Short-term optimal operation of wind-solar-hydro hybrid system considering uncertainties

Energy Conversion and Management 205 (2020) 112405

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Short-term optimal operation of wind-solar-hydro hybrid system considering uncertainties

T

⁎

Zhendong Zhanga, Hui Qina, , Jie Lia, Yongqi Liua, Liqiang Yaob, Yongqiang Wangb, Chao Wangc, Shaoqian Peia, Jianzhong Zhoua a

School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China Changjiang River Scientific Research Institute of Changjiang Water Resources Commission, Wuhan, Hubei, China c China Institute of Water Resources and Hydropower Research, Beijing, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Wind-solar-hydro hybrid system Daily power generation operation Uncertainty Complementarity

Due to the deterioration of non-renewable energy resources, the operation of wind-solar-hydro hybrid systems has become a prominent research topic. However, owing to the uncertainties in such a hybrid system, such as those in wind speed, solar radiation intensity, and power load, it is difficult for a dispatcher to develop the power generation plan of the day following the planning day (referred hereafter as the next day). The purpose of this study is to consider the uncertainties in a short-term optimal operation model and obtain for each state variable, the probability density function of the operation process of the next day. The latter can provide a dispatcher with a large amount of reliable decision reference information. In this study, simulation-estimation method is proposed to characterize the uncertainty and estimate the probability density function of the operation process. First, three short-term optimal operation models are established to provide flexible options to dispatchers. Second, a stochastic simulation method based on probabilistic forecasting is proposed to generate simulation scenarios for the next day. Third, each simulation scenario is input into the constructed optimal operation model for obtaining the solution. Fourth, the kernel density estimation method is used to estimate the probability density function of the operation process of the next day. Finally, the constructed optimal operation model and proposed simulation-estimation method are applied to the wind-solar-hydro Experimental Base of the Yalong river basin in China. In this case, the differences between the three operation models in three typical seasons are compared. Based on the verification of the prediction mean scenario and observation scenario, the experimental results show that the proposed model and method of this study are practical and effective.

1. Introduction Owing to the shortage of traditional fossil energy and the increasingly serious environmental problems caused by fuel consumption, renewable and clean energy sources such as wind, solar and hydro energy have received extensive attention [1]. However, because of the randomness, volatility, and intermittency of wind and solar energies, integrating them directly in a power grid may make it unstable [2]. Furthermore, wind speed, solar radiation intensity, and power load are uncertain [3], thereby making it difficult for dispatchers to develop the power generation plan for the day following the planning day (hereafter referred as the next day). Therefore, the two objectives of this study are to find a method to smooth the frequent fluctuations in both the wind and solar power outputs to ensure safe and stable operation of power systems, and to consider the uncertain components in the operation

⁎

model to avoid potential risks. Advantageously, these clean renewable energy sources exhibit certain complementarities [4]. In general, during the day, the solar radiation intensity is high and the wind speed is relatively slow; at night, there is no light and the wind speed is relatively high [5]. During the year, in the summer, the solar radiation intensity is high, the wind speed is relatively slow and the runoff is large; in the winter, the solar radiation intensity is low, the wind speed is relatively high and the runoff is small [6]. Building a hybrid system integrating multiple energies is one of the approaches to solve the power output fluctuation problem [7]. Representative multi-energy hybrid systems include windsolar (WS), wind-hydro (WH), solar-hydro (SH), and wind-solar-hydro (WSH) systems [8]. A hydropower station has high adjustment capability [9], similar to a large energy storage system. A hybrid system with a hydropower station will allow easy smoothing of the power

Corresponding author at: School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail address: [email protected] (H. Qin).

https://doi.org/10.1016/j.enconman.2019.112405 Received 7 October 2019; Received in revised form 7 December 2019; Accepted 11 December 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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Presently, the uncertainty research of WSH hybrid systems needs to be further strengthened, such as considering three types of uncertain components simultaneously and, obtaining the probability density function (PDF) of the operation process of the next day. Therefore, the second focus of this study was to develop a method to simultaneously consider three uncertain components in the operation model of a WSH hybrid system, and obtain the PDF for each state variable, the PDF of the operation process of the next day. In this paper, the simulation-estimation method is proposed to characterize the uncertainty and estimate the PDF of the operation process. The main contributions of this study are outlined as follows:

output. By computational simulations with idealized energy availability functions, Beluco et al. verified that the short-term complementarity of the PV and hydropower systems in an SH hybrid could improve the stability of the power supply [10]. Angarita et al. revealed that hydropower played a key role in the regulation of WH hybrid systems by maximizing expected hydro-wind profit [11]. For a WSH hybrid system, Zhang et al. maximized the 90th percentile reliable generation for the entire period to develop a daily power generation plan, and their research results presented significant guidance for complementary operation [12]. Han et al. proposed a complementarity evaluation method for WSH hybrid system by examining the fluctuation of the independent and combined power generation [13], which provided reference for the optimization of power grid dispatch and power supply planning of combined power stations. Xu et al. integrated a pumped storage hydropower to WSH hybrid system and analyzed the stability of system [14], and their research verified the feasibility of the pumped storage station in integrating the hybrid power system under steady and fault scenarios. Wang et al. proposed a double-layer model for coordinating the operation of cascaded hydropower and neighboring wind and PV facilities [15], whose findings demonstrated that the WSH hybrid system is beneficial to the decarbonization of electricity systems. Existing studies of multi-energy hybrid systems focused on the complementarity of different energy sources, with little focus on the differences in the complementary performance of hydropower in different seasons. However, it is well known that in different seasons, a reservoir has different tasks regarding its own hydropower aspect [16], its adjustment storage used to smooth the wind and solar power output also varies. For example, the flood control tasks of a reservoir will be heavier in the wet season than those in the dry season [17]. Therefore, the first focus of this study was comparing the ability of a hydropower system to adjust the power output stability in three different typical seasons (dry, normal, and wet). Maximally stabilizing the period output, maximally making the period output curve close to the power load curve, and maximizing the total power generation are the objectives that need to be completed when developing a daily power generation plan. However, there are some difficulties in achieving these objectives owing to the uncertainties in the wind speed, solar radiation intensity and power load of the next day [3]. In fact, the runoff of the next day is also unknown. However, the runoffs of the two consecutive days are typically extremely close, and the runoff uncertainty can be ignored compared to those in the previous three uncertain components [18]. Ming et al. proposed a three-layer nested framework to solve a generation operation model whose objective function was maximizing the expected energy production of a hydro-PV plant, while considering the uncertainty in the power load [19]. Yin et al. built a stochastic operation model to find a base-case solution with relatively stable operation cost in the presence of uncertain renewable generation [20]. Hu et al. proposed improved generative adversarial networks to represent the uncertainties in wind power and solar power, and further completed a short-term optimal operation of a WSH hybrid system [21]. The aim of their model was to achieve a tradeoff between maximization of the generating efficiency and minimization of the water spillage under the influence of wind and solar uncertainties. In a case study [22] by Ming et al., the uncertainty in PV power was characterized by multiple PV generation scenarios, and their results verified the applicability and effectiveness of the proposed methods by an operation model minimizing the average water consumption of a hydropower plant. Biswas et al. proposed multi-objective economic emission power operation problem formulation and solution incorporating stochastic WSH hybrid powers [23]. Yang et al. constructed two operation models that maximized the total generation output of a system and maximized the reliability of the output of the system [24]. They performed stochastic optimization to explore the long-term operating rules that could address the uncertainties in reservoir inflow and PV power and offer guidelines for the effective operation of an SH hybrid system [24].

(1) Three short-term optimal operation models focusing on stability, practicability and economy, respectively, are established to provide flexible options to dispatchers. (2) A stochastic simulation method based on probabilistic forecasting is proposed to generate simulation scenarios for the next day, which can characterize the uncertainties of three uncertain components well. (3) The kernel density estimation (KDE) method is used to estimate for each state variable, the PDF of the operation process of the next day. (4) The constructed optimal operation model and proposed simulationestimation method are applied to the WSH Experimental Base of the Yalong river basin. In this case, the differences between the three operation models in three typical seasons are compared. Moreover, the practicability and effectiveness of the model and the method of this study are validated using the prediction mean scenario and observation scenario. Compared to the existing research of the short-term optimal operation of WSH hybrid systems, the highlights and advantages of our study are as follows: (1) Most studies only focus on one operation model; however, here, three different operation models are studied. (2) In terms of uncertainty, the existing studies do not consider wind speed, solar radiation intensity and power load concurrently; however, this study considers the above three uncertain components simultaneously. (3) The existing research generally only estimate the uncertainty interval when quantifying uncertainty; however, this study obtains the entire probability density function, which can provide comparatively more information to dispatchers. (4) In addition, the ability of hydropower in the WSH hybrid system to adjust the complementarity is compared in different seasons, which is also one of the innovations. The remainders of this paper are organized as follows. In Section 2, three short-term optimal operation models are introduced in detail. In Section 3, uncertainty representation and simulation-estimation method are described. In Section 4, an application of WSH Experimental Base of the Yalong River Basin is presented. In Section 5, the work of this paper is summarized and the conclusions are given. The nomenclatures used in this paper are listed in Table 1. 2. Short-term optimal operation model of hybrid system Due to the randomness, volatility and intermittent of wind and solar, WSH hybrid system not only needs to maximize power generation efficiency, but also needs to balance the stability of the power grid output. Therefore, in this section, the methods for calculating the output of wind power, solar power and hydropower are first introduced. Then, different operation objectives are established based on the stability of power grid output and power generation efficiency. Finally, the constraints of the operation model are described. 2

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Table 1 Nomenclature. variable

meaning

variable

meaning

Nw ρ Aw Cp v Ns nr β Tc Tcref As G Nh K Qf H Zu Zd Hl Nt N¯

wind power output air density swept area by the turbine blades power coefficient wind speed solar power output reference module efficiency temperature coefficient cell effective temperature reference cell temperature solar power generator area solar radiation intensity hydropower output hydroelectric coefficient power generation flow water head of the hydropower station upstream water level downstream water level water head loss total output during the t-th period average of outputs N the number of wind farms the number of solar farms the number of reservoirs

T Pt E Δt Vk,t Ik,t Evk,t B K()

the number of operation periods power load during the t-th period total power generation duration of one period storage capacity of k-th reservoir during t-th period incoming flow of k-th reservoir during t-th period system losses bandwidth non-negative kernel function

abbreviation WSH WS WH SH PV PDF KDE min max std RMSE SWLSTM-GPR GA

meaning wind-solar-hydro wind-solar wind-hydro solar-hydro photovoltaic probability density function kernel density estimation minimum maximum standard deviation root mean square error Shared Weighted Long and Short-term Memory Network combined with Gaussian Process Regression genetic algorithm

Mw Ms Mh

where Nh is the hydropower output (W). K is the hydroelectric coefficient. Q f is the power generation flow (m3/s), and H is the water head of the hydropower station (m). Further, H = Zu − Zd − Hl , where Zu , Zd , and Hl are the upstream water level, downstream water level, and water head loss, respectively. The upstream water level, Zu = [Zu, t ], at each moment is a decision variable of the optimal operation model.

2.1. Power output calculation methods In order to lay the foundation for elaborating the objectives of the optimal scheduling model, wind, solar and hydro power output calculation methods are described in detail in this section. 2.1.1. Wind power output Wind power refers to the process of converting the kinetic energy of wind into electrical energy. The most important factor affecting wind power is the wind speed. The wind power output calculation method [25] is as follows:

Nw =

1 ρAw Cp v 3 2

2.2. Objective functions of optimal operation model In order to provide the dispatcher with flexible choices, the objective functions of the three scheduling models are introduced in detail. 2.2.1. Minimizing period output standard deviation Owing to the randomness, volatility and intermittency of wind and solar energies, integrating them into a power grid may pose risks to its stability. Indeed, there is a certain complementarity between wind power and solar power. In general, the solar radiation intensity is high and the wind speed is low during the day; at night, there is no light and the wind speed is high. However, this complementarity is relatively limited and simultaneously accompanied by randomness; thus, relying solely on wind power and solar power is not sufficient to make the output stable [28]. Therefore, it is necessary to introduce hydropower with strong adjustment capability to maximize smoothing the wind and solar power output, i.e. to minimize the period output standard deviation:

(1)

where Nw is the wind power output (W). ρ is the air density (kg / m3 ). Aw is the swept area by the turbine blades (m2). Cp is the power coefficient, and v is the wind speed (m/s). For safe fan operation, the wind speed in interval [vmin, vmax ] can be used for power generation. 2.1.2. Solar power output Solar power refers to the process of converting solar energy into electrical energy. The most important factor affecting solar power is the solar radiation intensity. The solar power output calculation method is [26] as follows:

Ns = nr [1 − β (Tc − Tcref )] As G

(2)

where Ns is the solar power output (W). nr is the reference module efficiency. β is the temperature coefficient. Tc is the cell effective temperature. Tcref is the reference cell temperature in degree Celsius. As is the solar power generator area (m2), and G is the solar radiation intensity (W/m2). Because of the capacity limitations of solar panels, the solar power output should be in interval [Ns,min, Ns,max ].

min f1 = min{std (N )} = min{ Mw

Nt =

T

∑ (Nt − N¯ )2 } t=1

(4)

Mh

∑ Nw,i,t + ∑ Ns,j,t + ∑ Nh,k,t i=1

j=1

k=1

(5)

where std (N ) is the period output standard deviation for outputs N = [N1, N2, ⋯, NT ]. Nt is the total output during the t-th period. N¯ is the average of outputs N . Nw, i, t is the wind power output of the i-th wind farm during the t-th period. Ns, j, t is the solar power output of the jth solar farm during the t-th period. Nh, k, t is the hydropower output of the k-th reservoir during the t-th period. Mw , Ms and Mh are the numbers of wind farms, solar farms and reservoirs, respectively. T is the number of operation periods.

2.1.3. Hydropower output Hydropower refers to the process of converting the kinetic energy of water into electrical energy. The most important factor affecting hydropower is the runoff. The hydropower output calculation method is [27] as follows:

Nh = KQ f H

Ms

1 T

(3) 3

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Vk, t + 1 = Vk, t + (Ik, t − Qk, t − Evk, t )·Δt

2.2.2. Minimizing root mean square error between period output and load In reality, the power demand at different times of the day is different, and it also varies from day to day. If the period output curve of a WSH hybrid system is close to the power load curve, then they can be easily integrated into the power grid. Therefore, minimizing the root mean square error (RMSE) [29] between the period output curve and power load curve is an extremely practical operation objective, which is expressed as follows:

min f2 = min{RMSE (N , P )} = min{

1 T

where Vk, t and Vk, t + 1 are the initial and final storage capacities of the kth reservoir during the t-th period, respectively. Ik, t and Qk, t are the incoming flow and discharge flow of the k-th reservoir during the t-th period, respectively. Evk, t is the system losses, such as evaporation. (5) Restrictions of wind power and solar power In the proposed short-term optimal operation model of a WSH hybrid system, the upstream water levels of the reservoir are the decision variables. The wind speed limitation and solar power output limitation do not limit the decision variables, therefore, they are not expressed in Section 2.3 but are presented in Section 2.1.1 and Section 2.1.2, respectively.

T

∑ (Nt − Pt )2 } t=1

(11)

(6)

where RMSE (N , P ) is the RMSE between period output curve N and power load curve P = [P1, P2, ⋯, PT ]. and Pt is the power load during the t-th period. Other variables have the same definition as mentioned before.

3. Uncertainty representation for hybrid system 2.2.3. Maximizing total power generation There is also a commonly established optimization operation model that maximizes the total power generation, which estimates the power generation efficiency limits of the model, but at the expense of the stability of the power system. This is expressed as follows:

In this section, the uncertainty components of a WSH hybrid system are first analyzed. Then the uncertainty is considered to the short-term optimal operation model and stochastic simulation method based on probabilistic forecasting is introduced to visualize this uncertainty model. Finally, kernel density estimation (KDE) is described to estimate the probability density function (PDF) of WSH hybrid system considering uncertainty.

T

minf3 = max{E (N )} = max{ ∑ Nt ·Δt } t=1

(7)

where E (N ) represents the total power generation. Δt is the duration of one period.

3.1. Uncertainty components analysis In the short-term optimal operation model of a WSH hybrid system proposed in this paper, the wind speed, solar radiation intensity, runoff, and power load need to be known before the optimization operation calculation is performed. However, these variables are unknown when developing the power generation plan for the next day. These four variables are the source of the uncertainties in the operation model. It is worth mentioning that compared to the change in the wind speed, solar radiation intensity, and power load, the difference in the runoff variation over a day is small. Concurrently, the average runoffs of two consecutive days are extremely close [19]. Therefore, the runoff of one day can be used to approximate that of the next day when developing a power generation plan, so that the uncertainty in the runoff can be ignored in the short-term (one day) power generation operation of a WSH hybrid system. The uncertain components vary in different operation models, as understood from Table 2. In the Model 1, since it does not involve power load, its uncertain components are wind speed and solar radiation intensity. In the Model 2, it considers the most comprehensive, including wind speed, solar radiation intensity and power load. In the Model 3, its operation objective is not directly related to the wind speed and solar radiation intensity at each period, instead it is directly related to the total power generation of the wind power and solar power during the entire operation period. Simultaneously, under this model, the wind speed, solar radiation intensity and power load at each period do not affect the change in the hydropower decision variables. This implies that maximizing the total power generation of a WSH hybrid system is equivalent to maximizing the total power generation of hydropower. Specifically, in this model, regardless of the value of the wind speed, solar radiation intensity, and power load in the future, the operation of hydropower is the same. Therefore, there is no need to consider

2.3. Constraints of optimal operation model The constraints of optimal operation model are described as follows: (1) Water level constraint max Zumin , k , t ⩽ Zu, k , t ⩽ Zu, k , t

(8)

where Zu, k, t is the upstream water level of the k-th reservoir during the t-th period, which is also the decision variable of the optimal operation max model. Zumin , k , t and Zu, k , t are the lower and upper limits of the upstream water level, respectively. (2) Discharge flow constraint max Qkmin , t ⩽ Qk , t ⩽ Qk , t

(9)

where Qk, t is the discharge flow of the k-th reservoir during the t-th max period. Qkmin , t and Qk , t are the lower and upper limits of the discharge flow, respectively. Qk, t consists of two parts, power generation flow (Qkf, t ), and abandoned water flow (Qka, t ). (3) Hydropower output constraint max Nhmin , k , t ⩽ Nh, k , t ⩽ Nh, k , t

(10)

where Nh, k, t is the hydropower output of the k-th reservoir during the tmax th period. Nhmin , k , t and Nh, k , t are the lower and upper limits of the hydropower output, respectively, which should be between the installed capacity and the guaranteed output. (4) Water balance equation Table 2 Uncertain components of the three operation models. model

objective

uncertain components

Model 1 Model 2 Model 3

minimizing period output standard deviation minimizing RMSE between period output and load maximizing total power generation

wind speed, solar radiation intensity wind speed, solar radiation intensity, power load none

4

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(1) Forecasting: The SWLSTM-GPR is used to obtain the PDF of the uncertain component at each period of the next day. (2) Simulation: Five hundred future scenarios are generated using the stochastic simulation method, based on the PDF of each uncertain component. (3) Operation: According to the actual needs, the corresponding shortterm optimal operation model of the WSH hybrid system is constructed. Five hundred future scenarios are input into the operation model, and a GA is used to solve the operation process of all the simulation scenarios, including the power outputs of each period and the objectives. (4) Estimation: The operation processes of all the simulation scenarios are regarded as the samples of the KDE. After using the grid search algorithm with cross-validation to select the appropriate bandwidth, the PDF of the operation process of the next day is obtained by the KDE.

uncertainty in Model 3. 3.2. Stochastic simulation method based on probabilistic forecasting Because the wind speed, solar radiation intensity and power load in the future are unknown, it is an effective solution to predict them before the operation calculations. Because of the errors in the forecasts, it is necessary to quantify their uncertainties by probabilistic forecasting to obtain their PDFs in the future [30]. In this study, the shared weighted long and short-term memory network combined with Gaussian process regression (SWLSTM-GPR) [31] was used for the probabilistic forecasting of wind speed, solar radiation intensity and power load. The future wind speed, solar radiation intensity and power load predicted by the SWLSTM-GPR exhibit independent Gaussian distributions at each period. Based on their distribution functions, random numbers can be used to simulate the wind speed, solar radiation intensity, and power load in numerous future scenarios. These scenarios simulated by random numbers are called simulation scenarios. The Gaussian distribution predicted for each period has an average value. The scenario with these average values is called the prediction mean scenario. Real values will become available in the future. The scenario with real values is called the observation scenario, which is not available in practical applications, and was used to verify the effectiveness of the method proposed in this paper. In each simulation scenario, the wind speed, solar radiation intensity and power load were determined, which were input into the proposed short-term optimal operation model of a WSH hybrid system. The operation process in this scenario can be obtained using optimization algorithms such as genetic algorithms [32], to solve the operation model, including the period power outputs, upstream water levels of the hydropower station, and model objective.

4. Case study In order to verify the effectiveness of the research model and method, the constructed optimal operation model and proposed simulation-estimation method are applied to the wind-solar-hydro Experimental Base of the Yalong river basin in China. 4.1. Research object introduction The study area was located in the WSH Experimental Base in the middle and lower reaches of the Yalong river basin, which is close to Yanyuan city, Sichuan Province, China, as shown in Fig. 2. In this area, there are four wind farms and one solar farm. Moreover, there is a hydropower station serving as an advanced pilot power station access WSH hybrid system. The four wind farms are Wodi (W1), Dahe (W2), Asa (W3) and Baiwu (W4). The solar farm is Zhalashan (S1). The reservoir is Guandi (H1). The data collected in 2010 was selected for the research. The statistical information of the WSH Experimental Base is shown in provided in Table 3. Mean wind speeds W1 to W4 are 6.20 m/s, 8.10 m/s, 7.01 m/s and 6.04 m/s, respectively. The average and maximum solar radiation intensity of S1 are 465 W/m2 and 1572 W/m2, respectively. The average runoff of H1 is 1353 m3/s. The installed capacities of the four wind power stations (W1-W4) are 91.5 MW, 60 MW, 80 MW, and 99 MW, respectively. The installed capacities of S1 and H1 are 700 MW and 2400 MW, respectively. H1 is a reservoir with monthly adjustment capacity, whose dead and normal water levels are 1328 m and 1330 m, respectively. Its total storage capacity is 760 million m3/s.

3.3. Kernel density estimation By stochastic simulation and optimization operation, the operation process in a specific scenario can be obtained; however, the distribution function of an operation process in a future entire operation period cannot be obtained. KDE [33] is used to estimate the PDF of the operation process for the entire operation period in the future, because it is a classic non-parametric estimation method and does not require a priori assumptions. Taking the period power output as an example, the sample of the KDE under the t-th period is Nt = [Nt1, Nt2, ⋯, Ntm, ⋯, NtM ], where Ntm is the power output in the m-th scenario under the t-th period. M is the total number of simulation scenarios. The estimated function is as follows:

1 ft ̂ (x ) = MB

M

∑ K( m=1

Ntm − x ) B

4.2. Experimental design (12) In order to design the experiment reasonable, the experimental purpose and experimental parameter details are described in this section.

where B > 0 is the bandwidth. K (·) is a non-negative kernel function. Epanechnikov kernel is used in this study [34], whose formula is shown as follows: 3

K (α ) =

⎧ 4 (1 − α 2) α ∈ [−1, 1] ⎨ α ∉ [−1, 1] 0 ⎩

4.2.1. Experimental purpose To verify the effectiveness and practicability of the model proposed in this paper, three operation models and three typical periods were used to estimate the operation of the WSH hybrid system for the next day. The three models are described in Table 2. The three typical days were 9 March, 27 August and 28 November, respectively, corresponding to the dry, wet, and normal water seasons, respectively. Because hydropower stations have different operation tasks, runoffs, and adjustment capability in different periods, it is necessary to explore the differences in their capability to adjust their complementarities in WSH hybrid systems in different seasons. In this study, five tasks t needed to be completed: Task I: Estimation of the PDF of the period output of the WSH hybrid system under the influence of forecast uncertainty.

(13)

The bandwidth B is an important parameter of KDE. Too wide bandwidth leads to the bias of the estimator while too narrow bandwidth leads to the noise of the estimator [35]. Grid search with crossvalidation is used to select an appropriate bandwidth [36]. 3.4. Operation model framework of hybrid system considering uncertainty The operation model framework of the WSH hybrid system considering uncertainty is shown in Fig. 1; it contains four modules: forecasting, simulation, operation and estimation. Its implementation details are as follows: 5

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Fig. 1. Operation model framework of the WSH hybrid system considering uncertainty.

Task II: Verification that the output curves of the prediction mean scenario and observation scenario were well within the confidence interval of the proposed method. Task III: Analysis of the complementarity of the output of the WSH hybrid system. Task IV: Comparison of the ability of hydropower to adjust the complementarity in the WSH hybrid system in different seasons (dry, wet, and normal seasons). Task Ⅴ: Comparison of the differences between the three optimal

operation models. 4.2.2. Experimental parameters Probabilistic forecasting of the uncertain components was required before completing the above five tasks. The prediction method used was the SWLSTM-GPR [31]. The short-term optimal operation model of the WSH hybrid system was solved by GA [32]. Grid search combined with cross-validation was used to select the optimal bandwidth of the KDE [33]. The corresponding parameters are listed in Table 4. In addition, 6

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Fig. 2. WSH Experimental Base of the Yalong river basin.

Additionally, a majority of the red observation line are located in the 95% gray confidence interval, indicating that the prediction method used in this study is highly reliable. Based on the probabilistic forecasting results of each farm, 500 sets of scenarios were randomly simulated, and 10 scenarios are plotted in second subgraph. It can be seen from the figure that the simulation results are consistent with the trend of the probabilistic forecasting results, indicating that the simulation results are representative. The probabilistic forecasting and simulation results in the dry and wet seasons are similar to these in the normal season.

Table 3 Statistical information of WSH Experimental Base. resource

flag

station

metric

unit

min

mean

max

wind

solar

W1 W2 W3 W4 S1

Wodi Dahe Asa Baiwu Zhalashan

m/s m/s m/s m/s W/m2

0.15 0.44 0.40 0.40 0

6.20 8.10 7.01 6.04 465

15.04 19.95 15.62 12.85 1572

water

H1

Guandi

wind speed wind speed wind speed wind speed solar radiation intensity runoff

m3/s

397

1353

3704

4.4. Results and discussion of model 1

the total number of simulation scenarios was set as 500.

In order to numerically prove the practicability and effectiveness of the models and methods, results and discussion of Model 1 are performed from task I to IV.

4.3. Stochastic simulation results The probabilistic forecasting results of the four wind farms (W1W4), one solar farm (S1), and power load in the normal season are shown in Fig. 3. Taking the first two subgraphs as an example, the first subgraph presents the interval prediction results of W1 and the second subgraph displays the results of the corresponding simulations based on the first subgraph. In the first subgraph, the blue prediction mean line is extremely close to the red observation line, indicating that the prediction method used in this study has high prediction accuracy.

4.4.1. Task I: Estimate probability density function of period outputs In Model 1, the wind speed and solar radiation intensity are unknown when developing the power generation plan for the next day, and they are uncertain. It is necessary to estimate the PDFs of the period outputs for the next day, which is beneficial in avoiding the risks causes by uncertain components. The PDFs of the period outputs in the three

Table 4 Experimental parameters. model

symbol

meaning

value

reason

SWLSTM-GPR

ni nh no η T Ep kf N pc ηc pm ηm I K B

number of input layer nodes number of hidden layer nodes number of output layer nodes fixed learning rate size of batch epochs of training kernel function population size crossover probability crossover distribution index mutation probability mutation distribution index iteration numbers K-fold cross validation in grid search for KDE's bandwidth bandwidth range for KDE in grid search

3 8 1 0.01 32 2000 ardmatern32 100 0.9 20 1/24 20 10,000 5 (0, 10, 0.5)

number of feature inputs common values [2,4,8,10,…] time series regression common values [0.001,0.01,0.05,0.1,…] common values [8,16,32,50,100,…] converged a competitive kernel function common values [30,50,100,…] recommended by original paper recommended by original paper recommended by original paper recommended by original paper converged common values [5, 10, …] commonly used range

GA

KDE

7

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Fig. 3. Probability forecasting and simulation results in the normal season.

(1) It can be seen from Fig. 5 that the power output stability in the dry season is better than that in the normal season, which in turn is better than that in the wet season. This is consistent with the conclusion based on Fig. 4. (2) Regardless of the season, the output processes of the prediction mean scenario and observation scenario are located in the 90% interval of the output simulations for most of the period. This indicates that the confidence interval obtained is reliable, and further, that the proposed method is effective.

seasons are plotted in Fig. 4, where the left part is the overall PDF for the next day and the right part is the PDF for the typical period. The following inferences can be drawn from the figure: (1) In the dry and normal seasons, the centerline of the projection of the overall PDF on the horizontal plane is nearly a horizontal line. This is because Model 1 minimizes the period output standard deviation, which makes the output of the next day stable. (2) In the wet season, the centerline of the projection of the overall PDF on the horizontal plane is undulating, and the output after the ninth period is significantly larger than that before the ninth period. The latter indicates that the capability of hydropower to smooth the output of the wind power and solar power is limited. The reason for this phenomenon will be discussed in detail in Section 4.4.4. (3) Regarding the PDF for the typical period, the center of the PDF in the dry season is approximately 1700 MW. The outputs of the prediction mean scenario and observation scenario are extremely close, and both are close to the center of the PDF, which verifies the effectiveness of the method proposed in this paper. (4) The two typical scenarios are extremely close during period 11 of the wet season, where the output of the observation scenario during period 15 is off center. However, it is clearly seen that the output of the observation scenario during period 15 is extremely close to the second peak of the PDF. In practice, if a bimodal type PDF is obtained by the simulation-estimation method, then significant attention should be paid to the output of the two peaks, which will help to avoid potential risks. This phenomenon verifies the practicability of the proposed method.

4.4.3. Task III: Analyze the complementarity of the output To analyze the complementarity of the output of the WSH hybrid system, the power output stacking diagrams in the two typical scenarios of Model 1 in the three seasons are presented in Fig. 6. The following can be deduced from the figure: (1) In general, the power output in the two typical scenarios of Model 1 is basically stable in the three seasons, and only a few periods exhibit fluctuations. (2) The output fluctuation during the dry season is the smallest, followed by that in the normal season, and finally, that in the wet season. The reason is that for hydropower stations, when the inflow is high, the hydropower tasks of the reservoir are extremely intense, and the ability to smooth the output of the wind power and solar power is limited. (3) The output stacking diagram of the prediction mean scenario is extremely close to that of the observation scenario, indicating that the former can provide a decision maker with a large amount of relatively accurate reference information.

4.4.2. Task II: Verify two typical scenarios To verify the effectiveness of the proposed method, the power output processes of Model 1 in two typical scenarios in the three seasons are plotted in Fig. 5, Here, the blue, orange, and yellow lines are the output of the prediction mean scenario, output of the observation scenario, and 0.5 quantile of the output simulations, respectively. The gray interval is the estimated 90% confidence interval. The following inferences can be analyzed from the figure:

4.4.4. Task IV: Compare the ability of hydropower in different seasons In order to further analyze the reasons for the differences in the ability of hydropower to smooth the output of the wind power and solar power in different seasons, the statistics of all the simulation scenarios are displayed in Fig. 7. The left part exhibits the objective statistic for all the simulation scenarios in the three seasons, including the minimum, mean, maximum, and standard deviation. The right part shows the number of periods in which the hydropower (H1) output is in 8

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Fig. 4. PDF of period outputs of Model 1.

output of wind power and solar power are to be maximally smooth, these outputs should be of the same order of magnitude. The hydropower (H1) output in the wet season is mainly concentrated in interval (2000, 2400] MW, which is much larger than 1030.5 MW. Therefore, hydropower has the worst complementarity in the wet season. In the dry season, the hydropower output is distributed in all the four output ranges, and most of the periods are located in interval (1500, 2000] MW; therefore, the hydropower has the best complementarity in the dry season.

a specific output range, for all the simulation scenarios in the three seasons. The following inferences can be drawn from the figure: (1) The objective mean of all the simulation scenarios in the dry season is the smallest, indicating that the output in this season is the most stable, which is consistent with the conclusions of the two typical scenarios discussed in Section 4.4.2 and 4.4.3. (2) The installed capacities of the four wind power stations (W1-W4) are 91.5 MW, 60 MW, 80 MW and 99 MW, respectively. The installed capacity of S1 is 700 MW. The maximum output of the wind power and solar power is 1030.5 MW. If hydropower output and the 9

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Fig. 4. (continued)

right corner is the PDF for the typical period. The following deductions can be made from the figure:

4.5. Results and discussion of model 2 In order to numerically prove the practicability and effectiveness of the models and methods, results and discussion of Model 2 are performed from task I to IV.

(1) The overall PDF for the next day of Model 2 is not as uniform as that of Model 1. It can be seen from the top view that they are not irregular but are extremely close to the shape of the power load, which exhibits that the operation model works effectively. (2) In typical period 18, the power output and power load in the two typical scenarios are basically located near the center of the PDF, which indicates that the estimated PDF is reasonable.

4.5.1. Task I: Estimate probability density function of period outputs In Model 2, the uncertain components in the operation model are wind speed, solar radiation intensity, and power load, so that there is one more uncertain component than those in Model 1. The estimated PDFs of the period outputs of Model 2 in the three seasons are presented in Fig. 8. In the figure, the left part is the overall PDF for the next day, the upper right corner is the top view of the left part, and the lower

4.5.2. Task II: Verify two typical scenarios To verify the effectiveness of the proposed method, the power

Fig. 5. Power output processes in the two typical scenarios of Model 1. 10

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Fig. 6. Power output stacking diagrams in two typical scenarios of Model 1.

deductions can be made from the figure:

output process and power load process in the two typical scenarios in the three seasons of Model 2 are plotted in Fig. 9. In the figure, the blue, orange, yellow and purple lines are the output of the prediction mean scenario, output of the observation scenario, load of the prediction mean scenario and load of the observation scenario, respectively. The gray interval is the estimated 90% confidence interval. The following inferences can be drawn from the figure:

(1) In general, in the three seasons, the power output curves of the two typical scenarios of Model 2 are basically close to the power load curves, and only a few periods exhibit differences. (2) Remarkably, it is difficult to achieve closeness to the load curve if it relies solely on the complementation of the wind power output and solar power output. Therefore, hydropower plays a key role in the regulation of the WSH hybrid system.

(1) The four curves are relatively close. This shows that Model 2 works and indicates that the prediction mean scenario can represent the observation scenario to a large extent. (2) The four curves are located in the gray 90% interval for most of the periods, indicating that the estimated interval is reasonable.

4.5.4. Task IV: Compare ability of hydropower in different seasons In order to further analyze the reasons for the difference in the ability of hydropower to smooth the output of the wind power and solar power in the different seasons, the statistics of all the simulation scenarios are shown in Fig. 11. The left part display the objective statistic for all the simulation scenarios in the three seasons, including the minimum, mean, maximum and standard deviation. The right part presents the number of periods in which the hydropower (H1) output is

4.5.3. Task III: Analyze complementarity of output To analyze the complementarity of the output of the WSH hybrid system, the power output stacking diagrams of the two typical scenarios in the three seasons of Model 2 are displayed in Fig. 10. The following

Fig. 7. Statistics of all simulation scenarios of Model 1. 11

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Fig. 8. PDFs of the period outputs of Model 2.

strongest adjustment ability.

in a specific output range, for all the simulation scenarios in the three seasons. The following results can be deduced from the figure:

4.6. Comparison of three models

(1) The objective mean of all the simulation scenarios is the smallest in the normal season, followed by that in the dry season and finally that in the wet season. This indicates that hydropower has a different adjustment ability in the three seasons. In Model 2, it has the strongest adjustment ability in the normal season, followed by that in the dry season, and the last in the wet season. (2) Similar to Model 1, the number of periods in interval (1500, 2000] MW during the normal season is the highest, therefore it has the

To compare the differences between the three operation models, their objectives in the three seasons are presented in Fig. 12. The objectives corresponding to the three subgraphs from the left to the right are the period output standard deviation, RMSE between the period output and load and total power generation, respectively. The values in the histogram are the averages of all the simulation scenarios. The following inferences can be drawn from the figure: 12

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Fig. 8. (continued)

Fig. 9. Power output processes and power load processes in the two typical scenarios of Model 2.

4.7. Real application method

(1) Regardless of the season, the objective of the period output standard deviation of Model 1 is the best among the three models. (2) Regardless of the season, the objective of RMSE between period output and load of Model 2 is the best among the three models. (3) Regardless of the season, the objective of total power generation of Model 3 is the best.

After verifying the practicability and effectiveness of the models and methods, the methods of how these results can be used for real applications are summarized as follows: (1) Train the SWLSTM-GPR probability prediction model and predict the PDF of wind speed, solar radiation intensity, and runoff for the next day. (2) Stochastic simulate 500 or more scenarios based on the predicted PDF. (3) Construct the optimal scheduling model of WSH hybrid system,

In an actual application, the corresponding model can be selected based on the specific requirements.

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Fig. 10. Power output stacking diagram of the two typical scenarios of Model 2.

is used to obtain the distribution of these uncertain components in the next day. Then, stochastic simulation is used to generate 500 sets of simulation scenarios for the next day. Next, each set of simulation scenarios is input into the constructed optimal operation model for solution. Finally, the kernel density estimation method is used to estimate the distribution function of operation process of the next day. The constructed optimal operation model and proposed simulation-estimation method are applied to WSH Experimental Base of the Yalong river basin. The six main conclusions of the work can be summarized:

input the randomly generated scenarios into the model and solve them with genetic algorithms to get the state variables of each simulated scenarios for the next day. (4) The KDE method is used to obtain PDF of state variable for the next day, and it is provided to the dispatcher as reference information for decision-making. 5. Conclusions In this study, three optimal operation models are constructed for the WSH hybrid system with the objective of minimizing period output standard deviation, minimizing RMSE between period output and load and maximizing total power generation, respectively. There are uncertain components of wind speed, solar radiation intensity and power load in the daily operation model of the WSH hybrid system, the simulation-estimation method is proposed to consider these uncertainties. Firstly, the SWLSTM-GPR probabilistic forecasting method

(1) The model and method of this study works well, and can well simulate the PDF of the operation process in the future, which can provide rich decision information for dispatchers. (2) The operation process of the prediction mean scenario is extremely close to the operation process of the observation scenario, which can represent the real situation to a large extent. (3) The operation process of prediction mean scenario and observation

Fig. 11. Statistics of all the simulation scenarios of Model 2. 14

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Fig. 12. Comparison of the objectives of the three models in the three seasons.

Hydropower Research, No. IWHR-SKL-KF201914), the Graduates' Innovation Fund, Huazhong University of Science and Technology (2019ygscxcy072), and special thanks are given to the anonymous reviewers and editors for their constructive comments.

scenario is located in the 90% interval for most of periods, which can avoid many potential risks, and also indicates that the estimated interval is reasonable. (4) In the WSH hybrid system, hydropower plays a key role in adjustment. This adjustment ability is different in different seasons. In Model 1, the hydropower station in the dry season has the strongest adjustment ability. In Model 2, the hydropower station in the normal season has the strongest adjustment ability. (5) The three operation models established in this study have different emphasis, which can be flexibly selected according to specific needs in practical applications. (6) This research model fully considers the uncertainty and power generation. On the one hand, it can optimize the economic benefit through the model objective; on the other hand, it can avoid the economic loss caused by the potential uncertainty by quantifying the uncertainty.

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CRediT authorship contribution statement Zhendong Zhang: Writing - original draft, Conceptualization, Data curation, Methodology, Visualization. Hui Qin: Writing - review & editing. Jie Li: Writing - review & editing, Visualization. Yongqi Liu: Writing - review & editing. Liqiang Yao: Writing - review & editing. Yongqiang Wang: Writing - review & editing. Chao Wang: Writing review & editing. Shaoqian Pei: Writing - review & editing. Jianzhong Zhou: Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is supported by the National Key R&D Program of China (2016YFC0402209), the National Natural Science Foundation of China (No. 91647114, U1865202, 51779013, 51709275, 51579107, 91547208), the National Public Research Institutes for Basic R & D Operating Expenses Special Project (CKSF2017061/SZ), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and 15

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