With the continuous increase in power consumption and the high penetration of renewable energy generations, peak load and power imbalance have become two major challenges for an electrical grid; these challenges significantly affect the reliability, quality and energy efficiency of the grid (Arteconi et al., 2019). The peak load usually results from end-user energy behaviors (e.g., the power demands of buildings or industrial production during office hours/peak hours). Power imbalances generally result from a sudden loss of power supply or an increase in power demand. Redundant capacities of power plants and adequate operating reserves are essentially required by power generation sectors. Energy storage devices/systems (e.g., electric vehicles, batteries, and pumped-storage hydroelectricity) can also be employed as operating reserves. However, these methods are usually limited by either geographic conditions or high initial/operation costs and low storage capacities (Yan et al., 2020). In contrast, methods that use incentive benefits (i.e., implement the power demand response programs) to encourage end-users to manage their power usage behaviors are considered a more promising solution for peak load and power imbalance of grids.

Buildings are the largest electricity consumers worldwide and have great potential for power demand management in practice. In the United States, China, and Europe, the proportion of electricity used in construction in total electricity consumption reached 39.1, 20.6, and 29.4%, respectively (Electrical and Mechanical Services Department of Hong Kong, 2012; DoE, 2014). With the wide applications of building automation systems, IT technologies, smart meters and energy storage, buildings have demonstrated their great capabilities and willingness to participate in the demand management of grids through the bidirectional interaction between buildings and smart grids (Reynders et al., 2018). “Energy flexible buildings” (EFBs), which have the capacity to manage their energy demand and production according to local climate conditions, user needs, and grid requirements, have been proposed by the International Energy Agency (IEA) (Jensen et al., 2017). More specifically, Wang proposed the concept of ‘grid-friendly and grid-responsive’ buildings in a research report, where energy flexible buildings are required to work in synergy with (i.e., be responsive to) the grid or avoid additional stresses (i.e., be friendly) on the power grid balance (Wang, 2016). The energy flexibility of buildings can be greatly enhanced with the use of passive/active thermal storage. For instance, building thermal mass is an inherent passive storage of building structures and internal furniture for building load shifting and demand limiting by using precooling and room temperature set-point reset (Liang et al., 2020). Wang summarized three typical categories of active storage used in buildings to enhance energy flexibility: conventional storage (e.g., chilled water storage), small-scale storage (e.g., phase-change material), and innovative use of existing building facilities (e.g., fire water tanks) for load shifting, demand limitation and management. The increasing usage of power generation in buildings is a trend for sustainable building design and significantly affects the demand and flexibility characteristics of buildings (Zhong et al., 2016). Above all, buildings have the potential to be an excellent carrier for demand-side energy consumption management to solve grid imbalance.

How to explore the energy flexibility of buildings and to coordinate a variety of buildings with different energy flexibilities for effective interactions with smart grids are challenging. The key issue is how to accommodate the interests of all participants involved in the interactions between grids and buildings (Xu et al., 2020). In fact, driven by attractive electricity prices and various incentive policies, buildings may change their power demand flexibly and responsively. The altered aggregate power demand of buildings will affect electricity prices once a dynamic pricing mechanism is adopted in a smart grid. In contrast, the adjusted electricity prices will also induce buildings to change their energy behaviors to lower their operation cost. Further adjustments to electricity prices and building demands will continue until optimal operation is approached (Saad et al., 2012; Huang et al., 2019). A dynamic pricing method based on genetic algorithm is proposed by Huang et al.to improve two-way interaction and reduce power imbalance (Huang and Sun, 2019). They also proposed the collaborative demand response of nearly zero energy buildings to respond to the dynamic pricing of cluster-level performance improvement, which provides decision makers with computationally efficient demand response control for almost zero-energy buildings, thereby realizing full collaboration and helping To improve performance (Basar and Olsder, 1999).

At the same time, as an iterative and interactive power demand management strategy, mutual matching of supply-demand between EFBs and smart grid can be analyzed by game theory. Game theory is a mathematical theory and method for studying interactive phenomena whose nature is characterized by struggle or competition (Huang et al., 2017). Previous studies have investigated the feasibility of using game theory to solve the supply-demand interaction problem. Huang et al. reviewed the related research on cluster energy consumption planning when EFB buildings are connected to the grid. The authors pointed out the importance of consumer participation in the interaction of supply and demand and proposed an information interaction platform structure based on game theory, thereby aiming to improve the reliability of energy planning strategies for building clusters (Chen et al., 2019). Chen et al. used game theory as a tool to define the strategies of participants in the Israeli construction market; the authors combined these strategies with various incentives in the interaction of supply and demand and analyzed the strategy combination that optimally improved the market to help the expansion of the Israeli EFB market (Najafi-Ghalelou et al., 2018). Afshin et al. conducted game modeling on the internal energy interaction problem of a building complex, ensured the global optimal solution through mixed integer programming, and determined the individual strategies in equilibrium through general algebraic modeling system optimization software. The results of this case study showed that the internal energy interaction strategy of the building complex can improve the power exchange capacity and reduce the power cost (Lv and Ai, 2016). Lv et al. proposed a new dynamic energy management strategy that interacts with an active power distribution system based on multigrid-connected microgrids; the strategy was aimed at a higher-level benefit distribution network and multiple smart grid units participating in the interaction. A high-level interaction between smart grid units and benefit distribution networks is described by two-level programming, and the smart grid units are modeled by using an innovative interactive energy game matrix (Li and Wang, 2020). In a study by Li et al., an online multi-objective coordinated control strategy composed of two control optimization schemes was proposed for predictive scheduling and real-time optimal control of the energy system of zero-energy buildings. The strategy is based on a cooperative game model and is tested and evaluated by simulating energy storage system scheduling in a typical period in a zero-energy building. The control variables and target weights are finally optimized, and energy costs and grid fluctuations are minimized (Zhao, 2001). The abovementioned studies regard the smart grid and buildings as two participants simultaneously engaged in decision-making and thereby provide a guiding idea for analyzing supply-demand interaction from the perspective of game theory. The traditional game model regards the building and the power grid as equal participants in the buying and selling relationship; however, this view differs from reality, and consequently, the final Nash equilibrium is inaccurate.

The economic competition relationship between the power grid and buildings is usually defined as a hierarchical planning problem in which one party is dominant and the other party is subordinate. Specifically, the power grid precedes buildings in making decisions on electricity prices, and the buildings then respond to the electricity price plans formulated by the grid and determine the power purchase demand to maximize the buildings’ own benefits. Additionally, because the power grid needs to consider the response of buildings to electricity prices when making decisions (excessive prices will cause buildings to be more self-produced and self-sold), the energy demand of buildings can also counteract the power grid’s pricing plan. This game model of interaction between different levels of decision-making is called the Stackelberg model (Yang et al., 2013). In the production and operation of some commodities with poor price elasticity, the company that decides the strategy first in the Stackelberg model does not have the first-mover advantage, but the company that determines the output later has the latter-mover advantage. Therefore, traditional electricity sales models adopt monopoly or national production and operation methods. However, when renewable energy and energy storage systems are connected, the price demand elasticity of electricity usage in buildings increases. Under the Stackelberg model, the grid side can ensure its own first-mover advantage while incentivizing the buildings to reduce their consumption, and the revenue of electricity is also higher than that under the traditional Cournot model, so it is beneficial to use the Stackelberg model to solve the game equilibrium in the game analysis.

In a study by Peng et al., the Stackelberg model was used to optimize the time-of-use (TOU) pricing strategy of the grid. The model satisfied equilibrium user demand and reduced the potential cost of the utility by encouraging buildings to purchase electricity through low trough and low pricing and by encouraging the self-production of buildings through high peak pricing (Yang et al., 2014). On this basis, Jie et al. optimized the utility problem of building user comfort based on the new effect function for determining the optimal power consumption and grid pricing under real-time electricity prices (RTPs) (Srinivasan et al., 2017). Srinivasan et al. selected dynamic pricing strategies based on game theory for the Singapore electricity market and compared the economic benefits of three pricing strategies: half-hour pricing, time-of-use electricity pricing, and day-and-night electricity pricing (DN). The results show that RTP can reduce the peak load of the residential and commercial sectors by 10 and 5%, respectively; and increase profits by 15.5 and 18.7%, respectively (Tang et al., 2019). Tang et al. used the Stackelberg model to maximize the profits of buildings and power grids by considering the impact of uncertainties (Zhang et al., 2019).

However, the game model used in the literature cited above does not classify the types of buildings that the game applies to and ignores the impact of different building system conditions on the interaction of supply and demand.

In previous studies, when considering grid interactions or games between EFBs and smart grids, buildings were often considered to have the same energy “flexibility”. In fact, buildings with different energy systems and different control strategies have different energy flexibilities and energy consumption patterns, which affect the results of the supply-demand interaction of the game with the power grid. To obtain better demand response optimization results with more realistic performances, this paper constructs three typical flexible buildings with different energy systems and energy control strategies and proposes a hierarchical demand optimization method based on game theory to coordinate these buildings with different energy flexibilities for effective grid interaction with smart grids. The remainder of this paper is arranged as follows. In Principle of the Hierarchical Optimization Method, the principle of hierarchical optimization methods will be explained in detail, and the specific interactive game model and internal strategy selection algorithm will be established in Hierarchical Optimization Implementation Based on Game Theory. Finally, in Case Study, the rationality of the two-tier optimization scheme will be analyzed by using case analysis.

As shown in Figure 1, the proposed hierarchical game theory-based demand optimization method consists of two optimization strategies at the grid and building levels. At the grid level, a demand-price interaction model between buildings and the grid is established to use game theory to identify the Nash equilibrium solutions, which are used to determine the optimized energy demand of buildings and the associated electricity prices by accommodating the interests of all participants involved. At this level, buildings can adjust their energy consumption patterns in response to the real-time electricity price or other incentive policies to pursue the lowest possible electricity cost. However, the power grid will also provide the corresponding RTP according to the energy consumption of the building at different times to ensure maximum profit for the building. This kind of supply-demand interaction level analysis of building energy strategy is a typical non-cooperative game problem. Building energy demand and grid quotations are bargained at the game level; when the demand and the quotations reach the Nash equilibrium, the mutual benefits of both parties can be maximized.

At the building level, three types of EFBs with different energy flexibilities are investigated to achieve their maximum interests by using appropriate control strategies during the interaction with the grid; the details of the building system conditions are shown in Table 1. Type-1 buildings are “passive storage buildings”, which can adjust their energy usage by changing the indoor air temperature of the air-conditioning system with a certain degree of thermal comfort sacrifice. Considering that the acceptable temperature change range is small (e.g., 2°C), the energy flexibility is limited. Type-2 buildings are “active storage buildings”, which can purchase excess electricity during periods of low electricity prices and use active energy storage systems to transfer the excess electricity to use during periods of high electricity prices. The energy flexibility is generally moderate, and buildings have a certain degree of initiative in the game, which requires the grid to set peak electricity prices with more consideration of the building’s acceptance. Type-3 buildings, which both generate and store energy, have relatively considerable energy flexibility by controlling both their own energy generation and consumption patterns. Such buildings can purchase low-priced or sell high-priced electricity as much as possible and therefore have a strong initiative in the game with the power grid. In summary, the building energy flexibility or the ability of a building to adjust energy consumption in response to electricity prices depends on the system conditions of the building. How to encourage buildings with different energy flexibilities to take part in the grid interaction game and maximize their own interests by using appropriate control strategies is the other key of the proposed optimization method.

The optimization objective of the grid level is to achieve the Nash equilibrium of the EFB-grid game interaction. The three elements that make up game G are its participants σ (two or more), their strategies S , and the benefits gained by strategies U ; game G = { σ , S , U } . The interactive participants of the supply and demand strategy proposed in this paper are the EFB cluster and the smart grid. The strategy determined by the grid is the electricity price ( P r ), and the strategy determined by the EFBs is its energy demand scheme ( q ). Grid pricing is based on the intensity of the demand of EFBs, and this demand is also affected by the acceptance of the current electricity price, which is P r = f ( q ) , q = g ( P r ) . The grid first quotes the EFBs, and then the EFBs adjusts their own demand based on their acceptance of the current electricity price and feeds the electricity price back to grid. After receiving the electricity price, the grid adjusts the quotation strategy and sends the price to the EFBs. Both parties repeat this process until P r ∗ = f ( q ∗ ) , q ∗ = g (   P r ∗ ) ; that is, the supply and demand strategies given by the grid and EFBs meet the expectations of both parties. The game process enters a dynamic equilibrium process; this equilibrium state is called the Nash equilibrium, and the process is shown in Figure 2. Under the Nash equilibrium, the strategies of both participants of the game will no longer change because breaking the balance will not be more beneficial to either of them. Unlike the “maximum profit,” which exists in an ideal state, the profit of both parties at this time is the real profit after concession to guarantee the transaction. The definition of the Nash equilibrium is as follows:

A strategy vector s ∗ = { s i ∗ , s − i ∗ } that is in the Nash equilibrium state needs to satisfy U ( s ∗ ) ≥ U ( s i ∗ , s − i ∗ ) .

In the above definition, s i ∗ is the strategy of game player i , s − i ∗ is the strategy of all other players, and U is the profit that the strategy can promote.

To model the game objective on the building side, the mathematical description of the game objective is as follows: { ∀ Q ∈ ∅ , Q ≠ Q ∗ , U b u i l d i n g ( P r ∗ , Q ) ≤ , U b u i l d i n g ( P r , Q ∗ ) Q ∗ = a r g m a x ( Q ) U b u i l d i n g (1) where ∅ is the value range of the building strategy, U b u i l d i n g is the building revenue, Q is the decision value of the building demand, Q ∗ is the optimal decision value of building demand under Nash equilibrium, P r is the dynamic electricity price set by the grid, and P r ∗ is the maximum value under Nash equilibrium. Building energy demand under this balance is the most conducive to the common economic benefits of the building complex and the power grid and can be used as a reliable energy optimization result under the demand response strategy.

The mathematical description corresponding to the grid strategy is: { ∀ P r ∈ P , P r ≠ P r ∗ , U g r i d ( Q ∗ , P r ) ≤ , U g r i d ( Q , P r ∗ ) P r ∗ = a r g m a x ( P r ) U g r i d (2) where P is the value range of the grid strategy and U g r i d is the grid revenue.

The premise of the existence of the Nash equilibrium is that the players of the game abide by the basic rules of the transaction, and any conflicting strategy that only considers unilateral interests will lead to the failure of the transaction. Therefore, it is necessary to define the value range of the game strategy set: { ∅ = { Q | Q ∈ R N , Q m i n ≤ Q ≤ Q m a x } P = { P r | P r ∈ R N , Q m i n ≤ Q ( P r ) ≤ Q m a x } (3)

In Equation 3, R N is the complete set of strategies, Q m i n , Q m a x is the value range of energy consumption under the rules, and Q ( P r ) is the building demand in response to electricity prices.

To determine the energy demand scheme that can minimize the overall cost of a building, the cost optimization objective function must be constructed first. The building cost is composed of three main parts: user dissatisfaction, mismatch cost (these two will not be directly reflected in the bill), and the electricity purchase cost of the transaction with the grid.

During the interaction between the EFB and the grid, biding of the grid will affect the motivation of the EFB to purchase electricity, while the degree of the EFB’s dependence on electricity will also affect the grid’s biding strategy. The grid’s actions always precede those of EFBs; this accords with the application conditions of the Stackelberg model. The principle of backward induction is used to determine the optimal energy use plan of the buildings under the Nash equilibrium of the game and the optimal price of the power grid.

In this paper, some typical buildings of Hong Kong Polytechnic University are selected to provide and generate necessary building energy consumption and energy flexibility data. Buildings adopt central air-conditioning systems and providing energy storage capacity for the building complex by installed phase change material (PCM) storage tank in series with chiller, charging during the low power period is used for the joint power supply during the peak period. In the optimization calculation of passive storage buildings, the PCM air-conditioning system is replaced with an ordinary central air-conditioning system with similar system parameters. At this time, the campus buildings will rely on the energy passive storage of building’s thermal mass during the peak period of electricity consumption to regulate demand. In the period of low electricity consumption, considering the marginal cost of sacrificing user dissatisfaction, the demand will be maintained at the baseline level. The renewable power generation system is connected to the building complex to construct a simulated building complex equivalent to generation and storage buildings, and the system parameters refer to the Hong Kong Zero Carbon Building (ZCB) (Jian and Wang, 2010). A distributed energy system that uses building integrated photovoltaics (BIPV), CIGS thin film solar cells and small wind power generation equipment to provide production capacity for buildings, and cooperates with PCM air-conditioning to complete energy output and transfer. The campus buildings can be divided into four areas according to different functions and locations; these areas are equivalent to four large buildings. The division of each area is shown in Table 2. The data sources, such as building benchmark energy consumption requirements, local meteorological parameters, and time-of-use electricity prices, are based on field observations created on July 3, 2017.

Figure 11 shows the electricity purchase cost of each building area under three different system conditions. For passive storage buildings, by sacrificing a certain degree of comfort, the peak energy consumption is reduced, and consequently, the electricity purchase cost is directly reduced by 3–4.4%. For active storage buildings, since the use of stored energy during peak periods reduces the demand for electricity, the cost of electricity purchases can be reduced, consider the increase in cost caused by excessive power purchase during the low electricity consumption period, the electricity bills of different area have been reduced by 5.5–8.8%. For generation & storage buildings, With the further improvement of building energy flexibility, peak electricity consumption has been greatly reduced, the total daily electricity purchase bill of the building decreased by 13.7–18%.

After adopting the hierarchical optimization method, although the direct sales revenue of smart grid will decrease because of the reduction of the building electricity purchase cost, the peak-to-valley difference is also significantly reduced due to building energy demand optimization, thereby effectively reducing the hidden costs caused by grid imbalance. As shown in Figure 12, the grid’s total income has increased by 8, 12.3, and 20%.