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Journal of Cleaner Production 195 (2018) 562e572

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Deriving operating rules for a large-scale hydro-photovoltaic power system using implicit stochastic optimization Zhikai Yang a, b, Pan Liu a, b, *, Lei Cheng a, b, Hao Wang a, c, Bo Ming a, b, Wenting Gong a, b a

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China Hubei Provincial Collaborative Innovation Center for Water Resources Security, Wuhan 430072, China c China Institute of Water Resources and Hydropower Research, Beijing 100038, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 March 2018 Received in revised form 16 May 2018 Accepted 19 May 2018 Available online 23 May 2018

Complementary operation is a new effective way to simultaneously manage hydropower and photovoltaic (PV) power. With the integration of a PV power into an existing hydropower reservoir system, the original operating rules need to be re-designed to improve operational performance. This study focuses on exploring long-term operating rules for such an integrated system using implicit stochastic optimization, which can address uncertainties in reservoir inflow and PV power. First, a long-term multiobjective optimization model for this system is established by maximizing the total energy production and assurance rate (i.e., reliability) simultaneously. The model is then solved using a dynamic programming technique. Operating rules are derived from the obtained optimal trajectory using a linear fitting method. Finally, a simulation-based optimization framework is used to refine the parameters of these rules. Our case study based on China's Longyangxia hybrid power system shows that: (1) a significant linear correlation between available energy and reservoir storage at the end of each time period, with fitting correlation coefficients above 0.9 for each month. Therefore, the available energy and reservoir storage at the end of each time period are selected, respectively, as independent variables and decision variables in the operating rules; (2) an improved average annual energy production and assurance rate are obtained for the hybrid system when considering complementary operations; and (3) the derived operating rules are effective in improving system benefits when compared with conventional operation. These findings are helpful to offer guidelines for the effective operation of the hydro/PV hybrid power system. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Renewable energy Hydro/photovoltaic hybrid power system Operating rules Implicit stochastic optimization

1. Introduction The global energy crisis is an international problem arising from the rapid development of the world economy and its growing demand for energy. The extensive use of fossil fuels has resulted in environmental deterioration, threatening the sustainable development of human society (Chen and Chen, 2015). Development of clean renewable energy is therefore a global priority (Barbosa et al., 2017; Farfan and Breyer, 2017). Solar energy is inexhaustible, globally distributed, clean and environmentally friendly, making it an ideal renewable energy resource (En, 2004; Kannan and Vakeesan, 2016). However, solar energy depends on the weather

* Corresponding author. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China. E-mail address: [email protected] (P. Liu). https://doi.org/10.1016/j.jclepro.2018.05.154 0959-6526/© 2018 Elsevier Ltd. All rights reserved.

conditions, and inherently stability in supply is poor. Therefore, solar energy sources should be paired with alternative forms of energy sources that can balance demand rapidly. Hydropower is another source of renewable energy that not only provides stable power supply but also provides peaking capabilities (Chang et al., 2017; Kaldellis, 2007). Hydropower turbines can quickly start and stop power production, enabling the hydropower plant to match time-varying demand. Specifically, the ramp rate can be as high as 20%e30% per minute of plant's installed capacity, with the peaking capacity close to the rated capacity of the plant (Feng et al., 2018; Kong et al., 2017). Hydropower can therefore complement photovoltaic (PV) power generation, an opportunity that has led to the recent construction of numerous hydro/PV hybrid power systems. In a hydro/PV hybrid power system, hydropower can compensate for PV power during periods of limited solar resources, and vice versa with electricity during dry seasons (An et al., 2015). The hydropower station acts as a fallback for the PV system; when PV

Z. Yang et al. / Journal of Cleaner Production 195 (2018) 562e572

Nomenclature

Qin ðtÞ Qfd ðtÞ

Abbreviations CORR correlation coefficient DP dynamic programming Hydro Hydropower PV photovoltaic PSO parameterization-simulation-optimization

Qqs ðtÞ

Indices k t

index of months (1, …,12) index of time periods (1, …,672)

Parameters/Variables ak 、bk operating rules parameters E* ðtÞ½VðtÞ  maximum cumulative power output from 1st period to t th period EðTÞ system's total generation (kWh) EðtÞ½VðtÞ; Qfd ðtÞ average output in t th period DHðtÞ net head (m) Hlose ðtÞ water head lose (m) IðtÞ total system input of potential energy system's total power output (kW) P ps ðtÞ power output of the PV (kW) P p ðtÞ power output of the hydropower (kW) P s ðtÞ P smin ðtÞ P smax ðtÞ PA ps ðtÞ Pfirm

lower limits for hydropower output (kW) upper limits for hydropower output (kW) limit imposed by transmission system (kW) required output minimum (kW)

output is not stable or sufficient, the hydropower station can rapidly adjust its power output to guarantee sufficient supply. Hydropower generation capacity depends mainly on the amount of runoff, which varies from year to year. The monsoonal climate of China also creates seasonal variation, with higher runoff during the summer flood season. In contrast, the inter-annual fluctuation of PV power generation is small, this generation being higher in winter and spring, Thus, PV and hydropower are complementary in their electricity generation. Specifically, hydropower can compensate short-term fluctuations in PV output, and PV can compensate for long-term fluctuations in hydropower capacity/output. Previous studies on the hydro/PV hybrid power system have explored its feasibility in the planning stage. For example, Dujardin et al. (2017) presented a set of calculations showing that hydropower can effectively complement intermittent energy sources. Bekele and Tadesse (2012) studied the feasibility of small-scale hydro/PV/wind-based hybrid electric supply systems in remote areas of Ethiopia, where they identified the component size of every energy source. For small hydropower plants, wind farms, and PV panels in Brazil, de Oliveira Costa Souza Rosa et al. (2017) assessed the potential of complementarity, using Pearson correlation coefficients and linear programming to comprehend and optimize the renewable mix. Daily complementarity was observed among the energy sources considered, especially between hydropower and solar resources. Beluco et al. (2012) proposed a theoretical performance limit for power plants as well as a method for the determination of this limit using computer simulations with idealized energy availability functions. They also used the method to study the effect over time of different degrees of

Q min ðtÞ Q max ðtÞ RðTÞ Rt Rb SðtÞ Ss ðtÞ

DTðtÞ T Tc Tb VðtÞ

563

reservoir inflow (m3/s) average reservoir release passing through the hydraulic turbines (m3/s) water spillage (m3/s) Lower limits for downstream discharge (m3/s) upper limits for downstream discharge (m3/s) system generation reliability actual intensity of solar radiation (kW/m2) intensity of solar radiation under standard test conditions (1 kW/m2) stored energy potential at the beginning of the t th period stored energy potential of hydropower time step (e.g., one month) total number of time periods actual temperature of solar cell modules ( C) temperature of the solar cell modules under standard test conditions (25  C) reservoir storage (m3)

V min ðt þ 1Þ lower limits for reservoir storage (m3) V max ðt þ 1Þ upper limits for reservoir storage (m3) b ðtÞ X independent variables k

Xp b ðt þ 1Þ Y k Zup ðtÞ Zdown ðtÞ

a ap

rated power output of PV station (kW) decision variables average fore-bay water level (m) average tail-race water level (m) penalty coefficient power output temperature coefficient of the solar cell modules (0.35%/ C)

complementarity in energy resources on the performance of hydro/ PV plants. From observations, the smallest failure indexes indicating the available energy supply to consumers are associated with the best complementary indexes over time. To determine the optimal size of a plant for integration, in Ming et al. (2017c), a nesting model was developed that incorporated both long- and short-term operating decisions in estimating delivered PV energy. The model was applied to determine the optimal size of a utilityscale PV plant for integration with a hydropower plant using cost-benefit analysis and considering variations in downstream water levels. Izadyar et al. (2016) proposed a list of potential areas concerning techno-economic factors, to design and install best combinations of hybrid renewable energy system. An effective energy management scheme is highly desirable for a hydro/PV hybrid power system. Conventionally, operating rules are widely used for hydropower operations. Specify operational decisions (e.g., power output, release) as a function of appropriate available information that includes current power storage, reservoir inflow and other hydro-meteorological conditions (Liu et al., 2006). Both single hydropower systems and single PV systems have been widely researched. For hydropower systems, various management schemes have been used to provide guidelines for reservoir releases, such as the operating rules and rule curves, to maintain the sustainability of reservoirs (Kaldellis, 2008; Ogayar et al., 2009; Zhou et al., 2015) For PV systems, optimal dispatches have been addressed in many studies using management models, such as a systematic model and an optimization model (Aghay Kaboli et al., 2017; Goroohi Sardou et al., 2018; Modiri-Delshad et al., 2016). Several studies have focused on the management of

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existing hydro/PV hybrid system. Meshram et al. (2013) proposed an energy management system to improve hybrid system power quality and to control the power distribution among the power generating systems, resulting in an energy management system control strategy that is suitable for implementation in remote or rural areas. Li and Qiu (2016) proposed a multi-objective optimization model for a hydro/PV hybrid power system taking into account the smoothness of the power output process and the total annual combined power generation. However, the study only simulated the hydro/PV hybrid power system in five typical years with deterministic inflow and PV inputs, and did not provide operating rules to make operational decisions for the hybrid system. Reservoir long-term operating rules are often derived using implicit stochastic optimization (ISO), which employs a deterministic optimization model to operate the system under different inflow scenarios. It then develops the operating rules for the reservoir based on the optimal trajectory (Celeste and Billib, 2009; Liu et al., 2014; Rani and Moreira, 2009; Zhang et al., 2017b). ISO is able to take the uncertainties of inflows into account in an implicit way and provide operating rules in an arguably simpler way (Celeste and Billib, 2009). For this reason, ISO has become one of the most reliable methods for deriving operating rules, which might be more popular to operators who are skeptical to use complex optimization approaches as a replacement to easier-to-understand simulation procedures (Celeste and Billib, 2012). With the construction of new large-scale hydro/PV hybrid power systems, attention should focus on improving the operational efficiency. The original reservoir operating rules need to be redesigned in pursuit of better operational performance, particularly with the integration of PV power into the existing hydropower reservoir system. Selecting the functional form for operating rules has turned out to be a challenge to derive (Zhou et al., 2015). Effective forms of operating rules for a hydro/PV hybrid power system are as yet unknown, and their independent and decision variables are difficult to determine. Therefore, this paper uses ISO to investigate the operating rules related to complementary management of hydropower and PV power plants. The remainder of this paper is organized as follows: Section 2 describes the deterministic optimization model of the hydro/PV hybrid power system, a solution of the model, and the resulting linear operating rules. Section 3 discusses the application of this method in a case study based on the Longyangxia hydro/PV hybrid power system. Section 4 derives the operating rules from the optimal trajectory, and compares the six operating scenarios before and after the implementation of complementary. Section 5 draws conclusions and discusses implications.

2. Methodology The proposed methodology for deriving hydro/PV hybrid power system operating rules (Fig. 1) consists of three steps: (1) Developing an optimal hydro/PV hybrid power system model: in this regard, a deterministic optimization model is established with two objective functions (Section 2.1). (2) Solving the model: using a dynamic programming (DP) technique to find a solution and its optimal trajectory is obtained (Section 2.2). (3) Deriving linear operating rules: independent and decision variables are selected using a cross-correlation analysis, then the operating rules are derived using a linear fitting method and parameterization-simulation-optimization (PSO) (Section 2.3).

Fig. 1. Outline of the methodology.

2.1. Deterministic hydro/PV hybrid power system optimization model For reservoir operations, optimal trajectory with deterministic inflow is essential for the derivation of operating rules using a fitting method (Bhaskar and Elbert. Whitlatch, 1980; Zhang et al., 2015). Similarly, optimal trajectory of a hydro/PV hybrid power system is used to derive the joint operating rules. Thus, in the following, a deterministic optimization model is established using objective functions and constraints. In what follows, “system” shall refer to hydro/PV hybrid power system unless otherwise stated.

2.1.1. Objective functions Economy and reliability are the twin goals of a system's operation and management. The maximization of its total power generation is an important operational objective. At the same time, the power output is expected to provide reliability over the power grid. Therefore, the dual objectives for optimization are the generation and reliability of the system as a whole, (1) Objective 1: maximize the total generation output of the system

EðTÞ ¼ max ¼ max

T h X

T X ½P ps ðtÞ  DTðtÞ t¼1

 i P ðtÞ þ P S ðtÞ  DTðtÞ

(1)

p

t¼1

where EðTÞ denotes the system's total generation (kWh), T denotes the total number of time periods, P ps ðtÞ denotes the system's total power output in the tth period (kW), P p ðtÞ and P s ðtÞ denote the power output (kW) of the PV and hydropower in the tth period, respectively, and DTðtÞ denotes the time step (e.g., one month). (2) Objective 2: maximize the reliability of the system's output

Z. Yang et al. / Journal of Cleaner Production 195 (2018) 562e572

RðTÞ ¼ max

  ps # P ps ðtÞ  Pfirm ðtÞ T

P smin ðtÞ  P s ðtÞ  P smax ðtÞ

during which the system power output P ps ðtÞ is equals or exceeds ps the required output minimum Pfirm ðtÞ. 2.1.2. Calculation of power generation The power output is calculated as follows: (1) hydropower generation: the hydropower output is calculated from

(3)

where K denotes the comprehensive output coefficient of the hydropower station (dimensionless), Qfd ðtÞ denotes the average reservoir release passing through the hydraulic turbines in the tth period (m3/s), and DHðtÞ denotes the net head of the hydropower station in the tth period (m), which is obtained from

DHðtÞ ¼ Zup ðtÞ  Zdown ðtÞ  Hlose ðtÞ

(4)

where Zup ðtÞ denotes the average fore-bay water level in the tth period (m), Zdown ðtÞ denotes the average tail-race water level in the tth period (m), and Hlose ðtÞ denotes the water head lose in the tth period (m). (2) PV generation: the PV power output is calculated based on a model developed by National Renewable Energy Laboratory (Li and Qiu, 2016), using the formula

 P p ðtÞ ¼ Xp

  Rt  1 þ ap ðTc  Tb Þ Rb

(5)

where Xp denotes the rated power output of the PV station (kW), Rt denotes the actual intensity of solar radiation (kW=m2 ), Rb denotes the intensity of solar radiation under standard test conditions (1kW=m2 ), ap denotes the power output temperature coefficient of the solar cell modules (0.35%/ C), Tc denotes the actual temperature of the solar cell modules ( C), and Tb denotes the temperature of the solar cell modules under standard test conditions (25  C). 2.1.3. Constraints The following operational constraints are taken into consideration in the system's optimization model. (1) Water balance equation:

h i Vðt þ 1Þ ¼ VðtÞ þ Qin ðtÞ  Qfd ðtÞ  Qqs ðtÞ  DTðtÞ

(6)

(7)

(3) Water release constraints:

Q min ðtÞ  Qfd ðtÞ þ Qqs ðtÞ  Q max ðtÞ (4) Power output constraints:

(5) Transmission system constraints:

P ps ðtÞ  P A

(10)

where VðtÞ and Vðt þ 1Þ denote the reservoir storage at the beginning and end of the tth period, respectively (m3), Qin ðtÞ denotes the reservoir inflow in the tth period (m3/s), Qfd ðtÞ denotes the average reservoir release passing through the hydraulic turbines in the t th period (m3/s), Qqs ðtÞ denotes the water spillage in the tth period (m3/s), V min ðt þ 1Þ and V max ðt þ 1Þ are the lower and upper limits for reservoir storage in the tth period, respectively (m3), Q min ðtÞ and Q max ðtÞ denote the lower and upper limits for downstream river discharge, respectively (m3/s), P smin ðtÞ and P smax ðtÞ denote the lower and upper limits for hydropower output, respectively (kW), and P A denotes the limit imposed by the transmission system (kW).

2.2. Method of solution A proper optimization method is important in resolving systemoperation problems (Ming et al., 2017a). As a multi-objective optimization mathematical model, the model is solved more easily as a single-objective problem by integrating Eqs. (1) and (2) (Liu et al., 2011b),

EðTÞ ¼ max

T X f½P ps ðtÞ þ gðP ps ðtÞÞ  DTðtÞg

(11)

t¼1

where gðP ps ðtÞÞ is the penalty function defined as

ps

gðP ðtÞÞ ¼

8    < a P s ðtÞ  P ps ðtÞ  P p ðtÞ ; P ps ðtÞ < P ps ðtÞ firm firm : 0; P ps ðtÞ  P ps ðtÞ firm (12)

with a denotes the penalty coefficient, which is adjusted to ensure that the assurance rate meets the specified requirement. Typically, when the overall output is lower than the required minimum output, the hydropower generation is used to compensate deficits from the PV station so as to adjust the overall output of the system needed to meet the output requirement. Therefore, the form of penalty function is as above. This deterministic operation model is a multi-stage problem, which can be solved by DP (Labadie, 2004; Liu et al., 2006). According to the multi-stage decision-making principle, the recursive equations are

h h i i 8 * * < E ðtÞ½VðtÞ  ¼ max EðtÞ VðtÞ; Qfd ðtÞ þ E ðt þ 1Þ½Vðt þ 1Þ  Qfd 2DðtÞ i h : Vðt þ 1Þ ¼ VðtÞ þ Qin ðtÞ  Qfd ðtÞ  Qqs ðtÞ  ΔTðtÞ

(2) Water storage capacity constraints:

V min ðt þ 1Þ  Vðt þ 1Þ  V max ðt þ 1Þ

(9)

(2)

where RðTÞ denotes the system generation reliability, and ps ðtÞÞ accounts the total number of time periods # ðP ps ðtÞ  Pfirm

P s ðtÞ ¼ KQfd ðtÞDHðtÞ

565

(8)

(13) where E* ðtÞ½VðtÞ  denotes the maximum cumulative power output from the 1st period to the tth period (kWh), EðtÞ½VðtÞ; Qfd ðtÞ denotes the average output in the tth period (kWh). The objective function is calculated from the Tth period to the 1st period by the DP technique using the above equation, from which the optimal trajectory is obtained.

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2.3. Operating rules derivation

b ðtÞ þ b ; k ¼ 1; 2; /; 12 b ðt þ 1Þ ¼ a  X Y k k k k

Independent and decision variables constitute the basic framework of operating rules. Depending on the selected variables, these rules can be divided into those related to energy and those related to water. Their proper selection is of great importance for model accuracy (Chang-Ming et al., 2010; Zhou et al., 2015). In a hydro/PV hybrid power system, energy inputs consists of those related to hydropower generation and PV generation. To enable the direct comparison of different quantities, the inflow and water storage capacity of the hydropower station can be expressed in the form of their energy potential.

(16)

where k indexes the month; ak and bk denote the operating rules parameters to be determined in the above regression equation by b ðt þ 1Þ denotes the decision variables at the the fitting method; Y k

end of the time period t, which may be the power output, water release during the time period, the reservoir storage or water level b ðtÞ denotes the independent at the end of each time period; X k

variables at the beginning of the time period t, and correspond to the available energy or available water. The appropriate decision variables and independent variables can be determined by the above cross-correlation analysis of variables.

2.3.1. Transformation to potential energy (1) The input of potential energy during the time period Assuming other water uses are negligible, the total system input of potential energy during the tth period can be written as

IðtÞ ¼ KQin ðtÞDHðtÞDTðtÞ þ P p ðtÞDTðtÞ

(14)

The first term on the right side of this equation is the total potential energy that is theoretically generated by the hydropower plant, whereas the second term refers to the input of energy during the tth period of the PV plant. (2) The initial total potential energy stored at the beginning of the time period The system can only store hydropower energy potential, in the form of a water reservoir; the PV power cannot be stored with large scale. The stored energy potential at the beginning of the tth period depends on the amount of water stored in the hydropower reservoir at the beginning of the time period and is calculated using

h i SðtÞ ¼ Ss ðtÞ ¼ K VðtÞ  V min ðtÞ DH0 ðtÞ

(15)

2.3.2. Cross-correlation analysis of variables According to the optimal trajectory, variables that affect system operation need to be identified. Variables that were considered are: available energy, available water, reservoir storage, water release, power output, reservoir water level. A correlation analysis of variables was performed to select independent variables and identify decision variables for the operating rules. To quantify the correlation between variables mathematically, a statistical measure called the correlation coefficient (CORR) was calculated. In this study, CORR uses the Pearson correlation coefficient. To analyze efficiently the correlation between multivariate, a cross-correlation analysis of variables was used to select independent and decision variables of operating rules. 2.3.3. Fitting operating rules The operating rules can be derived by a fitting method (Soltani et al., 2010; Wang et al., 2011), and is used here because of its ease of implementation. Widely used linear operating rules for a single reservoir are adopted (Liu et al., 2014; Stedinger, 1984); these are the simplest and effective in improving reservoir performance (Feng et al., 2017; Liu et al., 2011a). In addition, linear operating rules are as good as or even better than nonlinear operating rules in many cases (Bhaskar and Elbert. Whitlatch, 1980; He et al., 2018). Therefore, the initial form of the operating rules is expressed as

2.3.4. Refining operating rules The parameterization-simulation-optimization, PSO, is an efficient method by which to refine the operating rules of the reservoir (Koutsoyiannis and Economou, 2003; Ming et al., 2017b). In this study, the parameters to be optimized are the coefficients, ak and bk of the operating rules. The above objective functions and constraints are used to build a simulation-based optimization model (Chang et al., 2005; Liu et al., 2015). In the optimization part, many optimization methods can used to optimize the parameters, such as the Complex method, artificial cooperative search algorithm, gene expression programming, particle swarm optimization or other methods (Kaboli et al., 2016, 2017; Rafieerad et al., 2016, 2017; Sebtahmadi et al., 2017; Zhang et al., 2015). As the model is nonlinear, a nonlinear optimization technique, namely the Complex method, is used to maximize the objective function (Xie et al., 2017; Zhang et al., 2016). Complex method is an optimization algorithm to search for extreme values of a n-dimensional problem having equality and inequality constraints (Zhang et al., 2017a), which is a popular algorithm for multidimensional constrained optimization. The Complex method is based on a comparison of function values at the vertices, followed by the replacement of the worst point by another point. This method is widely used in the field of hydrology and water resources management, such as the calibration of hydrological-model parameters (Liu et al., 2006; Zhang et al., 2015, 2017a). A set of initialization of the parameters (i.e., ak and bk) is obtained from either the fitting method or a randomly generated scheme. Then, the optimal parameters are ultimately determined using the Complex method. Fig. 2 shows the main steps of the Complex method. 3. Case study 3.1. Overview The Longyangxia hydro/PV hybrid power system is located in eastern Qinghai province, China (Fig. 3) and is currently the world's largest of its type. The plant comprises the Longyangxia hydropower station and a nearby PV power station. Built in 1989, the hydropower station was the first cascade hydropower station on the upper reaches of the Yellow River. The station was originally built to generate power, control flooding, provide irrigation, and supply water. The reservoir's normal water level is 2600 m, corresponding to a capacity of 24.7 billion m3; the regulation capacity is 19.35 billion m3, and the storage capacity adjustment coefficient is 0.94. The hydropower station contains a total of four turbines, each with a capacity of 320 MW, resulting in a total capacity of 1280 MW. The huge adjustment capacity ensures it has a good multi-year adjustment performance. Located nearby is the PV power plant in the western part of the Gonghe County PV power generation park. Its total installed

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China. Most of the generated power is accommodated by the power grid. Research is still needed to determine the optimal medium-and long-term operations for complementary energy production. 3.2. Simulation data and setup The primary input data for this study included monthly reservoir runoff and hourly PV power output. The Longyangxia reservoir inflow was measured over a 56-year period from 1956 to 2011 at Tangnaihe hydrological station (Ming et al., 2017c). Hourly PV power output data were obtained from the 320-MW PV arrays for all of 2014 (Fang et al., 2017). For this study, the PV power output was calculated using a scaling from the hourly power output data from the 320-MW PV arrays, which assumes that the annual solar radiation is relatively stable. This study optimized the system on a monthly time base, the entire simulation covering a 672 month period. The time interval of the reservoir inflow is monthly. To match the time scale, the time base of the PV power output data is for a 1-h basis and is used to aggregate the monthly time scale data. In addition, the initial and final water levels for the entire 56-year simulation were set at 2560 m.

Fig. 2. Steps in the Complex method framework.

4. Results and discussion 4.1. Operational results obtained from DP A DP algorithm is used to find the optimal trajectory for the system. Fig. 4 shows an optimal trajectory in the reservoir water

a

Fig. 3. Location of the Longyangxia hydro-PV plant.

capacity is 850 MW, with a planned production operation period of 25 years. The first phase of the project was completed in 2013, with an installed capacity of 320 MW. The second phase of the project, which was completed in 2015, created the world's largest gridconnected PV power plant at 850 MW capacity. The system generates electricity at a voltage of 330 KV, which is transmitted to the grid through the Longyangxia hydropower station transmission lines. The parameters regarding the hydro-PV plant are given in Table 1. The Longyangxia hydro/PV hybrid power system was the first large-scale, grid-connected hydro/PV hybrid power system built in

b

Table 1 Relevant parameters for the Longyangxia hydro/PV hybrid power system. Hydropower reservoir Average annual inflow Minimum release requirement Normal pool level Storage capacity Installed capacity Firm output Power coefficient PV arrays Installed capacity Expected life-span Occupied area

580 m3/s 300 m3/s 2600 m 24.7 billion m3 1280 MW 589.9 MW 8.3 850 MW 25 years 24.33 km2

Fig. 4. Seasonal statistical results: (a) optimized water level, and (b) optimized system power output.

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level and system power output. For both, the median value and the interquartile range (25% and 75%) for every month are shown. Moreover, the variational range is also drawn using the trajectories of minimum and maximum values. The results for the optimal water level of the reservoir (Fig. 4(a)) show the filling of the reservoir is earlier and faster in refill periods and the emptying of the reservoir is later and faster in drawdown periods, thereby increasing the duration during which the water head remains high. Also, the interquartile range of the monthly water level and the profile of each value are indicated in Fig. 4(a). The optimal trajectory of the water level can be used to derive operating rules for the system. Fig. 4(b) shows the monthly variation in the system's optimal power output during the entire operating period. This output remains mostly close to the firm output, except for the flood season when there is more rainfall. 4.2. Operating rules 4.2.1. Cross-correlation analysis of variables The operating rules were derived from the optimal trajectory. Before deriving them, the appropriate decision variables and correlation factors need selecting using the cross-correlation analysis of variables. Fig. 5 shows the result for the cross-correlation coefficients among the six variables extracted from the optimal trajectory. The six variables are: available energy, available water,

reservoir storage, water release, power output, and reservoir water level. In detail, Fig. 5(a) and (b) presents the cross correlations for a part of non-flood season; Fig. 5(c) and (d) presents similar results for the flood season. The diagonals of the diagrams indicate the selfcorrelations for the six variables and are always equal to 1. The decision variables may be the power output, the water release during the time period, the reservoir storage or the water level at the end of each time period. From the diagrams (Fig. 5) and a comparison of the CORR values of the six variables, the direct correlation between the reservoir storage at the end of each time period and available energy is very strong. Moreover, the available water was also good correlated the former. Therefore, the reservoir storage at the end of each time period was selected as the decision variables. Concerning the operating rules involving the PV power output, the study chose the energy correlation factors, the available energy as the independent variables to better reflect PV output in the operating rules and improve the practicality of these rules. Therefore, their form may be expressed as

 bI ðtÞ þ b ; k ¼ 1; 2; /; 12 b ðt þ 1Þ ¼ a  b S ðtÞ þ V k k k k k

(17)

4.2.2. Fitted operating rules Next, the monthly operating results were used to derive the

a

b

c

d

Fig. 5. Cross-correlation coefficients among the six variables: available energy (AE), available water (AW), reservoir storage (ST), water release (WR), power output (PO), reservoir water level (WL): (a) January; (b) February; (c) August; (d) October.

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operating rules. Specifically, the reservoir storage at the end of each month, the input energy during the month, and the energy storage at the beginning of the month were used for the derivation of these rules using the linear fitting method. The fitting result of the operating rules (Figs. 6 and 7) are presented as scatter plots of the optimal reservoir storage at the end of each month versus the available energy. These points represent optimal decisions and the linear lines correspond to the monthly operating rules for the nonflood (Fig. 6) and flood (Fig. 7) seasons. From Figs. 6 and 7, several observations and implications follow: (1) The optimal decision can be fitted using linear operating rules, which are constrained by water storage capacity constraints. When the value of the month's final reservoir storage is greater than 24.698 million m3, its decision variable is set at 24.698 million m3; similarly, when the value of the month's final reservoir storage is less than 5.343 million m3, its decision variable is set at 5.343 million m3. (2) A significant linear correlation exists between the available energy and reservoir storage at the end of each time period. The deterministic coefficient for each operating rule is greater than 0.9 suggesting that the fitting accuracy of the operating rules is adequate. That apart, the fitting accuracy of the non-flood season is generally higher than that of the flood season. This is because during flood seasons than for non-flood seasons rainfall varies and the range of runoff is greater. (3) To use these operating rules, the energy stored at the beginning of the time period can be calculated first using Eq. (15), and, with the forecast inflow and PV data, the input energy during the time period then can be calculated. The sum of these quantities is the available energy. Specific operational decisions (i.e., reservoir storage at the end of each time period) as a function of appropriate available information (i.e., available energy), reservoir storage at the end of each time period can be calculated easily every month based on the function, and operational decisions can be made. Therefore, the operating rules can provide expedient guidelines for operating decisions.

Fig. 6. Operating rules for the non-flood season: (a) January; (b) February; (c) March; (d) April; (e) November; and (f) December.

Fig. 7. Monthly operating rules for the flood season: (a) May; (b) June; (c) July; (d) August; (e) September; and (f) October.

4.2.3. Refined operating rules From the foregoing analysis, the form of the operating rules of the hydro/PV hybrid power system have been identified. Nevertheless, the operational performance may be further improved using the PSO. The operation results of the refined operating rules are listed in Table 2. 4.3. Comparison of different operating scenarios The superiority of the hydro/PV hybrid power system and the effectiveness of the operating rules are revealed by comparing the six operating scenarios, the first three and the last three relate, respectively to after and before the implementation of complementary: Scenario 1: an integrated system complementary optimal operation, Scenario 2: an integrated system operation using refined operating rules, Scenario 3: an integrated system operation using fitted operating rules, Scenario 4: a hydropower station conventional operation plus directly PV station output, Scenario 5: a hydropower station conventional operation optimal operation plus directly PV station output, Scenario 6: a hydropower station using operating rules plus directly PV station output. For each scenario, the annual average generation and assurance rate were calculated and compared (see Table 2). Table 2 shows that of the six scenarios. By considering the conventional operation with added PV operations, this scenario yields poor benefits as the operation scheme has not considered complementary operations in managing hydropower and PV power, simultaneously. As expected, an optimal complementary operation is superior to other operation scenarios as it has the highest annual generation and assurance rates, with values of 7.850 billion kWh and 76.04%, respectively. This scenario increases power generation by 0.053 billion kWh, and the assurance rate by 8.33% compared with the optimal operation of a single reservoir plus PV. The enhancement arises because PV power can compensate for the hydropower with the electricity. It enables less electricity to be generated and more water stored during the dry season, and more electricity to be generated and less water stored during the flood season. Hence, the water head of the hydropower station increases

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Table 2 Comparison of annual average generation and assurance rates for the six operating scenarios. Operating scenarios

Power generation (billion kWh)

Assurance rate (%)

Complementary optimal operation Complementary operation using refined operating rules Complementary operation using fitted operating rules Single reservoir conventional operation & PV Single reservoir optimal operation & PV Single reservoir operation using operating rules & PV

7.850 7.454 7.303 7.283 7.797 7.420

76.04 74.85 63.54 66.96 67.71 68.01

and water consumption rate decreases thereby improving the performance index values. Moreover, the operational performance of the complementary operation using operating rules has improved after being refined using the PSO framework. The annual generation increased from 7.303 billion kWh to 7.454 billion kWh, along with an 8.33% increase in the assurance rate. Therefore, the PSO scheme (i.e., Complex method) can be used to refine the operating rules effectively. The performance of this complementary system using operating rules derived from the complementary optimal trajectory, while better than the conventional operation with added PV operations, is worse than that for the complementary optimal operation. From Table 2, the index values of the complementary implementation have increased with the annual generation and assurance rate increasing by 0.171 billion kWh and 7.89%, respectively. Therefore, with efficient complementary operating rules, the complementary operation is an effective way to manage a combined hydropower and PV power simultaneously. To further explore the effectiveness of the proposed operating rules, using the observed inflow and PV data, the operating rules were used to provide guideline of the system operation. The operation results for the 56-year period from 1956 to 2011 are presented in Fig. 8. The box plot shows the distribution of monthly water level. The top and bottom boundaries of the boxes represent the 25th and 75th percentiles, the central red line represents the median, and red crosses indicate the remaining outliers. Therefore, the monthly water level median, tail length, outliers, distribution intervals, and other shape information are contained in this box representation. In comparing Fig. 8(a) and (b), we find that the shape of the boxes for each month's water level are similar, indicating that the corresponding eigenvalues are similar. Therefore, operating rules can be used as guidelines to hydro/PV hybrid power system operations. Fig. 8 shows that the length of boxes during flood seasons is longer than that in non-flood season, indicating that the water levels during flood seasons have the larger variability. Hence the fitting accuracy of the operating rules in non-flood seasons is generally higher than that of flood seasons, suggesting that parameter optimization of the operating rules during flood season are particularly important. These findings demonstrate that operating rules are efficient and reliable for hydro/PV hybrid power system operation. 5. Conclusions This study focused on exploring the long-term operating rules for an integrated hydro/PV hybrid power system using implicit stochastic optimization. A deterministic optimization model of the system was established with two objective functions, which considered both total power generation and assurance rate simultaneously. The DP technique was used to obtain the optimal trajectory, and a linear fitting method was used to fit the operating rules from the obtained optimal trajectory. Based on the integrated objective, the parameterization-simulation-optimization

a

b

Fig. 8. Box plot of monthly water levels of the operation results: (a) optimal water level, and (b) water level using operating rules.

framework was used to optimize the parameters of the operating rules. The proposed method was applied to the Longyangxia hydro/ PV hybrid power system, and three main conclusions can be drawn: (1) The available energy and reservoir storage at the end of each time period are effective as independent variables and decision variables in the operating rules. Because there exists a significant linear correlation between the available energy and reservoir storage at the end of each time period, the fitting correlation coefficient for each month is greater than 0.9. (2) The complementary optimal operation of the whole system is superior to other operation scenarios, because PV power can compensate shortfalls in hydroelectric power supply during the dry season. Specifically, the complementary operation can optimize the generation process by increasing

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water use efficiency, thereby improving the operational performance. (3) The derived operating rules are able to improve the hybrid system's performance compared with the conventional operation, because they consider the complementary operation of hydropower and PV power. Meanwhile, the PSO framework was proven to be an effective tool to derive operating rules of such hybrid systems. Therefore, the resulting operating rules can be used as a guideline in the operations of the hydro/PV hybrid power system. Further work is still needed on short-term optimization, as well as operational optimization under climate change. Acknowledgments This study was supported by the National Key Research and Development Program (Grant No. 2016YFC0400907), the Innovative Research Groups of the Natural Science Foundation of Hubei, China (Grant No. 2017CFA015) and the National Natural Science Foundation of China (Grant No. 51579810). Our sincere gratitude is extended to the editor and anonymous reviewers for their professional comments and corrections, which greatly improved the presentation of the paper. References Aghay Kaboli, S.H., Selvaraj, J., Rahim, N.A., 2017. Rain-fall optimization algorithm: a population based algorithm for solving constrained optimization problems. J. Comput. Sci. 19, 31e42. An, Y., Fang, W., Ming, B., Huang, Q., 2015. Theories and methodology of complementary hydro/photovoltaic operation: applications to short-term scheduling. J. Renew. Sustain. Energy 7, 063133. Barbosa, L.S., Bogdanov, D., Vainikka, P., Breyer, C., 2017. Hydro, wind and solar power as a base for a 100% renewable energy supply for South and Central America. PLoS One 12, e0173820. Bekele, G., Tadesse, G., 2012. Feasibility study of small Hydro/PV/Wind hybrid system for off-grid rural electrification in Ethiopia. Appl. Energy 97, 5e15. Beluco, A., Kroeff de Souza, P., Krenzinger, A., 2012. A method to evaluate the effect of complementarity in time between hydro and solar energy on the performance of hybrid hydro PV generating plants. Renew. Energy 45, 24e30. Bhaskar, N.R., Elbert Whitlatch, J., 1980. Derivation of monthly reservoir release policies. Water Resour. Res. 16. Celeste, A.B., Billib, M., 2009. Evaluation of stochastic reservoir operation optimization models. Adv. Water Resour. 32, 1429e1443. Celeste, A.B., Billib, M., 2012. Improving implicit stochastic reservoir optimization models with long-term mean inflow forecast. Water Resour. Manag. 26, 2443e2451. Chang-Ming, J.I., Zhou, T., Huang, H.T., 2010. Establishment and evaluation of operation function model for cascade hydropower station. Water Sci. Eng. 3, 443e453 (in Chinese). Chang, F.J., Chen, L., Chang, L.C., 2005. Optimizing the reservoir operation rule curves by genetic algorithms. Hydrol Process. Hydrol. Process. 19, 2277e2289. Chang, J., Li, Y., Yuan, M., Wang, Y., 2017. Efficiency evaluation of hydropower station operation: a case study of Longyangxia station in the Yellow River, China. Energy 135, 23e31. Chen, S., Chen, B., 2015. Urban energy consumption: different insights from energy flow analysis, inputeoutput analysis and ecological network analysis. Appl. Energy 138, 99e107. de Oliveira Costa Souza Rosa, C., Costa, K., da Silva Christo, E., Braga Bertahone, P., 2017. Complementarity of hydro, photovoltaic, and wind power in Rio de Janeiro State. Sustainability 9, 1130. Dujardin, J., Kahl, A., Kruyt, B., Bartlett, S., Lehning, M., 2017. Interplay between photovoltaic, wind energy and storage hydropower in a fully renewable Switzerland. Energy 135, 513e525. En, Z., 2004. Solar energy in progress and future research trends. Prog. Energy Combust. Sci. 30, 367e416. Fang, W., Huang, Q., Huang, S., Yang, J., Meng, E., Li, Y., 2017. Optimal sizing of utilityscale photovoltaic power generation complementarily operating with hydropower: a case study of the world's largest hydro-photovoltaic plant. Energy Convers. Manag. 136, 161e172. Farfan, J., Breyer, C., 2017. Structural changes of global power generation capacity towards sustainability and the risk of stranded investments supported by a sustainability indicator. J. Clean. Prod. 141, 370e384. Feng, M., Liu, P., Guo, S., Shi, L., Deng, C., Ming, B., 2017. Deriving adaptive operating rules of hydropower reservoirs using time-varying parameters generated by the

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