Three-Phase inverter Controlled by ISCPWM and DPWM-S 1

Nowadays, it is possible to use sophisticated control techniques due to the permanent technical developments which, by means of microcontrollers, DSPs or FPGAs, allow solving complex equations characterizing various modulation techniques. Here are some of them: Third Harmonic Injection Pulse Width Modulation (THIPWM) [1], Discontinuous Pulse Width Modulation (DPWM) [2], Space Vector Modulation [3], etc. These modulation techniques are used in order to enhance the performances of the power electronic circuit, lower cost, reduce size and increase reliability. Implementing a complex control technique that runs in real time on a computer system implies using many resources such as RAM/ROM memory, work speed, internal blocks: PWM, ADC, PLL, DAC, Timers, UART, etc. This paper uses as a reference wave a Discontinuous Pulse Width Modulation S1 signal (DPWM-S1) modulated by an Inverted Sine Carrier Pulse Width Modulation (ISCPWM) carrier signal. The use of the DPWM-S1 signal is beneficial, since it has the value 1 or -1 on two intervals out of six (i.e. a full period). This is important because, in these time intervals, the power transistors within a threephase inverter are in continuous conduction or blocked, therefore there are no switching losses. Overall, the efficiency of the three-phase inverter will be higher, since the switching losses on the power transistors are lower and thus, they need smaller heat sinks, their life span will be longer and the price of such a circuit will be lower.


Introduction
Nowadays, it is possible to use sophisticated control techniques due to the permanent technical developments which, by means of microcontrollers, DSPs or FPGAs, allow solving complex equations characterizing various modulation techniques.Here are some of them: Third Harmonic Injection Pulse Width Modulation (THIPWM) [1], Discontinuous Pulse Width Modulation (DPWM) [2], Space Vector Modulation [3], etc.These modulation techniques are used in order to enhance the performances of the power electronic circuit, lower cost, reduce size and increase reliability.Implementing a complex control technique that runs in real time on a computer system implies using many resources such as RAM/ROM memory, work speed, internal blocks: PWM, ADC, PLL, DAC, Timers, UART, etc.
This paper uses as a reference wave a Discontinuous Pulse Width Modulation S1 signal (DPWM-S1) modulated by an Inverted Sine Carrier Pulse Width Modulation (ISCPWM) carrier signal.The use of the DPWM-S1 signal is beneficial, since it has the value 1 or -1 on two intervals out of six (i.e. a full period).This is important because, in these time intervals, the power transistors within a threephase inverter are in continuous conduction or blocked, therefore there are no switching losses.Overall, the efficiency of the three-phase inverter will be higher, since the switching losses on the power transistors are lower and thus, they need smaller heat sinks, their life span will be longer and the price of such a circuit will be lower.

Theoretical considerations
Fig. 1 presents the waveform of the Discontinuous Pulse Width Modulation S1 (DPWM-S1) reference signal (green-colored waveform), modulated by an Inverted Sine Carrier Pulse Width Modulation (ISCPWM) carrier signal (red-colored waveform).Each intersection between the two waveforms is marked with p1, p2, p3, etc.As long as the amplitude of the DPWM-S1 reference signal waveform is higher than that of the ISCPWM modulating signal, the control signal for the Q + A transistor has the value ON corresponding to its conduction state.Fig. 2 presents the electric circuit of a three-phase inverter, which includes the following transistors: The control signal for Q - A transistor is obtained by inverting the Q + A signal.For Q + B and Q + C transistors, control signals resulted from the intersection of other DPWM-S1signals with the ISCPWM modulating signal.These are phaseshifted by 120º and 240º respectively from the reference signal corresponsding to the Q + A transistor.

Fig. 2. Schematic of the three-phase inverter
The intersection points (p1, p2, p3, p4, p5, etc.) between   where M f is the frequency ratio, p x stands for the points of intersection between DPWM-S1 and ISCPWM and x represents the number of points.
If we consider the DPWM-S1 equations: 1; 0 / 6 and substitute for each interval of time equations ( 3) in ( 1) and ( 2), we can find intersection points p1, p2, p3, p4, p5, etc. [7].Based on these points we can draw the new ISCPWM-DPWM-S1 signal which can be seen in Figure 3. Next to this signal, the original DPWM-S1 signal is illustrated, used only for comparison purposes; it is thus obvious that DPWM-S has lower amplitudes than the new signal ISCPWM-DPWM-S1 at the same points in time.4 presents a period of an ISCPWM modulating signal and of a triangular PWM signal, respectively.These two modulating signals were compared only in order to show that the conduction time resulting from the intersections of ISCPWM and DPWM-S1 -marked as d 1is longer than the time resulting from the intersection between DPWM-S1 and a classic triangular PWM modulating signal -marked as d 2 .The d 1 time has the amplitude value 1 as long as ISCPWM has a higher amplitude than DPWM-S1, which means that one transistor within the three-phase inverter will be in conduction.

Software algorithm
The software was designed to be implemented on the C8051F120 microcontroller, made by Silicon Laboratories.It was chosen because it is fast (100MIPS) and has numerous internal blocks suitable for the implementation of our software (such us: PWM, ADC, Timers, PLL, Ports, XRAM).Fig. 5 presents the flowcharts underlying the C software applied for the C8051F120 microcontroller.For both the simulation and the practical part we used a 315V supply voltage, a 17,25Khz switching frequency and as a load -a 0,37KW motor.Fig. 7 shows the phase A voltage -simulation on the right and practical part on the left -for comparison purposes.Its frequency spectrum is presented below.The amplitude of the fundamental of the voltage between the A and B phases is 320V for the simulation and 321.28V for the practical circuit.
Fig. 9 shows the A phase voltage -simulation on the right and practical part on the left -for comparison purposes.Its frequency spectrum is presented below.

Conclusions
In this paper we used the ISCPWM-DPWM-S1 algorithm implemented on a microcontroller to command a three-phase inverter.This algorithm was tested by simulations and practically.We compared the results of the simulations to the results obtained with the practical circuit in order to emphasize the performances of this control algorithm.High performances were obtained in terms of low power losses on the power transistors within the threephase inverter and high amplitudes of the line and phase voltages fundamentals.However, this control technique has got a drawback: it requires a high calculation volume from the microcontroller.This paper presents the implementation of the ISCPWM-DPWM-S1 control technique on a microcontroller.This technique was developed due to the modulation of a discontinuous signal DPWM-S1 with an inverted sinusoidal signal ISCPWM.Good results were obtained for the switching losses on the power transistors, which are lower, and for the amplitudes of the fundamental frequency, which are higher for the phase and line voltages.Ill.9, bibl.7 (in English; abstracts in English and Lithuanian).Pateikiamas ISNIPM-NIPM-S1 valdymo metodas įdiegtas mikrovaldiklyje.Metodas buvo sukurtas panaudojant nenutrūkstamo signalo NIPM-S1 moduliaciją invertuotu sinusiniu signalu ISNIPM.Gauti geresni rezultatai vertinant galios tranzistorių perjungimo nuostolius, kurie yra mažesni, bei pagrindinio dažnio amplitudę, kuri yra aukštesnė.Il. 9, bibl.7 (anglų kalba; santraukos anglų ir lietuvių k.).

Fig. 1 .
Fig. 1.Waveforms of the Discontinuous Pulse Width Modulation S1 (DPWM-S1) reference signal, Inverted Sine Carrier Pulse Width Modulation (ISCPWM) carrier signal and command signal for Q + A transistor and THIPWM signals can be calculated based on the following equations:

Fig. 3 .
Fig. 3. Waveforms of the ISCPWM-DPWM-S1 and DPWM-S1 signals Fig.4presents a period of an ISCPWM modulating signal and of a triangular PWM signal, respectively.These two modulating signals were compared only in order to show that the conduction time resulting from the intersections of ISCPWM and DPWM-S1 -marked as d 1is longer than the time resulting from the intersection between DPWM-S1 and a classic triangular PWM modulating signal -marked as d 2 .The d 1 time has the amplitude value 1 as long as ISCPWM has a higher amplitude than DPWM-S1, which means that one transistor within the three-phase inverter will be in conduction.

Fig. 7 .
Fig. 7. Waveforms of the phase voltage and harmonic spectrum of this voltage obtained by simulations and from oscilloscopeThe amplitude of the fundamental of the phase A voltage is 185V for the simulation, and 184.18V for the practical circuit.
Fig. 8 shows the AB line voltage -simulation on the right and practical part on the left -for comparison purposes.Its frequency spectrum is presented below.

Fig. 8 .
Fig. 8. Waveforms of the line voltage and harmonic spectrum of this voltage obtained by simulations and from oscilloscope

Fig. 9 .
Fig. 9. Waveforms of the phase current and harmonic spectrum of this current obtained by simulations and from oscilloscope
spectrum of the phase current A (50 Hz,1.8 A)