# The Optimal Dispatch of a Power System Containing Virtual Power Plants under Fog and Haze Weather
## 6 Case Study
### The Dispatch under F-H Weather  
(1) Case description:  
There are two thermal power units (G\({}_{1}\) and G\({}_{2}\)) and two VPPs (VPP\({}_{1}\) and VPP\({}_{2}\)) supplying the total load, the forecast curve of which is shown in Figure 10, of a certain region in Baoding, China, on 27 March 2014 (AQI = 305, \(L_{\text{AQI}}=6\)). Some relative parameters of G\({}_{1}\) and G\({}_{2}\) are listed in Tables 4 and 5. VPP\({}_{1}\) consists of a wind power plant (WPP\({}_{1}\), 100 MW), a photovoltaic power plant (PPP\({}_{1}\), 80 MW) and an efficiency power plant (EPP, 90 MW); VPP\({}_{2}\) consists of a WPP (WPP\({}_{2}\), 80 MW), a PPP (PPP\({}_{2}\), 60 MW) and an electric vehicle charging station (EVCS, 70 MW). An EPP implements all kinds of electricity-saving strategies in a certain region, and the electricity saved becomes its virtual output, which is equivalent to building a new power plant or enlarging the capacity of an old one. The control strategies and implementation of an EPP rely on advanced communication and information technology [29]. An EVCS aggregates a large number of EVs, the charge-discharge patterns of which are rationally controlled to realize load shifting. Thus, the charge-discharge control strategies of EVs are the fundamental tasks of an EVCS [30]. The main focus of this case is the plan of green economic dispatch between the power system and VPPs under F-H weather. The characteristics of DERs inside VPPs will be researched in a future study. Therefore, it is hypothesized that the EPP and EVCS act only as special generation units, and their outputs could be controlled and adjusted according to demand within capacities, which could simplify the dispatch model. The output forecast curves of VPP\({}_{1}\) and VPP\({}_{2}\), which are shown in Figure 11, would be available by adding the forecast curves of the WPP and PPP and the capacity of the EPP (90 MW, VPP\({}_{1}\)) or the EVCS (70 MW, VPP\({}_{2}\)). The cost coefficients (yuan/MW) of the WPP, the PPP, the EPP and the EVCS are 414, 1170, 278 and 670, respectively [29; 30; 31]. In addition, financial subsidies have been used to encourage the development of DERs without pollution. To simplify the calculation, it is hypothesized that the basic rate of subsidization of all DERs is 40%. (2) Result analysis:  
The dispatch results are shown in Figure 12 (\(L_{\text{AQI}}=6\); the proportionality coefficient of the growth factor function of emission cost \(\alpha=1.5\); weights of the objective functions without AQI: \(\beta_{1}=0.1089\), \(\beta_{2}=0.2030\), \(\beta_{3}=0.6275\) and \(\beta_{4}=0.0606\); with AQI: \(\beta_{1}=0.1286\), \(\beta_{2}=0.0489\), \(\beta_{3}=0.8017\), \(\beta_{4}=0.0208\)). It is shown in Figure 12 that 70.35% of daily load is supplied by thermal power units (G\({}_{1}\) and G\({}_{2}\)) with a cost advantage, and the other 29.65% is left for VPPs (VPP\({}_{1}\) and VPP\({}_{2}\)) when F-H is ignored. The reasons could be described as follows. First, G\({}_{1}\) and G\({}_{2}\) receive less economic punishment according to Formula (18) and have a higher dispatch priority with their cost advantage when the effect of F-H is ignored. Second, the cost coefficients of DERs inside VPP\({}_{1}\) and VPP\({}_{2}\) are much larger. Thus, only VPP  
Figure 11: Maximum output forecasts of VPP\({}_{1}\) and VPP\({}_{2}\). with a lower cost shares more load requirements, and the output of VPP\({}_{2}\) is rarely adopted, which results in the waste of clean DERs. Conversely, if F-H is considered, 54.98% of the daily load is supplied by VPPs that contain many clean DERs, which is much larger than the former condition (>29.65%), and only 45.02% (<70.35%) is left for the thermal power units. G\({}_{1}\) and G\({}_{2}\) incur a much higher emission cost, because the AQI factor is considered, which greatly weakens the generation cost advantages of thermal power units. Therefore, VPP\({}_{1}\) and VPP\({}_{2}\) gain a higher dispatch priority, because DERs have less or even no pollution, which makes full use of clean energy.