PWM inverters Cont. Unipolar Switching of the Bridge inverter. Previously we have discussed Bipolar Voltage switching in which Leg A and Leg B are switched in exact Anti-phase. We have seen that this produces an output voltage ripple at the triangle wave frequency with peak to peak ripple voltage amplitude = 2xVd. An alternative scheme known as uni-polar voltage switching offers significant advantages. (Vcontrol) + TA+, TB- Bipolar Switching Carrier (Vtri) Pulse Width Modulated Output TA-, TB+ Unipolar Switching Modulation (Vcontrol) + Carrier (Vtri) -1 Inverse Modulation ( -Vcontrol) Pulse Width Modulated Output + Carrier (Vtri) TA+ TA- TB+ Pulse Width Modulated Output TB- Unipolar Switching cont. Unipolar Switching has 2 major advantages: 1) The lowest ripple frequency has doubled to 2 x ftri 2) The peak to peak ripple voltage is now only Vd rather than 2Vd. This frequency doubling will greatly reduce the size of inductor required to smooth the output current. Is it a harmonic or is it ripple? The terminology can be slightly confused here. In general the term hamonics is used to refer to unwanted low frequency components which are at integer multiples of the reference frequency. Low frequency components at non integer components of the reference frequency are known as interharmonics. If asynchronous modulation is employed and mf is small then a PWM inverter can generate low frequency interharmonics. It is rare to consider harmonics or interharmonics of more than 40 times the reference frequency (eg 2kHz for a 50Hz system). Ripple is the term usually used to refer to unwanted high frequency components (typically more than 40 x the reference frequency). It is quite common for a pwm inverter to have an mf of 100 or more. In this case it matters little whether or not the carrier is synchronous with the reference and we consider the frequencies centred around the triangle wave carrier to be ripple frequencies. Peak to Peak Current Ripple Calculation for Bipolar and unipolar operation fa = 50Hz ftri = 20kHz ma = 0.5 Vd = 300V Output Inductor = 200uH In both cases the worst case ripple will occur when the duty cycle of the output voltage waveform is to 50%. For bipolar operation this occurs at 0 output voltage. In unipolar operation this occurs at the instant when the carrier is 50% of the peak of the triangle wave. For the purpose of the calculation we assume that the inductor blocks all of the ripple. Example done in class. Answers: Peak to peak ripple current for Bipolar operation = (0.5*Vd)/(ftri.L) Peak to Peak Ripple for Unipolar operation= (0.125*Vd)/(ftri.L) Three Phase Bridge Inverter The capacitor midpoint is ficticious. Each leg uses the same triangle wave and produces an output voltage that swings between –Vd/2 and +Vd/2 with respect to the fictitious midpoint. The clever bit is that the reference voltagesfor leg a, b and c are all phase shifted by 120° from each other so the resulting outputs on leg A,B and C are three phase shifted sine wave – a proper 3 phase set. The fictitious midpoint actually represents the neutral pfor each phase. At maximum linear modulation (ma<1) the output voltage on any leg has a peak value equal to Vd/2. Thus the maximu rms phase voltage (for linear modulation) is Vd/(2√2). The line to line voltage is then √3.Vd/(2√2). For a modulation index of less than 1 then the output voltage magnitude is √3.ma.Vd/(2√2) = 0.612 ma.Vd (NB for ma <= 1.0) Three Phase inverter Waveforms It is important to note that the neutral is fictitious and cannot take any real current. This implies that the three phase inverter should always be used with a delta connected load where a neutral is not required. This has the added advantage that the harmonics (or ripple) at the triangle carrier frequency largely canacels out in the line to line voltage allowing us to benefit from the same frequency doubling effect we got with unipolar operation of a single phase inverter. If the frequency modulation index mf is low then perfect cancellation of the frequency component at ftri can be achieved if mf is an odd multiple of three. For high values of moulation index this is less significant and the dominant ripple frequency occurs at 2*ftri Over Modulation Just as in the Single phase inverter overmodulation can achieve a higher output voltage at the expense of (i) linearity and (ii) increased dstortion. In the extrem overmodulation will result in square wave output voltages. The maximu achievable line to line output voltage is (√6/π).Vd = 0.78*Vd.