## 6 Simulation Results
### Economic Assessment with the DR Program  
Section 6.1 outlined the optimal scheduling and operation for system security for the proposed study, whilst this section outlines the assessment of the effectiveness of the proposed incentive method alongside the customer's profit. Profits gained by customers from the incentive program of operation Cases 3 and 4 are shown in Figures 13 and 14, respectively. All customers who are providing coordination by participating in the incentive market can gain a profit throughout without changing their electrical energy consumption pattern. In Figures 13a and 14a, it can be confirmed that the obtained profit is small in the day-time when the inverter margin is small, but on the other hand, it gains higher profit at night when compensating for voltage deviation due to heavy load. It is different from the end-of-day profit for customers at each node from Figure 13b, due to the absence of voltage compensation from SVR in Case 3. Therefore, the contribution by cooperative control from customers is necessary, as it helps the customer to gain high profit for the end-of-nodes (Nodes 12-15). Otherwise, in order to levelize the distribution of incentives shown in Figure 13b, it is advisable to introduce SVR.  
Next, an analysis that changes the participation rate of the incentive market is shown in Figure 15. This figure provides three comparisons; (1) comparison of profits with the participation rate, (2) comparison of profits obtained by the contribution functions and (3) the participation rate for appropriate control. The participation rate of customer changes in Cases 3 and 4. The profit obtained by linear and sigmoid contribution functions is plotted for each case. First, as the participation rate increased, it can be confirmed that the profits of all the participants increased. Secondly, liner and sigmoid profits intersected about the 84% point. It is clear that the linear contribution function gave higher profit than the sigmoid contribution at a participation rate beyond 84%. In contrast, the sigmoid function showed a benefit for a lower participation rate. The vertical dotted lines indicate boundaries that satisfy all constraints. In other words, the area to the left of this boundary line indicates the impossibility to maintain a safe system. Therefore, on the operation points, the participation rate exceeded 82% in Case 3 and 73% or more in Case 4, which is necessary for maintaining the grid stability.  
Figure 14: Profit of the customer from reactive power incentive (Case 4). (**a**) Hourly profits of each node and (**b**) end-of-day profit for customers at each node.  
Figure 13: Profit of the customer from reactive power incentive (Case 3). (**a**) Hourly profits of each node and (**b**) end-of-day profit for customers at each node.  
Assuming that all consumers participated in the DR event in Case 3, the average profit of the sigmoid function decreased over the linear function, and the result is shown in Figure 16. However, in actual systems, it is difficult to meet an expectation of 100% participation from consumers in the market. In addition, several control devices have already been introduced, so in such a case, the sigmoid function is more likely to distribute profits to consumers. Since the sigmoid function has high flexibility, versatility is high even in real systems.