## 4 Case Study
### MOPSO-Based Problem Solution
#### 4.3.2 Discussion on Receding Horizon of Optimization  
This subsection tests the overall performance of the proposed bi-objective dispatch of ME-VPP. The mechanism of receding horizon is employed to incorporate the predicted external parameters (e.g., wind power) and the optimized decision variables (e.g., CCHP output). We investigate two strategies as follows:  
* Strategy A: \"Improvisational\", which operates ME-VPP on a 1-h receding horizon. * Strategy B: \"Foresighted\", which operates ME-VPP on a 5-h receding horizon. The flow diagrams of two strategies are illustrated in Figure 14. It should be emphasized that two strategies both operate ME-VPP in a 1-h-ahead framework, i.e., the bi-objective optimization problem is solved every hour and the dispatch solution is applied next hour. But they are discriminated by different prediction steps and optimization horizon: the \"improvisational\" strategy incorporates 1-h wind prediction result and only derives the dispatch solution of the next one hour; \"foresighted\" strategy utilizes 5-h wind prediction and computes dispatch solution for the next five hours (although only the first one hour is actually applied). Figure 14: Schemes of two strategies: (**a**) improvisational; (**b**) foresighted. Figure 13: One noninferior solution of the Pareto frontier—power production/consumption (MW) in ME-VPP in 24 h.  
Due to the relatively small scale of Hongfeng Eco-town, the IEEE 118-bus system is adopted as the benchmark to test the overall performances of the two aforementioned strategies. The IEEE 118-bus system is a large-scale and complex case consisting of 118 buses, 186 branches, 91 loads and 54 generators [30]. The simulation is performed by using 24 h of data of a typical day. The particle population is 200 and the maximal generation number is 50. The overall performance is quantified by EC and PQ. Each solution corresponds to a point on the EC-PQ plane and all optimal solutions forms the Pareto frontier. In each hour, the numeric simulation obtains two Pareto frontiers on EC-PQ plane. Each Pareto frontier corresponds to one strategy. For the ease of comparison, we select the two closest points on the EC-PQ plane, each from a Pareto frontier. These two points represents the performances of two strategies in each hour, and 24-h comparison results are listed in Table 4.  
There are four major columns in Table 4. The first indicates the sequence of 24 h in a day. The second and third are the selected Pareto optima of \"improvisational\" and \"foresighted\", respectively; each Pareto optimum represents the strategy performance in terms of EC and PQ. The fourth major column demonstrates the improvement of \"foresighted\" strategy. Two indexes, \"saved EC\" and \"enhanced PQ\", are investigated with respect to the \"improvisational\" strategy. The \"foresighted\" strategy has Pareto dominance if both indexes are positive numbers, i.e., achieving higher quality with lower cost. Otherwise \"improvisational\" strategy takes Pareto dominance if both indexes are negative numbers; and neither one takes Pareto dominance if one index is positive and the other is negative. Table 4 demonstrates that the \"improvisational\" and \"foresighted\" strategies take Pareto dominance in 3 h and 10 h of one day, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Time**} & \multicolumn{2}{c}{**“Improvisational”**} & \multicolumn{2}{c}{**“Foresighted”**} & \multicolumn{2}{c}{**Improvement of “Foresighted”**} \\ \cline{2-7}  & **EC (10\({}^{3}\)** & **PQ (Score** & **EC (10\({}^{3}\)** & **PQ (Score** & **Based EC** & **Enhanced PQ** & **Pareto** \\  & **CNY)** & **in 100)** & **CNY)** & **in 100)** & **(10\({}^{3}\)****CNY)** & **(Score in 100)** & **Dominance** \\ \hline
1 & 268.63 & 78.30 & 257.53 & 82.38 & 11.10 & 4.08 & Yes  
The last two rows at the bottom of Table 4 further compare the two strategies in terms of the total EC and average PQ in 24 h. It is shown that neither takes Pareto dominance.