Multi-objective optimization for integrated hydro–photovoltaic power system

Applied Energy xxx (2015) xxx–xxx

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Multi-objective optimization for integrated hydro–photovoltaic power system Fang-Fang Li a,⇑, Jun Qiu b,⇑ a b

College of Water Resources & Civil Engineering, China Agricultural University, Beijing 100083, China Institute for Aero-Engine, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

h i g h l i g h t s
A model optimizing both quality and quantity of hydro/PV power was proposed.
The dimension was reduced by decoupling hydropower and PV power in time scales.
Reservoir operations have been optimized for different typical hydrological years.
Hydropower was proved to be an ideal compensating resource for PV power in nature.

a r t i c l e

i n f o

Article history: Received 29 May 2015 Received in revised form 20 August 2015 Accepted 3 September 2015 Available online xxxx Keywords: Hydro–photovoltaic power system Multi-objective optimization NSGA-II Longyangxia hydro/PV project

a b s t r a c t The most striking feature of the solar energy is its intermittency and instability resulting from environmental influence. Hydropower can be an ideal choice to compensate photovoltaic (PV) power since it is easy to adjust and responds rapidly with low cost. This study proposed a long-term multi-objective optimization model for integrated hydro/PV power system considering the smoothness of power output process and the total amount of annual power generation of the system simultaneously. The PV power output is firstly calculated by hourly solar radiation and temperature data, which is then taken as the boundary condition for reservoir optimization. For hydropower, due to its great adjustable capability, a month is taken as the time step to balance the simulation cost. The problem dimension is thus reduced by decoupling hydropower and PV power in time scales. The modified version of Non-dominated Sorting Genetic Algorithm (NSGA-II) is adopted to optimize the multi-objective problem. The proposed model was applied to the Longyangxia hydro/PV hybrid power system in Qinghai province of China, which is supposed to be the largest hydro/PV hydropower station in the world. The results verified that the hydropower is an ideal compensation resource for the PV power in nature, especially in wet years, when the solar radiation decreases due to rainfalls while the water resource is abundant to be allocated. The power generation potential is provided for different hydrologic years, which can be taken to evaluate the actual operations. The proposed methodology is general in that it can be used for other hydro/PV power systems than those studied here. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction China’s energy demand will continue to grow rapidly in the early 21st century. According to the prediction of Chinese Academy of Sciences, the annual energy consumption of China may increase to 7 billion tonnes of coal equivalent (1 tce corresponds to 7.500 kW h) in 2050 from 3.84 billion tce in the year of 2014, ⇑ Corresponding authors. E-mail addresses: [email protected], [email protected] (F.-F. Li), qiujun07@ tsinghua.org.cn (J. Qiu).

and the total installed capacity of power generation will rise to 3 billion kW in 2050 from 1.36 billion kW in 2014. To utilize the energy resources sustainably and limit the environment pollution and greenhouse gas emissions, the portion of coal energy should be decreased, and the share of clean renewable energy needs to be greatly increased. 40% of the 3 billion kW installed capacity in the year 2050 is taken by coal energy, and the hydropower, nuclear power and the gas power take up to about 15%, 11%, and 4%, respectively. Hence, there are about 30% of the power needs to be provided by non-hydro renewable resources, corresponding to about 900 million kW installed capacity.

http://dx.doi.org/10.1016/j.apenergy.2015.09.018 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

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China has a large area of desert Gobi, which offers the probability of large-scale development of photovoltaic (PV) industry. It is estimated that the gross area of desert Gobi in China is about 1,280,000 km2, and the corresponding potential PV power output can be as high as about 130 billion kW. By the end of 2014, the accumulative installed capacity of PV power is 28.05 million kW, with annual power generation of 25 billion kWh. In the year of 2014, China added 10.6 million kW of the PV capacity, taking up to 1/5 of the global increment. Only for Qinghai province, the PV capacity integrated into power grid is increased by 1.01 million kW in 2014, and it has accomplished annual growth of over 1 million kW integration of PV capacity for consecutive four years. Qinghai Province locates in high latitudes with intense solar radiation, and long-time sunshine. The annual radiation is up to 56–74 MJ/m2, in which the direct radiation accounts for more than 60%, only ranking behind Tibet in China. Most of the Qinghai Province is sparsely populated with flat terrain. The population density is lower than 1 person/km2. The area of available desertificated land is more than 200,000 km2, mainly distributed in the Qaidam Basin and Sanjiangyuan region with rich radiation. Besides, a lot of desert is near electric power lines and load centers, facilitating electrical connection. For these reasons, Qinghai region is preferable for the construction of large-scale PV power plants. Photovoltaic power generation converts the solar radiation directly into electrical power without fuel consumption or rotating machinery. Thus it is simple to maintain with high safety and reliability. Nevertheless, since PV generation uses solar radiation as the energy resources, it depends greatly on the uncertain natural conditions. The largest disadvantage of the PV power lies in its instability and discontinuity on account of season and weather, and such changes of power flow in long-distance power transmission leads to the difficulty for voltage control in power grid. As a result, there has to be enough spare capacity in the power system to make adjustment. The majority of studies and most systems in operation use a renewable source backed up by a conventional one such as a fossil fuel based generator [1], causing coal consumption and greenhouse gas emissions. Recently, the integrated hydro/ PV/wind system has attracted interest of researchers, especially for the remote or isolated areas. Bekele and Tadesse studied the feasibility of small hydro/PV/wind hybrid system in Ethiopia [2]. Nfah and Ngundam contemplated pico–hydro and PV power systems in Cameroon [3], and Kenfack et al. suggested small hydro/PV hybrid system for rural electrification in developing countries as well [4]. Some pioneering resolutions have been put into operation, such as the PV–micro–hydro hybrid system in Taratak village of Indonesia, which was launched on June 10, 1989 [5]. As for the management of the existing hydro/PV hybrid systems, there also have been related studied. Meshram et al. developed an energy management system to improve the power quality of the hybrid system and to control the power distribution among the power generating systems [6]. A new approach to optimize the photovoltaic water pumping system for irrigation was presented by Campana et al. [7]. Campana et al. also developed a dynamic simulation tool combining the models of the water demand, the solar PV power and pumping system [8]. Many other studies on the hydro/PV hybrid system are published on its design [9], control strategies [10], as well as environmental effect [11,12]. Nevertheless, most of the studies are in view of the short-term operation for the small-scale system, or even off-grid power systems in some cases, where the quality requirements of power generation appear less important. Moreover, the PV power output depends on the solar radiation in hourly scale, while to estimate the long-term optimal operation by hours would result in a highdimensional non-linear problem, to which none of the current optimization algorithms is capable. Hence, the optimization of the whole integrated hydro/PV power systems instead of the

control techniques is seldom focus on, nor the analysis of the operational potential in a long term. This study is intended to focus on the estimation of the annual power generation of the whole hydro/PV system considering both the quality and the quantity of the power output. To maintain the accuracy of calculation, the PV power output is firstly evaluated day by day with hourly solar radiation and temperature data, the results of which is taken as the boundary condition for the reservoir optimization. As to the hydropower, because of its great adjustable capability, a month is taken as the time step to balance the simulation cost. Such decoupling of hydropower and PV power in time scales effectively reduces the problem dimensions with respect to the computational accuracy. Taking reservoir release as decision variables, both maximizing the power generation of the integrated system and minimizing the fluctuation of its power output are set as objectives. With the addition of other operational constraints, a multi-objective optimization model for long-term operation of hydro/PV power system is established, and it is then optimized by the modified version of Non-dominated Sorting Genetic Algorithm (NSGA-II). The proposed method is applied on the Longyangxia project, which is the largest integrated hydro/PV power system in the world. The power generation potential in different typical hydrologic years is provided. The results prove that the hydropower and PV power are able to complement each other significantly, especially in wet years. Hydropower can make the power output process of the whole system much smoother with an increment of total power generation by reallocating the temporal distribution of water resources. The results can be used to either evaluate the practice or guide the reservoir operation. The proposed model can be promoted to other hydro/PV power systems than the case in this study.

2. Methodology 2.1. Calculation of PV power generation PV grid-connected generation systems can be divided into two categories based on its function: one is unschedulable excluding energy storage components, and the other kind of PV systems is schedulable with energy storage elements. The energy storing device of the latter one introduces some operational defects, the primary of which is that the common storage battery has a short service life of about 3–5 years and is inconvenient to maintain. Besides, the battery will lead to environmental pollution. Due to the existence of these problems, the application of ‘‘schedulable type” of the PV system is far below that of the ‘‘unschedulable type”. Hence, this study mainly aims at ‘‘unschedulable” PV gridconnected generation systems. There is a typical PV power device in Fig. 1, a PV array with tracking stents. PV array is the key component of the device, formed by series–parallel connected PV solar cells. Its main function is to convert sunlight energy into electrical energy. The twin-shaft tracking stents bear the weight of the PV cells with controller, which is able to rotate the PV array to track the maximum energy point of incident rays. Detailedly, the angle of the solar wafer substrate is adjusted constantly to ensure that the substrate is always perpendicular to the incident solar rays so as to maximize the utilization of solar energy. The electric current and voltage of PV power varies with different solar intensity and environmental temperature, and thus the output of PV power is unstable. If the PV array is incapable to real-timely track the change of external environment, the overall efficiency of PC power system will decrease inevitably. The technology of Maximum Power Point Tracking (MPPT) is developed to continuously obtain the maximum power output at any

Please cite this article in press as: Li F-F, Qiu J. Multi-objective optimization for integrated hydro–photovoltaic power system. Appl Energy (2015), http:// dx.doi.org/10.1016/j.apenergy.2015.09.018

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Fig. 1. Hydro/PV hybrid power system.

sunshine and temperature. Existing MPPT methods mainly include: constant voltage method [13], perturbation and observation method, P&O [14], the incremental conductance method [15], variable step perturb and observe method [16], fractional short circuit current method [17], neural network [18], the optimal gradient method [19], etc. With the twin-shaft tracking device and MPPT, the power output of PV array is only determined by solar radiation and temperature. Comparing the standard test condition and general cases, the PV power output can be derived on the basis of the model in HOMER software developed by National Renewable Energy Laboratory (NREL) [20], as shown in Eq. (1).


PPV ¼ Y PV

 RT ½1 þ aP ðT C  T STC Þ RSTC

ð1Þ

where PPV and YPV are the actual and rated power output, respectively; RT is the actual intensity of solar radiation; RSTC represents the solar radiation intensity under the standard test conditions, equivalent to 1000 W/m2; aP is the temperature coefficients of power output of the solar cell module, which is 0.35%/°C in this study; TC is the actual temperature of the module, and TSTC is the temperature under the standard test conditions, equivalent to 25 °C. Power output of a PV power device can be derived from Eq. (1) as long as the solar radiation and temperature at each moment is given. Unfortunately, these data are not available for all the areas in the world, especially for small time scale. So as to establish a more propagable model, the data from NASA, which is of open access on [21], is used to modified the model. NASA provides daily insolation data on horizontal surface. However, due to the twinshaft tracking device and MPPT, the PV array is perpendicular to the solar direct rays, which changes from time to time in a day. The actual daily intensity of solar radiation on the PV array RT in Eq. (1) has to be calculated hourly with different solar incident angles. NASA also offers the monthly averaged hourly solar angles relative to the horizon. According to the geometrical relationships between radiations in different directions illustrated in Fig. 1, the RT can be calculated based on energy conservation as shown in Eq. (2).

Z

t¼t s

RT sin hðtÞdt ¼ RHorizon  24

ð2Þ

t¼t0

where RT is the actual daily solar radiation on the PV array; RHorizon is the daily average insolation on horizontal surface from NASA; h is the hourly solar angles relative to the horizon provided by NASA, which is a function of time t; t0 and ts are the times of sunrise and sunset, respectively. The other variable except for solar radiation determining the power output of PV in Eq. (1) is temperature Tc, which can be downloaded from [22] with the location information. With the

data of RT and Tc, the daily power output of PV can be derived by hourly calculation. 2.2. Calculation of hydropower generation Reservoirs are constructed to regulate the spatial and temporal distribution of the runoff to meet the power load demands, as well as many other demands, such as water supply, navigation, and flood control. Hydropower units convert the mechanical energy of water flow to electric energy, the power output of which can be calculated by Eq. (3) [23].

PH ¼ KQ DH

ð3Þ

where PH is the power output of the hydropower station; K is the synthetic output coefficient of the power station, while Q is the total discharge flow, and DH is the net water head of the power station, which is calculated by Eq. (4).

DH ¼ Lup  Ldown

ð4Þ

where Lup is the pool level and Ldown is the tailwater elevation. The basic state equations referring to the hydraulic and electric conditions and connections used in calculation process mainly includes: 2.2.1. Water balance equations Water balance equations shown in Eq. (5) imply the hydraulic relations between neighboring time steps:

St ¼ St1 þ It  Dt  Q t  Dt

ð5Þ

where t is time index; S is the storage volume in reservoir; I is the inflow, and Dt is the length of the time period t. 2.2.2. Water level-storage curves of the reservoir A nonlinear function f(x) is adopted to express the relationship between storage S and water level L according to the reservoir characteristic database:

St ¼ f ðLt Þ [ Lt ¼ f

1

ðSt Þ

ð6Þ

2.2.3. Tailwater elevation curves at the reservoir Tailwater elevation T is calculated based on discharge–elevation curve, which is also described by nonlinear function g(x), derived from the reservoir characteristics database. Together with Eqs. (4)–(6), Eq. (3) can be directly used for the hydropower plant where uniform hydropower units are installed so that the water head influences the output of the units equally.

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2.3. Optimization model the PV–hydro hybrid power system

2.4. Implementation

2.3.1. Objective functions The purpose of integrate hydro power and PV power is to avoid the uncontinuity and instability caused by solar radiation. The total power output of the hydro/PV hybrid system is expected to be reliable with variation as small as possible. On the other hand, the power generation of the whole system should be maximized by regulation of the reservoir. Therefore, there are two objectives selected in this study, as illustrated below.

The two objectives in Eqs. (7) and (8) is neither coincident nor comparable. A single solution optimizing all objectives simultaneously does not exist. Instead, the best trade-off solutions called the Pareto optimal solutions are of great significance. There have been a growing interest in apply evolutionary algorithms to deal with multi objective problems (MOPs). The modified version of Nondominated Sorting Genetic Algorithm (NSGA), NSGA-II, proposed by Deb et al. [24] was adopted in this study since it grants elitism and preserves diversity automatically without specifying any additional parameter [25]. Individuals shown in Eq. (9) are generated randomly at first with a population of size N. The objectives in Eqs. (7) and (8) are then evaluated for each individual respectively. Another offspring population of the equal size N is also generated using the parent population. The parent and offspring compose a mating pool with population of size 2N, and the individuals in such mating pool are classified in different Pareto Fronts by their own level of dominance, which is defined in Eq. (13).

Objective 1: minimizing the variance of the power output In order to guarantee the smoothness of the output into the power grid, the fluctuation of the power output should be as small as possible. Thus minimizing the variance of the power output of the hybrid system is selected as an optimizing objective, as described in Eq. (7): T X 2 Z 1 ¼ Min ðPt  PÞ =T

ð7Þ

t¼1

X ¼ fx1 ; x2 ; . . . ; xM g

where T is the total number of time periods being calculated, P is the total power output of the hydro/PV hybrid power system, P = PPV + PH; and P is the average value of P during the time period. Objective 2: maximizing total generated energy of the hydro/PV hybrid system Maximizing power generation of the whole system in the entire time period is an important operational objective for any power generation system. The objective function can be written as: T   X ~ ¼ Max Pt  Dt Z 2 ¼ MaxE Q t¼1 T   X ~ Þ  Dt PtPV þ PtH ðQ ¼ Max

ð8Þ

Y ¼ fy1 ; y2 ; . . . ; yM g X Dom Y () 8i : xi 6 yi

where X and Y are two individuals of population and xi and yi are objective functions that should be minimized and M is number of objectives. A new population with size N is then configured by the individuals in the mating pool, which is first built with the best nondominated Pareto Front, and continues with the solutions from the second front, and so on. When the last front is under consideration, those configurations at a scarcely populated area which is far away from the other solutions are selected to fill up the rest of the positions. Such diversity is measured by crowding distance as defined in Eq. (14).

t¼1

DðkÞ ¼

where E is the total generated energy.

   kþ1 k1  M f  fj  X j max

j¼1

2.3.2. Decision variables According to Eqs. (7) and (8), reservoir release is the only variable adjustable to optimize the objectives, which thus is determined to be the decision variables, shown in Eq. (9).

u¼

! Qt

ð9Þ

2.3.3. Constraints The main operational constraints of the hybrid system includes the constrains of reservoir pool level, reservoir release, as well as the capacity of the power grid to accommodate the power energy, as shown in Eqs. (10)–(12):

ð13Þ and 9j : xj 6 yj

fj

ð14Þ

min

 fj

k

where D(k) is crowding distance of individual k, f j is the j-th min

objective function value of k-th individual, zmax and f j are the j maximum and minimum values for the j-th objective function, respectively. The procedure is repeated until a certain number of generations have been evaluated. During the whole process, the constraints in Eqs. (10)–(12) are handled by either of the two ways: one is to set certain limit conditions when producing initial population and evolving new generation, the other is to check whether they are satisfied after the calculation and the unfeasible solutions are filtered out automatically. A scheme of the proposed optimization model is given in Fig. 2. 3. Case study: the Longyangxia hydro/PV hybrid power system

Ltmin 6 Lt 6 Ltmax

ð10Þ 3.1. Overview

Q tmin

t

6Q 6

Pt 6 A

Q tmax

ð11Þ ð12Þ

where Ltmin and Ltmax are the allowable lowest and highest level during time t, respectively; Q tmin and Q tmax are the lower and the upper limit of the reservoir release, respectively; and A represents the ability of the power grid to accommodate energy.

Qinghai province of China is located in the northeast of Tibetan plateau with an average elevation over 3000 m. Not only great solar radiation intensity but also long lighting time let to a high annual solar radiant of 5800–7400 MJ/m2, in which the direct radiation accounts for over 60%. The area of Qinghai province is 72  104 km2, about 27  104 km2 of which is unused. Both the abundant solar energy resources and vast desert land provide favorable conditions for PV power stations.

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Fig. 2. Multi-objective optimization of hydro/PV hybrid system.

Besides, Qinghai has rich hydropower resources. The theoretic reserves is as high as 2.16  107 kW. There have been 254 hydropower plants constructed or under construction until the end of 2011 with total installed capacity of 1.56  107 kW [26]. Longyangxia hydropower station is the leading reservoir of the upstream- Yellow River cascade development, as shown in Fig. 3. Except for the primary function of power generation, Longyangxia reservoir also gives consideration to flood control and irrigation. The natural annual runoff into the reservoir is 20.8  109 m3, while the normal storage level of the reservoir is 2600 m with a storage capacity of 24.7  109 m3, and its regulating capacity is 19.35  109 m3. The available storage balances the annual runoff, thus the surplus water in wet years can be stored for dry years and the reservoir has strong capacity of regulation over years. There are 4 hydropower units of 320 MW installed in Longyangxia hydropower station with the total capacity of 1280 MW. The general goal for the PV power station of Longyangxia hydro/PV hybrid system is 850 MW. The first part of the PV station with 320 MW has been put into operation in December of 2013, which is located in the desert of Gonghe county, 130 kW away from Xining city, as shown in Fig. 3. The PV power is loaded into the hydropower station by 330 kV, and translated to the power grid by the existed lines of hydropower station.

The Longyangxia hydro/PV hybrid power system satisfies the local load demand; moreover, most of the generated power is accommodated by the power grid. To optimize the power generation process of this hybrid system to provide electric energy of high quality is of great significance to the power grid. 3.2. Experimental setup The existing research results show that the inflow into the Longyangxia reservoir has great interannual variability, and generally presents a declining trend in recently years [27]. The yearly inflows are fit by Pearson-III distribution, the function of which is shown in Eq. (15).

F¼

ba CðaÞ

Z

1

ðx  bÞ

a1 bðxbÞ

e

dx

ð15Þ

b

where F is the frequency value; x is the random variable; b ¼ Xð1  2C v =CsÞ; a = 4/Cs2; b ¼ 2=ðXC v CsÞ. X is the mean of x; Cv, and Cs are the coefficients of variation and skew, respectively. Using the annual runoff data from 1956 to 2002 at the Tangnaihe station, which is the inflow hydrometric station of the Longyangxia reservoir, the statistical parameters in Eq. (15) are

Fig. 3. Study area.

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calibrated by optimal curve fitting method, as presented in Eq. (16).

C v ¼ 0:27;

C v =Cs ¼ 3:0

ð16Þ

The years are classified into five categories by hydrological frequency derived from Eq. (15), and Equation illustrates the classification criterion.

8 F < 12:5% Extremely wet years > > > > > > < 12:5% 6 F < 37:5% Wet years

ð17Þ

37:5% 6 F < 62:5% Normal years > > > 62:5% 6 F < 87:5% Dry years > > > : 87:5% 6 F Extremely dry years

The runoff corresponding to the representative years is shown in Table 1. Since 1987 when Longyangxia hydropower station was put into operation, most of the years are dry, except the year of 1989, 1993, and 1999. In this study, five years are selected as the study case, which are the year of 1989, 1993, 1998, 2000, and 1996, representing extremely wet years, wet years, normal years, dry years, and extremely dry years, respectively. The inter-annual change of solar radiation is relatively smooth, resulting in little inter-annual change of PV power generation. However, it has remarkable monthly variation within a year under the influence of plateau climate. Besides, the PV power output varies under different weather conditions. Thus, the PV output has to be calculated hourly day by day. Considering the computational efficiency, this study takes a month as time step in the multi-objective optimization model. Thus, there are 12 decision variables, the monthly reservoir release, for each of the selected years. The daily PV power output is worked out by hourly solar radiation and temperature, the sum of which in each month is added into the monthly power calculation of the hydro/PV hybrid system. To avoid the premature convergence problem of the genetic algorithm caused by random search in a large feasible domain [28], the candidate decision variables are generated month by month. For the optimization of NSGA-II, the initial population was set to 200, and the iteration stops after 500 times; Simulated Binary (SBX) Crossover [29] with the probability of 0.90 and polynomial mutation [30] with the probability of 0.10 were carried out.

Table 1 Runoff with representative frequency at Tangnaihe hydrometric station (109 m3). Frequency

12.5%

37.5%

62.5%

87.5%

Mean

Runoff

263.73

210.73

177.36

141.70

200.0

3.3. Results and discussion The application results of the proposed multi-objective model on Longyangxia hydro/PV power system for different typical years are presented in Fig. 4. Instead of providing a specific optimal solution like single objective optimization problems, a set of noninferior solutions known as Pareto Front are given in Fig. 4(a). Since the two objectives are minimizing the power output variance and maximizing the power generation respectively, optimal solutions should be as near as possible to the top left corner of Fig. 4(a). The Pareto optimal solutions are normalized, and the one approaches the closest to the ideal state is picked out to provide a reference for the operation, as illustrated in Fig. 4(b). The two objectives show an apparent counterbalance relationship. For a particular year, to maximize the total power generation needs to enhance the output efficiency by increasing water release in the time periods with high water head, which leads to power output variation. It can be seen that for the study case the hydro power plays leading roles in the hybrid power system, and the inflow condition determines the annual power generation. Table 2 presents the statistic results of the objectives on the Pareto Front in different typical years. Generally, the variance of the monthly power output is larger in wet years than in dry years, since there is abundant water for dynamic adjustment, which also results in larger power generation in wet years. It can be seen that the optimization is inclined to maximize the power output efficiency with large amount of water. Fig. 5 shows the hydro and PV power output process for the recommended optimal solution as shown in Fig. 4(b), as well as the corresponding natural environmental conditions for the extremely wet year of 1989, the extremely dry year of 1996, and the normal year of 1998. Basically, the PV power output is larger in summer than in winter, which has a positive correlation with the solar radiation. The flood season is also in summer, bringing about higher reservoir inflow from June to September. To minimize the variance of the power output, the total power output process should be a smooth convex curve with a crest in summer instead of a jagged curve with drastic fluctuations. Another interesting phenomenon Table 2 Statistics of the Pareto Front for different years. Year

1989 1993 1996 1998 2000

Variance of the monthly power output (1010 kW2)

Annual power generation (109 kW h)

Min

Max

Mean

STD

Min

Max

Mean

STD

19.82 13.87 9.35 12.84 11.76

24.80 17.73 12.68 16.01 15.37

22.16 15.53 10.72 14.30 13.18

1.47 1.07 1.0 0.94 1.12

8.13 7.18 5.70 7.11 6.41

8.67 7.66 6.03 7.45 6.86

8.42 7.45 5.89 7.29 6.69

0.16 0.14 0.09 0.10 0.13

Fig. 4. Optimization results (a) Pareto Front of the proposed multi-objective model for different years; (b) recommended optimal solution nearest to the ideal state.

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(a) Extremely wet year of 1989

(b) Extremely dry year of 1996

(c) Normal year of 1998 Fig. 5. Power output process and environmental condition for different hydrologic years. In each subgraph: (A) the monthly inflow and optimal outflow corresponding to the recommended optimal solution as shown in Fig. 4(b); (B) optimal hydropower output process corresponding to the recommended optimal solution as shown in Fig. 4(b); (C) daily normal solar radiation, and (D) monthly PV power output process.

is that the wet years are usually caused by abundant rainfall, when the solar radiation is spontaneously weaker. Hence, the hydropower can be an ideal compensation for the PV power in nature. For example, in Fig. 5(a), the PV power dropped significantly in June due to the low solar intensity, but there is a large amount of

water inflow in this month, and the hydropower output can be enhanced to compensate the drop of PV power by maintaining high water head with low outflow. In extremely dry year of 1996 shown in Fig. 5(b), there seems not too much adjustment space due to the water limitation. The reservoir outflow is basically synchronized to

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the inflow, while in flood season the optimization still tries to make the whole power output process as smooth as possible by reallocating the water resources in different months. For normal year as shown in Fig. 5(c), such compensation effect of hydropower on PV power is more obvious. Generally speaking, the hydropower is a desired compensating resource for PV power. The optimization degree as well as the compensating effect depends on the amount of the available water resources. The results not only give estimations of the power generation potential of the integrated system, but also provide operational references for practice. A more detailed short-term model is in need for the actual operation in the future. 4. Conclusions This study aimed to explore a long-term optimization model for hydro/PV hybrid systems, considering the stability of the power output and the total power generation simultaneously. By decoupling hydropower and PV power in time scales, the model had the balance right in terms of computational accuracy and cost. The PV power output is firstly worked out by hourly solar radiation and temperature data day by day, the result of which is taken as the boundary condition of the hydropower optimization. Taking the reservoir release as the decision variables, minimizing the variance of the power output and maximizing the annual power generation are then set as the objectives, which are optimized by NSGA-II. The application of the proposed model on the Longyangxia hydro/PV hybrid power system, the largest hydro/PV integrated system in the world verified its validity. The results proved that hydropower and PV power complement each other in nature. The advantages are particularly clear for wet years, when the solar radiation will be influenced by rainfalls, and there is abundant water resource to adjust the power generation of the whole system. The provided estimation of the power generation potential can be taken to evaluate the actual operation, as well as the reference for practice. The proposed methodology can also be generalized to other hydro/PV power systems than the study case. The future work would focus more on daily joint control of the integrated system, as well as the coupling between short-term and long-term optimization. Acknowledgements This research was supported by National Natural Science Foundation of China (Grant no. 51409248 & 11402136), and the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and Hydropower Research) (Grant no. WHR-SKL201409). References [1] Beluco A et al. 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 2012;45:24–30.

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Please cite this article in press as: Li F-F, Qiu J. Multi-objective optimization for integrated hydro–photovoltaic power system. Appl Energy (2015), http:// dx.doi.org/10.1016/j.apenergy.2015.09.018