Elsevier

Applied Energy

Volume 250, 15 September 2019, Pages 389-403
Applied Energy

Short-term optimal operation of hydro-wind-solar hybrid system with improved generative adversarial networks

https://doi.org/10.1016/j.apenergy.2019.04.090Get rights and content

Highlights

  • An improved deep neural network for capturing the high-dimensional features of wind-solar energy.

  • A refined model and a two-stage solution for cascade hydropower stations.

  • Proof of the applicability of only a hydro-wind-solar hybrid system to satisfy power transmission.

  • Improvement of the quality of generated scenarios helps enhance the hybrid system performance.

Abstract

The high penetration of variable renewable energy sources (RESs) has greatly increased the difficulty in power system scheduling and operation. To fully utilize the complementary characteristics of various RESs, a stochastic optimization model considering the strong regulation capacity of cascade hydropower stations and the uncertainty of wind and photovoltaic (PV) power is presented. Based on the improved generative adversarial networks, the spatial and temporal correlation characteristics between wind farms and PV plants are accurately captured via measured data. Due to the nonlinear features of the hydroelectric plants, linearization methods are adopted to reformulate the original model into a standard mixed integer linear programming (MILP) formulation. Then, the model is solved with a proposed two-stage approach, in which a heuristic algorithm is used to solve the first-stage unit commitment optimization. The cascade hydraulic connection and time delay of the water flow are established in the second stage to exploit the considerably controllable adjustment capability of hydropower generation. A renewable energy base in southwest China is chosen as a detailed case study. The simulation results reveal the potential of the large-scale application of only a hydro-wind-solar hybrid system to satisfy the power transmission demand with the guidance of the coordinated operation strategy, and the performance of the hybrid system can be further enhanced with high-quality scenarios from the proposed deep neural network.

Introduction

As fossil fuels are restricted by energy reserves and environmental issues, the utilization of renewable energy sources (RESs) has become an inevitable trend worldwide [1]. Wind, photovoltaic (PV), geothermal and wave energy have been widely applied and rapidly developed in recent years with the promotion of a positive electricity price mechanism for RESs. Among the RESs, wind and PVs are particularly considered because of their nonpollution, effective technologies and low costs. In China, the total installed capacity of solar energy exceeded 100 GW in 2017, while the installed capacity for wind energy reached 165 GW in the same year [2]. Nevertheless, the random, fluctuating and uncontrolled power output from wind and PVs significantly challenges the system balance and causes increased operating costs because of the added requirements for ancillary services from system reserves. If the penetration rate of wind and solar power exceeds a critical value, the safe and stable operation of the power grids may be seriously challenged [3]. Consequently, it is difficult to fully utilize the uncertain power generation from wind and PVs in the existing power systems. To enhance the applicability of wind and solar energy, the use of complementary sources can be an effective approach to lessen the renewable energy curtailment and improve the operational efficiency.

In China, the proportion of hydropower production has presented a notable increasing trend in the 21st century, and the installed capacity of hydropower reached 320 GW in 2016 [4]. As one of the low-cost and green energy sources, hydropower has gradually taken the lead in the electricity market worldwide. From a global perspective, hydropower can be commercially integrated with other uncertain energy sources, such as wind and solar, on a large scale [5]. With the flexibility provided by a large-capacity reservoir, hydropower generation can help balance electricity production and demand in real time because of its prompt startups and shutdowns. Expressly, the ramp rates of some hydroelectric plants can reach 30% per minute [6]. Thus, hydropower can be seen as an excellent resource to complement the intermittent power sources. Integrating a hydro-wind-solar hybrid system can be a promising option for future power systems with high proportions of RESs [7].

For multienergy hybrid systems, including hydro, wind and solar systems, a remarkably high-quality power output can usually be achieved with complementarity [8]. In general, rapidly adjusting hydropower stations can guarantee the power supply from the integrated system even with the volatile daily power output from wind or PVs. On the other hand, the hydroelectric power generation is mainly dependent on the state of runoff, which exhibits seasonal variations in China. Hence, a higher power generation from wind and PVs can compensate for the hydropower in winter and spring. At present, utility-scale hybrid systems with only RESs are a reality. In Longyaxia, a utility-scale PV-hydro integrated system was implemented and has brought enormous economic benefits [9]. The hydropower plant, with a capacity of 1280 MW, can cooperate with 320 MW PV arrays, thus delivering smoother power profiles to the grid. Currently, the practical application of large-scale RESs is hindered by their intermittency and uncertainty. These works provide the basis for realizing a future power system with a high penetration of RESs.

Recently, integrated multienergy systems have become a research focus due to their stronger power supply and increased operational efficiency compared to single energy systems [10]. Typical power source combinations include hydro-solar hybrid systems [11], [12], hydro-wind hybrid systems [13], [14], and hydro-wind-solar integrated systems [15]. Although much correlated research has been performed, these works focused chiefly on the feasibility analysis and design of small-scale multi-RES hybrid systems. Some regions rich in diversified RESs, such as Southwest China, have the potential to develop large-scale multienergy hybrid systems. As renewable energy-related technologies are evolving, region-level integrated multienergy systems are attracting growing interest from researchers. Previous studies have generally addressed the evaluation and utilization of the complementary characteristics of various RESs. References [16], [17] demonstrated an improvement in the power supply capability of a system by combining several RESs. Beluco et al. [16] found that the short-term temporal complementarity between PV power and hydropower could improve the stability of the energy supply. Angarita et al. [17] revealed that the energy balance would be enhanced with the regulation of hydropower stations. Regarding the optimal system configuration and operation strategy, Ming et al. [18] proposed a sizing model to determine the best proportion of PV plants to achieve an optimal operational performance and satisfy the demand. Silva et al. [19] developed a mathematical model to attain the configuration parameters for wind turbines and solar arrays via operation simulation. Refs. [20], [21] proposed operational strategies for hydro-PV hybrid systems in the short term and long term obtained through multiobjective optimization. However, few studies have estimated the detailed complementary characteristics in a systematic framework including large-scale wind farms, solar arrays and hydropower stations. In China, theoretical guidance for the short-term coordinated operation of large-scale hydro-wind-solar hybrid systems is urgently needed.

In addition to the abundant hydraulic resources in the Yangtze River, over 200 mega reservoirs and 1300 medium-scale reservoirs have been built along with hydroelectric plants in the last two decades [22]. Hydropower stations with cascaded structures were developed over a wide region of China. Commonly, cascade reservoirs can provide greater flexibility compared with single hydropower stations. Nonetheless, the management of cascade hydropower stations is highly challenging. The main obstacles lie in the nonlinearity and high dimensionality of the hydraulic-electrical connections between cascade hydroelectric plants. Furthermore, to accurately model the entire system, the reservoir water level, penstock losses, various power output curves for different units, and generating efficiency should be precisely described [23]. Owing to the complexity and intractability of the coordinated operation for cascade hydropower stations, various types of simplification methods and optimization algorithms have been proposed. Borghetti et al. [24] idealized the head effect and linearized the input-output power curves to transform the optimization problem into mixed integer linear programming (MILP) problems. In [25], the power generation characteristics of hydropower units at the same level were assumed to be identical, and this simplified problem could be solved by generic solvers with a stationary forebay elevation. In addition, the selection of algorithms is of great significance in attaining an accurate solution for these complex problems. Mathematical programming algorithms and heuristic algorithms have been the most commonly used approaches for realizing the optimal operation of cascade reservoirs. Mathematical programming methods, such as linear programming (LP), dynamic programming (DP), and nonlinear programming (NLP), have been widely used but are computationally inefficient if a result with high precision is to be acquired [26]. To overcome the bottlenecks of these high-dimensional problems, multiple decomposition algorithms, such as Lagrangian relaxation [27], successive approximation [28], and Benders decomposition [29], were proposed to ease the computational complexity. Moreover, heuristic rules and re-optimization are commonly used methods to ensure the feasibility of the solutions [30], [31]. In [31], the mixed integer nonlinear optimization problem was solved by a two-stage method; the second stage could transform the solution provided by the first stage into a feasible one. However, the curse of dimensionality was only partially overcome, and the hydraulic-electrical relations between multiple cascade hydropower stations could further limit the accuracy and efficiency of the simulation models considering their spatial and temporal characteristics. Alternatively, heuristic algorithms, such as genetic algorithms [32], differential evolution [33], ant algorithms [34], and the weighted non-dominated sorting genetic algorithm II [35], could be applied to address the optimal operation problem for cascade hydropower stations. These methods are especially advantageous for treating nonconvex and discontinuous problems; nevertheless, computational difficulties still exist, and the optimization of the joint operation of over 10 cascade hydropower stations is highly intractable [36]. In addition, heuristic methods easily become stuck in local optima, and the parameter tuning process is complicated. Hence, the accurate modeling and optimization of high-dimensional cascade hydropower stations are crucial for the coordinated operation of hydro-wind-solar hybrid systems.

In the short run, the wind speed and solar radiation are stochastic and affect the dynamics of power generation. However, they may display daily or seasonal patterns over longer time periods [37]. Accurately describing their long-term cyclicality as well as their stochastic short-term variations is significant for the optimized planning and operation of large-scale hydro-wind-solar hybrid systems. At present, three approaches, including scenario generation, the risk index and probabilistic forecasting, exist to represent the uncertainty of wind or PV power [38]. Among them, the scenario representation is the most appropriate when considering the spatial and temporal correlations between uncertain variables. Moreover, the generated scenarios can be directly applied in the latter stochastic programming models, and system participants can evaluate the impacts of uncertain RESs on the system reliability and cost more intuitively by using many possible scenarios. Previous works have mainly studied the model-based approach, which can generate scenarios of RES power via probabilistic distribution fitting and sampling. For wind and solar energy, considering their spatial and temporal characteristics, their high-dimensional correlation structure should be captured. Thus, the moment matching technique [39], copula-based methods [40], [41], [42], and the generalized dynamic factor model [43] have been used to fit the high-dimensional probabilistic distributions of multiple variables. Nonetheless, the temporal and spatial dynamics of wind and solar power could not be accurately fit by only first- or second-order statistical results. In addition, the accuracy of the distribution assumption and the applicability of the sampling methods could not be guaranteed. Recently, some machine learning-based methods, such as artificial neural network (ANN) [44], quantile regression convolutional neural network (QRCNN) [45], radial basis function neural network (RBFNN) [46] and support vector machine (SVM) [47], have also been adopted for RES scenario generation. These model-free approaches could potentially capture the high-dimensional and nonlinear dynamics of wind and solar energy compared with the copula-based methods. However, the feature extraction and parameter tuning processes are trivial, and the generalization ability is poor. In particular, generative adversarial networks (GANs) have been widely applied in computer vision [48]. The structure of a GAN can be seen in Fig. 1. A GAN can fully leverage the potential of neural networks to both capture the complex nonlinear correlations (the generator) and classify intricate inputs (the discriminator), and the game between the generator and discriminator promotes the progress of both networks. When a Nash equilibrium is reached, the generated scenarios for RESs can cover all the characteristics of the training data. In theory, a GAN is extremely suitable for scenario generation in the field of RESs. In 2018, Chen et al. [49] presented a Wasserstein GAN (WGAN) approach for generating wind and solar scenarios, taking into account multiple sites with spatial and temporal correlations. Before long a Bayesian GAN was proposed to generate scenarios that can reflect the dynamic patterns of wind and solar sources simultaneously [50]. Chai et al. [51] further improved the training stability of the WGAN by adding regularization and consistency terms to the objective function of the discriminator. However, the drawbacks of a GAN, including the training instability and mode collapse, still exist in these works, and the quality of the generated scenarios will be greatly influenced by the dynamics of the inputs.

To further demonstrate the potential of a large-scale cascade hydro-wind-solar hybrid system, this paper focuses on two main issues: proposing an improved deep neural network combining a GAN and variational inference to accurately capture the spatial and temporal dynamics of wind and PV power, after which high-quality scenarios can be generated, and exploring the strong regulation and storage capacity of cascade hydropower stations to balance the fluctuation and uncertainty of large-scale wind and PV power and to meet the export power transmission demands. Through the refined modeling of cascade hydropower stations and a two-stage method based on generated scenarios, the effectiveness of the proposed algorithms and the applicability of the large-scale hydro-wind-solar hybrid system are demonstrated.

In the remainder of the study, Section 2 introduces the detailed models and methods used for the coordinated operation of the cascade hydro-wind-solar hybrid system. A case study in Southwest China is provided in Section 3. In Section 4, the results of the proposed methods are given and discussed. Finally, conclusions are drawn in Section 5.

Section snippets

Methods

The presented approach for the coordinated operation of a large-scale hydro-wind-solar hybrid system consists of three parts (Fig. 2): (1) Development of a refined model for cascade hydropower stations coupled with wind and PV power (Section 2.1). (2) Proposal of a precise description of the stochastic dynamics of wind and PV power: the uncertainty of these variables can be represented by the generated scenarios based on the improved GAN combined with variational inference (GAN-VI) (Section 2.2

Case study

Recently, many renewable energy bases have been planned because of the abundant wind, solar and hydro energy sources in Southwest China. For these bases, the assurance of power transmission is one of the most important tasks. An appropriate multienergy joint operation strategy can further improve the efficiency of the system while accurately characterizing the spatial and temporal correlations and complementarities. Therefore, a base is chosen as the case study. The system under study includes

Scenario generation for wind and PV power

In addition to the proposed GAN-VI model, the Gaussian copula and variational automatic encoder (VAE) methods are also set up for scenario generation for comparison with our proposed approach. The Gaussian copula model is recursively estimated to capture the independence structure, while the VAE model is designed and trained according to [58]. Then, we are able to generate a group of scenarios for wind and PV power.

First, we need to prove that the proposed GAN-VI can generate scenarios with the

Conclusion

This paper presented a coordinated optimization model for a large-scale hydro-wind-solar hybrid system. A detailed model of cascade hydropower stations was established. The uncertainties of wind and PV power were incorporated into the model through scenarios generated by a novel deep neural network. Several linearization methods and a two-stage approach were used to solve the complicated coordinated optimization model.

The results of the scenario generation process indicated that the proposed

Acknowledgments

The authors thank the National Key R&D Program of China 2017YFB0902200 and Science and Technology Project of State Grid Corporation of China 5228001700CW.

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