In cases of unbalanced grid conditions, the controller has been tested with different voltage sags. As a result, the controlled signal starting could promote a rise in the error between the reference signal, and the controlled signal which can be identified as creating aberration from its nominal value. To overcome this concern, the adaptive PR control techniques have been used in the stationary reference frame to control the current based on look-up-table is implemented to obtain the optimal values of the control parameters. It establishes and associates the enactment of the adaptive PR controller during standard and irregular grid voltage conditions.
The performance of the adaptive PR controller has been implemented in abnormal grid condition. The adaptation mechanism applied allows low PR controller gains until there is a sudden change in the grid conditions. This means the error will appear eventually. If the error is less than the set value which is 5%, the adaptation mechanism still used low PR controller gains. If the error is higher than 5% and less than 8%, the adaptation mechanism will use medium PR controller gains and the new parameters are applied. If the error is higher than 8%, the adaptation mechanism will use larger PR controller gains and the new parameters are applied as can be seen in table Table 6.1. Figure 6.3 shows a screenshot of the adaptive PR controller in the Simulink.
Table 6.1 Adaptive PR controller simulation parameters
Parameter The proportional gain 𝑘𝑝 The integral gain 𝑘𝑖
α-axis, β-axis current controllers (low)
Chapter 6: PI and PR Current Controller
Figure 6.3 Screenshot of the adaptive PR controller
In order to test the controller dynamic performance under unbalanced conditions, three-phase voltage sag, single phase voltage sag and two-phase voltage sag fault conditions are investigated. Figure 6.4 and Figure 6.5 show the voltage and current waveform under voltage sag 30% for all phases. By applying the adaptation mechanism based on the error at the starting of the transient response, at a time of 0.15 sec, the 𝑘𝑝 and 𝑘𝑖 are varied from their set values in the look-up-table based on the error. The adaptation mechanism has been chosen the medium control gains. It can be seen from Figure 6.4 that the voltage drops when a voltage sag happens in the system at 0.1 sec until 0.15 sec. Figure 6.5 shows that the current has increased when the sudden voltage occurs at 0.1 sec in order to balance the active power transfer from the PV source.
Chapter 6: PI and PR Current Controller
Figure 6.5 The current waveform with 30% voltage sag
Figure 6.6 and Figure 6.7 shows the stationary reference frame alpha and beta current respectively for adaptive PR controller with medium controls gains. The adaptation mechanism based on the error at the starting of the transient response, at a time of 0.15 sec, the 𝑘𝑝 and 𝑘𝑖
are varied from their set values in the look-up-table based on the error. As can be seen from the figures, the measured current follows the reference current during steady state and transient states and the result is satisfactory in both transient and steady-state. It can be noticed that the when the control gains increased in the adaptive method, the settling time is reduced as well as the error is reduced between the reference and measured alpha and beta current waveforms compared to the conventional PR controller in Figure 5.26 and Figure 5.27, which illustrate the error between the reference and the measured current is approximately 8%.
Chapter 6: PI and PR Current Controller
Figure 6.7 The beta current waveform for adaptive PR controller using medium gains Figure 6.8 shows the voltage waveform during unbalanced grid condition with 50% voltage sag. Due to the clear unbalanced in phase a at 0.15 sec, the adaptation mechanism starting control the system and choose high gains. Unlike the PI controller, only one PR controller is needed to control the three-phase inverter under unbalanced grid condition. Here in the adaptive PR controller, the current components in the positive-sequence components is applied based on the adaptation mechanism as shown in Figure 6.9. As a result, it is observed that the current waveform is not affected by faults in the voltage and the control will work as designed and not distorted anymore.
Chapter 6: PI and PR Current Controller
Figure 6.9 The three-phase current waveform under unbalanced voltage sags
Chapter 6: PI and PR Current Controller
Figure 6.11 The beta current waveform for adaptive PR controller using medium gains To further validate the performance of the adaptive PR controller, another case was investigated based on unbalanced two-phase voltage sag as shown in Figure 6.12. Before introducing the adaptive PR controller, the current waveforms were distorted due to the unbalanced voltage and the effect of the unbalanced is visible as shown Figure 6.13. However, the control system will be significantly improving by obtaining the adaptive PR controller. The adaptive PR controller is applied and the output current waveform is shown in Figure 6.14. The control gains, 𝑘𝑝 and 𝑘𝑖were tuned depended on the error while observing the system response. The error over the limit and the test was carried out using the high gains. It can, therefore, be determined that the adaptive PR controller is able to achieve good performance during both balanced and unbalanced voltage sags.
Chapter 6: PI and PR Current Controller
Figure 6.12 The two-phase-to-ground voltage sag
Chapter 6: PI and PR Current Controller
Figure 6.14 The three-phase current waveform under unbalanced conditions
Figure 6.15 and Figure 6.16 show the reference and measured alpha and beta current respectively. It can be seen that the measured current follows the reference in both cases. It can be concluded that the measured current follows the reference current even in unbalanced grid conditions.
Chapter 6: PI and PR Current Controller
Figure 6.16 The stationary reference frame beta current