# The Optimal Dispatch of a Power System Containing Virtual Power Plants under Fog and Haze Weather
## 2 F-H Impacts on Photovoltaic Output and Load Forecasts
### The Influence of F-H on Load  
Several emergency warning policies are implemented by the Chinese government when F-H is serious, and the emergency warning levels, from low to high, are indicated by the colors yellow, orange and red according to forecast data of severity and continuous days of F-H. The influence of F-H on load could be divided into two parts:  
(1) Load directly influenced by emergency warning policies:  
The Chinese government forcibly shuts down some industries under conditions of heavy pollution and high energy consumption (or calls for reducing production) to reduce pollutant emission when emergency warning policies are implemented. The reduced portion of the load is directly influenced by the emergency warning policies. For instance, the daily load of a cement plant in Baoding, China, from 20-29 December 2014 is shown in Figure 3.  
As shown in Figure 3, although the air condition indicated serious pollution on 23 December, there was no emergency warning signal on 22 December, because the AQI value would drop in the foreseeable future. Thus, the cement plant did not reduce production or shut down. The AQI value would stay at a high level and continue to rise after 24 December. Therefore, the emergency warning signal became red on 24 December. As a result, production of the cement plant was reduced by nearly 50% on 25 December, and it was shut down forcibly from 26-29 December.  
(2) Load not directly influenced by emergency warning policies:  
The other portions of the load are not directly influenced by emergency warning policies, such as residential load and commercial load. These portions of load with higher randomness, which vary with people's subjective consciousness, are also affected by F-H. Considering the residential load as an example, the daily load of a residential quarter in Baoding, China, from 20-29 December 2014 is shown in Figure 4.  
Figure 3: Daily load of a cement plant in Baoding, China, from 20–29 December 2014.  
The Pearson's correlation coefficient, which is shown in Formula (1), is employed to analyze the correlation between curves of the AQI and load in Figure 4.  
\[r=\frac{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{ \sum\limits_{i=1}^{n}{(x_{i}-\overline{x})^{2}}}\sqrt{\sum\limits_{i=1}^{n}{(y_ {i}-\overline{y})^{2}}}} \tag{1}\]  
where \(x_{i}\) and \(y_{i}\) (\(i\) = 1,2,...,\(n\)) are the values of the AQI and the load.  
According to the raw data of Figure 4, the correlation coefficient \(r\) = 0.7164, which indicates that the AQI and daily residential load have a relatively strong positive correlation. Residents consciously stay home under F-H weather to keep healthy; therefore, residential load would increase to some degree.  
In all, industrial load is the main controllable load directly affected by emergency warning policies under F-H weather. The total power consumption of the whole Chinese society in the first quarter of 2014 was 1.28 \(\times\) 10\({}^{14}\) kW, a year-to-year growth of 5.4%, the growth rate of which increased by 1.1%. However, the growth rate dropped by 3% from the last quarter of 2013, because some industries with heavy pollution and high energy consumption were forced to reduce production or shut down by the government of North China to control F-H weather.  
For example, the AQI values of Baoding, China, from 17-28 November 2013 and the daily total load (including industrial load, residential load, commercial load, _etc._) of a region in Baoding, China, during the same period are shown in Figure 5.  
Figure 4: Daily load of a residential quarter in Baoding, China, from 20–29 December 2014.  
Figure 5: Daily total load of a region in Baoding, China, from 17–28 November 2013.  
According to the raw data of Figure 5, the correlation coefficient \(r=-0.8230\), which indicates that the AQI and daily total load have a relatively strong negative correlation, and the accuracy would be improved to some degree if the AQI factor is considered in the load forecast.