**Performance Evaluation**

*In previous publications, authors have reported about the performance of the single-phase inverter topology based on controlled charging of the capacitor. The dynamic performance was not available. This article presents the dynamic performance of the inverter for various types of load, which includes leading, lagging and unity power factor, and analysis for 'total harmonic distortion' has been included...*

**-K.Vijayakumar, S.Kannan and **

**S.Ponnayira Sundaravel**

Sinusoidal Pulse Width Modulation (SPWM) is used to digitize the output power, such that a sequence of voltage pulses can be generated by the toggling of power semiconductor switches. The sinusoidal modulated pulse widths enable the control of inverter output voltage and simultaneously reduce its harmonic content. A unipolar SPWM voltage modulation offers the advantage of doubling the switching frequency of the inverter that makes the output filter very smaller, cheaper and easier to implement. Conventionally, a triangle wave as a carrier signal is compared with the sinusoidal wave, and the SPWM gate signals are generated.

These gate signals are then distributed to power switches in a full bridge arrangement. The output voltage of the inverter is only a square waveform due to the switching, and the sine wave voltage is obtained via an LC filter that also reduces the harmonic content.

The control strategy can be digitized with the help of microcontroller for simpler hardware development, higher reliability and smaller filter size. Hence the operation with lower harmonic distortion can be achieved. Further the microcontroller based control strategy allows the flexibility of changing the control algorithms without any changes in the hardware setup. The block diagram of the entire system is shown in Fig. 1.

**FIG 1: Circuit diagram of the entire system...**

**Single phase inverter topology**

The single phase switch matrix topology (Fig. 2) has four power switching devices. The input DC supply voltage is given to the power switches of the switch matrix and the gate pulses (SPWM) are also given correspondingly to them via controller. The output of the inverter, which is normally a square pulse is then given to the LC component to make it sinusoidal for the required application as sine inverter. The inductor current and the capacitor voltage are the feedbacks to the controller and Vref is the reference voltage given by the user to the controller to reach the desired sinusoidal output voltage. Fig. 2 represents the single phase inverter topology.

**FIG 2: Single pahse inverter topology...**

The capacitor-charging power supplies are investigated in the literature. They were used for pulse-power applications, where a capacitor of sufficiently high magnitude is charged for a longer duration and the energy is discharged quickly to a load whenever required. Such a mechanism is not suitable for realising a sinusoidal power supply.

In previous publications, authors have reported about the performance of the single-phase inverter topology based on controlled charging of the capacitor. The dynamic performance was not available. This article presents the dynamic performance of the inverter for various types of load, which includes leading, lagging and unity power factor, and analysis for 'total harmonic distortion' has been included. The work is organised into five sections. The following section III presents the controller. Simulation results are discussed in Section IV and Section V concludes this article.

**Controller**

The controller forms the tracking mechanism to closely follow the output voltage and current waveform and compare this feedback (V&I) with the Vref. This comparator gives iref to be compared with iL to get the corresponding gate signals to synthesize the sinusoidal output voltage. Therefore, for successful operation of the controller, a reference sinusoidal wave Vref at power frequency (i.e., 50 or 60 Hz) is required. By using this signal as reference, the controller forms the PWM signals. Appropriate modulated gate pulse width signals are given to the Inverter switches so as to achieve better dynamic performance – and to reduce the size of the inductor. The controller continuously monitors the inductor current and capacitor voltage through feedback network. Fig. 3 shows a schematic representation of the controllers. The Voltage-mode control shown in Fig. 3 (a) senses the output voltage Vc and compares it with a reference Vref which can be practically synthesized from an exclusive standalone microcontroller. The result, suitably compensated to avoid instability, forms the control signal input to the PWM modulator. A slightly more advanced type, known as average current-mode control shown in Fig. 3 (b), uses a pair of nested loops. The inner loop derives an error signal from the difference of the inductor current – and the output of the outer loop, in which the error signal is derived as for voltage-mode control. Current-mode control carries a number of advantages over voltage-mode control – where selection of component values to optimise loop speed is concerned, and it is primarily with this form of control that this investigation is concerned.

a)

b)

**FIG 3: Controllers for the Inverter:**

**(a) Voltage - mode control... (b) Current - mode control...**

A block diagram of the average current-mode control is shown in the Fig. 4, where Vc is the feedback voltage signal across the capacitor and IL the feedback current signal. A block diagram of the complete embedded controller is shown in the Fig. 5 in which the voltage signal and the current signal are given as feedback to the controller – and it makes the PWM modulator to control the switches Q1, Q2, Q3 and Q4 correspondingly such that the output voltage is always maintained close to the desired reference input signal.

**FIG 4: Block diagram of the current-mode control...**

**FIG 5 Complete Embedded Controller...**

**Simulation results**

In this section, the computer simulation of the inverter has been carried out to evaluate their performances using a MATLAB-Simulink software package for single phase. From Fig. 6 to Fig. 9 shows the simulation circuits and results for single phase inverter and SPWM circuits without controller as open-loop and with controller as closed-loop circuit. Here the PWM is implemented as unipolar voltage switching; the switches in the two legs of the inverter are not switched simultaneously. Unipolar voltage switching has the advantage of doubling the switching frequency as far as the output harmonics are concerned, compared to the other switching schemes. Fig. 7 shows the Simulink model of SPWM circuit and Fig. 8 shows the gate pulse achieved by SPWM as unipolar voltage switching. The complete single phase inverter with closed loop control strategy is shown as Simulink model in the Fig. 9.

**FIG 6: Simulink model of single -phase inverter without controller (open loop)...**

**FIG 7: Simulink model of SPWM circuit...**

**FIG 8: Simulink result of gate pulse achieved by SPWM...**

**FIG 9: Simulink model of single-phase inverter with controller (closed loop)...**

The following Fig. 10 to Fig. 17 shows the simulation results obtained from single-phase inverter both without and with controller (open and closed loop operation) explaining that the output voltage gets maintained close to the reference in closed loop control, and drastically varying with change of loads in open loop control and the analysis is done for various resistive and resistive-inductive loads.

**FIG 10: Output voltage and output current for resistive load (R = 30 ohms) (Open loop)...**

**FIG 11: Output voltage and output current for resistive load (R = 40 ohms) (Open loop)...**

**FIG 12: Output voltage and output current for resistive load (R = 30 ohms) (Closed loop)...**

**FIG 13: Output voltage and output current for resistive load (R = 40 ohms) (Closed loop)...**

Further results in the Fig. 18 to Fig. 25 are concerned with the various THD values obtained explaining that the THD value is reduced with the controller showing the improved performance of the proposed inverter. This explanation is further summarised in the Table 1 to Table 4 giving the overall improved performance of the proposed inverter with controller in terms of voltage obtained and also with various improved THD values.

It can be observed from the Simulink results in the Fig. 10 and 11 that for resistive load of R=30Ω and R= 40Ω in the open loop performance, the output voltage is varied from 296Vrms to 366Vrms for respective variation of load. The same in the Fig. 12 and 13 shows the performance of the closed loop control of the inverter that the output voltage is maintained close to the reference as 230.5Vrms for the variation of resistive load R=30Ω and R=40Ω.

**FIG 14: Output voltage and output current for resistive-inductive load (R = 25 ohms, L = 20 mH) (Open loop)...**

**FIG 15: Output voltage and output current for resistive-inductive load (R = 30 ohms, L = 30 mH) (Open loop)...**

**FIG 16: Output voltage and output current for resistive-inductive load (R = 25 ohms, L = 20 mH) (Closed loop)...**

**FIG 17: Output voltage and output current for resistive-inductive load (R = 30 ohms, L = 30 mH) (Closed loop)...**

The open loop and closed loop comparative performance can also be seen from the Simulink results projected in the Fig. 14 and 15, that for resistive-inductive load of R=25Ω, L=20mH and R=30Ω, L=30mH, the output voltage (open loop) gets varied from 245.7Vrms to 286Vrms respectively. But in the closed loop performance (Fig. 16, 17) the output voltage is maintained as close as 230Vrms.

**FIG 18: THD value in % for resistive load ( R = 30 ohms) (Open loop)...**

**FIG 19: THD value in % for resistive load ( R = 40 ohms) (Open loop)...**

The analysis for THD is done for both the open loop and closed loop circuits. For open loop performance of resistive load R = 30Ω and R = 40Ω, the THD value in % is 2.72 and 3.50 respectively and is shown in the Fig. 18, 19.

The analysis for the same load of R = 30Ω and R = 40Ω in closed loop circuit, the THD value in % is 1.62 and 2.55 respectively, which is low compared to the open loop performance and is shown in the Fig. 20 and 21.

**FIG 20: THD value in % for resistive load ( R = 30 ohms) (Closed loop)...**

**FIG 21: THD value in % for resistive load ( R = 40 ohms) (Closed loop)...**

**FIG 22: THD value in % for resistive-inductive load ( R = 25 ohms, L = 20 mH) (Open loop)...**

For resistive-inductive load of R = 25Ω, L = 20mH, the value of THD in % for open loop performance is 4.68 and for R = 30Ω, L=30mH, the value of THD in % is 3.33. This is shown in the Fig. 22, 23. The THD analysis for the same load in closed loop performance is shown in the Fig. 24 and 25 and the value in % is 4.67 and 2.27 respectively.

**FIG 23: THD value in % for resistive-inductive load ( R = 30 ohms, L = 30 mH) (Open loop)...**

**FIG 24: THD value in % for resistive-inductive load ( R = 25 ohms, L = 20 mH) (Closed loop)...**

**FIG 25: THD value in % for resistive-inductive load ( R = 30 ohms, L = 30 mH) (Closed loop)...**

The open loop and closed loop performance of the single phase sinusoidal inverter with pulse width modulated control strategy is shown in tabulation from Table 1 to 4, explaining the improved performance of the inverter with simplified control strategy.

**Conclusion**

This article has evaluated the performance of the single phase sine inverter topology for its generation of desired sinusoidal waveform at its output and with lower harmonic distortions. The inverter is simulated in MATLAB-Simulink. The implementation of a single phase full bridge inverter with SPWM switching signal from a microcontroller minimises hardware requirement, with many functions performed through software. Implementation of SPWM control setup with microcontroller also enables flexibility in changing the algorithms without changing the hardware setup. The unregulated DC at the input side of the inverter can be obtained from the solar panel for the efficient operation as green technology with the implementation of MPPT algorithm along with Buck-Boost converter setup and the desired sine wave can be obtained from the proposed inverter with lower THD.

**The Authors **are Professors at Kalasalingam University.