# Experimental Validation of Peer-to-Peer Distributed Voltage Control System
## 6 Results of the Experiment
### Second Experiment: With P2P Voltage Control  
The inverters apply the same generation profile, but now the agents execute the distributed voltage control algorithm. This leads to the voltage profile shown by Figure 11. When an increase in generation causes an over-voltage issue, the agents bring the voltages back to the defined limits (\(\pm 10\%\)) within 3 min.  
Figure 10: Voltage profiles without voltage control for the 3 nodes in the microgrid (the generation profile causes over-voltages up to 1.145 p.u.)  
Figure 9: 30 min generation profiles of inverter 1 and inverter 2 (both inverters apply the same generation profile).  
The actions of the observer and actuator agents are reflected in Figure 12. The evolution of the control signals over time are presented in Figure 12c,d. The control signals for under-voltages (\(\lambda^{\text{min}}\)) are zero, because no under-voltages beyond the limits occur during this experiment. The control signals for over-voltages (\(\lambda^{\text{max}}\)) however, increase sharply after an increase in the voltages above \(V^{\text{max}}\). One can notice that the control signals \(\lambda^{\text{max}}\) return back to zero when the voltages return back to normal values without compensation, due to a decrease in the generation profiles.  
Figure 12a,b shows the actions taken by the actuator agents. As soon as an over-voltage occurs, nearly all reactive power is dispatched. This behaviour depends on the values of \(\alpha\), \(c^{p}\) and \(c^{Q}\). The step size \(\alpha\) controls mainly how fast the control signals will increase, and hence how fast compensation is dispatched. Since the cost of active power is set to be a lot higher than the cost of reactive power, the algorithm will dispatch first the available reactive power. \(\alpha\) is set high enough to get a fast response in the active power dispatch. However, this causes the dispatch of reactive power to be nearly instantaneous. \(\Delta P\) and \(\Delta Q\) return back to zero when the voltages return back to normal values without compensation.  
Figure 11: Voltage profiles with voltage control for the 3 nodes in the microgrid.  
Figure 12: (**a**) Active power curtailment of inverter 1 and inverter 2; (**b**) Reactive power compensation of inverter 1 and inverter 2; (**c**) The control signals for over-voltages; (**d**) The control signals for under-voltages.  
When the measured voltage \(V_{i}^{\text{meas}}\) is less than \(V^{\text{max}}\), \(\lambda_{i}^{\text{max}}\) starts to decrease till it reaches zero. One can explain this based on Equation (2). The Lagrangian multipliers drop back to zero because the underlying profile of the inverters change. The active power injection drops, and the voltage drops with it. The Lagrangian multipliers adapt to the new situation. When both \(\lambda_{i}^{\text{max}}\) and \(\lambda_{i}^{\text{min}}\) are zero at each observer, problem (1) can be written as:  
\[\underset{\Delta P,\Delta Q}{\text{argmin}}\quad c^{\text{P}}( \Delta P_{d}^{(t)})^{2}+c^{\text{Q}}(\Delta Q_{d}^{(t)})^{2}+\text{zero} \tag{3}\] \[\text{Subject to the local constraints of problem (1)}\]  
One can notice that the solution of the above optimization problem is: \(\Delta P_{d}^{(t)}=0\) and \(\Delta Q_{d}^{(t)}=0\). Hence, a stop mechanism can be designed to stop the solver of the optimization problem whenever the Lagrangian multipliers are zero at each observer. This should decrease the computational burden of the algorithm.