Small-Signal analysis of asymmetrical regular sampled PWM control loops

Raats, Wernich (2017-03)

Thesis (MScEng)--Stellenbosch University, 2017.

Thesis

ENGLISH ABSTRACT: In recent years it has become important to be able to design optimal PWM control loops to improve the performance of DC-AC power converters. This would depend on how accurate the stability margins of the control loops can be determined, especially the non-linearity introduced into a PWM control loop by the switching of the pulse-width modulator. By nding the small-signal models of pulse-width modulators it is shown that the stability margins of a control loop can be very accurately determined. However, the derivation of a small-signal model for an asymmetrical regular sampled pulse-width modulator is complicated by the duty cycle value getting updated each half of the switching period. Previously the small-signal model has been approximated by a zero-order hold model, but the accuracy of this approximation is questionable. In this research an accurate discrete-time small-signal model is derived for an asymmetrical regular sampled pulse-width modulator. It is shown that the proposed small-signal model is able to predict the gain margin of asymmetrical regular sampled PWM control loop more accurately than the original zero-order hold model. Two discrete-time state space small-signal models have been derived for single-phase and three-phase PI current regulator systems. The accuracy of the small-signal models are verified by incrementing the loop gain and finding the eigenvalues of the closed loop state space system through which the gain margin is predicted. The gain margin predicted by the small-signal model is compared to a bifurcation diagram to determine its accuracy. The single-phase small-signal model is then compared with the zero-order hold model, to show the in uence of the duty cycle value on the gain margin of a closed loop system. This approach differs from the zero-order hold model which assumes that the in uence of the duty cycle is negligible. It is further shown that the accuracy of the zero-order hold model is dependent on the time-constant of the RL-load, in that, for a small time-constant, it becomes inaccurate. However, the single-phase small-signal model derived is still able to accurately determine the gain margin. The accuracy of applying the zero-order hold model to a balanced three-phase PWM control loop is also investigated. Similar to the single-phase small-signal model, a threephase small-signal model is derived for the asymmetrical regular sampled pulse-width modulator in its stationary d-q frame. A Clarke's transformation is used to express threephase system into its equivalent α and β control loops. Again, the shortcomings of the zero-order hold model are pointed out. It is shown that the unstable operation of the α loop causes the β loop to go into unstable operation. Because the zero-order hold model assumes that the α and β loops are independent it is not possible to determine the influence of the α loop on the β loop.

AFRIKAANSE OPSOMMING: Gedurende die laaste paar jare het dit belangrik begin word om optimale PWM beheerlusse te kan ontwerp om die gedrag van GS-WS omsetters te verbeter. Die ontwerp van optimale PWM beheerlusse sal afhang van hoe akkuraat die stabiliteitgrense van die beheerlusse bepaal kan word om sodoende vir die optimale lus aanswins te kan ontwerp, veral in die geval wanneer daar nie-lineariteit binne 'n PWM beheerlus onstaan as gevolg van skakeling binne in 'n puls-wydte modulator. Vanaf die kleinsein-model van 'n puls-wydte modulator kan die stabiliteitgrense van 'n beheerlus baie akkuraat bepaal word. In hierdie navorsing word 'n kleinsein-model vir 'n asimmetries gemonsterde puls-wydte modulator toestandveranderlike model afgelei. As gevolg van die dienssiklus wat elke halwe skakel periode opgedateer word, raak die probleem meer kompleks. Voorheen is die kleinsein-model slegs deur 'n eenvoudige zero-order hou model voorgestel, maar die akkuraatheid van hierdie benadering word bevraagteken. In hierdie navorsing is 'n akkurate diskrete-tyd kleinsein-model afgelei vir 'n asimmetriese gemonsterde puls-wydte modulator. Dit word bewys dat die voorgestelde kleinsein-model in staat is om die aanwins grens van 'n asimmetriese gemonsterde PWM beheerlus meer akkuraat te voorspel as die oorspronklike zero-order hou model. Twee diskrete-tyd toestandveranderlike kleinsein modelle is afgelei vir beide enkelfase en driefase PI beheerde geslotelus stelsels. Die akkuraatheid van die voorgestelde kleinsein modelle is geveri eer deur die lus aanwins te verhoog en terselfdertyd die eiewaardes te bereken van die toestandveranderlike model om sodoende die geslotelus pole te analiseer waardeur die aanwins grens voorspel kan word. Die aanwins grens van die kleinsein-model word dan vergelyk met 'n bifurkasie diagram om te bepaal hoe akkuraat die model is. Die enkelfase kleinsein model word dan vergelyk met die zero-order hou model om die invloed van die dienssiklus waardes op die aanwins grens van die geslotelus van die stelsel te bepaal. In teenstelling met die zero-order hou model wat aanvaar dat the invloed van die dienssiklus geignoreer kan word. Daar word ook bewys dat die akkuraatheid van die zero-order hou model afhanklik is van die tydkonstante van die RL-las en waar 'n klein tydkonstante gebruik word die zero-order hou model 'n onakkurate model word. Die akkuraatheid van die zero-order hou model word ook ondersoek op 'n gebalanseerde driefase PWM beheerlus. Soortgelyk aan die enkelfase kleinsein model is 'n driefase kleinsein model afgelei vir die asimmetriese gemonsterde puls-wydte modulator in sy stationere d-q raamwerk. Clarke transformasie is gebruik om die driefase stelsel in sy ekwivalent α en β beheerlusse uit te druk. Weereens is die terkortkoming van die zeroorder hou model ook aangedui vir 'n gebalanseerde driefase sisteem. Dit is bewys dat onstabiliteit binne die α lus veroorsaak dat die β lus ook in onstabiele werking gaan. Indien die zero-order hou model gebruik word, word die α en β beheerlusse onafhanklik voorgestel en daarom is dit nie moontlik om met die zero-order hou model die invloed van die α lus op die β lus te bepaal nie.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/100979
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