Game-theoretical Energy Management for Energy ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2017.2658952, IEEE Access JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015

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Game-theoretical Energy Management for Energy Internet with Big Data-based Renewable Power Forecasting Zhenyu Zhou, Member, IEEE, Fei Xiong, Biyao Huang, Member, IEEE, Chen Xu, Member, IEEE, Runhai Jiao, Member, IEEE, Bin Liao, Member, IEEE, Zhongdong Yin, Member, IEEE, Jianqi Li, Member, IEEE

Abstract—Energy internet, as a major trend in power system, can provide an open framework for integrating equipments of energy generation, transmission, storage and consumption, etc., so that global energy can be managed and controlled efficiently by information and communication technologies. In this paper, we focus on the coordinated management of renewable and traditional energy, which is a typical issue on energy connections. We consider a conventional power system consisting of the utility company, the energy storage company, the microgrid, and electricity users. Firstly, we formulate the energy management problem as a three-stage Stackelberg game, and every player in the electricity market aims to maximize its individual payoff while guaranteeing the system reliability and satisfying users’ electricity demands. We employ the backward induction method to solve the three-stage non-cooperative game problem, and give the closed-form expressions of the optimal strategies for each stage. Next, we study the big data-based power generation forecasting techniques, and introduce a scheme of the wind power forecasting, which can assist the microgrid to make strategies. Furthermore, we prove the properties of the proposed energy management algorithm including the existence and uniqueness of Nash equilibrium and Stackelberg equilibrium. Simulation results show that accurate prediction results of wind power is conducive to better energy management. Index Terms—energy internet, Stackelberg game, microgrid energy management, wind power forecasting.

I. I NTRODUCTION A. Background and Motivation

D

ESPITE the unprecedented economic development achieved by human society, the world now has faced

Manuscript received XXX; accepted September 19, 2016. C. Xu is the correspondence author ([email protected]). This work was partially supported by the National Science Foundation of China (NSFC) under Grant Number 61601180, 61601181, Fundamental Research Funds for the Central Universities under Grant Number 2016MS17, National Key Research and Development Program of China under Grant Number 2016YFB0101900, and SGRIXTMMXS[2016]586 2016 State Grid Corporation Science and Technology Program: “Research on communication access technology for the integration, protection, and acquisition of multiple new energy resources”. Z. Zhou, F. Xiong, C. Xu, R. Jiao, B. Liao and Z. Yin are with the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China, 102206. (E-mal: zhenyu [email protected], [email protected], [email protected], runhai [email protected], [email protected], zhongdong [email protected]) B. Huang and J. Li are with Global Energy Interconnection Research Institute, State Grid Corporation of China, Beijing, China, 102209. (E-mail: [email protected], [email protected])

several challenging energy issues including energy inefficiency, environmental pollution, energy insecurity, and regional development imbalance [1]. Conventional energy systems are characterized by centralized energy generation and unidirectional energy flows, which are not well suited for high-level integration of distributed and diversified renewable energy sources [2]. Furthermore, due to the monopoly of state-owned energy distribution companies over energy sales, there lacks an effective pricing mechanism to enable the energy consumers to be actively involved in the energy trading process [3]. To address these issues, energy internet has been identified as a key enabler of the third industrial revolution [4], which represents a new paradigm shift for both energy industry and consumers. By analogy with the Internet’s characteristics [5], energy internet provides an open framework for integrating every pieces of equipment involved in energy generation, transmission, distribution, transformation, storage, exchange, and consumption with novel information and communication technologies (ICT) such as internet of things [6], [7], softwaredefined network [8], cloud computing [9], and so on. Thus, it can also be considered as an archetype example of cyber physical system, in which the underlaying physical infrastructures are monitored and controlled efficiently via millions of sensors and actuators in the field [10]. One of the most important capabilities enabled by energy internet is that standard and modular autonomous energy units such as solar panels, wind turbines, electric vehicles, fuel cells, batteries, hydrogen storage, etc., can be controlled through a standardized plug-and-play interface [11]. Open-standardbased communication protocols can also be incorporated into this plug-and-play interface to provide high level of syntactic and semantic interoperability for various products, solutions, technologies, and systems that build up the energy internet [12]. In this new paradigm, the energy provisioning and demand sides are connected more closely and promptly than ever before by implementing distributed and flexible energy production and consumption while hiding the diversity of underlaying technologies through standardized interfaces [13], [14]. In addition, energy consumers with co-located distributed energy sources and distributed energy storage devices within a limited area such as school, office building, industrial park, and residence community, etc., can form a local energy internet, i.e., the microgrid, which provides a promising way of relieving the stress caused by the increasing energy demands and penetrations of renewable energy sources.

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Microgrid is in essence an flexible and efficient network for interconnecting distributed renewable energy sources, load, and intermediate storage units at consumer premise [15]. It can be treated by the grid as a controllable load or generator and can operate in either islanded or grid-connected mode [16]. However, due to the intermittent and fluctuating characteristics of renewable energy sources and limited generation capacity, the large-penetration of uncontrolled and uncoordinated renewable generators into the microgrid especially distribution network will cause a high level of volatility and system disturbances. For an instance, the uncertainties brought by renewable energy sources will lead to significant mismatch between generation and load, which results in numerous critical problems such as power imbalance, interarea oscillations, voltage instability, and frequency fluctuations [17]. Hence, novel energy management methodologies are required to harness the full potentials of the microgrid for reducing the energy supply-demand imbalance by making efficient use of widespread renewable energy resources. Realizing efficient energy management in microgrid is not trivial. First of all, to achieve the optimal economic performance while guaranteeing reliability, various parts inside the energy internet including conventional small-scale fossil fuelbased dispatchable generators and renewable-based distributed generators must be coordinated from a high-logical control level. However, it would be infeasible to take every detail into consideration as the computational complexity increases dramatically with the number of optimization variables and stages [18]. Second, in real-world energy management problems, a small uncertainty, which arises from implementation, estimation, and measurement errors, can sometimes make the solution completely meaningless from a practical viewpoint [19]. For example, considering a microgrid with wind turbines, if the wind speed suddenly becomes stronger, more active power will be injected to the grid, which eventually causes the grid frequency to go up [20]. Last but not least, microgrid alone with limited generation capacity is not capable of satisfying users’ demands, and has to procure energy from alternate sources such as the utility company or the energy storage company, which involves multiple market players and makes the energy management problem more complicated [21]. In reality, each market player , e.g, the utility company, the microgrid, energy storage company, and users, might be selfish and only cares about the individual benefit rather than the total benefit of the overall system. Thus, it is not always possible to simultaneously optimize the objective functions of every market player by using a centralized energy management approach [22].

techniques to obtain the short-term prediction value [23]. Then, we focus on solving the distributed microgrid energy management problem by employing noncooperative game theory [24], which provides an effective mathematical tool for analyzing optimization problems with multiple conflicting objective functions. The major contributions are summarized as follows:

B. Contributions

The structure of this paper is organized as follows: In Section II, we give a brief review of related works on energy management and prediction technologies. The system model of energy management and problem formulation are provided in Section III. Section IV introduces the proposed gametheoretical and data-centric energy management algorithm, and provide the equilibrium analysis of the three-stage Stackelberg game. The simulation results and analyses are presented in

In this paper, in order to efficiently use renewable energy, we study a distributed energy management problem, with the aim of maximizing the individual objective function of each market player while guaranteeing the reliable system operation and satisfying users’ electricity demands. Due to the uncontrollability and uncertainty of renewable generation, we utilize the big data-based renewable power forecasting

•

•

•

We adopt a combination of game-theoretical and datacentric approaches to address the microgrid energy management problem in energy internet. To address the uncertainties brought by wind turbine, we propose a deep learning-based short-term wind power forecasting algorithm by combining stacked auto-encoders (SAE), the back-propagation algorithm, and the genetic algorithm. We employ SAE with three hidden layers in the pretraining process to extract the characteristics from the training sequence and the back-propagation algorithm to calculate the weights of the overall neural network in the fine-tuning process. Then, a genetic algorithm is adopted to optimize the neuron number of hidden layers and the learning rate of auto-encoders. The energy management problem is modeled as a threestage Stackelberg game to capture the dynamic interactions and interconnections among electricity users, the microgrid, the utility company, and the energy storage company. In the first stage, both the utility company and the energy storage company issue real-time electricity prices to the microgrid. In the second stage, the microgrid adjusts its electricity price offered to electricity users and the amounts of electricity procured form the utility and the energy storage companies. In the third stage, electricity users adjust their electricity demands based on the price offered by the microgrid. The objective function of each game player is well designed based on multi-objective optimization approaches, and practical constraints such as active power balance, power generation limits, electricity demands, etc., have been taken into consideration. Based on the short-term wind power prediction, we employ the backward induction method to analyze the proposed three-stage Stackelberg game and derive the closed-form analytical expressions for optimal energy management solutions. The properties of the proposed energy management algorithm including the existence and uniqueness of Nash equilibrium and Stackelberg equilibrium are analyzed theoretically. In the simulation, we compare the optimal payoff of the microgrid with different prediction errors of wind power forecasting. Numerical results show that accurate prediction results of wind power is conducive to better energy management.



Section V. Finally, Section VI gives the conclusion. II. R ELATED W ORKS This paper aims to solve the distributed microgrid energy management problem in energy internet by exploring both game theory and big data analysis. There has been a recent surge in the literatures that propose mathematical tools for dealing with uncertainties in energy management problems. Stochastic optimization and robust optimization are two main methodologies which have been widely employed for handling data uncertainties in energy management problems [25]. Stochastic optimization based energy management solutions provide an effective framework for optimizing statistical objective functions if the uncertain numerical data can be assumed to follow a well-known probability distribution. In [26], the authors proposed a multi-stage framework to minimize the cost of the total energy system based on stochastic optimization. A stochastic dynamic programming method was developed to optimize the multi-dimensional energy management problem in [27]. A stochastic optimization-based real-time energy management method was proposed to minimize the operational net cost in [28]. In [29], the authors developed a two-stage stochastic optimization framework of photovoltaic systems to reduce electricity costs of users. An online stochastic optimization scheme was proposed to reduce the expected electricity bill of users in [30]. However, the accurate estimation of the probability distributions of uncertain data can be a tremendous challenge in practical applications considering the complex operation details and various practical constraints. The impacts of data uncertainties on the optimality performance may not be sufficiently captured in the stochastic optimization based energy management approaches. On the other hand, robust optimization based energy management schemes only require moderate information and enable a distribution-free model of uncertainties [31]. The worst-case operation scenarios of energy systems have been considered during the optimization process. As a result, robust energy management can alleviate the negative effect of uncertainty on the optimality performance and thus overcome the aforementioned limitations of stochastic optimization. In [32], the authors proposed a novel pricing strategy that enables robustness against uncertain power input. A robust energy scheduling approach was proposed to overcome the uncertainty brought by electric vehicles in [33]. Robust energy management approaches were developed to optimize the energy dispatching problem in the worst-case scenarios of renewable energy integration [34], [35]. In [36], the authors presented a robust systematic framework to integrate renewable energy sources and distributed storage units for minimizing the total operation cost. However, the above works also inherit the drawbacks from robust optimization, i.e., the over-conservatism problem [37]. Due to the fact that the worstcase scenarios of all uncertain factors are considered to provide the highest protection against uncertainties, the optimality performance is also severely degraded as the price paid for robustness. Furthermore, the robust version of a tractable energy management problem is not guaranteed to be tractable, which

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mainly depends on the proper deign of objective function modeling and the construction of uncertainty sets. With the development of advanced information and communication technologies, large volumes of data are routinely collected in every aspect of the microgrid including consumer behaviors, demand profiles, battery states, renewable outputs, weather conditions, video surveillance and so on [38], [39]. Big data-based forecasting approach can learn from these massive amounts of real-world data and thus utilize the historical knowledge to adapt conventional energy management design to this new data-centric paradigm. Thus, we propose a big data-based forecasting approach to provide a short-term precise estimation of the uncertainties. Taking wind power forecasting as an example, the datacentric approaches mine the relationship between historical data and knowledge to build the prediction model through various approaches such as persistence methods, linear methods, and nonlinear methods. The persistence method, which assumes that short-term wind speeds are highly correlated, is one of the classic methods for wind power forecasting and is usually utilized as a benchmark method [40]. Linear methods such as autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA), which can efficiently capture the time relevance and probability distribution of wind speed data [41], have been shown to outperform most persistence methods in short-term forecasting [42]. Nonlinear methods such as support vector machines (SVM) [43], [44], artificial neural networks (ANNs) [45], etc., are demonstrated to outperform linear methods in nonlinear models. SVM is closed to ANNs and provides superior generalization ability and good performance even with relatively small training samples [46]. ANN is a simplified model of human brain neural processing, and has the advantage of easy implementation, fast self-learning capability, and high prediction accuracy [47]. The drawback of ANN is that the high-dimensional time series data of wind is hardly to be described with closed-form equations with precise parameters, which may significantly affect the learning convergence speed and the optimality performance. To efficiently handle the largevolume and high-dimensional nonlinear data, deep learning which is capable of extract high-level abstractions presented in data has been proposed [48]. In [49], the authors demonstrated that both short-term and long-term wind power forecasting can be realized by the proposed sophisticated deep-learning algorithm. As an essential deep learning architecture, SAE are auto-encoders which can be well adapted for unsupervised learning and the objective function can be solved efficiently by utilizing back propagation [50]. Hence, we propose a deep learning-based short-term wind power forecasting algorithm by combining SAE and the back-propagation algorithm. For energy management design in microgrid, there already exists some works. In [51], the authors proposed a doublelayer control model for energy management in microgrid, which consists of a dispatch layer to offer the output power of each unit based on real-time data and a schedule layer to provide the operation optimization based on predicting data. A fair energy scheduling strategy was proposed in [52] to maximize the overall system benefit while providing higher



energy utilization priorities to users with larger contributions. In [53], demand side management and generation scheduling were considered to ensure the real-time operation of energy system. A multi-agent energy management scheme was presented to optimize the energy exchange efficiency. A dynamic programming algorithm was proposed in [54] for coordinating deferrable demands with distributed renewable supply based on a stochastic unit commitment model. However, the above works mainly focus on the total benefit of the overall system, and ignore the interactions and interconnections among multiple market players. Game theory which provides a distributed self-organizing and self-optimizing solution for optimization problems with conflicting objective functions has been widely applied in microgrid energy management studied [55]. Games can be classified into two categories based on whether or not binding agreements among players can be enforced externally, i.e., noncooperative and cooperative games [56]. Noncooperative games focus on predicting players’ individual strategies and analyzing the competitive decision-making involving players to find the Nash equilibrium, which offer an analytical framework tailored for characterizing the interactions as well as decision-making process among multiple game players. The players with partially or even completely conflicting interests upon the result of a decision will influence the decision making process. In contrast, cooperative games provide mathematical tools to study the interactions of rational cooperative players. The strategic outcome among those players as well as their utilities can be improved under a common commitment. For noncooperative game-based microgrid energy management, a multi-user Stackelberg game model was employed to maximize the payoff of each player in [57]. In [58], the authors proposed a new model of electricity market operation and developed an adequate hourly pricing scheme to optimize the objective function of each market player. Time-of-use pricing and real-time pricing schemes were proposed to achieve optimal load control in [59] and [60], respectively. In [61], The authors presented a novel demand side management method based on dynamic potential game to address the uncertainty in wind power generation. In [62], the authors provided a gametheoretical distributed real-time energy management scheme to maximize the social benefit while minimizing the cost of each user. A dynamic noncooperative repeated game model was employed to optimize the energy trading amounts of users with distributed renewable generators [63]. For microgrid energy management schemes based on cooperative games, a cooperative demand response scheme was proposed to reduce the electricity bills of consumers in [64]. In [65], a multistage market model was proposed based on the cooperative game to minimize the operational cost of the utility company while maximizing the total profit of the market. A cooperative distributed energy scheduling algorithm was developed to optimize the power dispatch problem the integration of renewable generation and energy storage [66]. In [67], the authors proposed a cooperative energy trading approach for the downlink coordinated multi-point transmission powered by smart grids to reduce the total energy cost. Despite the various advantages of cooperative games, the noncooperative game

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model does not require a common commitment among various market players and has the advantage of a lower communication overhead. In particularly, among various noncooperative game models, the Stackelberg game can efficiently model the hierarchy among players, where the leaders have dominant market positions over followers, and can impose their own strategies upon the followers. Considering above two points, we employ the non-cooperative game-theoretical approach and model the microgrid energy management problem as a threestage Stackelberg game. In summary, most of the previous works are restricted to limited aspects of microgrid applications, which have not provided a comprehensive framework for how to utilize the real-world data to improve the energy management performance. Furthermore, the prior statistic knowledge of uncertain renewable power outputs was assumed to be perfectly known and the energy trading process among market players in the energy internet paradigm has been completely neglected. This motivates us to explore the integration of deep learning-based wind power forecasting technique with Stackelberg gamebased energy management strategy, so as to make a further step to enable data-centric energy management in future energy internet. III. S YSTEM M ODEL A ND P ROBLEM F ORMULATION A. System Model Fig. 1 presents a structure of a typical microgrid energy management system with the utility company, the energy storage company, users and various kinds of renewable energy sources. In this system, without loss of generality, we assume that there is a single conventional energy generation company which is denoted as the utility company and a single renewable energy storage company which is denoted as the storage company. Furthermore, we assume that there is a single microgrid and there are K users denoted as K={1, · · · , k, · · · , K} in this model. The utility company and the storage company are regarded as energy suppliers to meet the electric power demand of the microgrid and ensure the stability of power system. To implement efficient energy management, the microgrid should be in charge of energy dispatching and be responsible for meeting users’ electricity demands based on the forecasting of renewable energy generation. However, due to renewables’ uncontrollable fluctuations, variability, intermittent nature and the capacity limitation of the microgrid, the microgrid may not be able to meet the electricity demand of users by itself and has to purchase electricity from the utility company and the storage company. B. Objective Function 1) Objective Function of the Utility Company: The definition of the utility company’s objective function is rather flexible. Generally, we consider the cost function consisting of the electricity generation cost denoted as C(L) and the pollutant emission cost denoted as I(L) [68]. Each of them can be modeled as a quadratic function of the electricity demand L. Besides, line loss which is mainly caused by resistance of the transmission lines has been taken into consideration



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3) Objective Function of the Microgrid: We focus on renewable energy which is the main source of the microgrid and consider the satisfaction function based on quality of service of the electricity provided by the utility and storage companies [69]. Hence, the objective function of the microgrid is formulated as Um (Lm,g , Lm,s , pm ) = Rm,g (Lm,g ) + Rm,s (Lm,s ) − Cm,g (Lm,g , pg ) − Cm,s (Lm,s , ps ) + Rm (Lk,m , pm ) ˆ r + ∆) − Im (L ˆ r + ∆) + F | ∆ |, − Cm (L (5) where Fig. 1: System model of microgrid energy management.

to ensure energy supply. Hence, the objective function of the utility company is formulated as: Ug (Lm,g , pg ) = Rg (Lm,g , pg ) − Cg (εg Lm,g ) − Ig (εg Lm,g ), (1) where Rg (Lm,g , pg ) =Lm,g pg , (2)

Rg (Lm,g , pg ) denotes the electricity revenue. Cg (εg Lm,g ) and Ig (εg Lm,g ) are the cost functions of the power generation and the pollutant emission, respectively. Lm,g denotes the quantity of electricity bought from the utility company by the microgrid and pg is the unit electricity price of the utility company. ag , bg , cg , αg , βg are the cost parameters of Cg (εg Lm,g ) and Ig (εg Lm,g ). Assuming that ρg denotes the power loss percentage during power transmission, which is related to voltage, efficiencies of transformers and resistance of the transmission line. Hence, εg Lm,g is the actually generated electricity to satisfy the microgrid demand Lm,g , where εg = 1/(1 − ρg ). 2) Objective Function of the Storage Company: we consider the power loss inefficiency during the battery charging and discharging processes, as well as line loss, and the objective function of the storage company is formulated as Us (Lm,s , ps ) = Rs (Lm,s , ps ) − Cs (εs Lm,s ),

(3)

where Rs (Lm,s , ps ) = Lm,s ps , cs εs Lm,s . Cs (εs Lm,s ) = ηc ηd

k=1

Cm,g (Lm,g , pg ) = Lm,g pg , Cm,s (Lm,s , ps ) = Lm,s ps , ˆ r + ∆) = am (L ˆ r + ∆)2 + bm (L ˆ r + ∆) + cm , Cm (L ˆ r + ∆) = αm (L ˆ r + ∆)2 + βm (L ˆ r + ∆). Im (L

Cg (εg Lm,g ) =ag (εg Lm,g )2 + bg (εg Lm,g ) + cg , Ig (εg Lm,g ) =αg (εg Lm,g )2 + βg (εg Lm,g ).

dm,g (Lm,g )2 , 2 dm,s (Lm,s )2 , Rm,s (Lm,s ) = Xm,s Lm,s − 2 K ∑ Rm (Lk,m , pm ) = Lk,m pm , Rm,g (Lm,g ) = Xm,g Lm,g −

(4)

Rg (Lm,s , ps ) denotes the electricity revenue and Cs (εs Lm,s ) is the cost function of energy storage. Lm,s denotes the quantity of electricity bought from the storage company by the microgrid. ps is the unit electricity price of the storage company. ηc and ηd are the charging and discharging efficiencies of storage equipments, respectively. cs denotes the unit cost of operation and maintenance. The meaning of εs is the same as εg introduced above.

(6)

Rm,g (Lm,g ) denotes the satisfaction value and Cm,g (Lm,g , pg ) denotes the payment of the microgrid for electricity bought from the utility company. Xm,g denotes the satisfaction parameter for the utility company. As the satisfaction parameters depend on various factors, such as electricity demands, electricity prices, preferences in different energy sources, weather conditions, etc. it is hard to model the satisfaction parameters accurately. Thus, we assume that these parameters are predefined. Analogously, dc,m denotes predefined satisfaction parameters of the microgrid for the utility company. The definitions of Rm,s (Lm,s ) and Cm,s (Lm,s , ps ) are similar to those of Rm,g (Lm,g ) and Cm,g (Lm,g , pg ) introduced as above. Rm (Lk,m , pm ) denotes the electricity revenue acquired from users while Lk,m is the quantity of electricity bought by the k-th user and pm ˆ r + ∆) is the unit electricity price of the microgrid. Cm (L ˆ and Im (Lr + ∆) are the cost functions of wind power generation and wind power pollutant emission, respectively. ˆ r + ∆) am , bm , cm , αm , βm are the cost parameters of Cm (L ˆ ˆ and Im (Lr + ∆). Lr + ∆ denotes the prediction result ˆ r is the real wind power and ∆ is of wind power while L the prediction error. F denotes the penalty factor of the prediction error ∆ that satisfies F < 0. That is, the payoff of the microgrid will decrease when the result of wind power forecasting is not accurate, which reflects the restriction of power purchase agreement in the market. 4) Objective Function of Users: In a similar way, we also take the satisfaction function into consideration. Hence, the objective function of the k-th user is given by Uk (Lk,m , pm ) =Rk,m (Lk,m ) − Ck,m (Lk,m , pm ),

(7)



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as: max

Lm,g ,Lm,s ,pm

Um (Lm,g , Lm,s , pm ),

s.t. C1 : 0 ≤ εg Lm,g ≤ Lg,max , C2 : 0 ≤ εs Lm,s ≤ Ls,max , C3 : 0 ≤ pm ≤ pm,max , C4 : Lm,s + Lm,g = max{

K ∑

ˆ r − ∆, 0}, Lk,m − L

k=1

(11) where Lg,max denotes electricity generation capacity of the utility company. Ls,max denotes energy storage capacity of the storage company and pm,max is the maximum price users can afford. However, due to the intermittent nature, and the capacity limitation of renewables, microgrid alone may not be able to meet the electricity demand of users by itself and has to purchase electricity from ∑K the utility ˆcompany and the storage company. When k=1 Lk,m − Lr − ∆ ≤ 0, the three-stage Stackelberg game will be a two-stage Stackelberg game and there is no need to purchase electricity from the utility or storage companies for the microgrid. Hence, the constraints of ∑K ˆ L k=1 k,m − Lr − ∆ can be rewritten as

Fig. 2: The diagram of the three-stage Stackelberg game.

where Rk,m (Lk,m ) = Xk,m Lk,m −

dk,m (Lk,m )2 , 2

Ck,m (Lk,m , pm ) = Lk,m pm .

(8)

Rk,m (Lk,m ) denotes the satisfaction value and Ck,m (Lk,m , pm ) denotes the payment that the k-th user pays for electricity bought from the microgrid. The meanings of Xk,m and dk,m are similar to Xm,g and dm,g .

C5 :

K ∑

ˆ r − ∆ > 0. Lk,m − L

(12)

k=1 •

C. Problem Formulation As mentioned above, we propose a three-stage Stackelberg game which consists of leaders and followers to describe the interconnection of each stage and model the energy management process. The three-stage Stackelberg game can be described in a distributed manner as Fig. 2: •

Stage I: The utility and the storage companies, as leaders of the game, announce the unit electricity price pg and ps to the microgrid. By setting reasonable prices, the companies hope to maximize their own payoffs. Thus, we can describe the optimization problem for the utility and storage companies as:

max Uk (Lk,m ),

(13)

s.t. C6 : Lk,m ≥ Lk,b ,

(14)

Lk,m

where Lk,b is the basic electricity demand of the k-th user.

max Ug (pg ),

(9)

IV. A LGORITHMS AND A NALYSIS

max Us (ps ).

(10)

In this section, firstly, we propose a distributed energy management algorithm based on the three-stage Stackelberg game. Then, the big data analysis based wind power forecasting algorithm is derived by combining SAE, the back propagation algorithm, and the genetic algorithm. Finally, we provide the equilibrium analysis for the three-stage Stackelberg game.

pg

ps

•

Stage III: The k-th user (∀k ∈ {1, 2, ..., K}), as the follower of the microgrid, determines electricity amount Lk,m purchased from the microgrid based on pm to maximize its payoff. We can describe the optimization problem for the k-th user as:

Stage II: As the core node of the energy management system, the microgrid plays two kinds of roles in the threestage Stackelberg game. The microgrid can be assumed as the follower of the utility and the storage companies as well as the leader of users. On one side, microgrid determines electricity demand Lm,g and Lm,s based on the prediction result of the wind power and the unit prices pg , ps . On the other side, it announces electricity price pm to users. The objective of the microgrid is also to maximize its payoff by adjusting Lm,g , Lm,s and pm . We can describe the optimization problem for the microgrid

A. Distributed Energy Management Algorithm In this subsection, we propose a three-stage Stackelberg game to describe the interconnections of each stage and use the backward induction to capture the interrelation of the decisionmaking process in each stage.



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1) Analysis of the Third-Stage User Game: The optimization objective of the k-th user is defined in (13), which is a standard concave function. Hence we can use the KarushKuhn-Tucker (KKT) conditions to solve the optimization problem. The Lagrangian function associated with the k-th user is Lagk (Lk,m , µk ) = Rk,m (Lk,m ) − Ck,m (Lk,m , pm ) + µk (Lk,m − Lk,b ) dk,m (Lk,m )2 − Lk,m pm + µk (Lk,m − Lk,b ). = Xk,m Lk,m − 2 (15) By employing KKT conditions   ∂Lag k (Lk,m , µk ) = 0, ∂Lk,m  µk (Lk,m − Lk,b ) = 0,

k=1

Lk,m

(17)

′′

K K ∑ ∑ Xk,m − pm = + Lk,b . dk,m ′ ′′ k =1

ˆ   Lm,s1 = 0,   Xm,s − ps − µm,1 ˆ , Lm,s2 = dm,s     L ˆ m,s3 = Ls,max , εs

(16)

ˆ k,m1 denotes the optimal electricity procurement where L ˆ k,m2 denotes the scenario where the optimal quantities. L electricity procurement quantity lines on the boundary of the inequality constraint. 2) Analysis of the Second-Stage Microgrid Game: In State II, we assume user k ′ ∈ K′ ={1, · · · , i, · · · , K ′ } purchases ′′ electricity Lk,m1 and user k ′′ ∈ K′′ ={1, ∪ ′′· · · , i, · · · , K } ′ purchases electricity Lk,m2 . While K=K K , we can obtain ′

 ∂Lag m (Lm,s , µm,1 , µm,3 , µm,5 )   = 0,   ∂Lm,s     K  ∑ ˆ µm,1 (Lm,s + Lm,g + Lr + ∆ − Lk,m ) = 0,   k=1     µm,2 (εs Lm,s − Ls,max ) = 0,    µm,4 εs Lm,s = 0,

(22)

we can obtain the optimal solution as

we can obtain the optimal solution as  L ˆ k,m1 = Xk,m − pm , dk,m ˆ Lk,m2 = Lk,b ,

K ∑

quantities of electricity procured from the utility company line ˆ m,g2 denotes on the boundaries of the inequality constraints. L the interior solution. In a similar way, based on KKT conditions

(18)

k =1

The Lagrangian function associated with the microgrid can be written as (19) Based on KKT conditions  ∂Lag m (Lm,g , µm,1 , µm,2 , µm,4 )   = 0,   ∂Lm,g     K  ∑ ˆr + ∆ − µm,1 (Lm,s + Lm,g + L Lk,m ) = 0, (20)   k=1     µm,2 (εg Lm,g − Lg,max ) = 0,    µm,4 εg Lm,g = 0, we can obtain the optimal solution as  ˆ m,g1 = 0,  L    Xm,g − pg − µm,1 ˆ , Lm,g2 = dm,g     ˆ m,g3 = Lg,max ,  L εg

(21)

ˆ m,g1 denotes that the microgrid will only purchase where L ˆ m,g3 denotes that electricity from the storage company and L the electricity procurement quantity by the microgrid reaches the electricity generation capacity of the utility company. ˆ m,g1 and L ˆ m,g3 denote the scenario where the optimal L

(23)

ˆ m,s1 denotes that microgrid will only purchase elecwhere L ˆ m,s3 denotes that the tricity from the utility company and L electricity procurement quantity by microgrid reaches energy ˆ m,s1 and L ˆ m,s3 storage capacity of the storage company. L denote the scenario where the optimal quantities of electricity procured from the storage company line on the boundaries of ˆ m,s2 denotes the interior solution. the inequality constraints. L In the same situation, based on KKT conditions  ∂Lag m (pm , µm,1 , µm,6 , µm,7 )   = 0,   ∂pm     ˆ    µm,1 (Lm,s + Lm,g + Lr + ∆  ′ K k′′ ∑ ∑ Xk,m − pm (24)  − + Lk,b ) = 0,   dk,m   k′ =1 k′′ =1     µm,6 (pm − pm,max ) = 0,    µm,7 pm = 0, we can obtain the optimal solution as  pˆm1 = 0,    ∑K ′ ∑K ′ Xk,m ∑K ′′   k′′ =1 Lk,b − µm,1 k′ =1 k′ =1 dk,m + pˆm2 = ∑ ′ K 2   k′ =1 dk,m    pˆm3 = pm,max ,

1 dk,m

,

(25) where pˆm1 and pˆm3 denote the minimum value and the maximum value of electricity prices for the microgrid. pˆm1 and pˆm3 denote the scenario where the optimal electricity price of the microgrid line on the boundaries of the inequality constraints. pˆm2 denotes the interior solution. L and Lm,s = 0 When Lm,g = 0 or Lm,g = g,max εg L

or Lm,s = s,max , there is no price competition between εs the utility and storage companies. Thus, the analysis of the corresponding pg and ps is omitted here. Considering the price competition game between the utility company and the storage



8

Lagm (Lm,g , Lm,s , pm , µm,1 , µm,2 , µm,3 , µm,4 , µm,5 , µm,6 , µm,7 ) = Rm,g (Lm,g ) + Rm,s (Lm,s ) − Cm,g (Lm,g , pg ) ˆ r + ∆) − Im (L ˆ r + ∆) + F | ∆ | −µm,1 (Lm,s + Lm,g + L ˆr + ∆ − − Cm,s (Lm,s , Ps ) + Rm (Lc,m , pm ) − Cm (L

K ∑

Lk,m )

k=1

− µm,2 (εg Lm,g − Lg,max ) − µm,3 (εs Lm,s − Ls,max ) + µm,4 εg Lm,g + µm,5 εs Lm,s − µm,6 (pm − pm,max ) + µm,7 pm . (19)

company, µm,1 can be derived as µm,1 = ∑K ′

k′ =1

Xm,g −pg dm,g 1 dm,g

+

Xk,m −pm dk,m

−

+

where

Xm,s −ps dm,s 1 dm,s

∑K ′′

1 dm,g

k′′ =1 1 + dm,s

Ag,3 = Ag,1 − ε2g (ag + αg )A2g,1 ,

−

Ag,4 = Ag,2 [1 − 2ε2g (ag + αg )Ag,1 ] − εg (bg + βg )Ag,1 ,

ˆr + ∆ Lk,b + L

.

(26)

We can observe that pm can be viewed as a function of pg and ps based on (25). Thus, pm can be given as pm = Am,1 pg + Am,2 ps + Am,3 ,

Ag,5 = −ε2g (ag + αg )A2g,2 − εg (bg + βg )Ag,2 − cg .

Since Ug is a convex function of pg based on (31), we can obtain pˆg by solving the convex function that

(27)

pˆg = −

where Am,1 =

∑K ′

(1 + Am,2 =

1 k′ =1 dk,m 2 2 + dm,g dm,s

∑K ′

2 )( dm,g +

2 dm,s )

(1 + Xm,g dm,g

+

1 k′ =1 dk,m 2 2 + dm,g dm,s

Xm,s dm,s

)

where

(1 +

As,1 = −

∑K ′

∑K ′ − ( k′ =1 ∑K ′

2 k′ =1 dk,m

Xk,m dk,m

1 k′ =1 dk,m 2 2 dm,g + dm,s

+

ˆ k′′ =1 Lk,b ) + Lr + ∆

2

)( dm,g +

.

2

dm,s )

3) Analysis of the First-Stage Utility and Storage Company Game: In this case, defining Lm,g as a function of pg , we have ˆ m,g (pg ) = Ag,1 pg + Ag,2 , L (29)

Ag,1 =

Ag,2 =

∑K ′ +

k′ =1

Xk,m −Am,2 ps −Am,3 dk,m

1+

+

∑K ′′

dm,s

+

1 dm,s

− 1

∑K ′

Am,2 k′ =1 dk,m dm,s + dm,g Xm,g −pg dm,g dm,s dm,g

m,s Xm,s dm,s + As,2 = − dm,s 1+ ∑K ′ Xk,m −Am,1 pg −Am,3

+

k′ =1

+

dk,m

1+

,

∑K ′′

k′′ =1

ˆr − ∆ Lk,b − L

dm,s dm,g

,

k′′ =1

.

(35) Hence, Us can be written as a quadratic function of ps , which is given by Us (ps ) = As,3 (ps )2 + As,4 ps + As,5 .

∑K ′

Am,1 1 k′ =1 dk,m dm,g − − + d dm,g 1 + dm,g m,s Xm,g Xm,s −ps + dm,s Xm,g d − m,g d dm,g 1 + dm,g m,s 1

1

X

∑K ′′

(28)

where

(34)

,

1

∑K ′

(33)

ˆ m,s (ps ) = As,1 ps + As,2 , L

1 dm,s

k′ =1 d

Ag,4 . 2Ag,3

In the same way, defining Lm,s as a function of ps based on (21), we have

,

2 2 (1 + 2 + k,m + dm,s ) )( dm,g 2 dm,g dm,s ∑K ′ Xk,m ∑K ′′ k′ =1 dk,m + k′′ =1 Lk,b

Am,3 =

−

1 dm,g

(32)

(36)

We can obtain As,3 = As,1 , As,4 = As,2 − ˆr − ∆ Lk,b − L

dm,g dm,s

.

(30) Hence, Ug can be written as a quadratic function of pg , which is given by Ug (pg ) = Ag,3 (pg )2 + Ag,4 pg + Ag,5 ,

(31)

As,5 =

cs εs As,1 , ηc ηd

cs εs As,2 . ηc ηd

(37)

Since Us is a convex function of ps based on (36), we can obtain pˆs by solving the convex function that pˆs = −

As,4 . 2As,3

(38)



9

B. Algorithm of Wind Power Forecasting

Algorithm 1 The proposed genetic SAE Algorithm 1: Procedure: Genetic Algorithm 2: Begin 3: Initialize: P(0, 0) 4: Set t = 0 5: while t < T do 6: for d ∈ D do 7: The Pre-training Process: 8: Evaluate fitness of P(d, t): Calculate and store the best, worst and average objective value for current individuals. 9: Select operation to P(d, t): Select optimal individual for the next generation. 10: The Fine-turning Process: 11: Crossover operation to P(d, t): Do crossover operation on the selected individuals and obtain better individuals. 12: Mutation operation to P(d, t): Do mutation operation to P(d, t) based on a certain mutation probability. 13: end for 14: Update: t = t + 1 15: end while

In this subsection, we propose a deep learning-based shortterm wind power forecasting algorithm by combining autoencoders (SAE), the back-propagation algorithm, and the genetic algorithm. It is noted that the proposed forecasting model can also be applied for other distributed renewable energy sources such as solar energy and hydroenergy, etc. The reason why we study the wind power forecasting in this paper is mainly due to the illustration purpose and the availability of the wind big data. The core of the algorithm is to establish a forecasting model through training on the historical data. Exploiting the statistical relationship among the historical time series data can be divided into two processes: the pre-training process and the fine-tuning process. In the pre-training process, three stacked AEs which consist of one visible layer, one hidden layer, and one output layer form a neural network. In the fine-tuning process, one more layer is added to the end of the neural network and back-propagation algorithm is applied to obtain more appropriate initial weights of the whole network. Furthermore, for improving the forecasting accuracy, we adopt genetic algorithm to optimize the learning rate of each AE and the number of neurons of each layer. 1) Training Process of the Proposed Genetic SAE Forecasting Model: As shown in Fig. 3(a), SAE consists of one input layer x, the first hidden layer h1 and one output layer x ˆ. We adopt encoder function fθ 1 to transform x to a low or a high dimensional code h1 and adopt decoder function gθ 1 to reconstruct the original data as x ˆ. We can obtain the values of parameters θj ={wj , bj , wjT , dj }, j ∈ {1, 2, · · · , J}, (J denotes the number of layers in SAE) through back propagation, where wj and wjT are weight matrices of encoder and decoder, bj and dj are biases of encoder and decoder, respectively. We add a new hidden layer h2 to the whole network, new layer and the original layers are stacked into the existing AE in Fig. 3(b). There is a new AE illustrated since h1 and h2 are combined as the input layers. Hence, we can stack more

auto encoders by removing the last layer h1 and add one more layer. Considering computation complexity, three auto coders are stacked together in this section. The pre-training process is shown as Fig. 3(a) and Fig. 3(b), which consists of two hidden layers h1 , h2 and trains the initial weights of the whole network. In Fig. 3(c), to form the whole genetic SAE neural network, we add an output layer and initialize the set of parameter w4 , b4 between the last hidden layer and the output layer. The process which we adopt back-propagation algorithm to train all the weights and biases of the whole network is called the fine-tuning process. Hence, a deep network with three hidden layers can be trained to converge to a global minimum by the process we proposed. 2) Optimization of the Proposed Model: The learning rate of the network and the number of neurons in hidden layer are the key parameters which have a significant impact on the final prediction performance. Hence, we adopt the genetic algorithm to optimize the parameters of the SAE and the whole network for improving the performance of the models. We regard the historical time series data x as the individuals of population in genetic algorithm and we obtain a multidimensional vector P(d, t), where there are d individuals in the population denoted as d ∈ D = {1, · · · , d, · · · , D} and t ∈ T = {1, · · · , t, · · · , T } is the number of evolution. We assume the size of the population is D and the maximum of evolution is T . Firstly, we set the initial population as P(0, 0). Then, we calculate the objective value and the fitness value to select optimal individual for the next generation. After crossover and mutation, we can obtain optimal individual P(d, T). Algorithm 1 shows the optimization process of the proposed model. To make a fair comparison, we optimize the parameters of the BP algorithm and the SVM algorithm in

Fig. 3: The pre-training and fine-tuning process of genetic SAE.



10

the similar way. The BP algorithm, which repeats a two phase cycle, propagation and weight update, is combined with an optimization method such as gradient descent and is a general algorithm of training ANNs. The SVM algorithm is a machine learning algorithm of ANNs to analyze data which is used for classification and regression analysis. Furthermore, Mean Absolute Percentage Error (MAPE) is adopted to evaluate the accuracy of the model that 1∑ x î − xi ∗ 100 |, | n i=1 x î N

MAPE =

(39)

where x î denotes the real wind power value at i-th time point, xi is the forecasting result for the same point, and n is the number of forecasted points.

• Scalability: for all φ > 1, φˆ pg (ˆ ps ) > pˆg (φˆ ps ). The best optimum function pˆg (ˆ ps ) meets the positivity property obviously. To prove the monotonicity, we have to prove pˆg (ˆ ps ) is an monotonically increasing function of pˆs . The best optimum function pˆg (ˆ ps ) is defined in (33). It is observed that − 2A1g,3 > 0, thus we should prove Ag,4 defined in (32) is an monotonically increasing function of pˆs , which is equivalent to proving that Ag,2 is an monotonically increasing function of pˆs . Since Am,2 < 0, we can obtain that Ag,2 is a monotonically increasing function of pˆs . For scalability proof, we first rewrite pˆg = hg,1 ps + hg,2 and hg,2 is given by

hg,2 = C. Equilibrium Analysis In this subsection, we prove Nash equilibrium for the three-stage Stackelberg game. Since the microgrid provides renewable energy power on a priority and then prefers to purchase electricity on a lower price, a price competition game is played in the third stage between the utility and storage companies. These players who have partially or even completely conflicting interests make decisions independently and the price competition game between the utility and storage companies is a non-cooperative game. For any feasible electricity price p˜g and p˜s , there are the optimal strategies pˆm , ˆ m,g and L ˆ m,s in the second stage. The proof process of Nash L equilibrium is divided into three parts. Firstly, we prove the existence of the Nash equilibrium in this Stackelberg game. Secondly, the existence of Nash equilibrium is proved to be unique. Finally, we prove that the Stackelberg equilibrium is constituted by the Nash equilibrium at each stage. Theorem 1: A Nash equilibrium exists in this Stackelberg game. Proof: The function of the utility company is defined in (1) and the optimal variables including pg and Lm,g are continuous. Hence, the strategy space of the utility company is a non-empty compact convex subset of a Euclidean space. Furthermore, we prove the objective function can be expressed as a concave function of pg based on (31). Similarly, The same conclusion can be applied to the objective functions of the storage company, the microgrid and users. Therefore, there exists a pure strategy Nash equilibrium in the first and third stages of this three-stage Stackelberg game. Theorem 2: The existence of the Nash equilibrium in this Stackelberg game is unique. Proof: The Nash equilibrium in Theorem 1 is composed of the optimum strategies between the utility and storage companies. Taking the utility company as an example, we give the proof process that the Nash equilibrium is unique. To address the problem, we should prove that the best optimum function pˆg (ˆ ps ) is a standard function, where pˆs denotes the best response of the storage company to pˆg . pˆg (ˆ ps ) is considered to be a standard function while satisfying the following properties: • Positivity: p ˆg (ˆ ps ) > 0; • Monotonicity: if p ˆs ≥ (ˆ ps )′ , then pˆg (ˆ ps ) ≥ (ˆ pg (ˆ ps ))′ ;

−

1 − 2ε2g (ag + αg )Ag,1 Xm,g εg (bg + βg )Ag,1 − ( 2Ag,3 2Ag,3 dm,g ′ ∑K Xk,m −Am,2 ps −Am,3 Xm,g Xm,s −ps − k′ =1 dm,g + dm,s dk,m 1+ ˆ r + ∆ − ∑K′′ Lk,b L k =1

dm,g dm,s

′′

+

1+

dm,g dm,s

).

(40)

To prove the scalability, we only need to prove that 1−2ε2g (ag +αg )Ag,1 ε (b +βg )Ag,1 > 0, > hg,2 > 0. We have g g2Ag,3 2Ag,3 0 based upon the analytical framework we built above. Xm,g By setting pˆg = pˆs = 0, we can obtain ( dm,g − Xm,g dm,g

+

Xm,s −ps dm,s

∑ ′ − K k′ =1

Xk,m −Am,2 ps −Am,3 dk,m d 1+ dm,g m,s

∑ ′′ ˆ r +∆ − K L +L k′′ =1 k,b

)

> 0 easily. Hence, we complete the scalability proof and pˆg is a standard function. We can prove pˆs (ˆ pg ) is a standard function in the same way. For the best response functions pˆg and pˆs , ˆ m,g , L ˆ m,s and L ˆ k,m there are corresponding strategies pˆm , L in the second and third stages. Therefore, the Nash equilibrium in Theorem 1 is unique. Theorem 3: the Stackelberg equilibrium is constituted by the Nash equilibrium at the first and third stages. Proof: The Nash equilibrium of the first stage game is pˆg , pˆs , thus for any feasible price p˜g , p˜s , we have ˆ m,g ) ≥ Ug (˜ ˆ m,g ), Ug (ˆ pg , L pg , L ˆ m,s ) ≥ Us (˜ ˆ m,s ). Us (ˆ ps , L ps , L

(41)

ˆ k,m , thus The Nash equilibrium of the third stage game is L ˜ for any feasible electricity demand Lc,m , we have ˆ k,m ) ≥ Uk (L ˜ k,m ). Uk (L

(42)

Hence, the first and third stages Nash equilibriums constitute the Stackelberg game. V. S IMULATION R ESULTS In this section, we verify the proposed game-theoretical energy management algorithm with big-data based wind power forecasting through simulation results. The simulation parameters of the utility company, the energy storage company, the microgrid and users are shown in Table I. In order to evaluate the prediction accuracy of the proposed wind forecasting model, real data of wind turbines, which were collected form



11

TABLE I: Simulation Parameters.

a local micorgrid in Hebei Province, China, are employed to perform the training and forecasting processes. By excluding unnecessary information, the one-year data samples of active power, which spans from September 2015 to October 2016, are utilized for simulations. We assume that ag > am and αg < αm , which represent that the power generation cost of the utility company is lower, but the pollutant emission cost of the utility company is higher than the renewable energybased microgrid. In addition, we assume that Xm,s > Xm,g , which represents that the microgrid has a preference to use the stored renewable energy. The basic electricity demand Lk,b is assumed to be the same for every user k ∈ K. Fig. 4 shows the optimal electricity prices of the utility company, the energy storage company, and the microgrid, i.e., pˆg , pˆs , and pˆm , versus the basic electricity demands of users Lk,b . Lk,b is increased from 10 to 100 kW with a step of 10, and the corresponding pˆg , pˆs , and pˆm are obtained by the proposed algorithm. The simulation results demonstrate that pˆg , pˆs , and pˆm increase monotonically as Lk,b increases, which is reasonable since the electricity generation cost also increase dramatically as Lk,b increases. pˆs > pˆg is due to the preference of the microgrid to use clean renewable energy stored by the energy storage company. In addition, we have pˆm > pˆg and pˆm > pˆs . Since only one microgrid has been considered in the second stage, the microgrid is always able to make more profits by announcing higher prices towards users than those of the utility and the energy storage companies. Fig. 5 shows the optimal electricity procurement quantity ˆ m,g and the energy storage procured from the utility company L ˆ company Lm,s versus the basic electricity demands of users ˆ m,g Lk,b . From the simulation results, we found that both L ˆ m,s increase monotonically as Lk,b increases since the and L microgrid has to procure more electricity from both the utility and the energy storage companies to satisfy the increasing electricity demands of users. Furthermore, we can observe ˆ m,s > L ˆ m,g , which is due to the preference of the microgrid L to use clean renewable energy stored by the energy storage company.

50

Price (cents/kWh)

Value 0.03 0.08 1.5 0.5 0.5 0.05 0.05 5 0.21 10 0.21 50 0.15 200KW 100KW 50cents/kWh 20KW -50

the utility company pg the energy storage company p s the microgrid p

m

40

30

20

10

0 10

20

30

40

50

60

Basic Electricity Demand of Users L

70 k,b

80

90

100

*1 hour (kWh)

Fig. 4: The optimal electricity prices of the utility company pˆg , the energy storage company pˆs and the microgrid pˆm versus the basic electricity demands of user Lk,b .

60

Electricity Procurement Quantity (kWh)

Parameter Power generation cost parameter of utility company ag Pollutant emission cost parameter of utility company αg The unit cost of operation and maintenance cs Charging efficiencies of storage equipments ηc Discharging efficiencies of storage equipments ηd Power generation cost parameter of microgrid am Pollutant emission cost parameter of microgrid αm Satisfaction parameter for utility company Xm,g Satisfaction parameter for utility company dm,g Satisfaction parameter for storage company Xm,s Satisfaction parameter for storage company dm,s Satisfaction parameter for microgrid Xc,m Satisfaction parameter for microgrid dm,s Capacity of utility company Lg,max Capacity of storage company Lm,max The highest price users can afford pm,max ˆr The real wind power L The penalty factor F

60

55

50

45

40

35

the utility company L

m,g

the energy storage company L 30 10

20

30

40

50

60

70

80

m,s

90

100

Basic Electricity Demand of Users Lk,b*1 hour (kWh)

Fig. 5: The optimal quantity of electricity procured from the ˆ m,g and the energy storage company L ˆ m,s utility company L versus the basic electricity demands of user Lk,b .

Fig. 6 shows the optimal payoff of the utility grid company, the energy storage company, and the microgrid, i.e., ˆ m,g , L ˆ m,s ), Ug (ˆ ˆ m,g ), and Us (ˆ ˆ m,s ), versus Um (ˆ pm , L pg , L ps , L the basic electricity demands of users Lk,b . Simulation resultˆ m,g , L ˆ m,s ), Ug (ˆ ˆ m,g ), and s demonstrate that Um (ˆ pm , L pg , L ˆ Us (ˆ ps , Lm,s ) increase monotonically as Lk,b increases. The ˆ m,g and L ˆ m,s are all the monotonreason is that pˆg , pˆs , pˆm , L ically increasing functions of Lk,b as shown in Fig. 4 and Fig. ˆ m,g , L ˆ m,s ), 5, respectively. The relationships among Um (ˆ pm , L ˆ Ug (ˆ pg , Lm,g ) and Lk,b are highly related to the relationships ˆ m,g , L ˆ m,s and Lk,b . We also notice between pˆg , pˆs , pˆm , L ˆ ˆ ˆ m,s ) and Us (ˆ ˆ m,s ) > that Um (ˆ pm , Lm,g , Lm,s ) > Us (ˆ ps , L ps , L ˆ m,g ), due to the low transmission loss and monopoly Ug (ˆ pg , L position of the microgrid, and its preference to procure stored renewable energy, respectively.



12

3500

3400

3000

3200

2500

3000

L

k,b

=40 kW

Lk,b =60 kW

the utility company U

g

the energy storage company U

2000

the microgrid U

s

m

1500

1000

500

Payoff of the Microgrid

Payoff

Lk,b =80 kW

2800

2600

2400

2200

0 10

20

30

40

50

60

70

Basic Electricity Demand of Users L

k,b

80

90

100

2000 -10

-8

-7

80

L

3200

=40 kW

70

Lk,b =60 kW

60

k,b

-5

-4

-3

-2

-1

0

Fig. 8: The optimal payoff of the microgrid Um versus the prediction error of wind power forecasting ∆ < 0.

BP SVM Genetic SAE

3400 3300

-6

The Prediction Error ∆

Fig. 6: The optimal payoff of the utility company Ug , the energy storage company Us , and the microgrid Um versus the basic electricity demands of user Lk,b .

Lk,b =80 kW 50

3100

MAPE(%)

Payoff of the Microgrid

-9

*1 hour (kWh)

3000 2900

40 30

2800

20

2700 2600

10

2500

0 1

2400 0

1

2

3

4

5

6

7

8

9

10

The Prediction Error ∆

Fig. 7: The optimal payoff of the microgrid Um versus the prediction error of wind power forecasting ∆ > 0.

Fig. 7 and Fig. 8 show the optimal payoff of the microgrid ˆ m,g , L ˆ m,s ), versus the prediction error of wind Um (ˆ pm , L power forecasting ∆ for the two scenarios ∆ > 0, and ∆ < 0, respectively. ∆ > 0 represents that the actual wind power output is less than the predicted amount, and the microgrid has to procure more electricity from both the utility and the energy storage companies. In comparison, ∆ < 0 represents that the actual wind power output is more than the predicted amount, and the microgrid will not procure the specified amount of electricity from both the utility and the energy storage companies. Three cases where Lk,b = 40, 60, and 80 kW have been considered. Both Fig. 7 and Fig. 8 show that the optimal payoff of the microgrid decreases monotonically as | ∆ | increases. For example, if ∆ is increased from 0 to 10 kW or decreased from 0 to −10 kW, the optimal payoff will be decreased by 9.2% and 22.1% when Lk,b = 40

1.5

2

2.5

3

3.5

4

4.5

5

Step

Fig. 9: MAPE of three different models with wind power forecasting step varies.

kW, respectively. The reason is that the microgrid will be charged for the difference between the predicted and actual electricity procurement quantities, due to the restriction of power purchase agreement. It is also clear that the optimal payoff is degraded more severely when ∆ < 0 compared to ∆ > 0. The reason is that the electricity prices of the utility and the energy storage companies are higher when ∆ < 0 compared to the case of ∆ > 0. Fig. 9 shows the MAPE value of three different algorithms including BP, SVM and genetic SAE versus wind power forecasting step. The process of wind power forecasting based on historical data is called step=1. By adding the prediction result to the historical data, we can obtain a new result in the similar way and the process is called step=2, and so on. From the simulation results, we found that MAPE increases as prediction step increases. Thus, we can come to the conclusion that the result becomes inaccurate as the step



increases. Furthermore, the simulation results demonstrate we obtain a minimum prediction error by genetic SAE algorithm compared to the other two algorithms. More concretely, the prediction absolute error is decreased by 7.3% compared to the SVM algorithm and 32.4% compared to the BP algorithm when step=5. VI. C ONCLUSIONS In this paper, we focused on the energy management system that consisting of the utility company, the energy storage company, the microgrid, and electricity users. To make use of renewable energy efficiently, we proposed to utilize the big data-based power generation forecasting techniques to obtain the short-term wind power forecasting results that assist the microgrid to implement energy management strategies. Moreover, we innovatively formulated the energy management problem as a three-stage Stackelberg game, and each character in the electricity market, regarded as game player, hopes to maximize its individual payoff while at the same time guaranteeing the system operation reliability and satisfying users’ electricity demands. We solved the three-stage optimization problem by employing the backward induction method and derived the closed-form analytical expressions for the optimal price and demand strategies in each stage. Then, the properties of the proposed energy management algorithm including the existence and uniqueness of Nash equilibrium and Stackelberg equilibrium were analyzed theoretically. Finally, simulations validated the proposed algorithm and demonstrated that the optimal payoff of the microgrid will be decreased due to the prediction error. Furthermore, the performance of the proposed genetic SAE algorithm is demonstrated to be much better than other conventional algorithms, which is helpful for energy management. In future works, we will put emphasis on cooperative energy management among multiple microgrids based on the predictions of renewable power and electricity consumptions. R EFERENCES [1] B. Huang, Y. Li, and H. Zhang, “Distributed optimal co-multi-microgrids energy management for energy internet,” IEEE/CAA J. of Auto. Sinica, vol. 3, no. 4, pp. 357–364, Oct. 2016. [2] L. Jia and L. Tong, “Dynamic pricing and distributed energy management for demand response,” IEEE Trans. Smart Grid, vol. 7, no. 2, pp. 1128 – 1136, Mar. 2016. [3] M. Muratori and G. Rizzoni, “Residential demand response: Dynamic energy management and time-varying electricity pricing,” IEEE Trans. Power Syst., vol. 31, no. 2, pp. 1108 – 1117, Mar. 2016. [4] J. Rifkin, The Third Industrial Revolution: How Lateral Power is Transforming Rnergy, The Economy, and The World. New York, USA: Palgrave Macmillan Trade, Dec. 2011. [5] P. Yi, T. Zhu, B. Jiang, R. Jin, and B. Wang, “Deploying energy routers in an energy internet based on electric vehicles,” IEEE Trans. Veh. Technol., vol. 65, no. 6, pp. 4714 – 4725, Jun. 2016. [6] Z. Zhou, M. Dong, K. Ota, R. Shi, Z. Liu, and T. Sato, “A gametheoretic approach to energy-efficient resource allocation in device-todevice underlay communications,” IEEE Commun., vol. 9, no. 3, pp. 375–385, Feb. 2015. [7] Z. Zhou, K. Ota, M. Dong, and C. Xu, “Energy-efficient matching for resource allocation in D2D enabled cellular networks,” IEEE Trans. Veh. Tech., vol. PP, no. 99, pp. 1–1, Oct. 2016. [8] S. Zhou, T. Zhao, Z. Niu, and S. Zhou, “Software-defined hyper-cellular architecture for green and elastic wireless access,” IEEE Commun. Mag., vol. 54, no. 1, pp. 12–19, Jan. 2016.

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