Optimal Scheduling of Hydro–PV–Wind Hybrid System Considering CHP and BESS Coordination

: Coordination of a hydropower, combined heat and power (CHP), and battery energy storage system (BESS) with multiple renewable energy sources (RES) can effectively reduce the adverse effects of large-scale renewable energy integration in power systems. This paper proposes a concept of a renewable-based hybrid energy system and puts forward an optimal scheduling model of this system, taking into account the cost of operation and risk. An optimization method is proposed based on Latin hypercube sampling, scene reduction, and piecewise linearization. Firstly, a large number of samples were generated with the Latin hypercube sampling method according to the uncertainties, including the renewable resources availability, the load demand, and the risk aversion coefﬁcients, and the generated samples were reduced with a scene reduction method. Secondly, the piecewise linearization method was applied to convert nonlinear constraints into linear to obtain the best results of each scene. Finally, the performance of the proposed model and method was evaluated based on case studies with real-life data. Results showed that the renewable-based hybrid system can not only reduce the intermittent and volatility of renewable resources but also ensure the smooth of tie-line power as much as possible. The proposed model and method are universal, feasible, and effective.


Introduction
In recent years, with the increasing attention on global climate change and sustainable development, the penetration of renewable energy resources (RES) has steadily grown in the global electricity market. As renewable energy sources are starting to play a prominent role in revolutionizing modern power systems, the impact on their operation and reliability no longer goes unnoticed and neglected. However, because of their variability and difficult-to-predict nature, renewable resources are always considered an unreliable resource, and their scheduled generation cannot be ensured [1,2]. Therefore, it seems that after overcoming the impediments related to the cost, the next problem which should be solved is the reliable and economically justifiable integration of RES into the power system. This is especially important in the case of RES such as wind and solar, which tend to exhibit a significant temporal and spatial variability [3]. The problems of RES integration into the power system have been studied in several studies [4][5][6].
In order to provide stable generation, coordination of several kinds of energy sources may be an effective way to overcome these disadvantages above. Because of the large scale and good regulation performance, hydroelectric power can effectively restrain the fluctuations in wind and photovoltaic generation to improve their stabilities. Based on integrated technology, establishing a hydro-photovoltaic-wind hybrid system is seen as a promising method to realize the conception [7,8].
(1) Propose a concept of a renewable-based hybrid energy system along with a corresponding mathematical model which can be used to simulate and optimize its performance. (2) Introduce an optimal optimization model which focuses on minimizing the operating cost of energy service providers considering the environment as much as possible.
(3) Investigate the distinction of uncertainty variables volatility on the energy exchange with the power grid. (4) Research the impact of different risk aversion coefficients on the operation of energy service providers.
The remainder of this paper is organized as follows. Section 2 formulates the mathematical model for the operation of the hybrid power system. In Section 3, the solution method is described in detail. In Section 4, numerical simulations of the proposed model are applied to a test system on real-life data, and discussions are provided accordingly. Finally, the conclusions of the paper are drawn in Section 5.

Coordinated Optimal Scheduling Model of Hybrid System
The proposed day-ahead optimal scheduling model of the hybrid system in this paper focuses on three issues: Firstly, a coordinated scheduling model including wind, solar, electric vehicle, battery energy storage, CHP, and pumped-storage power is proposed, considering all the operation constraints. Secondly, the different energy exchanges with the power grid due to the volatility of uncertainty variables are considered in the scheduling process. Finally, the impact of different risk aversion coefficients on the operation of the hybrid system is studied.

Description and Framework of the Hybrid Energy System
The renewable-based hybrid energy system supplied by energy service providers studied in the paper is composed of PV, WT, BESS, EV, CHP, and a hydroelectric power station. The conceptual structure of the proposed hybrid system in this paper is shown in Figure 1. The operation of multiple energy resources in the hybrid power is subjected to different constraints in the day-ahead scheduling because of their different characteristics. Due to the stochastic nature of the renewable resources, finding a way to maximize the wind and solar power at the lowest cost is the key to the optimal operation of hybrid energy system. In this situation, with the help of hydroelectric power plant, CHP and BESS, formulating an effective scheduling strategy to ensure the power balance of power system considering wind, solar, water, and other forms of energy is a major issue to be addressed. (3) Investigate the distinction of uncertainty variables volatility on the energy exchange with the power grid. (4) Research the impact of different risk aversion coefficients on the operation of energy service providers. The remainder of this paper is organized as follows. Section 2 formulates the mathematical model for the operation of the hybrid power system. In Section 3, the solution method is described in detail. In Section 4, numerical simulations of the proposed model are applied to a test system on real-life data, and discussions are provided accordingly. Finally, the conclusions of the paper are drawn in Section 5.

Coordinated Optimal Scheduling Model of Hybrid System
The proposed day-ahead optimal scheduling model of the hybrid system in this paper focuses on three issues: Firstly, a coordinated scheduling model including wind, solar, electric vehicle, battery energy storage, CHP, and pumped-storage power is proposed, considering all the operation constraints. Secondly, the different energy exchanges with the power grid due to the volatility of uncertainty variables are considered in the scheduling process. Finally, the impact of different risk aversion coefficients on the operation of the hybrid system is studied.

Description and Framework of the Hybrid Energy System
The renewable-based hybrid energy system supplied by energy service providers studied in the paper is composed of PV, WT, BESS, EV, CHP, and a hydroelectric power station. The conceptual structure of the proposed hybrid system in this paper is shown in Figure 1. The operation of multiple energy resources in the hybrid power is subjected to different constraints in the day-ahead scheduling because of their different characteristics. Due to the stochastic nature of the renewable resources, finding a way to maximize the wind and solar power at the lowest cost is the key to the optimal operation of hybrid energy system. In this situation, with the help of hydroelectric power plant, CHP and BESS, formulating an effective scheduling strategy to ensure the power balance of power system considering wind, solar, water, and other forms of energy is a major issue to be addressed.

Objective of Optimal Scheduling Model in Hybrid System
To comprehensively consider economy, environment protection, and the renewable energy consumption level, the day-ahead optimal scheduling model is constructed as follows: The above objective is to minimize the operation cost consisting of four distinct terms, including the generation cost of all CHPs, the cost of BESS, the cost of power exchange with the utility grid, and the cost of risk valued by CVaR. The indices g, t, and s represent the CHPs, time periods, and the scenarios. The objective is subject to many system equality and inequality constraints, including the power balance constraint in Equation (2), utility grid power exchange limit in Equation (3), and the constraint of risk in Equation (4). Meanwhile, these costs are calculated by the following model of different energy resources, respectively: The power balance in Equation (2) ensures that the sum of power generated by local generations and exchanged with the utility grid matches the local load. The power exchange with the utility grid is limited by the flow limits of the associated connecting line, as presented in Equation (3). Equation (4) denotes that the factor of risk with auxiliary variables of CVaR.

The Model of Hydro Power Station
Hydro power is a traditional renewable clean energy. In accordance with the regulation ability of water, the hydropower station can be divided into two categories, a run-off hydropower station and a pumped storage power station. The latter has a certain capacity of reservoir, which can store the appropriate capacity of water and have a certain ability to adjust and control electricity. Therefore, we assumed the hydropower station in this paper is a pumped storage power station to complement the renewable resources effectively. The output power of the hydro unit follows a function with the water flow. The relationship can be expressed as: Vol min ≤ Vol t,s ≤ Vol max (8) Vol 0,s = Vol begin (10) The relationship between output power and the water flow is shown in Equation (5), and the output power is limited by the limits of capacity in Equation (6). Equation (7) represents the reservoir volume constraint at time t and t−1, and the right and left limits of the reservoir volume in each hour are expressed in Equation (8). Meanwhile, Equation (9) fixes the hydro reserve at the end of the period to be no less than the terminal volume limit.

The Model of PV and WT
Different from those of a conventional thermal power unit, the operation characteristics and uncertainties of renewable energy sources make it hard to adjust their grid power.
The output power of wind turbines is mainly determined by the speed of wind and based on the nature of the turbine's power curve. The energy output can be expressed as follows considering the character of wind turbine operation: As another renewable resource, the output of solar power mainly depends on factors such as temperature, light intensity, and panel area. The output of PV can be estimated as follows: Equation (12b) calculates the working temperature of photovoltaic cell components in order to estimate the output power in Equation (12a).

The Model of CHP
In contrast to wind and solar photovoltaic, CHP units are highly controllable. In addition, ramp-up and ramp-down times of CHP units are short. Therefore, they can be used to ensure balance and stability in the electric grid because of their flexibility. The cost of CHP as a function of output power is represented as follows: C g,t,s The cost of CHP in an objective function consists of the running cost and the start-up cost shown in Equation (13). Equations (14) and (15) represent the running state of CHP with state variables. The constraints of thermal load are shown in Equations (16) and (17). Equation (18) represents the limits of CHP output, which are subject to commitment status and operating characteristics. Equations (19) and (20) define the left and right limits of the CHP ramping rate according to parameters of CHP.

The Model of BESS
The battery energy storage component in power system not only can smooth the output fluctuation of some intermittent energy sources, such as wind power and photovoltaic power, but can also participate in demand side management and the schedule of the smoothing power system load curve to reduce security problems caused by the load fluctuation of power system. The principle of battery energy storage is the charging and discharging of the chemical reaction between across the electrodes inside the battery. The battery energy storage cost can be expressed as: The cost of BESS in an objective function consists of the depreciable cost of discharge and charge shown in Equation (21), and the output power is calculated in Equation (26). Equation (22) represents the SoC constraint at time t and t−1, and the right and left limits of the SoC in each hour are expressed in Equation (23). Meanwhile, Equation (25) fixes the SoC at the end of the period to be no less than the terminal limit. Equations (27) and (28) represent the right and left limits of discharge and charge power.

The Model of EV
Different from that of a traditional load, the charging and discharging power of electric vehicles is based on driving behavior of users, battery characteristics, and charging and discharging device. It is uncertain in the two dimensions of time and space, so it is necessary to simplify it in order to solve it in an actual situation. Equation (29) shows the limit of the charging power, not exceeding the maximum charging power of charging pile. Equation (30) represents the capacity relationship between t−1 and t moment. Equations (31) and (32) show the capacity limit, and Equation (33) expresses the charging time is assumed as 8 h.
Above all, the objective and constraints of hybrid energy system are shown in Equations (1)-(4). The hydro power constraints are shown in Equations (5)- (10), and the wind and photovoltaic power generation constraints are shown in Equations (11) and (12). Equations (13)- (20) represent the constraints of CHP, battery energy storage constraints are shown in Equations (21)- (28), and electric vehicles constraints are shown in Equations (29)-(33).

Solution Methodology
Regarding the proposed day-ahead optimal scheduling model of the hybrid system, two key issues need to be solved: Firstly, how to deal with multiple uncertainties influences the finally results of the proposed model. Secondly, how to incorporate the objective function into the mixed integer programming (MIP) problem affects the efficiency of solution.

Latin Hypercube Sampling and Scene Reduction (LHSSR) Method
The LHSSR method is an effective method to deal with the uncertainty of renewable energy sources. The method firstly samples the probability distribution of renewable energy sources, to get large samples to cover the random variable space. Then, combining it with the scene cutting method to cut scene and probability statistics greatly reduces the amount of calculation to satisfy the accuracy of the premise. Assume that sample size is N, number of random variables is z, and the Nth sample can be expressed as X n = [X n1 , X n2 , . . . , X nz ], n ∈ (1, n). The procedure of the LHSSR method is as follows in Table 1: Table 1. The procedure of Latin hypercube sampling and scene reduction (LHSSR) method.

Scene construction
Step 1 Assume Obtain sample by inverse transformation: Step 6 Initialization p i = 1

N
Step 7 Calculate distance as to any two scenarios d k (X i , Step 8 Search the nearest scene of X i expressed as min d k (X i , X j ), i = j Step 9 Calculate the product P KDi = min d k (X i , X j ), i = j × p i

Step 10
Search for the smallest P KD expressed as P KDs = min P KDi |1 ≤ i ≤ N

Step 11
Update scenarios probability p j = p j + p i and reduce scene X i from the scene set

Step 12
Update the scene number N = N − n i and return Step 7.

Piecewise Linearization of the Objective Function
Piecewise linearization is widely used in the nonlinear curve of the power unit for the convenience to solve and accelerate its convergence, as shown in Figure 2. The process of piecewise linearization of the cost curve can be expressed as the following formulas: The process of piecewise linearization of the cost curve can be expressed as the following formulas: where F l,i is the increased cost of the i-th generator at the l section of the piecewise linearization curve, is the output of the i-th generator at the l section in moment t, and L i is the number of the piecewise section.
In the objective function, only the cost of CHP is nonlinear. Based on the piecewise linearization method above, the nonlinear constraint (Equation (13)) can be converted into Equation (40) as follows: Therefore, the objective function and constraints are linearized, and the problem can be converted into an MIP problem, solved using commercial solver CPLEX 12.4 (IBM, Armonk, NY, USA).

Parameter and Settings
The developed model of a hybrid energy system was applied to a real demonstration project in China, which was conceptualized with representative costs and technical data from numerous previous studies. The hybrid energy system was composed of two photovoltaic modules, a wind turbine, two battery energy storage modules, four electric vehicle chargers, a combined heat and power, and a hydroelectric power plant, which is illustrated in detail in Table 2. The parameters of each module are represented in Tables 3-6. The power outputs of renewable resources, including wind and PV and local load in a typical day, are represented in Figure 3. The time interval of RES is assumed as 15 min, and the period is 96. The electricity prices in a typical day are shown in Figure 4.
Because of the influence of socioeconomic development and population growth, the demands can be described as parameters with a fluctuant interval. Hence, assume the fluctuating intervals of renewable resources and load demands as, respectively, ±20% and ±10% [39]. The confidence coefficient of risk is 0.95, and the risk aversion coefficient of the energy service provider is 0.3.       Because of the influence of socioeconomic development and population growth, the demands can be described as parameters with a fluctuant interval. Hence, assume the fluctuating intervals of renewable resources and load demands as, respectively, ±20% and ±10% [39]. The confidence coefficient of risk is 0.95, and the risk aversion coefficient of the energy service provider is 0.3.

Results of the Proposed Model
Depending on the parameters above, construct 1500 scenes using Latin hypercube sampling, finally getting 150 scenarios with the scene reduction technology. Combined with the piecewise

Results of the Proposed Model
Depending on the parameters above, construct 1500 scenes using Latin hypercube sampling, finally getting 150 scenarios with the scene reduction technology. Combined with the piecewise linearization method, the above proposed strategies are all MIP problems. Therefore, they can be solved by commercial solver CPLEX 12.4 efficiently, and the optimal results of the proposed model are shown in Tables 7 and 8.        Table 7 represents the optimal output power of each generator in a hybrid energy system. Along with the increase of the local load demand, CHP and hydro power gradually begin to be put into operation, and the CHP operates at its maximum output all the time from the 33th period, while the output of hydro power changes with the fluctuation of the electricity price. Due to the electric vehicles needing a full charge to work before 8:00 a.m., the power exchange with EVs focuses on periods 1 to 32. With regard to the BESSs, they charge at a low electricity price between periods 14 to 16 and 26 to 28. and discharge at a high electricity price at 8:00 p.m. from periods 77 to 80 to get more economic benefits. From periods 53 to 68 and 77 to 88, the hydro power works at a high output power level because of the higher electricity price, while the tie-line power is zero to reduce the total cost in the hybrid energy system. Table 8 shows the optimal results of the proposed model in the hybrid system, consisting of the cost of operation and the cost of risk.

Discussion
In order to show the advantages of the proposed model, the tie-line power performance and the comparison results of the hybrid energy system with different situations are given in the following part, in which the effectiveness and the economy improvement are verified.

Comparison of Different Models
Considering the high cost of investment about BESS and charging piles, we compared the optimal results without the BESS or charging piles. The results of four different models are shown in Table 9. The tie-line power with power grid is represented in Figure 5. BESS has the ability to store energy, so it can discharge at high prices and charge at a low price to reduce the economic cost and stabilize the tie-line power. Comparing scheduling models where BESS participates and where it does not, we found that the total cost and risk all dropped, and the economic objective was lower in Table 9, which is consistent with the fact. Regarding the hybrid energy system, the charging piles of EV are opposite to the BESS. The charging piles can be seen as a controllable load, so the total cost and risk will drop without them. Figure 5 shows the tie-line power curve of the compared model. Throughout the time of operation, the curve of the model including all is much smoother than the compared model without BESS and EV. At periods 28 to 42, 46 to 59, and 70 to 76, the power of the tie-line in the proposed model is lower than those of the compared models without BESS and EV, respectively. Therefore, with the diversification of load demands, expanding the types of energy is important to peak shaving and valley filling.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 14 of 20 BESS and EV. At periods 28 to 42, 46 to 59, and 70 to 76, the power of the tie-line in the proposed model is lower than those of the compared models without BESS and EV, respectively. Therefore, with the diversification of load demands, expanding the types of energy is important to peak shaving and valley filling. In order to show the advantages of the proposed method, the computational time and the comparison results of the hybrid energy system with different situations are given in the following part.

Comparison of Different Methods
It is important to compare the proposed method with traditional methods regarding the above model, including all energy modules. This paper illustrates and compares the following three cases to investigate the advantages of the proposed method. Case 1 is the method proposed in this paper, and case 2 is the method with Monte Carlo sampling, scene reduction, and piecewise linearization. Case 3 is the intelligent method (PSO). The results of the three different methods are shown in Table  10. The method in case 2 is similar to the proposed method in case 1, and the difference is the sampling method. In Table 10, the results of the objective and computational time in case 2 is slightly more than those in case 1. However, the computational time of the intelligent method (PSO) is much longer than that in case 1. The computational time in case 3 is nearly four times as long as that in case 1. The main reason is that piecewise linearization can effectively reduce the solving time. The objective result in case 3 is slightly equal to case 2. From Table 10, the proposed method has advantages in optimal results and computational time. In order to show the advantages of the proposed method, the computational time and the comparison results of the hybrid energy system with different situations are given in the following part.

Comparison of Different Methods
It is important to compare the proposed method with traditional methods regarding the above model, including all energy modules. This paper illustrates and compares the following three cases to investigate the advantages of the proposed method. Case 1 is the method proposed in this paper, and case 2 is the method with Monte Carlo sampling, scene reduction, and piecewise linearization. Case 3 is the intelligent method (PSO). The results of the three different methods are shown in Table 10. The method in case 2 is similar to the proposed method in case 1, and the difference is the sampling method. In Table 10, the results of the objective and computational time in case 2 is slightly more than those in case 1. However, the computational time of the intelligent method (PSO) is much longer than that in case 1. The computational time in case 3 is nearly four times as long as that in case 1. The main reason is that piecewise linearization can effectively reduce the solving time. The objective result in case 3 is slightly equal to case 2. From Table 10, the proposed method has advantages in optimal results and computational time.

Impact of the Fluctuation of Uncertainty Variables
According to different seasons and regions, the difference of load curve and renewable resources is obvious. Therefore, it is necessary to consider the fluctuation of uncertainty variables on the influence of the objective function. Considering three scenarios: Reduction of 10%, unchanged, and increase of 10%, the optimal results are shown as follows: Table 11 represents the effects of the fluctuation of uncertainty variables on the objective function of the proposed model in hybrid energy system. Wind and PV as renewable resources have the features of low cost and high risk. With the increasing output of wind or PV, the cost reduces from 111,275 to 111,114 and 111,135, while the risk increases from 120,306 to 120,471 and 120,429 in Table 11. The results are opposite as to the case of decreasing output. In addition, the fluctuation of local load results has much more of an impact on the optimal results. The relative change reaches 20% when the load fluctuates by 10%, while the relative change only reaches 1% when the renewable resources fluctuate by 10%. Therefore, it is particularly important to improve the forecasting accuracy of the load demand.

Impact of the Time Intervals of RES
According to different granularity requirements, the difference in time intervals of RES is obvious. Therefore, it is necessary to consider the different granularity requirements of RES on the influence of the objective function. Considering three scenarios: 5-min intervals, 10-min intervals, and 15-min intervals, the optimal results are shown as follows: Table 12 represents the sensitive studies of different time intervals of RES. Due to the small scale of RES compared to the whole scale of energy system, the impact of different time intervals on the optimal results can be negligible. The objective results of different scenarios are approximately equal.

Impact of the Coefficient of Risk Aversion
In the renewable-based hybrid energy system supplied by energy service providers, different providers have different coefficients of risk aversion. Consider five scenarios to study the impact of risk coefficient for optimization model. The optimal results are shown in Table 13. Table 13 represents the sensitive studies on the provider's risk aversion for the hybrid energy system. A larger coefficient of risk aversion for the energy service provider indicates less tolerance towards possible uncertainty in the model. With the increase of the coefficient of risk aversion, the system pays more attention to risk, leading to the increase in the cost of risk. Thus, the hybrid system's objective cost is increased by the increase in coefficient of risk aversion.

Conclusions
This paper proposed a concept of a renewable-based hybrid energy system which can effectively restrain the fluctuations in wind and photovoltaic generation to improve their stabilities. Taking into account the cost of operation and risk, an optimal scheduling model of this system was put forward. An optimization method was proposed based on Latin hypercube sampling, scene reduction, and piecewise linearization. The main achievements and conclusions are listed below: (1) A concept of a renewable-based hybrid energy system including PV, WT, BESS, EV, CHP, and hydroelectric power was proposed to solve the reliable and economically justifiable integration of RES into the power system. (2) An optimal scheduling model of this system was put forward considering the cost of operation and risk. (3) An optimization method was proposed based on Latin hypercube sampling, scene reduction, and piecewise linearization to deal with multiple uncertainties, including renewable resource volatility, the load demand, and different energy service providers' coefficient of risk aversion. (4) Based on the real data obtained in China, the performance of the proposed model and method was evaluated. Results showed that the renewable-based hybrid system can not only reduce the intermittent and volatility of renewable resources but also ensure the smoothness of the tie-line power as much as possible. The effectiveness and the economy improvement of the proposed model and method were verified. (5) In future studies, the environmental factors of the hybrid energy system and how to deal with uncertainty efficiently in a power system can be studied. Hence, how to improve the reliable and economically justifiable integration of RES into the power system is worth further research.
Funding: This research was jointly supported by the National Key R&D Program of China (grant No. 2018YFB0905200).

Conflicts of Interest:
The authors declare no conflict of interest.