Implementing Natural Pwm Digitally

For dynamic closed loop control of a multilevel converter with a low switching frequency, natural sampled PWM is the best form of modulation. However previous natural sampled PWM implementations have generally been analog. A digital implementation has advantages, particularly for a multilevel converter. Re-sampled uniform PWM, a modulation technique which approaches the performance of natural PWM, is implemented both in software and hardware. Results demonstrating the improvement over uniform PWM techniques are presented. 1 Multilevel Converters A multilevel converter has a multiple of the usual six switches found in a three phase inverter. The main motivation for such converters is that voltage (in VSI, current in CSI) is shared amongst these multiple switches, allowing a higher converter power rating than the individual switch VA rating would otherwise allow. This sharing is achieved by summing the outputs of several two level converters with transformers or inductors [1], or direct series connection; or by more complex topologies such as the diode clamped inverter and the flying capacitor inverter [2]. Another secondary but very important advantage is the extra degrees of switching freedom that the multiple switches permit. Each switch still has the same limited switching frequency, but by staggering the switching instants of the individual switches, the overall switching frequency of the multilevel converter effectively becomes a multiple of that of the individual switches [1]. A further gain comes since we switch between multiple voltage levels at this higher frequency rather than two, so the switching harmonics appear at a higher frequency and a lower level. This higher apparent switch frequency and improved frequency spectrum suggests a accompanying increase in controllable converter bandwidth. These combined advantages make multilevel converters suitable for implementing large active power filters. But which of the many possible ways of generating PWM waveforms is most suited to multilevel converter modulation, and specifically to ensuring an improved controllable bandwidth? 2 Review of SPWM Optimised PWM or selected harmonic elimination / minimization PWM (SHE/SHM-PWM) seems attractive to low switching frequency applications. However they cannot react to transients quickly [3]. This is because pulses do not occur at fixed points, that is, the switch period is not constant. The switching instants are generally precalculated offline and stored in lookup tables. Closed loop control is generally limited to cycle by cycle control of the fundamental frequency and modulation depth. Some work has been done on closing feedback loops around optimised PWM modulators to remove errors when they occur [3]. Recent work has been done on implementing regular sampled or on-line SHE-PWM [4]. This work has shown that the positions of edges can be calculated relatively simply online given the modulation depth. The calculation gives their displacement from the “sampling points”, the positions of the edges for a modulation depth of zero. The paper does not discuss whether there is now scope for closed loop feedback. SHE-PWM is limited to generating a precalulated waveform — generally a sinewave — and so is unsuitable to active power filtering. Non optimised carrier based PWM can generate a PWM waveform from an arbitrary input waveform online. Further, it can be placed in a more responsive closed loop, as the error input to the PWM modulator can affect the next switching edge, without upsetting the fundamental spectrum. Uniform sampled and space vector PWM are sampled data systems. They sample the signal input at the beginning of the switch cycle, before the actual switching edge reflects this value later in the cycle. This delay in response is significant at low switch frequencies. It leads to a frequency response roll-off which obeys a Bessel function (similar to the sinc function roll-off for PAM). Another unwanted effect of uniform PWM is odd harmonic distortion of the synthesised waveform [5]. The severity of these effects is a function of the ratio of control and carrier frequencies, f1/fc. This ratio may approach and pass unity in high power active filters (high f1, low fc), by which point these effects have become significant and limiting. Figure 1: Natural vs. Uniform sampling. Note the delay introduced by uniform sampling. Naturally sampled PWM is (traditionally) an analog technique where the input signal is naturally sampled by the carrier triangle waveform at the instant of the switching edge. Naturally sampled PWM can react instantly to changes in input command and produces no attenuation or distortion of the synthesised waveform [5]. However as the ratio f1/fc rises for a given modulation depth m, the slew rate of f1 will exceed that of the carrier triangle, and an extra pulse will be generated. If these can be tolerated, the integrity of the synthesised waveform is preserved. So for a multilevel, low switch frequency converter, natural sampled PWM offers the most promise for dynamic control and a wide control bandwidth. However natural sampled PWM is invariably implemented as an analog technique. 3 Digital Natural PWM An analog technique does not however lend itself to a high power multilevel implementation. Considering a multilevel converter consisting of a number of single level modules, a digital implementation would be preferred because • Switching instants are crystal accurate (at least before the switches, and switching delays can be compensated for). More importantly, they are repeatable from module to module. This is very important to ensure that good cancellation of the switching frequency terms in the combined multilevel output. • A Digital implementation can be interrogated, tuned, even reconfigured more easily than an analog.These changes could be made online, and again, would be consistent from module to module. • A Digital system can be distributed master slave style more easily than an analog implementation, which is an advantage for a modular approach. Digital signals are more easily shared amongst isolated modules. • Digital is more reliable than analog in a noisy high power environment. This is the motivation for seeking to create a digital implementation of naturally sampled PWM. 4 Re-sampled Uniform Micro-