Describing function applied to HVDC systems harmonic instability

The adoption of voltage-controlled oscillator based firing systems has almost completely eliminated the harmonic instabilities experienced in early HVDC systems. However, the basic feature of such systems (equidistant firing) is adversely affected by the feedback action of the current control loop, since the direct current may contain uncharacteristic harmonics which are not filtered out by the controller. Under certain circumstances (such as an imbalance and/or a distortion in the alternating voltage, DC-or AC-side resonances near DC or AC harmonic frequencies, respectively) instabilities may occur which are characterised by oscillations synchronised with the alternating voltage, i.e. harmonic instabilities. Nonlinear control-system theory, namely the describing-function method, was used to show that these oscillations are limit cycles whose conditions of occurrence can be predicted. A detailed computer model for an hvdc link was developed which allows the calculation of both the DC and the AC harmonics in the steady state and the describing function for subharmonics of the firing frequency of the convertor. Limit cycles can be predicted by the Nichols chart technique.