Mathematical and Control Scientific Issues of Smart Grid and Its Prospects

Mathematical and Control Scientific Issues of Smart Grid and Its Prospects Sheng-Wei MEI1

Jian-Quan ZHU2

Abstract: Taking into account the connotation and engineering demand of smart grid, this paper summarizes and extracts several basic scientific issues of smart grid during its construction and development process, including prediction, energy storage, control, dispatching, planning, assessment, and their common engineering game theory. These basic scientific issues respectively belong to the mathematics, control science or their cross discipline. The solution of these issues not only is the precondition of the realization of smart grid, but also can promote the application perspective of mathematics and control science. Thus, it possesses a significant value in the theory and engineering research. Keywords:

Smart grid, engineering game theory, control science, artificial complex system, survivability assessment

Smart grid has been an overall solution of electric power industry driven by various factors such as the global energy, environment, economy, technology and so on. At the current stage, the facts that the energy shortage problem has become more and more prominent, the climate warming pressure is increasing and users are requiring higher power supply service level bring new challenges to the electric power industry. On the other hand, new technologies such as measurement, communications, information technology (IT) and control are making continuous progress, and account providing opportunities for power industry to make a transformation. Just under this circumstance, the power industry steps into a new development stage. It can absorb more renewable energy sources through smart grids to improve power supply reliability and power quality. At the same time, it can also focus more attention to users satisfaction, social benefits in energy saving and environmental protection, as well as energy economy development. At present, numerous countries in the world are committing in smart grid construction. The smart grid construction in the United States mainly focuses on three aspects. The first one is to upgrade and update power grid infrastructure to guarantee reliable power supply. The second one is to apply technology advantages of information, communication, and computer science into power systems. The third one is to further realize the interaction between power companies and users through infrastructure improvement with advanced smart meters. As early as in 2001, the United States began its smart grid study on the above points. And after that, in 2003, the Department of Energy (DOE) released “Grid 2030” program and established the Smart Grid Alliance[1] . In 2004, DOE launched smart grid research work. In 2005, GE, IBM, Siemens, Google, Intel and other enterprises began smart grid research[2] . In 2008, Boulder city in Colorado State began to build itself into a smart grid demonstration city[3] . In 2009, along with Obama s economic recovery plan, smart grid was regarded Manuscript received October 31, 2012; accepted November 8, 2012 Supported by National Natural Science Foundation of China (50977047) Recommended by Academician Lin HUANG Citation: Sheng-Wei Mei, Jian-Quan Zhu. Mathematical and control scientific issues of smart grid and its prospects. Acta Automatica Sinica, 2013, 39(2): 119−131 1. State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 10084, China 2. School of Electric Power Engineering, South China University of Technology, Guangzhou 510640

as a national strategy of the United States. According to the relevant plans of United States, the household electrical equipment in the United States may be gradually remote controlled during the years of 2010 ∼ 2020, and all of the electrical equipments in the United States will be automatically controlled by 2030. The European union emphasize on constructing the smart grid as an important platform to improve the utilization rate of renewable energy, so as to solve the issues of energy, climate and environment[4] . In 2004, the countries of EU initiated the European Technology Forum on Future Grid to promote European power grid development. In 2005, the European Technology Forum on Smart Grid was established. In 2006, the European Technology Forum on Smart Grids released “A European Strategy for Sustainable, Competitive and Secure Energy”, in which the prospect of smart grid construction was described[5] . In 2009, the EU announced Strategic Energy Technology Plan (SET-Plan). According to the plan, the EU renewable energy will be able to 35 % of the power supply in 2020 and EU power will be mainly supplied by new energy resources by 2050. By that time, the European grid will become a super power grid with renewable energies. The focus of smart grid in China is to ensure sufficient energy supply to satisfy high speed development of national economy. This includes two aspects: one is to strengthen the transmission link to realize large scale energy distribution via smart grid technology, so as to further solve the imbalance between energy and load in China. And the other is to strengthen the power distribution and utilization link to improve power supply reliability and quality. In 2005, the digital power grid construction plan was proposed by China State Grid Corp in its “SG186” project. At the same time, Tsinghua University joined the China Southern Power Grid Corp to carry out “digital China southern power grid” research and construction[6] . In 2007, China North Power Grid Corp approved a project on smart grid study[7] . In 2009, the China State Grid Corp formally proposed the target of smart grid construction, that is, to construct the “strong smart grid” in three steps, namely, by applying UHV power grid as its main frame, developing all levels of power grid coordinately, and uniting information technology, digitization, automation and interactive characteristics on the smart grid[8] .

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To sum up, the research and construction of smart grids in China and Western countries have been carried out with different focuses. Just under such circumstances, there has not been a unified definition of “smart grid” so far. Nevertheless, the basic scientific issues that smart grid contains are common, and the differences are mainly in external forms or specific technologies. In the early 1980 s, Mr. Tsien presented one paper regard the natural science research as basic research of mathematics discipline and physics discipline in essence. Upon some scholars objection, Mr. Tsien revised his perspective to “regard natural science as basic research of mathematics and systems science”. Even so, that article brought about a great impact in the academic circle due to his novel argument, unique views and careful logic. The best science students at that time chose mathematics or physics as their major. Mr. Tsien s point of view greatly inspired the confidence of researchers, especially young students (including the author, of course), to carry out researches on science and technology. Time flies, and the smart grid has appeared today. Following Mr. Tsien s ideas, this paper aims to summarize the technical connotation of the smart grid, extract basic mathematics and control issues closely related to smart grids in the hope of developing a new growing point of this subject and further providing scientific basis for smart grid construction.

1

Connotation of smart grid

The smart grid is also known as the future grid or the next generation power grid. According to the smart grid development in Western countries and Japan, with a view to guarantee energy supply, construct reliable power grid and strengthen the interaction between users and grid, these countries are committed to apply the advanced technologies such as measurement, communication and control in energy field, so as to upgrade and improve the traditional power grid. China is also not an exception. For better understanding smart grid, this paper will make a detailed analysis on smart grid connotation in the aspects of smart grid source, characteristics, differences from the traditional grid, main research contents, key technology and so on, and further summarize and refine the basic science issues related to smart grids.

1.1

Two main sources of the smart grid

The smart grid can be traced back to the “digital power system”[9] proposed by Prof. Qiang Lu, the academician of Chinese Academy of Sciences and professor of Tsinghua University, and “the friendly power grid”[10] proposed by Tokyo Power Company. Lu defined the digital power system as a fully digitized description and reproduction of physical power system, including power system physical configuration, operation, technical performance, management and enterprise culture and so on. This definition is the earliest one that pointed out the development direction of power industry from the angle of informatization. It can be regarded as the prototype of the smart grid. Tokyo Electric Power Company put forward the development concept of the friendly distribution power grid upon users demands. In 2009, Lu clearly defined smart grid on the basis of his

original digital power system and the latest development of power grids, that is, the smart grid is an intelligent power system at 110 kV and below, with multi-index selfoptimization operation capability[11−12] .

1.2

Seven characteristics of smart grids

The smart grid has seven characteristics when interacting with power users, adapting to various power demands, supporting the mature power market, satisfying high-quality power demands, asset optimization, self-healing and preventing external damage and attack[13] . Through interactions with power users, the electric equipments in power grids can be included in power grid design and operation management. The characteristics of adapting to various power demand means that the power system can meet requirements of different power distribution and generation modes. Supporting mature power market refers to support the fully competitive power market. Satisfying the highquality power demands means to provide high-quality uninterrupted power for residents living and production. Asset optimization means continuous capital asset optimization via information system and monitoring technology so as to reduce maintenance cost. Self-healing means quick recognition, analysis and handling of faults so as to recover power supply as soon as possible. Preventing the external damage and attack means the power system is capable of avoiding and resisting external physical and cyber attack.

1.3

Differences between smart grid and traditional grid

As the next generation power grid, smart grids have significant differences from traditional power grids in aspects of electric generation, transmission, distribution, utilization and communication means. Table 1 shows the details. We can see from Table 1 that smart grid has the advantages of flexible power generation, strong power grid structure, various control modes, more renewable energy absorption, highly efficient operation and management in the perfect power market environment due to the utilization of advanced materials, equipments and technologies. It can also stimulate users to have more interactions with power grids to realize two-way flow and control between energy and information. Compared with the traditional power grid, the smart grid has more advanced modes and ideas in the development and utilization of power grid equipments, technologies, and energy sources.

1.4

Social and economic benefits of smart grids

The smart grid leads to a great innovation of the power system with advanced technologies and concepts. It brings about significant benefits to users, investors and the society through applying new system, new elements (new energies and equipments, power system staff and users), new technology (information technology, system analysis technology and control technology), new policies and new ideas (the concepts of electric power system management and energy utilization). Thus, users will get higher-quality power supply, better service and less electricity expenditure. In-

Sheng-Wei MEI et al./ Mathematical and Control Scientific Issues of · · · Table 1 Item

Comparison between smart grid and traditional grid Traditional grid

Smart grid

Centralized power generation;

Co-existence of centralized

Power

transforming traditional

and distributed power generation;

generation

fossil energy to electric

transforming the renewable

energy

energy to electric energy

Transmission

Extra high voltage (EHA)

Vltra high volage (VHV)

Distribution

Conventional distribution substation

Smart distribution substation

Utilization

One-way utilization

Interaction between power supply and demand

Communication mode

One-way communication

Two-way communication

Control method

Conventional control

Smart control

Power system

Mal-mature

Mature

vestors can reduce infrastructure investment, transmission loss, maintenance expenditure and improve power grid efficiency. As for social benefits, the smart grid will avoid unnecessary blackout losses, improve energy security, provide more energy and environmental benefits and promote economic development. Therefore, the development of smart grids will create a win-win situation and bring significant social and economic benefits.

1.5

Main content and key mathematical and control issues of smart grid

Smart grid is a comprehensive upgrade of traditional power generation, transmission, distribution and consumption. To better develop smart grid, excessive research should be carried out. At power generation side, the research indudes new energy power plant planning, site choosing, investment, cost and equipment management, etc. At power transmission side, the main researches include power grid planning, interconnection of renewable energy to the grid, operation dispatching, wide area control and security defense. At distribution side, the main researches include advanced measurement system, communication technology, information security technology, network technology, microelectric vehicle charging station, advanced distribution automation and so on. At power utilization side, the main researches include intelligent building, intelligent electrical apparatus control mode, user electricity consumption characteristics, supply and demand interaction mode and incentive strategy, etc.

2 2.1

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Key mathematical and control problems Prediction technology

There are a lot of uncertainties in both the power supply side and load side of smart grid. In order to deal with these uncertainties, the service providers should precisely predict the demand and reasonably make power supply schedule and real-time fault solutions. Although the load prediction technology has been improved significantly, its accuracy is still not high enough and the power suppliers have to backup units to guarantee the power balance, which usually causes waste of resources and environmental pollution. A great challenge in smart grid comes from the uncertainties of power sources. The connection of large-scale renewable power with fluctuation and intermittency will impact

the power grid and bring about security and stability problems. This poses a great challenge to the prediction technology. We will briefly discuss this by taking wind power as an example. 2.1.1 Background of wind power Wind power is abundant and clean renewable source of energy. According to statistics, the total amount of wind power around world is around 130 billion kW, out of which there is 1.6 billion kW in China. In recent years, the world witnessed a rapid development of wind power, especially under the background of energy shortage and global warming. At the end of 2009, the global wind power installed capacity has increased to 158 million kW, including 44 million kW in China. China s wind power installed capacity became the largest in the world with a year-on-year growth rate of 108 %. Due to the uncertainties and fluctuation of wind power, its connection to the power grid will lead to two problems. Firstly, it will be more difficult to make precise generation schedule. Secondly, it will bring about large impact to the power grid. Without doubt, if wind power output can be predicted more precisely the security and stability problems caused by its uncertainties and fluctuation will be greatly eased. 2.1.2 Wind power prediction Wind power prediction refers to making a prediction to the future power output of wind plant by establishing the output prediction model with various data of wind plant such as meteorological data, topography, wind generator operational state, etc[14−15] . Considering the importance of wind power prediction for the wind energy development and utilization, scholars both at home and abroad have made tremendous studies on it and put forward various representative algorithms. The three most typical algorithms are power prediction algorithms based on the time series[16] , BP artificial neural network[17] and combined algorithm[18] . The time-series based algorithm builds a time series model (autoregressive integrated moving average model, ARIMA) mainly based on historic data, and then generates the prediction on wind power output according to the wind speed statistic law described by the time series model. The second algorithm makes a prediction based on the correlation between wind power and the influencing factors such as weather, temperature, etc, which has advantages of simple operation and good nonlinear fitting ability. The third method makes a wind power prediction by combining the prediction results from different prediction models through equal weight combination, variance combination, regression and other com-

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bination methods in accordance with their characteristics, and this method can improve prediction accuracy. Wind power prediction accuracy is actually influenced by many factors and the accuracy of wind speed prediction is the most important one. According to the research result of Dr. Lorentz, a meteorologist of the United States, long-term weather forecast often deviates hugely due to tiny change of environmental factors[19] . Since it is hard to obtain the influence of the weather factor changes, long-term weather forecast becomes extremely difficult. This finding is known as the “butterfly effect”, which reveals the root reason for poor accuracy of climate forecast. Up to now, the wind power management system developed by German Solar Energy Research Institute is a relatively mature prediction system for commercial application, but its prediction error still reaches 7 % ∼ 19 % of the installed capacity[17] . And the average error of other wind power prediction methods is generally higher than 15 %[20] . Fortunately, the wind power “cluster effect” is an important mean to overcome the wind power prediction problems. Affected by a large number of determinate and indeterminate factors, the power generation and utilization of power systems including wind power is highly uncertain in essence. For example, a sudden weather change will cause millions of people of Beijing to start or stop heating and lighting. Another example is that tens of millions of people in North China will switch on/off lamps, TV, computers and other electrical apparatus for living or working needs. Power supply reliability may also be affected by power plant or transmission line faults or extreme weather (such as transmission lines discharging power into fallen trees, ice up on transmission lines, and severe dry weather influencing hydroelectric or nuclear plant, etc). Therefore, power generation and utilization both have uncertainties. It can be seen that the key issue of wind power utilization efficiency is not its instability or intermittency, but how to predict this uncertainty and provide basis for advanced management and control technology. In other words, researches can only be meaningful when the wind energy instability is considered in a whole power system instead of simple analysis and smooth output control on a wind plant or a wind turbine. Although wind does not blow continuously, when the wind stops at one place, it blows at other places. Therefore, it brings about little effect to the whole. A reliable power can still be obtained as a whole although a certain place does not have continuous wind. This is why we make use of “cluster effect” of wind power. For example, the 300 km long Sanbian Wind Power Plant in North Shannxi province is with the wind velocity error 11 %. And the wind velocity error of the 2 500 km long east coast of North America is 5 % when the cluster effect is not considered. According to current technical level, it is difficult to achieve accurate local wind power prediction through wind power modeling. But the high accuracy prediction can be achieved in large scale power grid by using wind power “cluster effect”. It can offset the wind power uncertainty of a single wind turbine and obtain more accurate prediction results as a whole. 2.1.3 Other prediction issues Prediction technology is mainly used to solve electricity imbalance issues in smart grids. Therefore, in addition to above wind power prediction issues, it is also involved in the photovoltaic power generation prediction, local load prediction, railway transportation capacity prediction and

the influence of large range climate change to prediction results. Taking photovoltaic power generation as an example, as more and more photovoltaic power is interconnected to power grids, prediction of photovoltaic power generation becomes increasingly important[21] . Since photovoltaic power generation will be influenced by meteorological conditions such as solar radiation intensity, its output is random and it is difficult to make an accurate prediction. At present, the research on photovoltaic power generation prediction is rather limited and the main existing methods only include autoregressive moving average model, neural network method and so on[22] . Relatively speaking, the load prediction is a traditional problem in power systems, and has attracted much attention and research interest over a long time. Depending on users demand, load capacity has the characteristics of complexity, variability and randomness. Thus, it is difficult to predict single load conditions with a high accuracy. Generally, the overall prediction is adopted in accordance with its “cluster effect”. The prediction methods include time series method, trend extrapolation method, regression analysis, grey model method and so on. Solving these prediction problems will no doubt make significant effect on smart grid development planning and operation dispatching. In a word, prediction technology is the foundation of the game among interested parties in smart grid when they are pursuing for their maximum benefits. The power plant can formulate the bidding strategy according to the power generation and bidding behavior of other power plants. The power company can formulate dispatching control schedule according to the prediction of supply and demand situation. Electric vehicle holders and other users can take a part in power system interaction in accordance with electricity price prediction. The prediction and decision-making behaviors constitute a complex game relationship.

2.2

Energy storage technology

2.2.1 Classification of energy storage technology Energy storage technology can be classified into three kinds in accordance with the storage modes, that is, mechanical energy storage, electromagnetic energy storage and electrochemical energy storage. Specific energy storage type, capacity and application mode are shown in Table 2[23] . Energy storage technology belongs to physics category essentially. Owing to the instantaneous equilibrium of electrical energy (power), developing a storage device with high capacity and fast throughput capacity becomes a priority for smart grid construction and implementation. It also plays a significant role in smart grids especially for self-healing realization, robustness, interaction, and compatibility functions. But it should be noted that the research on energy storage device with high capacity and fast throughput functions can hardly achieve a breakthrough progress in the foreseeable future. A feasible idea is to study and develop control and dispatching method of advanced small capacity energy storage equipment group (including the management of charging and discharging), thus, the storage technology can be included into the category of mathematics and control science. 2.2.2 Storage technology application in smart grid Interconnection of new energy into power grid brings various adverse effects to the safe operation of power grid. Strong randomness and intermittency of wind and solar

Sheng-Wei MEI et al./ Mathematical and Control Scientific Issues of · · ·

power due to the influence of natural conditions such as wind speed and sunshine intensity, makes them as disturbance sources in power systems. For example, wind turbine may easily cause a chain of failure since it cannot make low voltage through. In addition, wind fluctuation will cause voltage flicker in power systems and reduce power quality. In theory, the application of energy storage equipment can greatly help power systems accept and consume more wind and photovoltaic power, and reduce their negative effects on the power system. The energy storage devices can store excess energy from new energy plants and release energy to overcome power shortage trouble. Therefore, the power fluctuations from renewable energy power plant can be significantly reduced in the entire system. However, the research and development level of large capacity storage technology is still insufficient and the construction and maintenance costs are relatively high. In addition, the environmental issues caused by storage equipment like various batteries in the process of production, operation and waste treatment, is also difficult to be well solved, which greatly restricts the energy storage equipment from being widely applied in power systems. The electric vehicle is an important energy storage resource in smart grids which can be used as a controllable power supply or load to regulate the peak and low points of power grid[24−27] . To make full use of the storage resources and achieve mutual benefits of the electric vehicle holders and power grid, it becomes necessary to well guide the electric vehicle to be charged and discharged following the key principle “discharging at peak point and charging at low point” upon charging and discharging demand of power systems. It turns out to be a kind of typical nonlinear mixed integer programming issue actually. In addition to electric vehicles, conventional pumped storage is also an important energy storage mode in smart grids. Electric vehicles and pumped storage both have the characteristics of power source and load, and relate to the interests of power plants, power grids and users. A random dynamic game pattern is formed by them. Renewable energy, such as wind and solar, can obtain economic benefits through power generation, but it needs energy storage devices to balance their own uncertainty. The benefits of electric vehicles and pumped-storage power plants are closely related to the uncertain situation caused by power generation of wind power plants, solar power plants and other renewable energy power plants. Thus, there exist mutual interdependence and restriction between renewable energies and energy storage devices. At the same time, there also exists competition between wind power and solar power and so it does between electric vehicles and pumped storage. Therefore, the energy storage issue in smart grids can be formulated as a game among various interested parties to pursuing their maximum profit. Then, energy storage equipment in power grid can be effectively managed and operated through solving the game problem, so as to realize peak clipping and valley filling.

2.3

Control technology

Smart grid is a major research direction of advanced control technology[28] . This section will mainly introduce

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network control, decentralized control, hybrid control and coordinated autonomous control under smart grid background. Among them, the former two control theories are mainly used to solve control issues of power grid parameters and various decentralized resources in power grids; the latter two control theories are important ways to control large power grids intelligently, and can provide significant references for constructing “strong smart grid” with UHV in China. They will be introduced respectively below. 2.3.1

Network control technology

Network control is a new method for smart grid control. The conventional network control method concentrates only on nodes (such as power plants and substations in power systems) and is powerless with tie-lines. After FACTS (flexible AC transmission system) technology is introduced into power grid, the power grid control efficiency is greatly increased. Through controlling FACTS devices such as SVC (static VAR compensator), STATCOM (static synchronous compensator), TCSC (thyristor controlled series compensation), SSSC (static synchronous series compensator), TCPST (thyristor controlled phase shifting transformers) and UPFC (unified power flow controller), power grid parameters can be continuously adjusted upon the system need, flow distribution can also be effectively improved without changing the grid structure, power transmission capacity can be increased and voltage and power angle stability can also be improved. For example, effective control of UPFC can overcome the “power bypass” and “power against flow” problems in transmission network, reduce power loss and improve utilization efficiency. Further, the control of TCSC can effectively reduce the electric power transmission distance by about half (like from 1 000 km to 500 km) and double transmission power limit without additional investments. This is particularly important for China to realize the “long distance and large capacity” power transmission strategy. It is obvious that power control method will extend the control objective from nodes to tie-lines, and thus bring a huge challenge to the traditional complex network control technology itself. Wide area measurement system (WAMS) has been worldwide implemented ever since it was successfully applied in the United States in 1990 s. As WAMS can collect realtime information of wide area power grids with the same time benchmark, it can provide reliable basis for power grid control. The modern power systems have two important characteristics. On the one hand, its scale becomes larger and larger (for example, China has the largest AC synchronized power grid in the world after national power grid interconnection). On the other hand, the electrical power system has been interconnecting more and more closely. In this case, the local fault in power systems may cause a serious impact to the whole power grids. For example, low frequency oscillation problem induced by small disturbance has occurred many times in power systems like in North America, Europe and Japan. The large scale blackout in North America on August 14, 2003 is the most serious one, in which 1/7 population of United States and 1/3 population of Canada were involved[29−31] . The emergence of

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Acta Automatica Sinica, 2013, Vol. 39, No. 2 Table 2

Applications of energy storage technology in power systems

Type Pumping energy storage (ES) Compressed air energy storage (CAES)

Typical rated power Typical rated time Application 100 ∼ 2 000 MW 4 ∼ 10 h Daily load adjustment, frequency control and system backup 100 ∼ 300 MW

6 ∼ 20 h

Peak-regulating power plant and system backup power Peak-regulating

Mechanical Micro-CAES flywheel-ES (FES)

10 ∼ 50 MW

1∼4h

Flywheel-ES

5 kW ∼ 1.5 MW

15 s ∼ 15 min

Peak regulating, frequency control, uninterruptible power system (UPS), power quality regulating

Electromagnetic

Superconductive magnetic energy storage (SMES)

10 kW ∼ 1 MW

5 s ∼ 5 min

UPS, power quality regulating, power transmission system stability

Capacitor

1 ∼ 100 kW

1 s ∼ 1 min

Power quality regulating, power transmission system stability

Ultra-capacitor

Combined with flexible alternative current transmission systems (FACTS)

Lead-acid battery Electrochemical

Advanced cell technology, such as VRLA, NaS, Li, etc Liquid cell, such as ZnBr, NaBr, etc

1 kW ∼ 50 MW kW scale to MW scale

Power quality, reliability, frequency control, backup power, blackout start, UPS

1 min ∼ several hours All kinds of application

100 kW ∼ 100 MW

the WAMS system brings new chances and challenges to traditional power systems. Since the WAMS system can dynamically measure the electrical parameters in different regions, the overall analysis and control of power systems can be realized. With the WAMS system being successfully applied in state estimation, stability monitoring, model validation, fault recording, relay protection and so on, it has been playing an important role in promoting the development of modern power systems[32−34] . But considering the time delay occurred in signal acquisition and transmission, protocol conversion, parameters adjustment of timing equipment and so on, wide area signals have not realized real synchronization in the whole grid. In poor conditions, the transmission of wide area measurement signals at different regions may be delayed by hundreds of milliseconds, which will cause the controller failure[35] . The existence of these delay issues, to a certain extent, makes the power system security analysis and stability control more complex, and becomes one of the root causes of power systems instability[36−37] . The delay of wide area measurement system includes fixed delay and random delay. The former can be described from linear and nonlinear angles. Some scholars have considered the linear delay effects when carrying out research on small disturbance problem[38−39] , but the research on nonlinear delay effect of wide area measurement system is still relatively insufficient. In short, the application of WAMS technology provides a brand new horizon for complex network in aspects of analysis and control, as well as simulation research. 2.3.2 Decentralized control based on multi-agent technology Multi-agent technology is a kind of distributed artificial intelligent technology. It can respond flexibly to the various external changes by the collaboration behaviors between agents[40] . It has characteristics of autonomy, reactivity, initiative and sociality. At present, it has been relatively successfully applied to power system distributed calculation, power market simulation and computation, relay pro-

1 min ∼ 3 h

1 ∼ 20 h

Power quality, reliability, peak regulating, energy management, renewable energy integration

tection and so on[41] . With the development of smart grids, more and more micro-grids will be constructed. It contains various distributed generation sources such as wind power, photovoltaic power and fuel cell, etc. Micro-grids can operate in parallel to the bulk grid or can operate in island, providing utility power station services. Since micro-power grids also possess characteristics of autonomy and sociality, the multi-agent technology can be adopted for their distribution control. According to multi-agent technology, each micro-grid can be treated as an agent that gets coordinated control with bulk grids through processing integrated data, formulating plans and issuing orders[42] . For example, the micro-grid with photovoltaic generation and battery storage can be further subdivided into photovoltaic cells agent, fuel cell agent, and battery agent and so on. The photovoltaic cell agent can track the maximum power points, monitor cell plate and work as grids-connected inverter. The fuel cell agent can achieve functions of fuel processing, hydrogen and oxygen content monitoring, thermal treatment and power regulation. And the battery agent can control the micro-grid in aspects of voltage, current and start-stop determination. Thus, the multi-agent technology can solve micro-grid coordination and control problems through information and energy interaction. This technology can make a large number of dispersed resources in smart grids easier to be managed. And it can also enhance the self-healing capability of smart grid through the rapid response of each autonomous and heuristic agent to external environment changes. 2.3.3 Hybrid control Professor Qiang Lu once pointed out that Chinese power grids will face many new challenges with more and more power type micro-grids, distributed power generations, large scale renewable energy power generation bases, as well as new customers such as electric vehicles and load type micro-grids. Therefore, to solve these problems, it becomes necessary to construct power grids with “self-approximate-

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optimal operation ability according to multi-index” to control the large power grid as a wide area robot[43] . Prof. Yaonan Yu, a tenured professor of Canada Vancouver B.C University, once called the power system in North America as the largest industrial robot created by human. In fact, modern power systems are far more complex than a general industrial robot. It has pulse (frequency), blood pressure (voltage) and brain (dispatching control center). Since power system is a big system with dynamic partitioned blocks and multiple layers, it needs to be described with strong nonlinear high dimensional differential equations. It is hard to solve such a complicated problem with pure mathematics method. An innovation thought is needed. Hybrid control provides an important theoretical basis for wide area robot, the highest intelligent level of power grids. According to hybrid power system control theory, the power system can be divided into decision-making layer, intermediate layer and control layer to solve its control issues. Wherein, the information analysis subsystem at decisionmaking layer collects information from the dynamic power system (controlled layer), determines whether an “event” is formed in accordance with the event definition, and then, generates corresponding control commands through the intelligent decision-making system. The intermediate layer converts received control commands to operation instructions and delivers them to the execution layer. The controlled layer includes direct dispatching hydroelectric plants or power plants, transformer taps, FACTS equipments, electric vehicles, intelligent buildings and so on. With hybrid control theory, a simple framework can be used for solving complex issues of power system multi-objective optimization. All layers have clear functions. It is an ideal engineering realization method. Thus, as a realization method for large scale power grid control, hybrid control can provide not only an important reference for solving complex mathematical optimization issues under engineering background, but also an important theoretical support for China strong smart grid construction and operation management. 2.3.4 Coordinated autonomous control Coordinated autonomous control has become an important way to realize smart grids[44] . In smart grids, the coordinated autonomous control manifests the coordination and cooperation between smart grid components, as well as their independent adaptive behavior to different systems. Wherein, coordination means the support function at the system normal operation and automation refers to that one subsystem fault will not influence the other subsystems. With the construction of smart grids, there will be more and more controllable resources groups. Coordinated autonomous control method can be used to decentralize and coordinate these resources under physical and economic constraint conditions of power systems. There is great difference between coordinated autonomous control and traditional centralized control strategy. As for centralized control strategy, it will collect and analyze all information of the whole grid to further analyze and process all events in the system, which needs more calculation and analysis tasks and reduces the overall control efficiency. By comparison, coordinated autonomous control strategy is faster and more efficient since it can complete the coordination control only with a small amount of information. It is also quite reliable because faults in one autonomous control center will not influence those of others.

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As a large complex system, power system includes a large number of components and covers wide geographical ranges, so global analysis will need more information exchanges and more calculations. Thus, coordinated autonomous control has a better application prospect than centralized control. It is obvious that the general system control faces the same challenge as the smart grid control. Although different methods are adopted to solve different issues, they also have a common problem, that is, how to use game theory to design closed loop system controller. In fact, any control problem can be classified as game problem[45] . The control objective is to keep the controlled objects work in the expected operation mode and state through human intervention. But, the control process faces some uncertainties due to external disturbance and the threat from opposing interest parties. Therefore, the control engineer must comprehensively consider these factors when formulating control strategies, so as to achieve the predetermined control target. From the angle of game theory, the external influence factors can be regarded as static opposing players, and then the control problem will actually turn out to be a “single game”. Considering the threat from opposing interest parties, the whole control process will become the classic “two-person zero-sum game” issue. In the power system, the electrical relationship and the interest relationship between various controlled objects are more complex which include cooperation, competition, and conflict, etc. Therefore, it is one of the most challenging research problems to apply game theory to power system control.

2.4

Dispatching technology − dynamic game theory

Power dispatching automation system can monitor the real-time voltage, current, frequency and phase angle of the whole system, and automatically (or manually) adjust active power and reactive power through various regulation methods and devices, or ensure the power balance through network structure changes and load switching. The core task of the power system dispatching is to make judgments, decisions and commands in accordance with current operation condition and predicted changes of power system so as to ensure power system operate in a safe, high quality and economical state. According to Wiener cybernetics, dispatching also belongs to the power system control category with its time constant at minute level[46] . The uncertainty in conventional power system is usually at load side, so generally the power grid dispatching center copes with this load uncertainty based on load prediction results and controllable power source to realize the reasonable and efficient power transmission and distribution. Under smart grid background, power supply also brings out very strong uncertainties with increasing renewable energy power generation[47] . This will make the power dispatching center face bilateral uncertainties of both power supply side and load side of smart gild. Thus, random dynamic game will be a possible choice. For example, the competition-cooperation game of wind power station group, power station group and energy storage is a typical dispatching issue in future smart grids. On one hand, the wind-photovoltaic-energy storage power plant can effectively suppress the randomness and fluctuation of each single power field through complementary effect of various energies. Thus the impact on the power grid can be

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significantly decreased, but the energy storage unit costs more. On the other hand, wind and photovoltaic power generation has considerable cluster effect, so the two can be effectively integrated to solve the key issues of new energy ultra-distance transmission and optimal dispatching. In order to solve the issue of renewable energy output fluctuation, the power grid should be equipped with more backup and make adjustment to conventional units when large scale renewable energy sources are long-distance transmitted, all of which will increase the power grid operation cost to some extent and is contrary to the original intention of developing large-scale renewable energy. Therefore, when wind and photovoltaic power generation cause power fluctuation, random game theory can be adopted to determine how to allocate the reserve capacity, how to coordinately dispatch the peak regulating power units by making full use of time complementary characteristics of wind and photovoltaic power generation and regulating characteristics of energy storage systems, so as to further improve the accommodation capability of large scale renewable energy[48−49] .

2.5

Operation technology − smart grid benefit evaluation

The smart grid can be regarded as an energy transmission “speedway” and provides an important platform for the development and utilization of various renewable energies such as solar energy, wind power and so on. It started a new energy revolution in the production, transmission and utilization aspects through changing people s consumption habits and electric power company s management philosophy based on the interaction methods. In addition, the smart grid is also an integration of cross-domain, crossindustry, inter-discipline, which will lead to the development of information, communication, computer, new materials, equipment manufacturing, and further derive intelligent home furnishing, intelligent buildings, intelligent transportation and other new industries. It will promote all-around development of economy and society. So far, the smart grid has been become an important measure to solve energy issues and reshape economic influence in the United States, European Union and other countries. China has also formulated a definite target to promote smart grid development in “The Twelfth Five-Year Plan for National Economy and Social Development”. According to relevant data, China s investment on smart grid will reach 1 500 billion during 2010 ∼ 2015[50] . But as an important project, smart grid construction has the characteristics of huge investment, numerous influence factors, long construction period and wide involvement. Therefore, it needs careful planning and arrangement to achieve the desired comprehensive energy utilization effect. And once the decision-making is inappropriate, it will bring tremendous negative effect, cause a waste of capital, and make industry development stagnant or even decline. The operation related technologies will be introduced below with combination of smart grid characteristics. 2.5.1 Coal transportation VS power transmission Coal transportation and power transmission are two different ways for energy transferring, and they have caused great arguments in China power grid construction[51] . The people supporting coal transportation insist that coal should be delivered through train, ships and so on to the power plants near load center to generate electricity, while

those supporting power transmission insist that the power plant should be constructed close to coal base and then the power can be transmitted via EHV or VHV to load centers. Reference [52] made a comparison between coal transportation and power transmission with the third coal conveying channel in China and Yinchuan-Caofeidian VHV transmission line, which is 1 319 kilometers long. To make the coal transportation capacity reach 200 million tons per year, the investment of railway construction, port construction and locomotive purchase for coal transportation will reach about 100 billion, while the power transmission method requires more than 20 VHV transmission lines with the total investment being about 160 billion. In the aspect of land resource occupation, coal transportation scheme requires a corridor width of 20 m ∼ 22 m, mainly crossing steppe and desert, while power transmission scheme with 1-tower double-circuit transmission lines occupies 900 m ∼ 1 500 m, crossing some cities. In the aspect of transmission cost, the annual cost for coal transportation is about 87.6 billion, while power transmission will bring about 22 billion kWh power loss (the power price is about 0.4/kWh). Only considering from the above results, it seems that coal transportation is superior to power transmission. But, the actual situation is not so simple. Transmission line construction also has unique advantages in aspects of hydropower development, grid-connection of renewable energy, utilization of inferior coal for power generation and so on[53] . In conclusion, the disputes on coal transportation and power transmission involves many aspects like transportation, electric power and national environmental resources and so on. Whether coal transportation or power transmission should be adopted essentially belongs to operational research category. The reason for coal transportation and power transmission disputes is the fact that both sides make “operation” argument from their own industrial interests, whereas, the game theory provides an effective solution for this class of issues. As a matter of fact, if taking the coal transportation and power transmission as opposing players, their mutual relationship and boundary conditions can constitute constraints of game issues. Then, coal transportation and power transmission can further play game in accordance with the behavior targets of two sides. Although there are various relations between them, such as cooperation, competition, antagonism, and master-slave, one can still find a solution to balance their different benefits, so long as Nash equilibrium can be achieved. It can not only settle the disputes but also form a reasonable coexistence of coal transportation and power transmission. 2.5.2 Solar power and wind power Solar power and wind power are the two most important means for renewable energy power generation. The clean and renewable solar power is an important way to solve power supply issue in remote areas. Its cost is related to photovoltaic component price, operation and maintenance cost, depreciation period, sunlight condition and so on. In China, Lasa and Guiyang are the two cities with the lowest and highest power generating cost respectively. Lasa has strong and long-time sunshine and the cost of solar power generation is only about 0.65/kWh, while Guiyang s cost is about 1.37/kWh. It is worth mentioning that, crystal silicon cells are used in 95 % of the solar power generation and this will cause toxic and high-polluting by-products such as four silicon chloride, and consume a lot of energy in

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production process. The production of wind turbines will also consume a large amount of steel and produce a certain CO2 . Statistics show that one 3 MW wind turbine will consume about 270 ton steel in a whole, about 160 ton for its tower, 70 ton for its cabinet and 40 ton for its blade. But suppose that the service life of the wind turbine is 40 years and the average rates is 50 %, then, its energy consumption is only 0.42 g standard coal/kWh and 1.07 g CO2 /kWh. So wind power has significant advantages compared with thermal power generation in the aspect of energy saving and emission reduction. On the other hand, the integrated benefit of solar power and wind power generation is also related to their interconnection state. Taking wind power for example, the data in “Investigation Report on China s Wind Power Development” (published by the State Electricity Regulatory Commission of PRC) show that nearly 1/3 China s wind power generator are idle[54] . At the end of 2010, the installed wind power capacity in China was 41.827 million kW. The unit cost of wind turbine is about 7 000 ∼ 8 000/kWh. Therefore, with 1/3 idleness rate, at least 97.6 billion yuan are wasted. A single new energy generation will bring about great random fluctuation to power grids. If various new energy generation methods are adopted at the same time, their complementary advantages will effectively suppress the fluctuation as a whole. In view of natural complementarities of wind power generation and solar power generation in time and region, they can be combined to make power generation much smoother. This is actually a kind of cooperative game. Solar power and wind power form a coalition in a cooperative way to obtain the maximum coalition benefits by using their complementary characteristics. Then, each maximizes their interests through a reasonable allocation scheme. This is a kind of typical cooperative game issue. 2.5.3 Operation planning of major projects Smart grids cover nearly all aspects of power systems. As a large-scale construction project, smart grid should both solve technical problems and adjust related industries and political and economic policies. The construction of smart grid will promote the research and development of a series of new materials and equipments such as battery, sensor, communication, electric vehicle and so on. It can also promote energy economy industry chain development, achieve the energy structure optimization and ensure national energy security fundamentally. Major projects should be rigorously and strategically planned. Generally, major projects involve various fields and make extensive and far-reaching influences on economy and society. Besides, the external environment is dynamic and uncertain and the decision-making information is usually imperfect. Therefore, only careful analysis and argumentation can lead to scientific decision results. China had undergone some experiences and lessons in aspect of major construction decision-making. According to the World Bank statistics, the error rate of investment decision-making in China is about 30 %, and from “The Seventh Five-Year Plan” to “The Ninth Five-Year Plan”, economic loss was up to 400 ∼ 500 billion[55] . Sanmenxia Water Project, known as the “The first dam in Yellow River” has played an important role in flood control, power generation and irrigation since its completion. But due to mistakes in decision-making, it has been re-

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constructed twice and adjusted three times during its 50year operation, which made great resource waste. After the event of “a normal flood causes a tremendous disaster” occurred in Weihe River Basin in 2003, disputes were aroused even on the existence of Sanmenxia Dam[56] . In addition, the South-to-North Water Transfer Project has also been disputed since it was started at the end of 2002. According to reports, this project is about 3 500 km long with water volume being about 44.8 billion cubic meters and its total investment reached 500 billion. This water transfer project is an effective measure to improve water storage level in North China[57] . This major project involves various complex issues in aspects of national economy, society, zoology, geology, water conservancy and so on. But this project also contained some defects due to lack of feasible scheme comparison in aspects of seawater desalination and so on during the feasibility demonstration stage[58] . With the development of the seawater desalination technology, developed countries like the United States and Japan have taken seawater desalination as their national important industry. The fresh water in Israel, Saudi Arabia and other countries in the Middle East mainly comes from seawater desalination. Because China has mastered the key technology for seawater desalination at present, the cost can be limited at about 7/ton. And according to the estimation of Academician Hao Wang, who was responsible for the general planning of South-to-North Water Transfer Project, the price for transferred water is more than 10/ton[59] . If take the expenses of land occupation, equipments and immigration into consideration, the cost of South-to-North Water Transfer Project will be much higher than that of seawater desalination. In this case, many experts and scholars suggest to use the seawater desalination as a solution to water supply in Beijing and Tianjin areas. Some people even call for applying seawater desalination instead of South-toNorth Water Transfer Project. The Central Committee of the Communist Party proposes the principle of “developing marine economy”, in the name of central government. Then, the seawater desalination was included in the important files such as “Circular Economy Promotion Law of People s Republic of China” and “Several Opinions on Accelerating Circular Economy Development” successively. But the definite policy on coordinating the South-to-North Water Transfer and seawater desalination has not yet been formulated[60] . Actually, game theory can be an effective method to solve the controversial issues such as Sanmenxia dam, South-toNorth Water Transfer Project and seawater desalination projects and so on. Sanmenxia dam is good for power generation, irrigation and so on, but it can also cause sediment deposition and bring potential safety problem to downstream cities during flood. Therefore, the conflict among power efficiency, irrigation efficiency and sediment deposition can be described by a typical “three-person zero-sum game”. When the dam has been built, the benefit conflict of power generation, irrigation and flood prevention can also be analyzed and solved through game theory. Similarly, the relation between South-to-North Water Transfer Project and seawater desalination has developed to be a very complex water resources allocation issue. It involves society, economy, environment and other interests in Yangtse River and Yellow River basin. They have both conflict and complementary relations, so the game theory can also be applied

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to analyze them and look for the Nash equilibrium solution with various interests considered. Thus, it can eliminate disputes and form an optimization scheme to solve the water crisis problem in North China. Smart grid development also needs reasonable operation planning, that is to analyze and model this major project, and get corresponding planning results, so as to achieve the maximum economic and social benefits. This is actually to refine and solve the related problems in the process of smart grid construction and operation management by using mathematical methods. Or in other words, it is a specific application of mathematics discipline in smart grid. Just as mathematics plays a fundamental role in celestial and fluid motion calculation, the development of applied mathematics also determines related scientific decision-making in smart grid to a large extent.

2.6

Assessment technology — risk/survivability/intelligent maturity assessment

Reliability, vulnerability and survivability are three basic issues of system science. As the largest artificial industrial system in the world, the power system also undergoes the above aspects in its development process. Wherein, reliability and vulnerability belong to risk assessment category. They are mainly used to explore the power system operation. Survivability assessment is mainly used to measure the development process of power grids, which plays a central role in the smart grid assessment. In addition, the power grid is related to huge systems engineering, involving many fields and various industries. Its comprehensive development is also an important issue and it is necessary to evaluate smart grid maturity. 2.6.1 Risk assessment During smart grid development process, new components, devices and structures appear in power systems, which bring more uncertain factors and risks. Among them, the new components and equipments include new energy power generation equipments, primary devices and secondary devices for power transmission and distribution, smart meters and intelligent apparatus. The frequent switching on or off of these devices will bring bigger influence to power system. The new structure refers to a flexible power grid connection mode of new energy, electric vehicles and micro-grid. These new structures also make the power grid more complex and increase the operation risk. Advanced risk assessment technology can help to keep safe and stable operation of smart grids. At the generation side, it monitors and evaluates real-time operation state of the generation devices to form corresponding risk information. At the transmission side, it establishes risk assessment system based on complex network theory with combination of wide area measurement systems. At the distribution side, it establishes risk warning system of power distribution grids to improve healing ability. At user side, it releases risk warning signals to users based on the equipment operational information measured by smart meters. Considering informatization is an important characteristic of smart grids, risk assessment on cyber security is also of great significance[61−62] . In fact, the problem of cyber security can be considered as a “two-person zero-sum game” between cyber protector and intruder. In the game

pattern, information invaders try to illegally obtain benefits through reading and processing power grid information, while information protectors protect the power grid information system from invasion to minimize the losses caused by information security problem. Therefore, power companies can decide the application method of information security technology based on game theory to get the best results. In this process, the offensive and defensive game model, cost and profit of the game players and the Nash equilibrium solution can be categorized according to the issues of application mathematics. 2.6.2 Survivability assessment The survivability assessment on smart grid is a new assessment concept of power system. According to “control theory” written by the Wiener and “engineering control theory” written by Tsien Hsueshen, we can know that survivability essence lies in the feedback results[63−64] . In a smart grid, the new sensors such as smart meter and phasor measurement unit (PMU) can collect abundant information from the power grid and transmit them to the dispatching center through fiber, wireless network and so on, which can significantly improve the feedback ability and enhance the survivability of the smart grid. Smart grid has three main characteristics of a living body, that is, growth, metabolism and immunity. In a smart grid, online expansion is a construction form of smart grid, corresponding to the growth character of a living body. Fault-tolerant ability embodies smart grid survival capability, corresponding to the metabolism character of a life body. On-line maintenance mainly solves the problems of smart grid self-healing, corresponds to immunity character of a life body. With these three characteristics, the smart grid can achieve efficient energy development, transmission and utilization, and can flexibly process all kinds of unexpected events to guarantee the power system security, economy and high quality. The smart grid that has the main characteristics of the life body is actually a wide area robot. Therefore, the smart grid development depends on the formation state of growth, metabolism and immunity. We can take the wide area robot as a target of smart grid construction, so as to maximize the intelligence level of power systems. 2.6.3 Assessment on intelligent maturity The smart grid represents power system development direction under the conditions of economical progress, environmental changes and rise in scientific and technological level. It can only be realized after long-term construction. Whereas, it is not to say that the previous power systems have no intelligence characteristic and we can build a smart grid after some years. The smart grid construction is a long-term process. In fact, the process of using centrifugal pendulum to measure generator velocity and automatically regulating steam (water) volume for frequency stability, made the power system with a certain degree of intelligence in early years. With the energy management system (EMS), distribution management system (DMS) and other advanced analysis management system being applied in power systems, people began to use the computer to realize power system analysis and control, which further raise the intelligence level. Under the promotion of computer, communication, control and other advanced technologies, power system intelligent level becomes higher and higher and its connotation is more and more abundant. But it

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is still far away from the smart grid realization. In order to better plan and construct smart grid, we should assess smart grid maturity to make its development stages and corresponding contents clear. IBM research shows that smart grids can gradually become mature through five development stages[65] . At the initial stage, people begin to put forward the construction plan. At the second stage, electric power enterprises invest in and construct smart grids. At the third stage, smart grids will realize business integration and industry chain extension. At the fourth stage, smart grids will achieve comprehensive control on a variety of business and derive new commercial modes and economic growth points. At the fifth stage, smart grids will have a new round of development in new business and environment. Smart grid maturity can be accessed from the following 8 aspects: organizational structure, technical level, management level, power grid operation state, personnel and assets, development and integration level of the industrial chain, users interaction level, social factors and the external environment[7] . At present, nearly 200 smart grid maturity assessment indices have been sorted up during the smart grid projects of American Productivity and Quality Center, Global Smart Grid Alliance, IBM and 6 electric power companies, which are suitable for different aspects of all stages of smart grids construction. However, the whole assessment system is still under constant improvement. In addition, Tsinghua University has established a 2-level index system for smart grid in accordance with the development characteristics of power grid in China, that is strategic index set and process index set. The strategic index set belongs to macro-scope and process index set belongs to micro-scope. These two sets form a close index chain[66] which is clear in logic and layers and easy to use, and provides useful references to smart grid maturity assessment. The risk assessment, survivability assessment and maturity assessment of smart grids can describe the survival and development process of power systems very well. Evolutionary game theory provides a novel tool for this kind of problem. It helps the game players to make strategic selection with competition evolution rules of biological species or groups[67] . “Evolution” can better explain the development process of growth, metabolism and immunity of smart grid. And “game” can help different decision-makers in smart grid to make a coordinated development to maximize their benefit respectively.

2.7

Engineering game theory

As for the above six key technologies (energy storing technology, control technology, dispatching technology, operation technology and assessment technology), every technology has its own characteristics with different objects and realization methods. They are consistent in the safety of operation target, but competitive for economic benefit. Since there exists conflict between safety and economy, and renewable energy will cause fluctuation and intermittency, the issue becomes very complex. From the view of game theory, the renewable energy power generation, energy storage systems, traditional power system and so on can be regarded as game players with certain behavioral patterns. They have common targets but self-interests. There exists coordination, conflict, cooperation and competition among them, which forms static or dynamic game relationship with

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conflict, competition, cooperation between two or more parties. These gaming relations in smart grid engineering issues are based on information prediction and treatment (prediction technology). This can enormously enrich the study objective and scope of traditional game theory in aspects of power grid development (energy storage technology and operation technology), object abstraction and control (control and dispatching technology), and self-assessment and evolution (assessment technology). Because of its distinctive engineering background and characteristics, and the formation of a complete system including information processing and object abstraction, control, assessment, development and so on, we can consider it as a new theoretical system, a prototype of engineering game theory. The traditional game theory has disadvantages of having too broad content and excessive mathematical orientation. With the systematic development of engineering game theory, it can not only solve these problems but also provide an effective solution for systems of smart grids. Especially in the market environment, it is inevitable to consider the “game” factor in smart grid control[68] . However, any new subject has a long development process. In the future smart grid construction process, we can start with the three typical problems of smart grids, that is, smart grid distributed dispatching with incomplete information, multi-index selfoptimization among different parties in smart grids, and robust dispatching in uncertain environment. Thus, we can constantly enrich and improve the related theories of engineering game theory under the smart grid engineering background, and gradually take it as the main analytical tool for smart grids.

3

Conclusions and prospects

The development of engineering science and technology is always following a certain process. Firstly, engineering issues are proposed. Then, physical laws are set after the physical essence is clear. And further, mathematical models (including control model) are constructed. Finally, the model is solved. All the above mentioned mathematics and systems science issues involved in smart grids follow this law. In 2005, Prof. Kalman, a famous scientist, made a more incisive address in his report at the 16th IFAC: “when we recall the development of system theory during the past of more than 100 years, we can get an indisputable conclusion, that is, when the basic physical essence is clear, the solution to engineering issues of system theory depends on the solution to their intrinsic pure mathematics issues”[69] . This paper discusses the basic scientific issues in smart grid construction, emphasizing not only on the realization of smart grids, but also on the development of mathematics, control science and other related disciplines through solving these issues. To conclude, with smart grid development, a series of major smart grid projects are being planned and constructed, such as Jiuquan Wind Power Three-Gorges Project in Gansu province, Yellow River Pumped Storage Project in Qinghai province, Bohai Sea Wind Power Project, and “Four-major and One-special” Development Plan by China power industry. How to develop and apply the key mathematics and control science tools of smart grid upon engineering construction requirements, is of vital concern to the successful construction of future smart grid.

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Sheng-Wei MEI Received his B. E. degree in mathematics from Xinjiang University, the M. S. degree in operations research from Tsinghua University, and the Ph. D. degree in automatic control from Chinese Academy of Sciences, in 1984, 1989, and 1996, respectively. He is currently a professor at Tsinghua University. His research interest covers power system analysis and control. E-mail: [email protected] Jian-Quan ZHU Received his B. S., M. S. and Ph. D. degrees in electrical engineering from Fuzhou University, Guangxi University and Tsinghua University, in 2005, 2008 and 2012,respectively. He is currently a Lecturer of South China University of Technology. His research interest covers power system optimization, operations and control. Corresponding author of this paper. E-mail: [email protected]