven level output, along with the harmonic output are shown in Figure 8(a), and Figure 8(b) respectively.


6 PV panel compensation

Compensation for obtaining a higher number of levels and consequently, lower THD is made by using a series connection of a PV panel feeding a standard single phase bridge inverter. The PV model used is according to Schönberger (2013). Starting with values for luminance of one sun, and using PV strings for a 127VRMS grid, we should divide the maximum amplitude in five for using the five-level inverter proposed in cascade with a three-level inverter. This means V_low, and V_high on Figure 5 should have same values, as presented in (9), while the compensation voltage has to accomplish the amplitude expected for the total, as presented in (10). On this way, the maximum amplitude gotten by adding these three DC sources (V_low + V_high + V_comp) will be 127 2,A = as expected for the single phase grid.

( )2_ _ 127 25

V low V high= = (9)

( )1_ 127 25

V comp = (10)

The switching strategy for V_comp is generated via trapezoidal rule for the angle of level change, producing a voltage output of 11 levels, as presented in Figure 9, with a THD of 7.93%, which is now within IEEE Std 519–2014 for residential applications. In order to complete this study, a PV string with the same characteristics is added to a seven level inverter using trapezoidal rule for the changing angles. The voltage levels needed for a 127VRMS grid are presented in (11), (12), and (13). Adding these three DC sources the maximum obtained will be 127 2,A = as on the previous array but with 15 level on the output, bringing the THD to 6.97%, as illustrated in Figure 10.

( )2_ 127 27

V low = (11)

( )4_ 127 27

V high = (12)

( )1_ 127 27

V comp = (13)

With the conditions of DC voltage needed for producing the amplitude and THD pursued, we can validate the results for partial events with 1 sun and 0.1 sun. For this study, we are considering the two PV-strings with the same sun, but having the arrays presented, we can use a boost converter to ensure the voltage levels obtaining two degree of freedom. This verification and the optimisation of these controllers for two degree of freedom are subject to further research, but using the difference between the reference voltage and the summation of the voltage of the main inverter, and the one gotten on the compensation the duty cycle of the boost can be linked obtaining the same amplitude and a THD of 7.05% for the 15 level array, which is still within standard, as presented in Figure 11.


Figure 11 Fifteen level output with 1.0 and 0.1 sun

7 Conclusions

This paper has introduced the idea of phasor relationships for the generation of two quadrature signals utilised for the arctangent method for synchronisation of single phase inverters. The difference on the zero of the grid signal and zero on the synchronising scheme is compensated via software. Having a precise angle tracking is easy to verify optimised angles presented on the literature and obtained with several strategies. The lowest THD obtained for five and seven levels is out of IEEE Std. 519-2014, so it is needed to introduce an extra module to drop this THD and be able to regulate voltage output. Having two strings for producing the needed voltage amplitude allow the possibility of having two degree of freedom for obtaining the best performance. In this work, the combination of voltage values allows to have amplitude for voltage regulation even with values of 0.1 sun of radiance. Combination of different strategies on a cascaded structure brings the possibility of having a reduced number of switches and low blocked voltage on them. The simulation results demonstrate the viability of the proposal for residential applications in islanding and non-islanding inverters.

Acknowledgements

This paper was supported by Universidad Panamericana under grant “Fomento a la Investigación UP 2013, project, Inversor vía punto neutro”.


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single phase low thd optimized inverter for pv voltage regulation

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