Gain limits for current loop controllers of single and three-phase PWM converters

Optimized tuning method of stationary frame Proportional Resonant current controllers

“…References [2] and [6] have demonstrated that the power converter plus the PWM block may be expressed by an averaged model, which consists of a voltage controlled source �o (s ) with unitary gain, since �om,F (s ) is divided by the DC link voltage. Thus, the per-phase closed loop system is represented by Fig.…”

“…OJ o = kOJ, (5) kR =k;u 'OJ, (6) where k is the relation between the resonant frequency and the base (or fundamental) frequency OJ, kf:u is the normalized proportional gain defmed in [6], and k�m is the normalized resonant gain.…”

“…This method defmes a discriminant d given by d = oi [ e + 2 k P U k i ' " _ ( k; " t ]3 + 27 P R 3 + ( k P u )z Oi [ k 2 + 2 k; " k; " Jk; U t _ � . z P 6 27 2 (7) Considering that the coefficients of the denominators proportional gain kJ," is chosen to be the maximum pennitted value for a two-level PWM and a single-phase converter, for a switching frequency of 12 kHz, according to [6]. The fIrst reason to choose high values for k;" is that it is important to assure that the three resonant gain regions will always occur, and simulations of (7) show that, for given values of OJ and k , this is true only if k;":2: 5k .…”

“…For a two-level converter, [6] states that kl'MAX = 21m] . L , where 1m is the switching frequency; (2) If the tracking response must be optimized, the resonant gain must be set In the range 0< k;" :s; O.Ollk]:/I;…”

“…These expressions allow to analytically obtain optimized gains, settling time and overshoot when designing PR current controllers, extending the results to other power converters; 2) Low, medium and high resonant gain regions are defined in Section III for the closed loop system operation and it is shown that the transient performance highly depends on which region the resonant gain lies. Moreover, this approach mathematically explains the pole behavior observed, but not detailed in [1]; 3) Charts of normalized proportional and resonant gains versus overshoot and settling time parameters are built in Section IV, as it is done in [6], allowing to clearly visualize the effect of the variation of gains on the transient response. Since these gains are normalized in terms of grid and converter parameters, the results can be extended for any grid connected power converter with an inductor filter;…”