Long-Term Optimal Operation of the Cascade Hydro-Wind-Photovoltaic Hybrid System considering Transmission Section Constraints

Su, Huaying; Wei, Huoqing; Wei, Xingchen; Wang, Guosong; Zhang, Yan; Wang, Rongrong

doi:https://doi.org/10.1155/2023/8484804

Mathematical Problems in Engineering

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Abstract Introduction Methods Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 8484804 | https://doi.org/10.1155/2023/8484804

Long-Term Optimal Operation of the Cascade Hydro-Wind-Photovoltaic Hybrid System considering Transmission Section Constraints

Huaying Su,¹Huoqing Wei,²Xingchen Wei,²Guosong Wang,¹Yan Zhang,¹and Rongrong Wang¹

Academic Editor: Bo Yang

Received07 Nov 2022

Revised08 Jan 2023

Accepted16 Jan 2023

Published28 Apr 2023

Abstract

With the sharply increased development of variable renewable energy resources (VRERs) in recent years, the hydro-wind-photovoltaic (PV) hybrid system (HWPHS) has the prospective to enhance the grid integration of VRERs. Nevertheless, the intense variation associated with wind and PV generation causes uncertainties in the long-term operation of the HWPHS. To overcome this drawback, this paper develops a novel method to derive adaptive operating rules for a cascade HWPHS. First, a scenario-generating method coupling Kernel density estimation with the copula function is proposed to characterize the wind and PV forecast errors. Second, based on the power generation scenarios, an optimal scheduling model for the cascade HWPHS considering transmission section constraints is proposed to simulate the hydro-wind-PV complementary operation; finally, the long-term operating rules for the cascade HWPHS are extracted by grey relational analysis and BP neural network. As a case study, the HWPHS of the Wu River basin in China is chosen. Results demonstrate that the proposed model can effectively utilize the flexibility of cascade hydropower stations, improve transmission section utilization efficiency, and promote clean energy absorption.

1. Introduction

Recently, the energy demand has increased rapidly as the global economies and populations continue to grow [1]. Variable renewable energy resources (VRERs), like wind and photovoltaic (PV) power, have developed sharply because of their green properties and resource-abundant characteristics [2, 3]. Nevertheless, the climate highly influences their energy resources, such as wind and solar energy. The inherent fluctuations of VRERs can cause severe imbalances between power supply and demand at different temporal scales [4]. Consequently, when unsteady VRERs are integrated straight into the power grid, the security and economics of the power grid are at risk [5]. It is possible to overcome this challenge by combining VRERs with other power sources [6, 7].

Hydropower, a cheap and clean energy source, has steadily led the electricity market worldwide. Globally speaking, hydropower may be extensively and profitably combined with VRERs, such as wind and solar [8]. Hydropower stations can assist in balancing electricity production and demand in real-time because of their advantages in dispatchability, quick start-up, fast ramping, and storage in the reservoirs [9]. Hence, hydropower can be considered an exceptional flexible resource to supplement intermittent power sources. With a growth portion of VRERs in tomorrow’s power systems, the hydro-wind-PV hybrid system (HWPHS) could be a viable scheme [10].

In the past few years, several researchers have explored how hybrid energy systems (HESs) operate in the short term. Due to the uncertainty of the forecast, nonlinearities, multidimensionality, and multiple objectives, the optimal operation of HESs is a difficult task [10, 11]. Chen et al. [12] presented a robust distributional model with two stages to solve the hydro-thermal-wind economic-dispatch problems. Ming et al. [13, 14] proposed approaches for multilayered nested to optimize the daily generation schedules of large hydro-PV hybrid power stations. Biswas et al. [15] investigated the trade-offs between the economic and environmental performance of a wind-solar-hydro HES. Despite their focus on increasing HES short-term complementary profits, these research studies are unable to ensure suitable long-term performance due to the limited scope of short-term forecasts. [16–18]. As a result, it is crucial to explore the long-term complementary operation of hydro-based HES that could coordinate different energy sources over a relatively long period of time.

A lot of scientific papers have investigated the optimal long-term operations of hydro-solar, hydro-wind, or hydro-wind-solar renewable energy resources. Xu et al. [19] presented simulation and optimization models to maximize the power generation for a hybrid system. Wang et al. [20] developed a double-layer model to minimize the fluctuation in output for a hybrid system, which can reduce intraday peak-valley differences and smooth out hourly volatility. Yang et al. [21] created an in-station economic operation model to minimize water consumption and guarantee the secure operation of the hydro-wind hybrid system. The above researchers offered valuable references for the long-term operation of hydro-based HESs. However, the “wait-and-see” dispatching strategies derived from deterministic optimization are not capable of dealing with extreme events in a timely manner, resulting in frequent violations of electrical or nonelectrical constraints [22].

One of the most challenging aspects of the operation of a HWPHS is considering runoff, wind, and solar radiation uncertainties. A typical approach uses measured or simulated data to implicitly account for resource uncertainties before applying the deterministic optimization method to determine the best course of action. Willis et al. [23] utilized the deterministic optimization model to acquire optimal scheduling strategies. Celeste and Billib [24] acquired the optimal release policy by a quadratic programming method. Another popular approach for managing uncertainties is explicit stochastic optimization. Lei et al. [25] and Tan et al. [26] obtained more accurate inflow transition probabilities via the copula method. Xu et al. [27] divided the prediction period into two periods, with different magnitudes of inflow uncertainty treated differently over the two periods. Tan et al. [28] proposed a two-stage stochastic optimal operation model by approximating the utility function of the carryover stage. These studies have been conducted on a single reservoir integrating wind power or PV power. Moreover, because of the complicated hydraulic-electrical relationships, it will become more challenging to dispatch wind and PV power at large scales into cascade hydropower stations, and relevant studies are rare.

This study proposes a novel method for the long-term operation of a cascade HWPHS. First, the wind and PV power forecast uncertainties are described by typical scenarios and then incorporated into the generation scheduling model. Second, the generation scheduling model is constructed for the cascade HWPHS, considering transmission section constraints. Finally, the long-term operating rules of the cascade HWPHS are obtained by grey relational analysis and BP neural network.

2. Methods

2.1. Describing the Uncertainties of Wind and PV Power

2.1.1. Kernel Density Estimation

Kernel density estimation belongs to the nonparametric probability prediction methods, which do not need any prior knowledge and assumptions about the form of probability distribution. Kernel density estimation can fit the distribution of the data according to its own characteristics and properties.

Let be samples of random variables x with probability density function , then the kernel density estimate of is shown in equation (1) [29].where n presents the sample size and h presents the smoothing coefficient. means the kernel function, which is usually chosen as a symmetric single-peaked probability density function centered at 0.

2.1.2. Copula Function

A copula function can describe the joint distribution by connecting the marginal distribution function of these N variables based on Sklar’s theorem. The multivariate copula function is shown as follows:where and are the marginal distribution function and the density function of , respectively.

Ellipse copulas and Archimedean copulas are the most commonly used copula functions. Among the ellipse function families, the common ones are normal copula functions and t-copula functions, and the common ones of the Archimedean function family species are Gumbel, Clayton, and Frank copula functions. Different types of copula functions have different function structures and also fit different types of variable descriptions because of their different shape characteristics. In this study, Kendall’s rank correlation coefficient , Spearman’s rank correlation coefficient , and Euclidean distance (d) were employed to estimate the imitative effect of the joint distributions. Parameter estimation of joint distribution uses maximum likelihood estimation (MLE).

2.1.3. Scenario Generation

After obtaining the wind-PV joint copula function, a Monte Carlo random sampling method is employed to develop the wind-PV output scenarios randomly. The main steps are as follows [30]:(1)Randomly generating numbers in the interval [0, 1].(2)Let the first random variable marginal distribution function value be to find the second random variable marginal distribution function value , then find the solution of the following equation:(3)For the nth random variable with marginal distribution function value , find the solution of the following equation:(4)Repeat steps (1) to (3) k times, then the marginal distribution function values of n random variables in k groups are obtained.(5)Using the inverse function operation , is converted into a joint distribution function scenario, where j = 1, 2, …, 12.

To evaluate the complementary of the generated wind-PV output static scenarios, this study uses the coefficient of variation (CV) for characterization.

2.2. Modeling Generation Scheduling of the Cascade HWPHS

2.2.1. Objective Function

where W is the sum of power consumption (kW∙h) of hydro-wind-PV during the year; represents the power output (kW) of ith hydropower station during period t; presents the power consumption (kW∙h) of wind power during period t; denotes the power consumption (kW∙h) of photovoltaic during period t; T is the sum of periods, which is taken as 12 in this study; n presents the sum of cascaded hydropower stations, which is taken as 7; means the output coefficient of the ith hydropower station; denotes the average power generation flow (m³/s) of the ith hydropower station in the tth time period; and presents the average water head (m) of the ith hydropower station during period t.

2.2.2. Constraints

According to the model, there are the following constraints:(1)Transmission section constraints Hydro-wind-PV complementary power systems still use the original hydropower transmission channels after wind and PV are connected to the grid. where is the ultimate transmission power of the transmission channel.(2)Water balance constraint where and are the initiatory and last volume (m³) of the ith reservoir at period t, respectively, is the inlet flow (m³/s) of time t of ith hydropower station; presents the discharge flow (m³/s) of time t of ith hydropower station; presents the discharge flow (m³/s) of time t of ith hydropower station; means the generation flow (m³/s) of time t of ith hydropower station; and is the abandoned flow (m³/s) of ith hydropower station at time t.(3)Hydraulic relationship of upstream and downstream where presents the discharge flow (m³/s) of the upstream hydropower station of ith hydropower station; denotes the interval flow (m³/s) of the range between i-1th and ith hydropower stations.(4)Hydropower station characteristics where presents the downstream water level (m) of the ith hydropower station at period t; is the relationship function between water level and reservoir capacity of ith hydropower station; and is a function which describes the relationship between the tailwater level and discharge flow of ith hydropower station.(5)Reservoir water level constraint where presents the lower water level (m) restricts of ith hydropower station at period t, and denotes the upper water level restricts (m) of ith hydropower station at period t. In this study, they are scheduling underline and scheduling upline, respectively.(6)Outflow constraint where presents the minimum quoted flow (m³/s) of ith hydropower station at time t; denotes the minimum ecological flow (m³/s) of the reservoir at time t for the ith hydropower station; presents the minimum quoted flow (m³/s) required by the turbine unit at time t for the ith hydropower station; and is the maximum quoted flow (m³/s) at time t for the ith hydropower station.(7)Hydropower output constraint where denote the minimum hydropower output (kW) of ith hydropower station during period t; denotes the maximum hydropower output (kW) of ith hydropower station during period t; and presents the generation head (m) of ith hydropower station during period t.

2.2.3. Solution

It is a great challenge to make large-scale grid-connected consumption of wind-PV because of the intermittent and fluctuating characteristics of these two power generation. To transform the uncertainty of wind-PV power output into deterministic constraints, this study uses the Monte Carlo method to produce wind and PV power output prediction data obtained by random sampling according to the copula function obtained from 2.1.2 characterizing the wind-PV correlation and participating in the water-scape complementary scheduling calculation. With regard to power consumption, wind and PV power output are preferentially delivered, and the remaining channel capacity is used by hydropower. This study uses the optimization solver LINGO to solve this nonlinear model. The global nonlinear optimization method provided by the LINGO solver can avoid the “dimensional disaster” problem associated with the use of dynamic programming-type algorithms and the problem that the traditional method of solving the nonlinear model tends to fall into local optimal solutions.

2.3. Extracting the Long-Term Scheduling Rules of the Cascade HWPHS

2.3.1. Grey Relational Analysis (GRA)

GRA involves analyzing the geometric similarity between the change curves of each factor to acquire the degree of correlation between the factors.

The implement of the GRA is as follows:(1)A comparison series and a reference series are selected. There are mth evaluation objects and nth evaluation indicator variables, and each indicator variable is a benefit type indicator variable. The comparison series are as follows: where means the value of ith evaluation object with respect to the jth indicator variable . The reference series are and generally.(2)The dimensionless treatment of the data set. Normalization was performed using the initial value method in this study. The data in both the reference and comparison series were divided by the first value in the series, which was used to eliminate the differences in absolute values caused by the difference in magnitudes between the different elements.(3)Calculate the grey correlation coefficient. The formula is showed as follows: where presents the correlation coefficient of the comparison series to the reference series at the jth index; is the resolution coefficient (the smaller resolution coefficient means the larger resolution), and is taken as 0.15 in this study; and and are the two-level minimum and two-level maximum differences, respectively, which are constant values for the given comparison and reference series.(4)Calculating the grey-weighted correlation: the calculation formula is as follows: where denotes the grey-weighted correlation of ith comparison series to the reference series. The indicator variables in this study are given equal weights, .(5)Correlation ranking: Based on the magnitude of the grey-weighted correlation, the correlation order of the comparison series can be established by sorting. Comparison series have a more significant influence on reference series when there is a greater correlation. According to the abovementioned steps, the feature vectors that have a notable impact on the decision variables of each participating regulating power station can be calculated and filtered out by month using the results of the scheduling of the cascaded power stations. It helps that the models trained by the subsequent BP artificial neural network can have more accurate predictions.

2.3.2. BP Neural Network (BPNN)

BPNN are multilayer feedforward networks based on the error backpropagation algorithm [31]. Generally, there are three or more layers in a network, each layer is composed of several neurons. A general network is presented in Figure 1.

Assume the network has n inputs, m outputs, and s neurons in the hidden layer. Then, and are output and threshold value of this layer, respectively. In addition, is the threshold value of the output layer where and are the transfer functions of the hidden layer and output layer, respectively. Moreover, is the weight from the input layer to the hidden layer, and is the opposite. Then, the output of the jth neuron of the hidden layer is as follows:

The output of network is calculated by

The desired output is , and the error function is defined as follows:

During network training, weights and thresholds are continually readjusted to decrease the network error to a predetermined minimum or halt at a predetermined training step. Furthermore, the prediction results can be obtained once the forecasting samples have been input into the trained network.

3. Case Study

3.1. Cascaded Hydropower Reservoirs on the Wu River

The Wu River is the largest tributary on the south bank of the upper reaches of the Yangtze River, with a basin area of 87,920 km² and a total length of 1,037 km. The Wu River basin is rich in rainfall, and the distribution of precipitation varies greatly from region to region, with an average precipitation of 1163.0 mm over the years. Precipitation from May to August accounts for 58.1% of the year and from April to October accounts for 85.1% of the year. Moreover, the basin is rich in hydropower resources, with a theoretical hydropower reserve of 10,225 MW. There are 11 hydropower stations built in the main stream of the Wu River, including PD, YZD, DF, SFY, WJD, GPT, SL, ST, PS, and YP, with a total installed capacity of 11,589 MW. The overall performance of the gradient regulation is good, which greatly improves the stability of power generation in the regional power grid.

In this study, HJD, DF, SFY, WJD, GPT, SL, and ST power stations and their surrounding areas are selected as the objects of the study. This study focuses on the regulating role of the above four power stations in the hydro-wind-PV complementarity in the basin. The study area is shown in Figure 2, and Table 1 shows the essential information about the cascade hydropower stations.

3.2. Scenario Generation via Monte Carlo

The marginal distributions of monthly wind and PV power output were obtained by kernel density estimation using the data from the Wu River basin during 2013–2018. The frequency histograms, kernel density estimates, and the cumulative probability distribution for the wind and PV power outputs are displayed in Figure 3.

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From Figures 3(a) and 3(b), the probability density curve obtained by using the kernel density estimation method is basically in line with the trend of the sample frequency histogram. It is easy to know that the cumulative probability distribution is fundamentally consistent with the empirical distribution from Figures 3(c) and 3(d). The effect of the overflow of the obtained density function on the sample probability distribution can be ignored, and the resulting curve can be used to express the sample’s characteristics.

In this study, Kendall’s rank correlation coefficient , Spearman’s rank correlation coefficient , and Euclidean distance (d) were employed to estimate the goodness of fit of the joint distributions. Results were shown in Table 2.

From Table 2, the correlation coefficient calculation results of the Gumbel copula and Clayton copula functions are small, indicating that the sample data are not strongly correlated with these two functions. Among the remaining three functions, and of the Frank copula function are closer to the calculated results of the empirical copula, and the Euclidean distance of the Frank copula function is the smallest. Thus, the Frank copula function is chosen to construct the joint distribution function of wind-PV output to ensure the fitting accuracy of the proposed model. The joint probability density and cumulative probability distribution of the Frank copula function of the wind-PV power output are shown in Figure 4.

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In this study, 10 sets of complementary wind-PV output scenarios were generated using a joint probability distribution model and Monte Carlo sampling.

The CV values of each set of data are derived to measure the complementary characteristics of the generated scenic output, and the comparison of CV is shown in Table 3.

As shown in Table 3, the CV values for the wind-PV output are the smallest.

3.3. Analysis of Optimal Scheduling Results in Typical Year

In order to verify the generalizability of the proposed model, three typical years were selected from the 56-year long series of historical runoff data of the cascaded hydropower reservoirs at the Wu River: dry, normal, and wet years, which correspond to 75%, 50%, and 25% of the incoming water frequency, respectively. The incoming water data of the three typical years are substituted into the model proposed in the previous paper for optimal scheduling calculation. In order to save space and consider the maximum influence of water volume on the transmission section, the dispatching result with 75% water frequency is selected for analysis. The comparison of power generation statistics before and after hydro-wind-photovoltaic complementarity in wet years is shown in Table 4. The comparison of the total output of the hydro-wind-PV system is shown in Figure 5.

In the wet year, hydropower occupies most of the transmission channels due to a large amount of hydropower output during the flood season. Wind and PV power consumption space is very limited, so wind and PV abandonment are very likely to occur. As shown in Table 4, the participation of hydropower stations in the complementary terraces reduces the amount of abandoned wind and PV during the year. The phenomenon of wind and PV abandonment even does not occur at all. Thus, the hydro-wind-PV complementary promotes the consumption of clean energy. It is worth mentioning that the total hydropower generation after the complementation of the cascaded hydropower stations is less than before the complementation. The reason for this phenomenon is that the cascaded hydropower brings the flood power generation to the preflood, reserving the transmission capacity for the flood scenery consumption and reducing the abandoned power of the whole system. It indicates that giving full play to the flexible regulating role of the cascaded hydropower station can better support the consumption of renewable energy resources and increase the total power generation.

As shown in Figure 5, from June of the flood season, due to the increase of incoming water, hydropower generation surges, and the transmission section constraints, much wind and PV power was abandoned before the complementation. In July and August, hydropower even filled the channel, resulting in these two months of scenery power that cannot be consumed. Moreover, a small part of the abandoned PV power in February of the dry season, because of the beginning of the season regulation and above the water level hydropower plants are in a higher position with the limited regulation capacity. To pursue hydropower generation, the maximum operating principle can only produce a small amount of abandoned PV power. When the cascaded hydropower station plays its power complementary regulation role, hydropower will originally cause crowded channel power that was evenly dispersed over the previous months which did not reach the transmission capacity limit. At this time, whether the flood season (June, July, and August) or the beginning of the year (February), including March, April, and May, the entire power generation base is within the transmission line capacity limit, and wind and PV power annual consumption rates have reached 100%. The goal of maximum clean energy power consumption on the premises and maximum power generation is achieved.

The reservoir water level process and water abandonment comparison of the power stations before and after the seasonal regulation and above hydro-wind-PV complementary regulation in the wet year are shown in Figure 6. As shown in Figure 6, DF and GPT power stations are running with the dispatch line to pursue the maximum power generation capacity before the hydro-wind-PV complementary. After the complementary regulation, the water level fluctuated downward before the flood to reduce the flood output and free up the wind and PV power consumption capacities. The water level fluctuated downward before the flood. As a leading power station, the HJD power station has been operating at a low water level in March, April, and May before complementary regulation. The water level increased suddenly after entering the flood season in June while generating and storing water during the flood season. After complementary regulation, the HJD power station operates at a low water level before the flood season. It increases output in May to keep the water level low, and the water level rises rapidly in the flood season, reducing output to consume the scenery. The seasonal regulating power station WJD and multiyear regulating power station GPT also increase their output to lower the water level in March and April before the flood to ensure that sufficient capacity is reserved to consume the wind and PV power during the flood. There is no abandonment of water in the whole year before and after the hydro-wind-PV complementation in the wet year. It indicates that the overall regulating ability of the cascaded hydropower stations is good and can effectively adjust the distribution of hydropower output in the basin.

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3.4. Long-Term Scheduling Rules of Cascade HWPHS

This study focuses on the 7 hydropower stations in the main stream of the Wu River. HJD and GPT power stations are annual regulating power stations, while DF and WJD power stations are seasonal regulating power stations. This section mainly discusses the operation rules of the four power stations with strong regulating capacity in the long-term complementarity of hydro-wind-PV in the Wu River basin. The remaining three power stations (SFY, SL, and ST) are daily regulating power stations, which do not play an obvious role in the long-term scheduling of the reservoirs. The hydropower output of the long series of complementary hydro-wind-PV was calculated using the monthly runoff data of the main stream of the Wu River from 1952 to 2007. Additionally, the long series of wind power and photovoltaic output prediction data are generated by using the copula function of wind-PV output and Monte Carlo method sampling.

The maximum model of clean energy consumption is constructed in Section 2.2. Results of the long series from 1952 to 2007 can be obtained from the above information. The year-by-year power generation curves are shown in Figure 7.

With complementary hydro-wind-PV scheduling, the average annual power generation capacity of hydro-wind-PV system in the Wu River basin is 32.770 billion kW h over 56 years, and the average annual power generation capacity of step-level hydropower is 24.043 billion kW∙h.

In this study, GRA is used to select the influencing factors that are highly correlated with the operation status of the power station by month for neural network training to avoid introducing redundant factors that may affect generalization performance. According to the GRA method, the long series of optimal scheduling results for 56 years from 1952 to 2007 were compiled in 12 months, and the reservoir capacity at the beginning of each time period, the interval flow at the time period, the wind power output at the time period, and the photovoltaic output at the time period of HJD, DF, WJD, and GPT power stations were taken as the reference series in the results. As a comparison series, totaling 12 × 10 series, and the reservoir capacity at the end of each time period of the four power stations as a reference series, totaling 12 × 4 groups (there are ith hydropower stations and tth time periods involved in the calculation, i = 1, 2, 3, 4; t = 1, 2, 3, …, 12). The MATLAB was used to program the correlations between the selected ten impact factors and the decision variables for each month and to rank and filter the impact factors with higher correlations. The results of the influence factors were filtrated for each month and displayed in Table 5.

In this study, the optimized scheduling results for a total of 42 years from 1952–1993 are used as the training set, and 14 years from 1994–2007 are used as the validation set. Four statistical indices, mean absolute error (MAE), mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of fit (R²), are used in this study to describe the generalization performance of the training model. Table 6 presents the results of the BPNN model month by month for the calculation of the metrics.

From Table 6, the MAE and RMSE values of each power station fluctuate around 200–23,000, among which the average MAE value of HJD power station is around 9000, the average MAE value of DF power station is around 2000, WJD is around 4000, and GPT is around 7000. The impact of this degree of deviation is minimal for the hydropower stations, which have a capacity of ten million cubic meters or even a billion cubic meters. Moreover, the RMSE value of HJD power station is generally higher than the MAE value because the RMSE is more sensitive to the abnormal values in the data set. The overall average of R² is 0.8528, which means that the trend of the predicted value is consistent with the trend of the actual value. In summary, the BP neural network model is with high accuracy, which has a good fit for the optimal operation trajectory of the Wu River main-stem power stations in the long-term complementary process of hydro-wind-PV, which can be used as a reference for actual scheduling.

To test the practicality and operability of the dispatching rules obtained by BPNN, the runoff data from 2014–2020 were selected for long-term complementary hydro-wind-PV simulation dispatching of the Wu River main-stem power stations. Moreover, the optimized dispatching results and the simulation dispatching results of the dispatching rules were compared. Table 7 shows a comparison of power calculations.

Table 7 shows that the total generation capacity of the cascaded hydropower simulated by the neural network model is 4.172 billion kW h more than the optimized scheduling result, with a relative error of 3.12%, which is within the engineering allowable range. For the prediction results of individual power stations, the relative errors of all power stations are within 10%, indicating that the neural network prediction results are more accurate, with stable prediction performance and good generalization performance. Table 8 presents the values of each error indicator in the simulation dispatch results.

From Table 8, the prediction of the reservoir capacity at the end of the decision variable period is relatively accurate, and the MAE and RMSE values of the four power stations are generally small, with MAPE values within 5% and R² above 0.95, except for the GPT power station, and the training model has a good prediction effect. The MAE and RMSE of the predicted output values of each power station are commonly 80, and the RMSE is not much different from the MAE, which indicates that the deviation of the predicted values is stable and the outliers are less, and the prediction stability of the network model is well. The reason why the power output of each power station fits better than the reservoir capacity is as follows: on the one hand, the prediction process is not limited by the basic constraints of the power station, and the predicted value may happen to be higher than the flood level or lower than the dead level, but the water level is in the constraint during the calculation, which will lead to the power output calculated by the predicted reservoir capacity is not equal to the power output corresponding to the predicted reservoir capacity; on the other hand, because the water level reservoir capacity curve is calculated by fitting a quadratic function, there is a certain error in the conversion process of water level and capacity in the regulation calculation. All in all, the difference between the simulated and optimized scheduling results is small. The errors are in the appropriate range, indicating that the BPNN-trained scheduling function model maintains the generation efficiency of joint-optimized scheduling well and has high practical value.

The comparison of predicted storage capacity and the optimized scheduling storage capacity of each power station is shown as Figure 8. Figure 9 shows the comparison between predicted power generation and optimized scheduling power generation.

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4. Conclusions

Cascade hydropower stations present significant challenges in maintaining optimal long-term performance because of the significant wind and PV power uncertainties. This paper proposes a novel method to derive adaptive operating rules for a cascade hydro-wind-PV hybrid system, considering the transmission section constraints and the uncertainty of wind and PV power. A case study implemented the cascade HWPHS in the Wu River basin, China. The main results of this study are as follows:(1)The wind-PV output scenarios generated by Monte Carlo random sampling using the proposed Frank copula function have been tested by the CV and have corresponding negative correlation characteristics, which can accurately reflect the complementary wind-PV output characteristics of the region and can provide prediction data for subsequent complementary scheduling.(2)To address the problem of transmission channel crowding caused by large-scale wind-PV grid connections, this paper establishes a long-term optimal dispatching model of complementary hydro-wind-PV systems, considering the transmission section limitation and aiming at the maximum system power generation. The model can reduce the abandonment of water in the flood period, enhance the utilization rate of hydro energy, and increase the output of the cascaded hydropower station in the dry period to compensate for the renewable energy resources and improve the application rate of transmission lines.(3)From the model evaluation process, it can be seen that using GRA to filter the simplified influence factors to build the neural network model can not only reduce the training time but also enhance the model’s prediction performance. The trained BPNN has accurate predictions and stable results in hydro-wind-PV complementary simulation scheduling, which can be used as a reference for actual scheduling.

Data Availability

The data used to support the finding of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

Acknowledgments

This research was funded by the Key Science and Technology Project of China Southern Power Grid, grant number GZKJXM20210372.

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