Keywords

1 Introduction

One of the efficient solution for the utilization of resources is the use of systems delivered by photovoltaic solar energy. Among different machines, induction machines are most widely used due to many advantages such as low cost, ease of operation, durability, high starting torque etc. In this paper, a three level dual inverter fed open end winding induction motor (OEWIM) is proposed to overcome the shortcomings of conventional induction motor. Vast works were carried out for different inverter topologies [5,6,7,8] and different modulation schemes [9, 10] for OEWIM. In this machine stator windings are open and the supply is given from both sides and inverters are connected at either ends to obtain the multilevel output. Vast works has being carried out about the different modulation schemes used for open end winding induction motor [11, 12]. This works proposes a zero sequence elimination pulse width modulation scheme for the machine. The system is supplied by solar panel and MPPT algorithm is also used to path the maximum power and space vector modulation scheme is also used for switching of inverters efficiency etc. But the induction motors has certain disadvantages such as difficult to control, occurrence of common mode voltages, high starting current etc. Several multilevel converter topologies have also remained analysed and suggested during several periods [1,2,3]. To improve the overall performance neutral point clamped inverters was used which is beneficial over two level H bridge inverter [4]. The multilevel inverter is a feasible.

2 Control Algorithms of OEWIM

The proposed system includes control algorithms for an open end winding induction motor (OEWIM) besides modified Dickson charge pump. OEWIM is simply an induction motor with both the ends of the stator windings are opened. The Fig. 1 shows the block illustration of the proposed system.

Fig. 1.
figure 1

Block illustration of control algorithms of OEWIM

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Nowadays OEWIM received large attention in many applications and has many advantage over conventional induction machine. The proposed system is powered by solar photovoltaic panel and to track the maximum power MPPT algorithm is used. A great voltage gain DC- DC converter is also used to acquire a stable output. The proposed converter is Dickson charge pump voltage multiplier. An OEWIM contains dual inverters on either side of the machine to achieve a 3 level output voltage and supply is provided from both sides of the inverter. The machine can be used for variable speed applications, grid applications, hybrid vehicles etc. Figure 2 illustrates an induction machine with both ends of stator windings are open.

Fig. 2.
figure 2

OEWIM

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Since both ends of stator windings are open the switches can be rated at half of the machine power rating and it removes the common mode voltage generated due to switching.

3 Simulation and Results

3.1 Modeling of Induction Motor

Modelling of OEWIM is similar to conventional induction motor. For simulating the proposed system, a 4 kW induction motor is modelled with the parameters specified in Table 1.

Table 1. Motor parameters
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The stator and rotor voltage equations are showed below.

$$ V_{qs} = R_{s} i_{qs} + \frac{{d\varphi_{qs} }}{dt} + \omega_{e} \varphi_{ds} $$
(1)
$$ V_{ds} = R_{s} i_{ds} + \frac{{d\varphi_{ds} }}{dt} + \omega_{e} \varphi_{qs} $$
(2)
$$ V_{qr} = R_{s} i_{qr} + \frac{{d\varphi_{qr} }}{dt} + \omega_{e} \varphi_{dr} $$
(3)
$$ V_{dr} = R_{s} i_{dr} + \frac{{d\varphi_{dr} }}{dt} + \omega_{e} \varphi_{qr} $$
(4)

The equation for determining torque and rotor speed of induction motor is given by

$$ T_{e } = \frac{3}{2}*\frac{p}{2}*\frac{1}{{w_{b} }}\left( {F_{ds} \,i_{qs} - F_{qs} \,i_{ds} } \right) $$
(5)
$$ T_{e } = T_{l } + \frac{2}{p}*{\text{J *}}\frac{{dw_{r} }}{dt} $$
(6)

Figure 3 shows the modeling of induction motor according to the above voltage and torque equations. The results obtained are as follows. Figure 4 shows the input voltage given to the induction motor with an amplitude of 325 V.

Fig. 3.
figure 3

Modeling of induction motor

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Fig. 4.
figure 4

Input voltage of induction motor

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Figure 5 shows the waveforms of output current, of an induction machine. A step time of 0.6 s is given to the machine, as a result up to 0.6 s the graphs shows the no load reading and after 0.6 s loaded condition is depicted here. The topmost value of the current of about 10.2 A obtained (Figs. 6 and 7).

Fig. 5.
figure 5

Output current of induction motor

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Fig. 6.
figure 6

Torque Vs Time graph

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Fig. 7.
figure 7

Speed Vs Time graph

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3.2 Modeling of PV System

Solar photovoltaic system is used to supply the machine and is modeled for running a 4 kW OEWIM. It is modeled according to the voltage current characteristic equation.

Figure 8 shows the modeling of photovoltaic system in MATLAB according to the voltage current characteristics equation given below:

Fig. 8.
figure 8

Modeling of PV system

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$$ {\text{I}} = {\text{I}}_{\text{ph}} - {\text{I}}_{\text{s }} \left[ {{ \exp }\left( {\frac{{{\text{q}}\left( {{\text{V}} + {\text{IR}}_{\text{s}} } \right)}}{{{\text{kT}}_{\text{c}} {\text{A}}}}} \right) - 1} \right] - \frac{{{\text{V}} + {\text{IR}}_{\text{s}} }}{{{\text{R}}_{\text{sh}} }} $$
(7)

Figures 9 and 10 shows the PV and VI characteristics obtained during varying temperatures such as 25 °C, 35 °C, 45 °C etc. To obtain the required output power, in 3 rows about 23 panels should be connected in series.

Fig. 9.
figure 9

PV characteristics

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Fig. 10.
figure 10

VI characteristics

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3.3 Modeling of MPPT Algorithm

MPPT algorithm can track maximum power and P&O method, one of the most simplest method is proposed here. Figure 11 shows the modeling of MPPT algorithm and the output obtained is used to trigger the converter switches.

Fig. 11.
figure 11

Modeling of MPPT algorithm

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3.4 Modeling of Converter

To obtain a stable output a converter is also proposed in this circuit. A Dickson charge pump voltage multiplier is used which had a high voltage gain and removes the need of chemical storages such as batteries (Table 2).

Table 2. Converter parameters
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Figure 12 shows the circuit of conventional and modified Dickson charge pump and Fig. 13 shows the different modes of operation of Dickson charge pump.

Fig. 12.
figure 12

Dickson charge pump voltage multiplier

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Fig. 13.
figure 13

Input and output of dickson charge pump voltage multiplier at 1000 W/m2 and 25 °C

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The circuit works by the charging and discharging of the capacitors in the circuit. It has three modes of operation, either two switches will be ON or either of the switches will be ON. The graph shows the input and output voltage at 1000 W/m2 and 25 °C is shown in Fig. 13.

3.5 Modeling of OEWIM and Space Vector Modulation

Modeling of OEWIM is given by subtracting the difference of pole numbers of both the inverters which can be seen in Fig. 14. The equations below are used for converting abc to dq coordinate

Fig. 14.
figure 14

Modeling of OEWIM

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$$ {\text{V}}_{\text{d}} = \frac{2}{3}\left( {{\text{V}}_{\text{a}} \,{ \sin }\upomega{\text{t }} + {\text{V}}_{\text{b}} \,{ \sin }(\upomega{\text{t}} - \frac{{2\Pi }}{3}) + {\text{V}}_{\text{c}} \,{ \sin }(\upomega{\text{t}} + \frac{{2\Pi }}{3})} \right) $$
(8)
$$ {\text{V}}_{\text{q}} = \frac{2}{3}\left( {{\text{V}}_{\text{a}} \,{ \cos }\upomega{\text{t}} + {\text{V}}_{\text{b}} \,{ \cos }(\upomega{\text{t}} - \frac{{2\Pi }}{3}) + {\text{V}}_{\text{c}} \,{ \cos }(\upomega{\text{t}} + \frac{{2\Pi }}{3})} \right) $$
(9)
$$ {\text{V}}_{ 0} = \frac{1}{3}\left( {{\text{V}}_{\text{a}} + {\text{V}}_{\text{b}} + {\text{V}}_{c} } \right) $$
(10)

The below equations shows the determination of time duration

$$ {\text{T}}_{\text{a}} = \frac{{\sqrt 3 \, *\,{\text{T}}_{\text{Z}} \, *\,{\text{V}}_{\text{ref}} }}{{{\text{V}}_{\text{dc}} }}\left( {{ \sin }\frac{\text{n}}{3}\Pi { \cos }\upalpha - { \cos }\frac{\text{n}}{3}\Pi { \sin }\upalpha} \right) $$
(11)
$$ {\text{T}}_{\text{b}} = \frac{{\sqrt 3 * {\text{T}}_{\text{Z*}} {\text{V}}_{\text{ref}} }}{{{\text{V}}_{\text{dc}} }} \left( { - { \sin }\frac{{{\text{n}} - 1}}{3}\Pi { \cos }\upalpha + { \cos }\frac{{{\text{n}} - 1}}{3}\Pi { \sin }\upalpha} \right) $$
(12)

Figure 15 shows the space vector model of the dual inverter. The inverters are pulsed by space vector modulation scheme and is modeled rendering to the above equations.

Fig. 15.
figure 15

Modeling inverter and space vector modulation scheme

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The modulation scheme has a total of space vector locations of about 64 which can be depicted from the Fig. 16. Figure 17 shows the dual inverter output voltage obtained by space vector modulation.

Fig. 16.
figure 16

Space vector of dual inverters

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Fig. 17.
figure 17

Dual inverter voltage

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Figures 18, 19 and 20 shows the output current, speed and torque of an OEWIM. The dual inverter is modeled and the difference in voltages of inverters is given to induction motor to obtain the modeling of OEWIM. A 0.6 s a step load is applied and the variation during load can be shown in the figure. The use of OEWIM over conventional machine excludes the common mode voltages generated.

Fig. 18.
figure 18

Output current of OEWIM

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Fig. 19.
figure 19

Speed characteristics

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Fig. 20.
figure 20

Torque characteristics

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4 Conclusion

Induction machine with stator end windings open are analysed with dual inverters connected to the open end winding induction machine. This machine offers many advantages over conventional induction machine and can be used for many applications such as variable speed, grid, pumping applications etc. Modeling of OEWIM with three level inverter, PV system, MPPT are modeled and different output waveforms are analyzed.