## 6 Results and Discussions
### Study System
#### 6.2.3 Analysis of Results Under Grid Price and Optimized Price  
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2. Reliability and Stability of the System  
Figures 7 and 8 show the net load demand of each MG under the grid price and the optimized price, respectively. It can be observed from Figure 7 that some MGs needed to buy electricity from the DNO, and the other MGs needed to sell electricity to the DNO in the time slots 9-10 and 16-17, which indirectly promotes energy sharing between the MGs. Figure 9 shows the comparison of the total net load demand of the three MGs. In time slots 1-2 and 4-5, the net load demand was higher than the original one due to the low selling price, where the energy storage system was charged and the transferable load was increased. In the other time periods, the optimized net load demand was lower than the original one. Consequently, the peak-to-average ratio of the net load demand was reduced from 5.48 to 3.77. This will improve the reliability and stability of the DN. Figure 6: Optimized transferable load demand. Figure 7: Net load demand under grid price. Figure 10 shows the voltages of all the nodes in the IEEE-33 bus system at each hour of the day. It can be seen that the bus voltages at all nodes were quite stable, where the minimum node voltage of the DN was 97% of the rated voltage, and the maximum voltage was near the rated voltage. Figure 11 shows the comparison of the maximum powers of all the branches in the IEEE-33 bus system at each hour of the day under the optimized price and grid price, respectively, where the power limit was set to 1000 kW. We can see that the maximum powers of all braches under the grid price exceeded the power limit three times (i.e., in time slots 7, 17 and 19), while those under the optimized price only exceeded the power limit two times (i.e., in time slots 17 and 19). Since almost all of the maximum power flow of the branch was less than 1000 kW, the reliability and stability of the DN was improved. Figure 8: Net load demand under optimized price. Figure 10: Voltage of all the nodes in the IEEE-33 bus system. Figure 9: Comparison of total net load demand before and after optimization. 2. Economic Benefits of the System Figure 12 shows the comparison of the transaction costs between the MG and the DNO under the grid price and optimized price. As can be seen from Figure 12, the transaction costs of the MG under the optimized price was lower than those under the grid price in the time slots 0, 3 and 6-24. In the time slots 1-2 and 4-5, the transaction costs under the optimized price were a little higher than those under the grid price because the energy storage was in charge, and the load was increasing. We can see that during most of the time, the transaction cost under the optimized price was lower than that under the grid price. This proves that the proposed electricity price strategy effectively reduces the cost of the MGO. Figure 13a shows the transaction costs of the DNO and the DN. In time slots 1-2 and 4-5, since the grid price was in the valley period, the DNO purchased more electricity from the DN and sold it to the MGO to meet the load demand and to charge energy into the battery, which increased the transaction cost between the DNO and the DN. In time slots 21-24, the transaction cost was also increased because the amount of electricity transactions between three MGs and the DNO increased (see Figures 7 and 8). Figure 11: Comparison of maximum power of all the branches in the IEEE-33 bus system under optimized price and grid price. Figure 12: Comparison of transaction costs between microgrid operator (MGO) and DNO. Figure 13b shows the transaction cost of the DNO and the MGO. To encourage the MG to participate in the operation of the DN, the buying price of DNO was higher than that of the DN, and the selling price of DNO was lower than that of the DN, so the cost of the DNO under the optimized price was slightly higher than that under the grid price.