6.1 Conclusions
In this thesis, detailed studies have been done on the dynamic response of a three-phase voltage source inverter (VSI) when operating in parallel with various ac voltage sources (Stiff grid, Inverter and Genset). The main contributions and conclusions of this thesis are as follows:
A three-phase VSI with an output LC filter, for attenuating the switching harmonics, and a closed loop voltage control scheme, for regulating the output voltage magnitude and frequency, has been designed. A simple PI type-3 controller using the dq (vector) control approach has been used. It has been shown by means of time domain simulations in Simulink that the inverter performs very well under various conditions including: Heavy balanced and linear load variations and voltage and frequency references variations.
Small-signal models of two systems, based on their average dq model, have been developed. The first system consists of a droop controlled three-phase VSI, with a local load, connected in parallel to a stiff grid through a tie-line. The second system consists of two parallel droop controlled VSIs, with their local loads, connected through a tie-line. It has been shown for both systems that the fast elements (Voltage controller and LC filter) can be neglected in the modeling and analysis since they have negligible influence on the system’s dominant poles. Therefore, reduced small-signal models have been derived confirming the previous statement. After varying the most influencing elements of the systems’ behavior, which are the droop controllers’ gains, the line impedance and the LPF of the active and reactive power calculator, it has been shown that both systems tend toward stability when decreasing mp and nq, (droop
factors) and when increasing Xg and Rg (components of the tie line) and fc (of the power calculator). This has been verified by means of time domain simulations in Simulink. Regarding the systems’ steady-state response, the main element which affects the accuracy of the power sharing between inverters is the ratio Xg/Rg. The larger the latter is, the smaller the steady-state error will be.
The conventional virtual impedance (VI) control loop has been designed and implemented in the system, which is composed of two droop controlled VSI, since the line impedance characteristics of the system generates high oscillatory dynamic responses for both inverters. It has been shown in the thesis that the conventional VI provides a good solution to the dynamic issue. However, its design is difficult because it depends on the inverter’s ratings and the line impedance. Moreover, it affects the inverters’ output voltage amplitudes because of the way it is implemented. Therefore, a new VI control loop has been proposed, which is based on the variation of the inverters’ output voltage phase angle. It has been shown, by means of frequency domain analysis (root locus) and time domain simulations that the new VI loop is more performing than the conventional one, it allows better voltage regulation, and it ensures good transients for a large range of line impedance values.
Regarding the system where the droop controlled VSI shares local loads with a Genset through a tie-line, no frequency domain analysis (root locus) has been conducted. It has been investigated only by means of simulations in Simulink. In this system, the studies focused on the dynamic response issue since both ac voltage sources behave differently in terms of speed response. Because the inverter is much quicker than the Genset, large overshoot can be generated in the inverter’s output active power even if the load variations occur at the Genset side of the tie-line. In order to avoid overloading the inverter, a new control loop has been conceived. This latter allows varying the inverter’s settling time by a factor of “Kd” to make its speed response as close
as possible to the one of the Genset. This technique consists of adding a negative angle to the inverter’s output voltage phase angle in order to curb the angle δ generated physically between the two sources. Moreover, this settling time variation technique uses only local measurement, unlike previous attempts, making its implementation simple. It has been shown, using a simplified small-signal model of two ideal ac voltage sources, that this new control loop creates an additional degree of freedom to the system dynamics improvement. The system performance verification has been done by means of time domain simulations in Simulink, which showed that the overshoot appearing in the inverter output active power decreases by increasing Kd. Although this generated at first high frequency oscillations in inverter’s dynamics, the use of the new (proposed) VI loop allowed the mitigation of the oscillations, resulting in an overall well damped and smooth response for the entire system.
6.2 Future work
The following topics are suggested for a future work.
The three-phase three-leg VSI should be capable to regulate its output voltage under unbalanced and no-linear loads conditions when the Genset is off. For this, a new voltage control loop should be designed.
The small-signal model of the system in chapter 5 needs to be developed for a better understanding of the parameters influencing its dynamic behavior under variable perturbations. This will lead to a better analysis of the new control loop benefits and limits on the system. Modeling and analysing bigger systems which regroup the three ac voltage sources (the two