1. Introduction
With the increasing clean energy penetration, the power grid’s security, stability, and economy have been severely affected by the intermittent and fluctuating nature of power sources. The large-scale transmission and consumption of clean energy face the challenge of a shortage of reliable power sources. This issue is especially prominent for some clean energy bases where clean energy production and transmission are the primary industry [
1], such as the Gonghe Basin. This region has tens of millions of kilowatt-level clean energy bases with abundant wind, solar, hydropower, and geothermal power resources. However, because of the lack of flexible and stable power sources, it is difficult to expand the scale of clean energy development further.
Among the various types of clean energy sources, hot dry rock (
HDR) power stations have the most stable and reliable operational characteristics [
2]. The development of a more flexible operational mode to form a new type of energy storage system, coupled with the vast amount of thermal energy in the geothermal reservoir, would be instrumental to ensure the reliability of grid-connected photovoltaic (
PV) plants and to support clean energy transmission. In [
3], geophysical methods were used for geological characterization of the Gonghe Basin on different scales. Finally, the scope and volume of Gonghe
HDR resources were evaluated. According to preliminary estimates, the amount of
HDR geothermal energy in the Gonghe Basin is equivalent to 55.909 billion tons of standard coal [
4]. Considering environmental protection requirements and realization of carbon neutrality constraints [
5], comprehensive utilization of
HDR geothermal energy will become an essential aspect of the global clean energy supply.
However, the large-scale development of
HDR resources still faces several technical and cost constraints [
6]. The experimental results and the critical technical challenges of
HDR geothermal energy development were summarized in [
7]. The hydraulic fracturing method assisted by micro-computed tomography was addressed in [
8], which improved the development of
HDR geothermal resources. Focusing on the geothermal resources of
HDR in Daqing oilfield, China, the research carried out a numerical simulation on reservoir stimulation and economic analysis of
HDR power stations [
9]. The results show that economy is key for restricting the development of
HDR geothermal resources. The geothermal generators in the
HDR power stations have low theoretical efficiency limited by the
HDR temperature [
10]. In order to improve the economics of low-temperature
HDR power stations, the energy efficiency and exergy loss of the Kalina cycle were analyzed in detail, and the maximum energy efficiency of 12.7% was obtained [
11]. In [
12], the adaptability of the organic Rankine cycle (
ORC) and Kalina cycle in low-temperature
HDR scenarios were further compared and analyzed. The energy efficiency of the geothermal generator was increased to 13.2%. Previous studies have shown that research in improving the efficiency of
HDR power station has been lagging owing to the limitations of physical and chemical properties. Therefore, coordinated operation of hybrid power systems with other energy sources, such as
PV plants, provides a new technical path for
HDR power stations to exploit their potential better and reap better economic benefits.
Extensive research has been conducted by scholars worldwide on the coordinated operation of hybrid power systems [
13]. Some studies have been conducted from the perspective of complementation. In [
14], a stochastic two-stage unit commitment model and a rolling look-ahead economic dispatch model were established based on the concentrated solar power plant and the wind turbine complementation mechanism. To further improve the reliability of the hybrid power systems, the robust optimization theory was introduced into the optimization dispatch for a hybrid wind-
PV-hydropower-thermal system to balance reliability and economy [
15]. Considering the scenario of time-of-use (
TOU) electricity price and randomness of wind power, a stochastic hourly combinational approach for effective dispatching of the wind plants, cascaded hydropower station, and pumped-storage units was proposed in [
16].
With the development of electrochemical energy storage technology, batteries have been widely used to coordinate renewable energy systems [
17]. A linear model was used to describe the energy storage dispatching model that minimized the power demand and verified the feasibility of lithium-ion battery storage [
18]. In [
19], the load following strategy and cycle charging strategy of battery are combined to explore the feasibility of a joint dispatching strategy for
PV/diesel/battery hybrid power system. A model for optimizing AC-coupled and DC-coupled
PV-battery hybrid power system was proposed in [
20], which proved the economics of large-scale lithium battery storage plants under appropriate conditions.
The research on geothermal hybrid power systems is still relatively few. Geothermal generation was used as the power source to optimize the dispatch of wind-
PV hybrid power system in the island scenario [
21]. An
HDR power station scheme combining geothermal generation, absorption refrigeration, and waste heat heating systems was further proposed in [
22]. For specific applications, an
HDR cogeneration system that combines wind and
PV energy as power sources to meet the cold, heat, and electricity demands of an independent micro-energy grid was proposed in [
23]. In [
24], a new type of combined cooling and power supply system was proposed in order to meet the energy demand of buildings, which can meet the seasonal cooling and power demand of buildings and maximize the utilization of hot dry rock resources.
The above research can well solve the coordinated dispatching problem and improve the system economy, but the interaction of the hybrid power system participants is not entirely reflected [
25]. Therefore, other scholars have discussed the hybrid power system’s coordinated operation based on game theory [
26]. In [
27], game theory was introduced to model a hybrid power system comprising wind turbines,
PV plants, and batteries to optimize the dispatching strategy of energy storage systems. The Stackelberg game was used to obtain the charging strategy of electric vehicles and the pricing strategy of charging stations [
28]. Cooperative and non-cooperative game methods were used to study automatic distributed optimal economic of automatic generation control in multi-region power systems [
29]. A non-cooperative game dispatching model composed of wind power, thermal power, and pumped storage power plants was established to optimize the combined operation effects in different seasons [
30]. Through non-cooperative game theory, a power generation dispatch model of a hybrid power system containing wind, wind, and heat was established to maximize the overall profits in the long-distance transmission scenario [
31]. A general framework for power system flexibility analysis based on cooperative game theory was proposed for risk design and energy policy design [
32]. The potential cooperative behaviors of multiple grid-connected micro-grids were simulated to achieve higher efficiency and better economy [
33]. In [
34], the payoffs of wind turbines, thermal power stations, and electric vehicles in the power market were studied based on cooperative game theory, and the imputation of the cooperative game was rationally allocated based on the Shapley value. The profit allocation of the hybrid power system in the cooperative game was analyzed in [
35]. The results show that the Shapley value is the most stable allocation strategy.
Previous studies have provided extensive theories and methods for the hybrid power system dispatching. However, the characteristics of HDR power stations observed in the energy extraction and conversion process lead to different operational strategies compared to thermal power stations and energy storage power stations. The existing coordinated dispatching models and payoff allocation mechanisms for multi-energy sources are not entirely suitable for HDR power stations. Accordingly, the coordinated operation model and payoff allocation strategy for HDR power stations require further research.
Therefore, the major contributions of this paper are: (1) a new method for designing HDR power stations is presented to reduce the power fluctuations of PV plants and improve the reliability of the power grid; (2) a hybrid power system composed of HDR, TS, and PV plants is constructed, and the coordinated operational characteristics of HDR power stations in the hybrid power system are analyzed; (3) a game pattern with HDR power stations, TS power stations, and PV plants as players is proposed. The non-cooperative game’s payoff function and the characteristic function of the cooperative game are then defined; and (4) the game dispatching models are simulated with the case of the Gonghe Basin of Qinghai. Finally, a sensitivity analysis of the two critical parameters of the allowed fluctuation rate, and the penalty coefficient is carried out.
The remainder of this paper is organized as follows. The architecture of the
HDR-
TS-
PV hybrid power system and characteristics of the
HDR power station are given in
Section 2. The
HDR-
TS-
PV game model is proposed in
Section 3.
Section 4 simulates a case based on actual data of the Gonghe Basin. An in-depth discussion of the simulation results is carried out in
Section 5. Conclusions and further developments are discussed in
Section 6.
3. HDR-TS-PV Game Model
3.1. ElemenTS of the Game
Compared with other coordinated dispatching methods, game theory can better clarify the internal mechanisms of multi-agent competition and cooperation to quantify each party’s benefits. The elements of the game include Player, Strategy, and Payoff.
- 1
Player
The HDR power station, TS power station, and PV plant are the three players, denoted by H, T, and P, respectively.
- 2
Strategy
The operational goal of the
HDR power station is to obtain as much profit as possible to rapidly recoup the high costs of construction by changing the mass flow of brine to dispatch the power. Therefore, the strategy set of the
HDR power station is
where
represents the installed capacity of the
HDR power station, and
is the output power that meets the minimum power generation requirements of the
ORC generator, which is generally 10% of the installed capacity.
The
TS power station primarily realizes the arbitrage of the electricity price peak-valley difference by dispatching purchased power and generating power. Therefore, the strategy set of the
TS power station is
where
is the electric power purchased from the grid during the low
TOU price period and limited by the maximum power
of the electric heating device.
represents the power generation capacity of the
TS power station, and its upper and lower limits are the installed capacity
and the
ORC generator and the minimum power generation condition
, respectively.
The operational goal of a
PV plant is to formulate a credible output power plan based on the weather forecast data to increase the credible capacity connected to the grid as much as possible so as to reduce the loss of surplus power and penalty incurred by abandoning loads. its strategy set is
where
is the credible output power of the
PV plant, and its corresponding installed capacity is the credible capacity of the
PV plant, denoted by
.
represents the installed capacity of the
PV plant.
- 3
Payoff
All three players profit by selling electricity to the grid so that we can define the payoff vector of the game as
where
,
and
represent the payoff of the
HDR power station,
TS power station, and
PV plant, respectively.
Each player has an independent and equal status and can either compete in a non-cooperative game or try to increase profits through cooperation. The coordination dispatching models of the two types of games are given below.
3.2. HDR-TS-PV Non-Cooperative Game and Payoff Functions
If all three players are independent and try to maximize their profits, they naturally constitute a non-cooperative game of competition with each other. This paper first presents the payoff functions of the three players in non-cooperative games in order to compare and analyze the results of the subsequent cooperative game dispatching model.
3.2.1. Payoff Function of HDR Power Station
Owing to the continuity of the geothermal mining cycle, the brine mass flow of the
HDR power station cannot be adjusted in the non-cooperative game in order to avoid heat loss. The flexibility of the
ORC generator cannot be fully utilized, and only the continuous power generation mode can be adopted. Therefore, according to Equation (1), the payoff function of the
HDR power station is
3.2.2. Payoff Function of TS Power Station
In the non-cooperative game, the
TS power station purchases electricity from the power grid during the low
TOU price period and converts it into thermal energy. During the high
TOU price period, the
TS power station generates electricity for arbitrage. The payoff function is
The output power of the
TS power station to the power grid can be modeled as
where
is the mass flow of the
HTO during the power generation period and
is the specific heat capacity of the
HTO.
and
represent the temperature of the
HTO used for power generation and its temperature after power generation, respectively.
The operation of the
TS power station must also account for the following thermal storage state constraints and thermal energy store/release constraints:
where
is the thermal storage energy in the tank,
is the input thermal power when the
TS power station is storing thermal energy,
is the released thermal power,
is the thermal preservation coefficient of the thermal energy storage tank,
is the efficiency of the thermal release process,
is the electric heating efficiency, and
is the time interval.
3.2.3. Payoff Function of PV Plant
The output power of the
PV plants can be modeled using solar irradiance and the installed capacity [
39]. According to the weather forecast, the
PV plant obtains the predicted output power as the credible power generation in the first stage. The curtailed electricity and the abandoned loads are obtained from the actual solar irradiance in the second stage. This type of problem can usually be described by a Bayesian game model [
34]: the two players of the game are the
PV plants and nature, where the
PV plants make decisions based on predicted values, and nature determines the joint probability of the actual solar irradiance. The payoff function of the
PV plant is
where
is the number of types of solar irradiance,
is the probability of each type,
represents the predicted value of the output power based on the solar irradiance in the non-cooperative game.
and
are the curtailed power and the abandoned loads under each type, and
is the penalty price for abandoned loads. The models of
,
, and
are
where
is the power generation coefficient of the
PV plant predicted according to the solar irradiance [
39] and
is the actual output power corresponding to the non-cooperative part of the
PV plant.
is the power predicted error of the
PV plant.
The penalty price for abandoning loads,
is expressed as the product of the penalty coefficient for abandoning loads
and the
TOU price
, namely,
3.3. HDR-TS-PV Cooperation Game Pattern
If the three players in the hybrid power system intend to form coalitions, such as coordinated dispatching with a PV plant, the HDR power station can obtain greater benefits by providing auxiliary services and by the coordinated dispatching with a TS power station, and the HDR power station can use the TOU prices for arbitrage. The three players participate in cooperation under these conditions. Due to the limitations caused by the efficiency of the ORC generator, it is difficult for the TS power stations to profit from the TOU prices. Therefore, the TS power stations need to cooperate with the HDR power station or the PV plant to profit from waste geothermal or surplus PV power with zero marginal costs. Concurrently, because of the requirements of power grid assessment for the PV curtailment power and the abandonment load, the PV plant also cooperates in order to reduce the loss of the curtailed power and the penalty for abandoning the load.
It is observed that through cooperation, the three players can obtain a greater payoff and allocate extra profits through energy settlement, which is only related to the cooperating players. Therefore, cooperation between HDR, TS, and PV can be modeled by the characteristic function game (CFG). CFG uses the tuple to describe the cooperative game relationship, where is a set representing the number of players in the coalition. represents the characteristic function that reflects the payoff of the coalition, which is represented by the mapping relationship . For any of , or represents the overall payoff of the coalition.
In the cooperative game, the three players can form four different coalitions denoted by [{H, T}, {P}], [{H, P}, {T}], [{P, T}, {H}], and [{H, T, P}]. The payoff of the players is defined by the tuple
, where
is the coalition structure and
is the payoff vector.
must meet the individual rationality
where
is the payoff received by the player
in the coalition, and
represents the payoff of the player
in the non-cooperative game.
3.4. Characteristic Functions of HDR-TS-PV Cooperative Game
In the non-cooperative game, each player can only achieve their best profits through their independent dispatching strategies. By forming coalitions, players have more options for coordinated dispatching, thus expanding the strategy set. Based on the original profit model,
HDR and
TS power stations can also profit by providing reserves for the
PV plant, but their primary strategies are to dispatch output power. Therefore, the strategy sets of the
HDR and
TS power stations are still
and
, respectively. The
PV plant can reduce the curtailed power and penalty for abandoning the load by purchasing reserves; therefore, its strategy set also includes
where
represents the reserves purchased by the
PV plant, and
represents the power fluctuation rate allowed by the grid. In the case of purchasing the reserves, the constraint in Equation (22) always limits the
PV plant’s output power within a range of
around the predicted value. Therefore,
can be considered as the credible output power of the
PV plant, and its corresponding installed capacity is the credible capacity of the
PV plant, denoted by
.
represents the actual output power corresponding to the credible capacity part of the
PV plant.
Because the actual installed capacity of the
PV plant may be greater than the reserve capacity provided by the
HDR power station, the installed capacity can be divided into non-cooperative and cooperative parts in the cooperative game.
In a non-cooperative game, the players cannot use their respective resource characteristics and operating modes to achieve complementary advantages. Through cooperation, players can fully coordinate the dispatching of resources to maximize profits. The operating models and the profit models can be innovated to expand payoff sources, thereby increasing the overall payoff of the hybrid power system. The characteristic function of each coalition is described below.
3.4.1. Characteristic Function of HDR-TS Coalition
In the
HDR-
TS coalition, the
TS power station stores part of the
HDR geothermal mining cycle’s thermal energy in the low TOU price periods and then reuses the stored thermal energy to generate power in the high TOU price periods for arbitrage. The characteristic function of the
HDR-
TS coalition is
According to the flexible generation model of the
HDR power station described in Equations (2)–(4), the heat exchange constraints for the
TS power station to obtain geothermal energy from the
HDR power station are
where
represents the thermal energy storage temperature of the HTO,
represents the waste heat power of the
HDR power station, and
is the heat exchange efficiency of the TESE. Additionally, the constraints of the optimization problem Equation (24) also include Equations (1), (12) and (14).
3.4.2. Characteristic Function of HDR-PV Coalition
In the
HDR-
PV coalition, the
HDR station flexibly distributes the mass flow of the brine to provide reserves for the
PV plant, which can then increase the overall payoff of the coalition by reducing the curtailment power and penalty for abandoning loads. The characteristic function of the
HDR-
PV coalition is
where
represents the payoff of the non-cooperative game part of the
PV plant, which is calculated according to Equation (15).
The reserve dispatching constraints for the
HDR-
PV coalition are
where
represents the reserves provided by the
HDR power station, and
is the brine mass flow required when the reserves are dispatched.
3.4.3. Characteristic Function of TS-PV Coalition
In the
TS-
PV coalition, the
TS power station converts the electricity purchased from the grid during the low
TOU price periods and the surplus
PV power into thermal energy for storage. During the high
TOU price periods or shortage periods of the
PV plant, the stored thermal energy is used to generate revenue and provide reserves for the
PV plant. The
TS power station achieves profitability through the zero-cost electricity generated by the surplus
PV power. Simultaneously, the
PV plant increases its credible capacity and reduces the penalty for abandoning loads by purchasing reserves, thus forming a cooperative game pattern. The characteristic function of the
TS-
PV coalition is
The
TS power station provides an up-reserve through the
ORC generator to realize the profits and a down-reserve through electric heating devices to absorb surplus
PV power. The reserve constraints of the
TS-
PV coalition are
where
represents the up-reserve provided by the
TS power station,
is the mass flow of
HTO that needs to be adjusted when the up-reserve is dispatched, and
represents the surplus
PV power consumed when the
TS power station provides a down-reserve for the
PV plant. The constraints also include Equations (1) and (12).
3.4.4. Characteristic Function of HDR-TS-PV Coalition
When the
HDR power station,
TS power station, and the
PV plant are coordinated for dispatch, the
TS power station can store geothermal energy in the thermal energy storage tank for the subsequent generation, which improves the flexibility of the
HDR power station and realizes the peak regulation of the geothermal energy. Both the
HDR power stations and the
TS power stations can simultaneously provide reserves for the plants through flexible output power dispatching strategies, thereby increasing the credible capacity of the
PV plant, reducing the curtailment of
PV power and the penalty for abandoning loads, and further improving the overall payoffs. The characteristic function of the
HDR-
TS-
PV coalition is
The constraints of the HDR-TS-PV coalition include the operating constraints, thermal storage state constraints, and reserve constraints of their respective systems, including Equations (1)–(4), (12), (25), (28)–(30), (32)–(34). They are not repeated here.
5. Discussion
Further analysis of payoff and extra profits was carried out to reveal the role of the players in the hybrid power system and the source of the extra profits. It can be seen from
Table 2 that under the
TOU price given in
Figure 3, the arbitrage operation of the
TS power station cannot be profitable due to the low power generation efficiency of the
ORC generator. As a result, the
TS power station can only benefit by abandoning heat and electricity with zero marginal cost through cooperating with
HDR power station or
PV plant. Therefore, its dispatching strategy is to always adopt a minimum generation operation in low TOU price periods and
PV generation periods in order to store as much as possible the waste heat and surplus power, as shown in
Figure 7. It can be seen from the actual operation shown in
Figure 6 that under this operating strategy, the
TS power station can play a peak shaving role by storing geothermal energy, which realizes its payoff and makes the geothermal energy mainly generated in high TOU price periods, thereby creating extra profits. Simultaneously, the
TS power station can recover the waste heat of the
HDR power station when the down reserve is provided to the
PV plant, further improving the system profits. As can be seen from the allocation results in
Table 4, the extra profits of the
TS power station accounted for 50.04% of the total extra profits. This result further shows that the
TS power station has the most considerable marginal contribution to the extra profits, reflecting the decisive role of the
TS power station in the game relationship.
Due to its operating characteristics, the
HDR power station cannot cooperate with the
PV plant without abandoning heat, so it cannot provide auxiliary services for the
PV plant alone. Since the
TS power station can directly store geothermal energy, it can help the
HDR power station realize arbitrage.
Table 3 shows that when the
HDR power station and the
TS power station cooperate, the payoff of the
HDR-
TS coalition increases by 8.04% relative to the non-cooperation operation, and the overall payoff of the grand coalition only increases by 1.95% relative to the
HDR-
TS coalition when the
PV plant joins. The extra profits in
Table 4 show that the
HDR power station is allocated 42.02% of the overall extra profits. This result shows that the increased profits of the hybrid power system in the cooperative game mainly come from the peak shaving arbitrage of geothermal energy.
Figure 10 and
Figure 11 also show that the
HDR power station is not affected by grid parameters
and
, which further clarifies that the payoff and extra profits of the
HDR power station mainly come from its geothermal energy.
Table 3 shows that when the
PV plant and the
TS power station cooperate, the overall payoff of the hybrid system only increased by 1.12%. In the grand coalition, the extra profits of the
PV plant accounted for only 7.94%. It can be seen that the contribution of the
PV plant to the extra profits of the hybrid system is small. The main interest of
PV plants participating in the coordinated dispatch of the hybrid power system is to increase the credible capacity and reduce the impact on the grid so as to obtain the priority of grid connection. This result is also reflected in
Figure 10 and
Figure 11. The increase in the allowed fluctuation rate and the penalty coefficient decrease indicates that the grid’s ability to absorb fluctuating power has increased. A strong power grid increases the non-cooperative payoff of the
PV plant and decreases the cooperative extra profits, thereby reducing the willingness of the
PV plant to cooperate.
Moreover, since the temperature of the geothermal reservoir is a critical parameter that restricts the operating performance of the
HDR power station, we conducted a preliminary simulation on the influence of the temperature change on the overall payoff of the hybrid power system. According to previous research [
38], when the temperature is 170 °C, the energy efficiency of
ORC is 12.7%. Simulation with these parameters shows that when the temperature drops to 170 °C, the overall payoff of the hybrid power system is 54,285
$/day, a drop of 12.28%. The credible capacity of
PV plants participating in cooperative games is reduced by 28.78%. The preliminary results indicate that after the
HDR power station has been operating for about 10 years, the three players’ willingness to participate in the cooperative game will decrease. More in-depth research on the influence of more
HDR power station parameters on the hybrid power system is needed in future research.
6. Conclusions
For the grid-connection requirements of large-scale PV plants, we first proposed the technical route of using HDR power stations to provide reserves for PV plants in this study. The operating characteristics of conventional HDR power stations were analyzed, and a scheme for using TS power stations to improve the operating flexibility of HDR power stations was proposed. In this study, a hybrid power system consisting of an HDR station, a TS station, and a PV plant was designed, and a coordinated dispatching method was provided based on game theory. First, taking HDR power station, TS power station, and PV plant as players, the non-cooperative game model and the characteristic function game model of the hybrid power system dispatching were established. The optimization of the dispatching models describes the decision-making processes of the players.
Consequently, the coordinated dispatching strategy of the players was obtained by calculating the optimal value of the payoff functions and the characteristic functions that can be transformed into linear optimization problems or mixed-integer linear optimization problems. The case analysis was based on actual data in the Gonghe Basin. The results show that only cooperation can maximize the overall payoff and the individual profits of the system. Due to heat loss, the HDR power station cannot form a coalition with the PV plant alone, reflecting the significant role of the TS power station in the system. Finally, the sensitivity analysis of the allowed fluctuation rate and the penalty coefficient shows that they significantly influence the overall payoff of the system and the operating strategies of each player. However, the profits of the HDR power station are not significantly affected by the two parameters, which reflects its stable characteristics. The main goal of PV plants in the cooperative game is to increase credible capacity and reduce the impact on the grid, and TS power station is the key to achieving extra profits for HDR power station and PV plant. This study provides an essential theoretical basis for developing power generation systems based on HDR geothermal energy in the Gonghe basin of Qinghai, China.
One limitation of this study is that the grid topology and capacity constraints are simplified when constructing the game dispatching model and calculating the payoff allocation of the hybrid power system. The influence of the grid structure on the hybrid power system will be further investigated in future studies.