The Optimal Dispatch of a Power System Containing Virtual Power Plants under Fog and Haze Weather

Abstract: With the growing influence of fog and haze (F-H) weather and the rapid development of distributed energy resources (DERs) and smart grids, the concept of the virtual power plant (VPP) employed in this study would help to solve the dispatch problem caused by multiple DERs connected to the power grid. The effects of F-H weather on photovoltaic output forecast, load forecast and power system dispatch are discussed according to real case data. The wavelet neural network (WNN) model was employed to predict photovoltaic output and load, considering F-H weather, based on the idea of “similar days of F-H”. The multi-objective optimal dispatch model of a power system adopted in this paper contains several VPPs and conventional power plants, under F-H weather, and the mixed integer linear programming (MILP) and the Yalmip toolbox of MATLAB were adopted to solve the dispatch model. The analysis of the results from a case study proves the validity and feasibility of the model and the algorithms.


Introduction
Challenges in the energy industry, such as rapidly growing demands for electricity, low efficiency of energy utilization and deteriorating environmental conditions, have attracted increasing global attention.Currently, thermal power plants (TPPs) of multiple sizes located all over the country are the major generators of power in China's electricity market.TPPs are characterized by a high consumption of coal resources, which is one of the main factors of air pollution.The air pollution, which contains harmful gases, solid particles in the air and the greenhouse effect resulting from excessive emissions of CO 2 , has affected people's livelihood and caused many problems in the operation, maintenance and dispatch control of power systems.
The air quality in China continues to deteriorate, and fog and haze weather (F-H) has become a new weather condition that is attracting much attention by the government and the public because its influence area has gradually increased.In 2013, more than 100 cities in 25 provinces in China, which represent 25% of the national territorial area, were covered by F-H [1].The severity level of F-H can be quantitatively described by the Air Quality Index (AQI), which is a dimensionless index calculated by the contents of SO 2 , CO 2 , PM10 (inhalable particle matter, diameter <10 µm), PM2.5 (fine particulate matter, diameter <2.5 µm), CO and O 3 [2].The AQI level (L AQI ) ranges from Level 1-Level 6 (0-50, 51-100, 101-150, 151-200, 201-300 and >300), which correspond to excellent condition, good condition, slight pollution, moderate pollution, severe pollution and serious pollution.People should consciously avoid outdoor activities when L AQI is above Level 4, especially children, the elderly and patients with heart, respiratory and lung diseases.generations (DGs), fees of battery aging and system power balance constraints [9,10].On the other hand, the methods by which the VPP internally controls the aggregated DERs, based on a mathematical programming model and a multi-agent system, have been researched, as well [6,11].The internal control of the VPP has three different structures: centralized structure (all of the information of the power generation and consumption is available to the VPP center), centralized-decentralized structure (there are several subordinate control units of the VPP center) and decentralized structure (the information transformation relies on the multi-agent system).In conclusion, previous studies emphatically researched measures for capacity allocation, coordinated operation, operation control and market bidding participation to maximize the benefits of VPPs or power systems from the perspective of VPPs.In this paper, the VPP dispatch strategies at the grid level that consider the impacts of F-H weather are discussed.
F-H weather would still exist in vast areas of China, and strategies of the operation, maintenance, prediction and dispatch control of power systems under F-H weather need improving.As for the predictions, the early studies about photovoltaic output and load forecasts only consider traditional meteorological factors, such as temperature, humidness and all kinds of weather types, rarely focusing on F-H [12,13].The literature [14] has proven that illumination intensity is directly blocked by F-H, and the instantaneous output and effective operating time of photovoltaic panels (PV panels) are greatly restricted.Residents' modes of production and life are affected by F-H, as well.People would stay indoors for health reasons, and industries with high energy consumption and high emission would be shut down by the government's contingency plan to reduce pollutant emission when the air is seriously polluted [15].Therefore, a suitable prediction model that considers the F-H factor is urgently needed, which would increase the reliability of photovoltaic output and load forecasts.Besides, the power system control center should distribute more power load to the generation with low emission during dispatch periods when L AQI is high, yet this has been addressed by few studies.
In this paper, the impacts of F-H on photovoltaic output and power load are first analyzed, and the wavelet neural network (WNN) model is adopted to predict photovoltaic output and load under F-H, based on the idea of similar days of F-H.On that basis, the power system multi-objective optimal dispatch model containing VPPs under F-H is employed to achieve the goals of energy conservation and emission reduction.The main contents in this paper comprise the following six parts: F-H impacts on photovoltaic output and load forecasts (Section 2); the dispatch of power systems containing VPPs (Section 3); the mathematical model of dispatch under F-H weather (Section 4); solving the optimal dispatch model based on mixed integer linear programming (MILP) (Section 5); case study (Section 6); conclusions (Section 7).

F-H Impacts on Photovoltaic Output and Load Forecasts
On 7 December 2015, the Moderate Resolution Imaging Spectroradiometer on NASA's Aqua satellite captured an image of eastern China being inundated by thick F-H, seen in the gray area of Figure 1.(shut-down) costs of distributed generations (DGs), fees of battery aging and system power balance constraints [9,10].On the other hand, the methods by which the VPP internally controls the aggregated DERs, based on a mathematical programming model and a multi-agent system, have been researched, as well [6,11].The internal control of the VPP has three different structures: centralized structure (all of the information of the power generation and consumption is available to the VPP center), centralized-decentralized structure (there are several subordinate control units of the VPP center) and decentralized structure (the information transformation relies on the multi-agent system).In conclusion, previous studies emphatically researched measures for capacity allocation, coordinated operation, operation control and market bidding participation to maximize the benefits of VPPs or power systems from the perspective of VPPs.In this paper, the VPP dispatch strategies at the grid level that consider the impacts of F-H weather are discussed.F-H weather would still exist in vast areas of China, and strategies of the operation, maintenance, prediction and dispatch control of power systems under F-H weather need improving.As for the predictions, the early studies about photovoltaic output and load forecasts only consider traditional meteorological factors, such as temperature, humidness and all kinds of weather types, rarely focusing on F-H [12,13].The literature [14] has proven that illumination intensity is directly blocked by F-H, and the instantaneous output and effective operating time of photovoltaic panels (PV panels) are greatly restricted.Residents' modes of production and life are affected by F-H, as well.People would stay indoors for health reasons, and industries with high energy consumption and high emission would be shut down by the government's contingency plan to reduce pollutant emission when the air is seriously polluted [15].Therefore, a suitable prediction model that considers the F-H factor is urgently needed, which would increase the reliability of photovoltaic output and load forecasts.Besides, the power system control center should distribute more power load to the generation with low emission during dispatch periods when LAQI is high, yet this has been addressed by few studies.
In this paper, the impacts of F-H on photovoltaic output and power load are first analyzed, and the wavelet neural network (WNN) model is adopted to predict photovoltaic output and load under F-H, based on the idea of similar days of F-H.On that basis, the power system multi-objective optimal dispatch model containing VPPs under F-H is employed to achieve the goals of energy conservation and emission reduction.The main contents in this paper comprise the following six parts: F-H impacts on photovoltaic output and load forecasts (Section 2); the dispatch of power systems containing VPPs (Section 3); the mathematical model of dispatch under F-H weather (Section 4); solving the optimal dispatch model based on mixed integer linear programming (MILP) (Section 5); case study (Section 6); conclusions (Section 7).

F-H Impacts on Photovoltaic Output and Load Forecasts
On 7 December 2015, the Moderate Resolution Imaging Spectroradiometer on NASA's Aqua satellite captured an image of eastern China being inundated by thick F-H, seen in the gray area of Figure 1.As shown in Figure 1, the thick F-H would certainly block out sunlight, which would affect the output of PV panels to a great extent.The previous day in Beijing, the Chinese government issued a first-ever "red alert" for the city, which resulted in power plant and factory closures and the change of power load.
The generation output forecast (photovoltaic power, wind power, thermal power, etc.) and load forecast of power systems are the basic tasks of dispatching, in which improved prediction accuracy would efficiently reduce the complexity and uncertainty of dispatch control to ensure the system's safe, economic and green operation.The impacts of F-H on photovoltaic output and power load are discussed as follows.

The Influence of F-H on Photovoltaic Output
The discontinuity, instability and uncertainty issues surrounding photovoltaic output are directly affected by meteorological factors, in which different weather conditions lead to different incident light intensity on PV panels.The incident light on PV panels is weakened only by atmosphere and clouds when no F-H is present.Otherwise, some light intensity is reflected and absorbed by F-H.Light intensity and photovoltaic output are further weakened with a high AQI level.Moreover, more dust appears on PV panels with increasing AQI level, which greatly restricts photoelectric conversion efficiency, as well.Thus, timely dust cleaning is needed.
The AQI values of Baoding, China, from 24-26 February 2015 are shown in Table 1, and the photovoltaic outputs of the polycrystalline silicon photovoltaic array (PSPA, 10 kW) in the State Key Laboratory of New Energy Power System (SKL of NEPS) at the North China Electric Power University (NCEPU, Baoding) during the same period are shown in Figure 2.  As shown in Figure 1, the thick F-H would certainly block out sunlight, which would affect the output of PV panels to a great extent.The previous day in Beijing, the Chinese government issued a first-ever "red alert" for the city, which resulted in power plant and factory closures and the change of power load.
The generation output forecast (photovoltaic power, wind power, thermal power, etc.) and load forecast of power systems are the basic tasks of dispatching, in which improved prediction accuracy would efficiently reduce the complexity and uncertainty of dispatch control to ensure the system's safe, economic and green operation.The impacts of F-H on photovoltaic output and power load are discussed as follows.

The Influence of F-H on Photovoltaic Output
The discontinuity, instability and uncertainty issues surrounding photovoltaic output are directly affected by meteorological factors, in which different weather conditions lead to different incident light intensity on PV panels.The incident light on PV panels is weakened only by atmosphere and clouds when no F-H is present.Otherwise, some light intensity is reflected and absorbed by F-H.Light intensity and photovoltaic output are further weakened with a high AQI level.Moreover, more dust appears on PV panels with increasing AQI level, which greatly restricts photoelectric conversion efficiency, as well.Thus, timely dust cleaning is needed.
The AQI values of Baoding, China, from 24-26 February 2015 are shown in Table 1, and the photovoltaic outputs of the polycrystalline silicon photovoltaic array (PSPA, 10 kW) in the State Key Laboratory of New Energy Power System (SKL of NEPS) at the North China Electric Power University (NCEPU, Baoding) during the same period are shown in Figure 2.   As shown in Table 1 and Figure 2, the daily photovoltaic outputs (kW) of 24 February, 25 February and 26 February are 34.31(L AQI = 2), 43.64 (L AQI = 4) and 58.06 (L AQI = 6), which indicates that photovoltaic output decreases with increasing AQI level.
In addition, the number of effective power generating hours (NEPGH) of PV panels may decrease with increasing F-H, which could also reduce photovoltaic output.Data from an empirical research platform of a photovoltaic system at the Chinese Academy of Sciences (Shanghai) indicated that the NEPGH was 2.79 on 4 December 2013 when F-H did not exist.However, the NEPGH was reduced to only 0.7, which was a reduction of 74.91%, on 6 December 2013, when the air condition included severe pollution.Therefore, the impact of F-H should be considered during the prediction process of photovoltaic output.

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 Table 1 and Figure 2, the daily photovoltaic outputs (kW) of 24 February, 25 February and 26 February are 34.31(LAQI = 2), 43.64 (LAQI = 4) and 58.06 (LAQI = 6), which indicates that photovoltaic output decreases with increasing AQI level.
In addition, the number of effective power generating hours (NEPGH) of PV panels may decrease with increasing F-H, which could also reduce photovoltaic output.Data from an empirical research platform of a photovoltaic system at the Chinese Academy of Sciences (Shanghai) indicated that the NEPGH was 2.79 on 4 December 2013 when F-H did not exist.However, the NEPGH was reduced to only 0.7, which was a reduction of 74.91%, on 6 December 2013, when the air condition included severe pollution.Therefore, the impact of F-H should be considered during the prediction process of photovoltaic output.

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.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.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.
where xi and yi (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 × 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.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.
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 ˆ10 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.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.
where xi and yi (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 × 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.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.

Selection of "Similar Days of F-H"
The prediction accuracy of photovoltaic output and load forecasts would improve to some degree if input data were selected from days with a similar temperature, light intensity, weather type, day type, etc.The above analysis indicates that there are great similarities in photovoltaic outputs (or loads) under the same AQI level, which cannot be ignored.Therefore, the idea of similar days of F-H is introduced in this paper, which emphasizes F-H weather based on the former research.
(1) Select similar days of F-H for photovoltaic output: Step 1. Data preprocessing: The order of magnitudes of different data varies greatly, which makes it difficult for any model to implement predictions.Therefore, data should be normalized or mapped to the range of [0,1] before calculating according to Formula (2): where X is one of the samples; X max and X min are the maximal and minimal values of samples; Y is the normalized value of X.
Step 2. Principal component analysis (PCA): Traditional methods to select similar days need more calculation time on account of the enormous raw data volume.The PCA is a statistical method that could convert multiple variables X i (i = 1,2, . . .,n) into a few comprehensive independent variables Y k (k = 1,2, . . .,m), as shown in Formula (3): where n and m are the numbers of variables X and Y, and m is set according to demand; Y C is the integrative factor; a ki (k = 1,2, . . .,m, i = 1,2, . . .,n) are principal component coefficients; and v k (k = 1,2, . . .,m) are component contribution rates, the calculations of which could refer to [15,16].
The integrative factor Y C , which reflects the summarized information of original data and deletes unimportant factors, could replace original photovoltaic output in the following analysis.
Step 3. Grey correlation analysis (GCA): In order to select similar days, the correlations between photovoltaic output and relative factors need to be analyzed first.The GCA, which has a good effect to solve the problem of multi-variables without obvious regularity, is a mature theory in this field and employed in this section [15,17].
The values of the integrative factors Y C of the photovoltaic outputs form a basic sequence y, and the relative factors form compared sequences z i (i = 1,2, . . .,p), the curve similarities of which reflect the degrees of relation.
y " typkq |k " 1, 2, ¨¨¨n u , z i " tz i pkq |k " 1, 2, ¨¨¨n u where ∆ i (k) min and ∆ i (k) max are the minimal and maximal values of ∆ i (k); ρP(0, 8) is the distinguish coefficient; n is the sequence length; p is the number of compared sequences; γ i is the degree of correlation between y and z i .
Step 4. Weighted similarity formula (WSF): The WSF combined with all values of the degree of relation in Step 3 is adopted to calculate the degree of similarity sim(k) between the day to predict and a given historical day [15].
where p is the number of relative factors; n is the number of historical days; z i (k) is the normalized value of the i-th factor on day k; z i (0) is the normalized value of the i-th factor of the day to predict; θ i is the weight of the relevant factor; γ i is the degree of correlation above.
The sample data are sorted in descending order according to the similarity, and the front days would be selected as the similar days of the predicted day.
(2) Select similar days of F-H for load: Step 1. Data preprocessing: The factors that affect load mainly include the AQI value, temperature, humidity, weather type and day type.The factor data should be normalized or mapped to the range of [0,1] before calculation.The relation of day types, which include workdays and weekends, and their values are shown as follows: workday, 0.3; weekend, 0.8.In addition, emergency warning levels are added into the factors because the load would be greatly influenced by emergency warning policies: yellow alert, 0.3; orange alert, 0.6; red alert, 0.9; and none, 0.
Step 2-Step 4 are the same as above.

Prediction Model of the Wavelet Neural Network
There are various prediction models and algorithms suitable for photovoltaic output and load forecasts, such the artificial neural network (ANN) and its modified versions, the support vector machine, the extreme learning machine, etc.In this section, the WNN model that combines the ANN and the wavelets theory is selected to be the predictor because it is familiar to our team and it has the following advantages [18][19][20][21][22]: (1) The ANN has characteristics such as self-learning, self-adaption and fault tolerance, and it is a universal function approximator.
(2) The motif and the whole structure of the WNN are set according to the theory of wavelet analysis, which could effectively extract the local information of the signal by multiresolution analysis and avoid the blindness of the structure design of the back propagation (BP) neural network.
(3) The WNN model has better learning ability and higher accuracy.In the same prediction tasks, the WNN with a simpler network structure possesses faster convergence speed.
The concepts of the ANN, the BP neural network and the wavelets theory are explained as follows to form the basic foundation framework of the WNN.
(1) Artificial neural network: The ANN is a mathematical model that has the ability of parallel distributed information processing, based on the representation of neural activity in the human brain [18].The most popular design for the ANN is the multi-layer feed forward network, which has an input layer, an output layer and one or more hidden layers.Each layer has a number of nodes or neurons, which consist of multiple inputs and a single output.A weight is associated with each input, while the input signal is multiplied by these weights.The neuron is responsible for the combination of these weighted inputs, and in accordance with an activation function, the output is determined.
(2) Back propagation neural network: The BP neural network is a feed forward neural network, the signals of which are transmitted forward while the errors in reverse.Its basic learning rule is the steepest descent method, which minimizes the sum of squared errors according to the back-propagation to continuously adjust the weights and thresholds of the network [19].
(3) Wavelets theory: The popularity of wavelets with compact supports is due mainly to their relation to the dyadic multiresolution analysis that dominates wavelet research [20].Historically, the continuous wavelet transform came first, which is defined as below: where φ(a, b) is a mother wavelet from which a family of wavelet daughters is obtained by scaling and translating it, thus by changing b (controlling the location) and a (determining the width of the wavelet and the frequency resolution).
(4) Wavelet neural network: The WNN, based on the topology of the BP neural network, selects a certain wavelet basis function as the transfer function of nodes in the hidden layer, where the signal propagates forward while the error returns [21,22].The basic structure of the WNN is shown in Figure 6.
The ANN is a mathematical model that has the ability of parallel distributed information processing, based on the representation of neural activity in the human brain [18].The most popular design for the ANN is the multi-layer feed forward network, which has an input layer, an output layer and one or more hidden layers.Each layer has a number of nodes or neurons, which consist of multiple inputs and a single output.A weight is associated with each input, while the input signal is multiplied by these weights.The neuron is responsible for the combination of these weighted inputs, and in accordance with an activation function, the output is determined.
(2) Back propagation neural network: The BP neural network is a feed forward neural network, the signals of which are transmitted forward while the errors in reverse.Its basic learning rule is the steepest descent method, which minimizes the sum of squared errors according to the back-propagation to continuously adjust the weights and thresholds of the network [19].
(3) Wavelets theory: The popularity of wavelets with compact supports is due mainly to their relation to the dyadic multiresolution analysis that dominates wavelet research [20].Historically, the continuous wavelet transform came first, which is defined as below: where ϕ(a, b) is a mother wavelet from which a family of wavelet daughters is obtained by scaling and translating it, thus by changing b (controlling the location) and a (determining the width of the wavelet and the frequency resolution).
(4) Wavelet neural network: The WNN, based on the topology of the BP neural network, selects a certain wavelet basis function as the transfer function of nodes in the hidden layer, where the signal propagates forward while the error returns [21,22].The basic structure of the WNN is shown in Figure 6.As shown in Figure 6, X 1 , X 2 , . . ., X n are inputs of the WNN; H 1 , H 2 , . . ., H l are outputs of the nodes of the hidden layer; Y 1 , Y 2 , . . ., Y m , are outputs of the forecast; and n, l and m are the node numbers of the input layer, hidden layer and output layer.
If the input signals are x i (i = 1,2, . . .,n), the output h(j) of node j in the hidden layer is shown as follows: where w ij is the connection weight between node i in the input layer and node j in the hidden layer; h j is the wavelet basis function; and a j and b j are the scalability factor and shift factor of h j .Several wavelet basis functions have been proposed in the wavelets theory.Each basis function has its suitable application.In the WNN model of this paper, the Morlet wavelet, which is a non-orthogonal wavelet base without a scaling function, serves as the wavelet basis function because it is symmetrical and has a simple expression as below: where δ = 1.75, generally.
The output of node k in the output layer is shown as follows: where w jk is the connection weight between node j in the hidden layer and node k in the output layer.
Step 2. Import data on photovoltaic output (or load) and relative factors, which should be normalized or mapped to the range of [0,1].
Step 3. Select similar days of F-H for photovoltaic output (or load) forecast based on the PCA, the GCA and the WSF.
Step 4. Organize photovoltaic output (or load) data of similar days, three days before the day to predict and 3 h before the moment to predict to form the input and output data of the WNN.
Step 5. Initialize the parameters of the WNN, according to demand, such as node numbers (n, l and m), connection weights (w ij , w jk ), wavelet parameters (a j and b j ), error limit (e 0 ), iteration precision (∆y 0 ) and maximum number of iterations (N max ).
Step 6. Repeatedly train the WNN through input and output data, according to Formulas (10) and (11).When the total forecast error e < e 0 or the iteration number r > N max , the training stops, and the network parameters that have a better fitting capacity for the original data are obtained.
where y 0 (k) is the real values; η 1 , η 2 , η 3 and η 4 are the learning rates of w ij , w jk , a j and b j , which are set according to demand.
Step 7. Conduct the forecast for photovoltaic output (or load) using the WNN trained by Step 6 and analyze the results.
Step 8.The mean absolute percentage error (MAPE) and the mean squared error (MSE) are employed in this section to evaluate the forecast accuracy, which are shown as Formulas ( 12) and ( 13): where N is the number of samples; y i is the real value; y' i is the forecast value.
The MAPE and the MSE will be small if the predicted values are very close to the true values and will be large if for some of the observations, the predicted and true values differ substantially.

The Construction of the VPP
The DERs that form the VPP could be the same or diverse, and their layout may be either concentrated or scattered.Information networks and high-level software architecture are employed inside the VPP to connect and control DERs.Therefore, there is no need to change the grid-connected structure and the distributed topology of DERs.
The construction of a VPP that consists of various DERs is shown in Figure 7.
Sustainability 2016, 8, 71 11 of 22 Step 8.The mean absolute percentage error (MAPE) and the mean squared error (MSE) are employed in this section to evaluate the forecast accuracy, which are shown as Formulas ( 12) and ( 13): where N is the number of samples; yi is the real value; y'i is the forecast value.
The MAPE and the MSE will be small if the predicted values are very close to the true values and will be large if for some of the observations, the predicted and true values differ substantially.

The Construction of the VPP
The DERs that form the VPP could be the same or diverse, and their layout may be either concentrated or scattered.Information networks and high-level software architecture are employed inside the VPP to connect and control DERs.Therefore, there is no need to change the grid-connected structure and the distributed topology of DERs.
The construction of a VPP that consists of various DERs is shown in Figure 7.As shown in Figure 7, DERs that form the VPP in this paper could be wind power plants (WPP), photovoltaic power plants (PPP), demand side resources (DSR), electric vehicle charging stations (EVCS), distributed energy storage (DES), etc.The output of a VPP is the sum of all DER outputs, which can be predicted separately, inside the VPP.The characteristics of different DERs could be complementary, and the uncertainties could be offset to some degree, which gives the VPP better external characteristics, similar to conventional power plants, than scattered DERs.

The Dispatch Model Containing VPPs
The schematic diagram of VPPs participating in the dispatch is shown in Figure 8.As shown in Figure 7, DERs that form the VPP in this paper could be wind power plants (WPP), photovoltaic power plants (PPP), demand side resources (DSR), electric vehicle charging stations (EVCS), distributed energy storage (DES), etc.The output of a VPP is the sum of all DER outputs, which can be predicted separately, inside the VPP.The characteristics of different DERs could be complementary, and the uncertainties could be offset to some degree, which gives the VPP better external characteristics, similar to conventional power plants, than scattered DERs.

The Dispatch Model Containing VPPs
The schematic diagram of VPPs participating in the dispatch is shown in Figure 8.The VPP, as an autonomous entity, connects to the power grid just like other conventional power plants (CPP), such as thermal power plants (TPP), hydraulic power plants (HPP), geothermal power plants (GPP) and nuclear power plants (NPP).After the process of output prediction, the VPP uploads its output and other relevant information to the dispatch center and the electricity market through information and communication technology and receives instructions from the system.
Energy conservation and emissions reduction are the main objectives of the power system in the dispatch considering F-H weather.On the premise of satisfying the needs of the total load, the system preferentially takes in power generated by units with low emission and restricts (or even shuts down) units with high emission to some degree according to the operational constraints and economic characteristics of the units.In addition, several economic incentive measures are taken to encourage the development of new clean energy, such as wind power and photovoltaic power.Therefore, the VPP demonstrates its priority in dispatch via its advantage of low pollution and policies of fiscal subsidies.Generally, the higher the AQI level is, the more obvious the VPP's priority.

The Mathematical Model of Dispatch under F-H Weather
A multi-objective optimal dispatch model of a power system, containing several VPPs and conventional power plants (take the TPP as an example), is employed in this paper, comprehensively counting four objective functions (f1-f4) and six constraints (C0-C5) [23][24][25][26][27].
where M is the number of thermal power units; T is the number of time intervals during the dispatch period; PGi,t and Ai(PGi,t) are the output and generation cost of unit i in period t; IGi,t is the running state of unit i in period t, with unit i on/off in period t when IGi,t = 1/0; aQi, bQi and cQi are the cost coefficients (constants) of unit i; SUi,t and SDi,t are the start-up and shut-down costs of unit i in period t; CSUi and CSDi are the cost coefficients of the start-up and shut-down of unit i; and yGi,t = 1 (zGi,t = 1) means that unit i is in the process of start-up (shut-down) in period t; otherwise, yGi,t = 0 (zGi,t = 0).The relations among yGi,t, zGi,t and IGi,t (constraints C0) are shown as Formula (15), which are additional equality constraints (C01) and inequality constraints (C02), because of the added variables (yGi,t and zGi,t).The VPP, as an autonomous entity, connects to the power grid just like other conventional power plants (CPP), such as thermal power plants (TPP), hydraulic power plants (HPP), geothermal power plants (GPP) and nuclear power plants (NPP).After the process of output prediction, the VPP uploads its output and other relevant information to the dispatch center and the electricity market through information and communication technology and receives instructions from the system.
Energy conservation and emissions reduction are the main objectives of the power system in the dispatch considering F-H weather.On the premise of satisfying the needs of the total load, the system preferentially takes in power generated by units with low emission and restricts (or even shuts down) units with high emission to some degree according to the operational constraints and economic characteristics of the units.In addition, several economic incentive measures are taken to encourage the development of new clean energy, such as wind power and photovoltaic power.Therefore, the VPP demonstrates its priority in dispatch via its advantage of low pollution and policies of fiscal subsidies.Generally, the higher the AQI level is, the more obvious the VPP's priority.

The Mathematical Model of Dispatch under F-H Weather
A multi-objective optimal dispatch model of a power system, containing several VPPs and conventional power plants (take the TPP as an example), is employed in this paper, comprehensively counting four objective functions (f 1 -f 4 ) and six constraints (C 0 -C 5 ) [23][24][25][26][27].

Objective Functions
(1) Minimizing generation cost and start-up (shut-down) cost of TPPs: where M is the number of thermal power units; T is the number of time intervals during the dispatch period; P Gi,t and A i (P Gi,t ) are the output and generation cost of unit i in period t; I Gi,t is the running state of unit i in period t, with unit i on/off in period t when I Gi,t = 1/0; a Qi , b Qi and c Qi are the cost coefficients (constants) of unit i; SU i,t and SD i,t are the start-up and shut-down costs of unit i in period t; C SUi and C SDi are the cost coefficients of the start-up and shut-down of unit i; and y Gi,t = 1 (z Gi,t = 1) means that unit i is in the process of start-up (shut-down) in period t; otherwise, y Gi,t = 0 (z Gi,t = 0).
The relations among y Gi,t , z Gi,t and I Gi,t (constraints C 0 ) are shown as Formula (15), which are additional equality constraints (C 01 ) and inequality constraints (C 02 ), because of the added variables (y Gi,t and z Gi,t ).
Gaseous pollutants, such as SO 2 , NO x , PM10 and PM2.5, are the main emissions considered in this paper.The concept of nominal environmental compensation cost is introduced to transform the pollutant emission of the thermal power unit into emission cost.
B i pP Gi,t q ¨IGi,t s, B i pP Gi,t q " a Wi ¨pP Gi,t q 2 `bWi ¨PGi,t `cWi (16) where B i (P Gi,t ) is the emission amount of unit i in period t; a Wi , b Wi and c Wi are the pollutant discharge coefficients of unit i; and C Fi is the cost coefficient of pollutant emissions of unit i.
In addition, the AQI level (L AQI ), as a penalty term, is added to the calculation of C Fi to consider the effect of F-H in the dispatch.The economic punishment varies with L AQI and the emission characteristic of the unit; namely, a unit with heavier pollution would receive more serious punishment when L AQI is higher.
where ϕ(L AQI ) is the growth factor function of emission cost and C Bi is the cost coefficient of the pollutant emission of unit i when L AQI = 1 (the air condition is excellent); namely, ϕ(1) = 1 and C Fi = C Bi .Generally, the worse the emission characteristics of a unit is, the larger the C Bi value, which causes the unit to stay in an inferior position in the dispatch considering the environmental benefits.Therefore, it could be deduced according to the above analysis that ϕ(L AQI ) might be an increasing function, which would be supposed to be a linear one since there are no studies on this expression.ϕpL AQI q " 1 `α ¨pL AQI ´1q, L AQI " 1, 2, ..., 6 (18) where α is the empirical value of the proportionality coefficient of ϕ(L AQI ), obtained from the comprehensive analysis of the policies, F-H condition and emission characteristic of the units.
Carbon emission is namely greenhouse gas emission, which mainly includes CO 2 , N 2 O, CH 4 and O 3 .Only CO 2 is discussed in this paper, because the other greenhouse gases could be converted into CO 2 equivalent.
where C Xi , c ei and e Gi are the cost coefficient of carbon emission, the coal consumption rate and the carbon discharge coefficient of unit i.
It is assumed that the generation cost of a DER and that of its output have a linear relationship to simplify the dispatch model, based on a comprehensive consideration of the basic construction cost, operation and maintenance costs and control cost of DERs.Similarly, the generation cost and output of a VPP have a linear relationship.
where n is the number of VPPs; w k is the generation cost coefficient of VPP k ; P VPPk,t is the output of VPP k in period t; m k is the number of DERs inside VPP k ; δ k,j is the capacity proportion of DER j inside VPP k ; and w k,j (constant) is the generation cost coefficient of DER j inside VPP k .Therefore, w k would be a constant if the types of DERs and δ k,j are known.
where P Dt is the total load in period t.
P min´Gi ¨IGi,t ď P Gi,t ď P max´Gi ¨IGi,t , P min´VPPk ď P VPPk,t ď P max´VPPk i " 1, 2, ..., M, t " 1, 2, ..., T, k " 1, 2, ..., n where P min´Gi and P max´Gi are the minimum and maximum outputs of thermal power unit I; the counterparts of VPP k are P min´VPPk and P max´VPPk .
where S Dt is the total system reserve in period t.
The VPP is in the running state all of the time, except during maintenance in the dispatch period, so the start/stop constraints consider only TPPs.These constraints are expressed as minimal on/off time limits in published research works, which are transformed into maximal start/stop counts to simplify the complexity of calculation in this paper.
where J max´i is the maximum start/stop count of unit i.

Solving the Optimal Dispatch Model Based on MILP
Mixed integer linear programming (MILP) [24] and the MATLAB toolbox Yalmip are employed to solve the above multi-objective optimal dispatch model.The MILP, which has no iteration process, is good at handling power system optimal dispatch problems because of its nice astringency, good optimality and simple expression of constraints.Yalmip is a free toolbox developed by Lofberg, and the greatest advantage lies in its simple and general modeling language.

Model Simplification
The objectives in this paper are all about costs that could be added up to form a total cost; the linear weighted sum method [28] is adopted to simplify the calculation in the early study.
where X and F are the decision variable set and the comprehensive objective function; β r is the weight of f r ; C 0 -C 5 are constraints; H p (p = 1,2, . . .,MT+T) are equality constraints; G q (q = 1,2, . . .,Q) are inequality constraints; and Q is the number of inequality constraints.Usually, the selections of the weights depend on the choices of the decision maker or field practical experience.Besides, Formula ( 27) is adopted to calculate weights, as well.
where f r (X * ) is the optimal value of the single objective problem of f r (X).

Linearization of Objective Functions
The objectives, such as generation cost and emission of thermal power units, could be linearized based on the piecewise linearization, which has better performance on the functions with low nonlinearity degree, to fit the solver Yalmip and simplify the calculation [25].The linearization formulas are shown as follows: (28) where x min and x max are the minimum and maximum values of variable x; X u is the value of the segment point of segment u; U is the number of segments; and k u is the slope of segment u.
If x is in segment u (X u´1 ď x ď X u ):

Model Solving
The Yalmip toolbox is employed on the MATLAB 2014a platform to solve a power system optimal dispatch model containing VPPs under F-H weather, according to the steps as follows: Step 1. Start; Step 2. Import data of load, AQI level (L AQI ), outputs and relative information of thermal power units and VPPs, basic parameters of DERs inside VPPs and other useful information; Step 3. Define column vector X of unknown variables and calculate row vector V of coefficients of the comprehensive objective function according to Formula (26): F = V ˆX; Step 4. Set all constraints W according to Formula (26): W = W + set(C i ), i = 1,2,...,5; Step 5. Set the empirical value of proportionality coefficient α of ϕ(L AQI ) according to Formula (18); Step 6. Solve the model by the Yalmip toolbox in MATLAB: result = solvesdp(W, F); Step 7. Export results and analyze; Step 8. End.

Photovoltaic Output and Load Forecasts under F-H
According to the methods mentioned in Section 2, the data of the AQI value, temperature (minimum and maximum), weather type, day type, photovoltaic output and load of a certain region in Baoding, China, during the period from 1 December 2013-26 March 2014 were gathered to conduct photovoltaic output and load forecasts.To verify the analysis of the influence of F-H, the prediction results of 27 March 2014 (AQI = 305, overcast) are shown as follows (both considering and ignoring F-H).
As shown in Figure 9, the red curve (with AQI) is closer to the black curve (real value) than the blue curve (without AQI); in Table 2, the MAPE and the MSE with AQI are much smaller than those without AQI, which indicates that the prediction accuracy of the photovoltaic output is higher if F-H is considered.Step 5. Set the empirical value of proportionality coefficient α of φ(LAQI) according to Formula (18); Step 6. Solve the model by the Yalmip toolbox in MATLAB: result = solvesdp(W, F); Step 7. Export results and analyze; Step 8. End.

Photovoltaic Output and Load Forecasts under F-H
According to the methods mentioned in Section 2, the data of the AQI value, temperature (minimum and maximum), weather type, day type, photovoltaic output and load of a certain region in Baoding, China, during the period from 1 December 2013-26 March 2014 were gathered to conduct photovoltaic output and load forecasts.To verify the analysis of the influence of F-H, the prediction results of 27 March 2014 (AQI = 305, overcast) are shown as follows (both considering and ignoring F-H).
As shown in Figure 9, the red curve (with AQI) is closer to the black curve (real value) than the blue curve (without AQI); in Table 2, the MAPE and the MSE with AQI are much smaller than those without AQI, which indicates that the prediction accuracy of the photovoltaic output is higher if F-H is considered.As shown in Figure 10, the blue curve (without AQI) is higher on average than the black curve (real value), especially in the period of peak load, while the red curve (with AQI) is closer to the black curve; in Table 3, the MAPE and the MSE with the AQI are also smaller than those without AQI, which indicates that the prediction accuracy of the load is higher if F-H is considered.
In other words, the prediction accuracy is higher because photovoltaic outputs and loads of similar days are much closer to those of the day being predicted when the AQI factor is included.During the similar days of F-H, the atmosphere factors, the operating states of PV panels, the electric power consumption of the whole society and the macroscopic readjustment of the Chinese  As shown in Figure 10, the blue curve (without AQI) is higher on average than the black curve (real value), especially in the period of peak load, while the red curve (with AQI) is closer to the black curve; in Table 3, the MAPE and the MSE with the AQI are also smaller than those without AQI, which indicates that the prediction accuracy of the load is higher if F-H is considered.
In other words, the prediction accuracy is higher because photovoltaic outputs and loads of similar days are much closer to those of the day being predicted when the AQI factor is included.During the similar days of F-H, the atmosphere factors, the operating states of PV panels, the electric power consumption of the whole society and the macroscopic readjustment of the Chinese government are similar, as well.The WNN model with better learning ability is able to catch the change pattern of photovoltaic outputs and loads to form more accurate predictions.There are two thermal power units (G1 and G2) and two VPPs (VPP1 and VPP2) 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, LAQI = 6).Some relative parameters of G1 and G2 are listed in Tables 4  and 5. VPP1 consists of a wind power plant (WPP1, 100 MW), a photovoltaic power plant (PPP1, 80 MW) and an efficiency power plant (EPP, 90 MW); VPP2 consists of a WPP (WPP2, 80 MW), a PPP (PPP2, 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  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 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%.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 VPP1 and VPP2, 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, VPP1) or the EVCS (70 MW, VPP2).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%.
It is shown in Figure 12 that 70.35% of daily load is supplied by thermal power units (G1 and G2) with a cost advantage, and the other 29.65% is left for VPPs (VPP1 and VPP2) when F-H is ignored.The reasons could be described as follows.First, G1 and G2 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 VPP1 and  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 1 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.Although G 1 and G 2 could at least run with minimal output at a much higher expense to satisfy the load requirement, they would be shut down if VPPs have larger capacities or there are other units with lower pollution and cost.The curves of variations of cost and emission under different AQI levels are shown in Figure 13 (the proportionality coefficient of the growth factor function of emission cost α = 1.5).It can be seen in Figure 13 that the total cost increases with increasing AQI level (1-6) because the emission cost increases significantly according to Formulas (17) and (18).When the AQI level is smaller than four, G1 and G2 could still afford the rising emission cost.Therefore, the outputs of the units remain unchanged, and the total carbon emission and total pollution emission remain at the same level.However, when the AQI level increases from 4-6, the total carbon emission and pollution emission decrease significantly because G1 and G2 cannot endure a heavy emission The curves of variations of cost and emission under different AQI levels are shown in Figure 13 (the proportionality coefficient of the growth factor function of emission cost α = 1.5).The curves of variations of cost and emission under different AQI levels are shown in Figure 13 (the proportionality coefficient of the growth factor function of emission cost α = 1.5).It can be seen in Figure 13 that the total cost increases with increasing AQI level (1-6) because the emission cost increases significantly according to Formulas (17) and (18).When the AQI level is smaller than four, G1 and G2 could still afford the rising emission cost.Therefore, the outputs of the units remain unchanged, and the total carbon emission and total pollution emission remain at the same level.However, when the AQI level increases from 4-6, the total carbon emission and pollution emission decrease significantly because G1 and G2 cannot endure a heavy emission It can be seen in Figure 13 that the total cost increases with increasing AQI level (1-6) because the emission cost increases significantly according to Formulas (17) and (18).When the AQI level is smaller than four, G 1 and G 2 could still afford the rising emission cost.Therefore, the outputs of the units remain unchanged, and the total carbon emission and total pollution emission remain at the same level.However, when the AQI level increases from 4-6, the total carbon emission and pollution emission decrease significantly because G 1 and G 2 cannot endure a heavy emission punishment and must reduce their outputs to control emission, which allows the clean DERs inside VPPs to be fully used.
The above situations are consistent with the emergency warning policies of the Chinese government.When the air condition is worse than moderate pollution (L AQI > 4), the Chinese government forcibly restricts the outputs of conventional thermal power units (or even shuts them down).Therefore, the method that modifies the emission cost by adding the AQI factor has a certain practical significance and research value.
The curves of variations of cost and emission under different values of α (the proportionality coefficient of the growth factor function of emission cost) are shown in Figure 14 (L AQI = 6).
α is an empirical value that could be drawn from the comprehensive analysis of policies, F-H condition and emission characteristics of the units.It can be seen in Figure 14 that the total cost increases with increasing α according to Formulas (17) and (18).However, the total carbon emission and total pollution emission are not always decreasing.Therefore, an optimal value of α must be selected to both control the total cost and reduce emissions of carbon and pollutants.The optimal value of α is 1.5 (L AQI = 6) in Figure 14, which is adopted in this paper.The above situations are consistent with the emergency warning policies of the Chinese government.When the air condition is worse than moderate pollution (LAQI > 4), the Chinese government forcibly restricts the outputs of conventional thermal power units (or even shuts them down).Therefore, the method that modifies the emission cost by adding the AQI factor has a certain practical significance and research value.
The curves of variations of cost and emission under different values of α (the proportionality coefficient of the growth factor function of emission cost) are shown in Figure 14 (LAQI = 6).α is an empirical value that could be drawn from the comprehensive analysis of policies, F-H condition and emission characteristics of the units.It can be seen in Figure 14 that the total cost increases with increasing α according to Formulas (17) and (18).However, the total carbon emission and total pollution emission are not always decreasing.Therefore, an optimal value of α must be selected to both control the total cost and reduce emissions of carbon and pollutants.The optimal value of α is 1.5 (LAQI = 6) in Figure 14, which is adopted in this paper.

Conclusions
With the growing harmful effects of F-H around China, this paper has employed the WNN prediction model to forecast photovoltaic output and power load based on the analysis of the influence of F-H.On that basis, the concept of the VPP is adopted to handle the dispatch problem of multiple DERs connecting to the power grid, and a multi-objective optimal dispatch model of a power system containing VPPs, with the goals of energy conservation and emission reduction under F-H weather, is constructed based on traditional unit commitment.Several conclusions have been drawn from the above study: (1) The influence of F-H on the photovoltaic output and load forecasts cannot be ignored, and the prediction accuracy could be improved effectively by selecting similar days of F-H to account for the influence of F-H.

Conclusions
With the growing harmful effects of F-H around China, this paper has employed the WNN prediction model to forecast photovoltaic output and power load based on the analysis of the influence of F-H.On that basis, the concept of the VPP is adopted to handle the dispatch problem of multiple DERs connecting to the power grid, and a multi-objective optimal dispatch model of a power system containing VPPs, with the goals of energy conservation and emission reduction under F-H weather, is constructed based on traditional unit commitment.Several conclusions have been drawn from the above study: (1) The influence of F-H on the photovoltaic output and load forecasts cannot be ignored, and the prediction accuracy could be improved effectively by selecting similar days of F-H to account for the influence of F-H.
(2) F-H has a great influence on the power system dispatch with the goals of energy conservation and emission reduction.If the AQI factor is considered, VPPs would generate more electricity, and thermal power units would be restricted, based on the comprehensive consideration of the overall benefit of the power system and macro policies, such as emission punishment, financial subsidies and emergency warning measures.Therefore, clean DERs would be fully used, and air pollution would be controlled to some degree.
(3) The influence of F-H on the output characteristics and control strategies of DERs inside VPPs has not been discussed in this paper; this will be studied in later papers.

Figure 1 .
Figure 1.The spatial distribution of fog and haze of eastern China on 7 December 2015.

Figure 1 .
Figure 1.The spatial distribution of fog and haze of eastern China on 7 December 2015.

Figure 2 .
Figure 2. Photovoltaic outputs of the polycrystalline silicon photovoltaic array (PSPA) (10 kW) in the State Key Laboratory of New Energy Power System (SKL of NEPS) at the North China Electric Power University (NCEPU) from 24-26 February 2015.

Figure 2 .
Figure 2. Photovoltaic outputs of the polycrystalline silicon photovoltaic array (PSPA) (10 kW) in the State Key Laboratory of New Energy Power System (SKL of NEPS) at the North China Electric Power University (NCEPU) from 24-26 February 2015.

Figure 5 .
Figure 5. Daily total load of a region in Baoding, China, from 17-28 November 2013.

Figure 5 .
Figure 5. Daily total load of a region in Baoding, China, from 17-28 November 2013.Figure 5. Daily total load of a region in Baoding, China, from 17-28 November 2013.

Figure 5 .
Figure 5. Daily total load of a region in Baoding, China, from 17-28 November 2013.Figure 5. Daily total load of a region in Baoding, China, from 17-28 November 2013.

Figure 6 .
Figure 6.The basic structure of the wavelet neural network (WNN) prediction model.Based on the strict theoretical background of wavelet analysis and the BP neural network, the WNN is able to adjust the weight and threshold values of the network and the scalability factors and shift factors of the wavelet function, which gives the WNN more sensitive approximation capability and better fault-tolerant capability than the BP neural network.As shown in Figure 6, X1, X2, …, Xn are inputs of the WNN; H1, H2, …, Hl are outputs of the nodes of the hidden layer; Y1, Y2, …, Ym, are outputs of the forecast; and n, l and m are the node numbers of the input layer, hidden layer and output layer.If the input signals are xi (i = 1,2,…,n), the output h(j) of node j in the hidden layer is shown as follows:

Figure 6 .
Figure 6.The basic structure of the wavelet neural network (WNN) prediction model.

Figure 7 .
Figure 7.The construction of a virtual power plant (VPP).DER, distributed energy resource.

Figure 7 .
Figure 7.The construction of a virtual power plant (VPP).DER, distributed energy resource.

Figure 8 .
Figure 8. Schematic diagram of VPPs participating in the dispatch.TPP, thermal power plant; HPP, hydraulic power plant; GPP, geothermal power plant; NPP, nuclear power plant.

Figure 9 .
Figure 9. Result comparison of the photovoltaic output forecast with and without AQI.

Figure 9 .
Figure 9. Result comparison of the photovoltaic output forecast with and without AQI.

Figure 10 .
Figure 10.Result comparison of the load forecast with and without AQI.

Figure 10 .
Figure 10.Result comparison of the load forecast with and without AQI.

Figure 12 .
Figure 12.Comparison of daily dispatch results without and with AQI.

Figure 13 .
Figure 13.Variations of cost and emission under different AQI levels.

Figure 12 .
Figure 12.Comparison of daily dispatch results without and with AQI.

Figure 12 .
Figure 12.Comparison of daily dispatch results without and with AQI.

Figure 13 .
Figure 13.Variations of cost and emission under different AQI levels.

Figure 13 .
Figure 13.Variations of cost and emission under different AQI levels.

Figure 14 .
Figure 14.Variations of cost and emission under different values of α.

Figure 14 .
Figure 14.Variations of cost and emission under different values of α.

Table 2 .
MAPE and MSE of the photovoltaic output forecast.

Table 2 .
MAPE and MSE of the photovoltaic output forecast.

Table 3 .
MAPE and MSE of the load forecast.

Table 4 .
The cost and emission coefficients of G1 and G2.

Table 5 .
The other information of G1 and G2.

Table 3 .
MAPE and MSE of the load forecast.

Table 4 .
The cost and emission coefficients of G 1 and G 2 .

Table 5 .
The other information of G 1 and G 2 .
Therefore, VPP1 and VPP2 gain a higher dispatch priority, because DERs have less or even no pollution, which makes full use of clean energy.Although G1 and G2 could at least run with minimal output at a much higher expense to satisfy the load requirement, they would be shut down if VPPs have larger capacities or there are other units with lower pollution and cost.
Therefore, VPP1 and VPP2 gain a higher dispatch priority, because DERs have less or even no pollution, which makes full use of clean energy.Although G1 and G2 could at least run with minimal output at a much higher expense to satisfy the load requirement, they would be shut down if VPPs have larger capacities or there are other units with lower pollution and cost.