Distributed Photovoltaic Systems Research Articles

Solar potential for social benefit: Maps to sustainably address energy poverty utilizing open spatial data in data poor settings

Access to affordable sustainable energy is a significant challenge for many lowincome countries experiencing energy poverty. The United Nations (UN) Sustainable Development Goal (SDG) 7 aims to “ensure access to affordable, reliable, sustainable and modern energy for all.” Simultaneously, the European Union (EU) seeks to reduce emissions by 55 % by 2030. Decarbonization policies must be carefully considered to avoid adverse effects on vulnerable groups experiencing energy poverty. Solar technology offers a viable solution to decarbonize the building sector, reduce energy dependence on fossil fuels, and provide financial benefits to the public. Mapping solar potential is crucial to determine where investment in solar photovoltaic (PV) technology is most advantageous to the populations who stand to benefit the most. We combine a solar potential mapping approach incorporating socio-economic indicators indicative of energy poverty, using off-the-shelf Geographic Information Systems (GIS) tools that are easily replicated across cities facing energy poverty. Utilizing lowest common denominator data and analysis approaches, we offer creative and innovative mapping solutions. The socio-economic factors help to contextualise the benefits of distributed PV systems and highlight the need for mapping solar potential, in combination with energy poverty indicators for sustainable planning and policymaking. Our results for a case study in the city of Plovdiv, Bulgaria, demonstrate high solar energy potential that could meet 29 % of the city's electricity needs, save citizens about M€ 43.84 annually, and pinpoint where to invest first for the highest gains. Finally, we offer suggestions on how to use these results to inform decarbonization policies to benefit low-income populations that are often missed in existing energy policies.

Techno-economic assessment of grid-connected residential photovoltaic systems considering overvoltage-induced generation curtailment

Grid-connected residential photovoltaic (PV) systems are continuously installed in worldwide communities, predominantly to reduce electricity bills. However, the rapid growth of distributed PV systems inevitably causes overvoltage in distribution networks. Conventionally, PV curtailment is implemented in a grid-connected inverter to prevent the system from overvoltage. Nevertheless, previous studies have failed to consider PV curtailment caused by overvoltage when conducting techno-economic assessments. Therefore, this study conducts a comprehensive techno-economic assessment of grid-connected residential PV systems, considering overvoltage-induced generation curtailment. A volt-watt curtailment strategy is designed based on a droop characteristic. Simulation studies are conducted using real-world load profiles and electricity tariffs retrieved from the Metropolitan Electricity Authority in Thailand. Furthermore, a typical low-voltage distribution feeder in Bangkok, Thailand, is employed using Thailand’s grid code. Simulation results indicate that the optimal PV size could be reduced by up to 58.33% (depending on the numbers and locations of PV systems) when considering overvoltage-induced generation curtailment, resulting in a profitability reduction of 21.34%. It is concluded that considering overvoltage-induced generation curtailment can accurately determine the PV size, preventing oversizing and overvoltage.

Sensitivity analysis of distributed photovoltaic system capacity estimation based on artificial neural network

Residential solar photovoltaic (PV) system installations are expected to continue increasing due to their growing cost competitiveness and supportive government policies. However, excessive installations of unknown behind-the-meter solar panels present a challenge for accurate load prediction and reliable operations of power networks. To address such growing concerns of distribution network operators (DNOs), this research proposes a novel model for distributed PV system capacity estimations. Innovative extracted features from 24-hour substation net load curves were fed into a deep neural network to estimate the PV capacity linked to the substation feeder. A comprehensive study into the sensitivity of the model’s accuracy to specific temporal scales of data collection, number of households served by a substation, and proportion of PV-equipped properties was conducted. This study revealed that a model developed to be used exclusively in summer achieved a 18.1% decrease in estimation root mean squared error (RMSE) compared to an all-year model, whilst using only a third of the training data amount. Similarly, compared to an all-year model, RMSE decreased by 26.9% when only data from Mondays to Thursdays were used to train and test the model. Also, for the all-year model, the most accurate estimations occur when 20% to 80% of households have PV systems installed and estimation percentage error tend to remain constant at around 10% when more than 20% of households have PV systems installed. A machine learning-ready dataset of substations with known PV capacity and experiment results are both useful to inform DNOs on the potential of the proposed method in reducing grid operation costs.

Residual learning-based robotic image analysis model for low-voltage distributed photovoltaic fault identification and positioning.

With the fast development of large-scale Photovoltaic (PV) plants, the automatic PV fault identification and positioning have become an important task for the PV intelligent systems, aiming to guarantee the safety, reliability, and productivity of large-scale PV plants. In this paper, we propose a residual learning-based robotic (UAV) image analysis model for low-voltage distributed PV fault identification and positioning. In our target scenario, the unmanned aerial vehicles (UAVs) are deployed to acquire moving images of low-voltage distributed PV power plants. To get desired robustness and accuracy of PV image detection, we integrate residual learning with attention mechanism into the UAV image analysis model based on you only look once v4 (YOLOv4) network. Then, we design the sophisticated multi-scale spatial pyramid fusion and use it to optimize the YOLOv4 network for the nuanced task of fault localization within PV arrays, where the Complete-IOU loss is incorporated in the predictive modeling phase, significantly enhancing the accuracy and efficiency of fault detection. A series of experimental comparisons in terms of the accuracy of fault positioning are conducted, and the experimental results verify the feasibility and effectiveness of the proposed model in dealing with the safety and reliability maintenance of low-voltage distributed PV systems.

Evaluation Model of Distributed Photovoltaic Utilization in Urban Built-Up Area

Photovoltaic (PV) power generation is emerging as a key aspect of the global shift towards a more sustainable energy mix. Nevertheless, existing assessment models predominantly concentrate on predicting the overall capacity of PV power generation, often neglecting temporal dynamics. Drawing upon the urban energy substitution rate, utilization rate, and power supply stability, this study has devised a comprehensive evaluation model for the utilization of distributed photovoltaic systems (SUS). This model integrates the quantification of spatio-temporal features inherent in urban settings and buildings. Using Hohhot city as a case study, this study conducted simulations to analyze how the installation of PV systems affects the electricity consumption patterns across different land plots within the urban core. The study additionally examines how urban planning influences the adoption of PV power, taking into account both the timing of PV power usage and the stage of PV technology development. The evaluation model surpasses the constraints of current urban PV assessments, which primarily emphasize enhancing power generation potential without adequately quantifying supply–demand dynamics or spatial and temporal variations. This breakthrough significantly improves the precision and reliability of assessing the efficiency of distributed PV systems. Its implications extend widely to subsequent comprehensive evaluations of urban PV applications.

SPATIAL INVENTORY OF SOLAR PHOTOVOLTAIC (PV) INSTALLATIONS USING REMOTE SENSING AND MACHINE LEARNING: CASE OF PAMPANGA PROVINCE, PHILIPPINES

Abstract. In recent years, the cost of photovoltaic (PV) technologies significantly declined, boosting the expansion of solar PV installations in the country. This rapid development in solar PV utilization necessitates an effective detection method capable of delineating both utility-scale and distributed PV installations to generate a complete inventory of solar PV installations for status monitoring and implementation of appropriate programs of stakeholders and decision-makers. This study aims to detect and delineate solar PV installations in Pampanga, Philippines using different band combinations of Sentinel-2, Sentinel-1, and indices (NDVI, NDWI, and PVSI) through machine learning with the aid of open-source geographic information system and remote sensing software. Moreover, an alternative approach to identifying solar PVs using the combination of pixel-based classification (PBC) and object-based classification (OBC) was introduced. Training and validation data were acquired from the satellite images. The accuracy of each approach in PV detection was then compared using three classifiers: Support Vector Machine (SVM), Random Forest, and Naive Bayes. Results showed that SVM has the best performance for PBC while Random Forest demonstrated the highest accuracy for OBC. A post-processing procedure was also implemented using a set of spectral rules to further refine the results of image classification. The delineation accuracies of the post-processed data over the ground-truth data showed that the methodology is effective in delineating utility-scale installations for both Sentinel-2 and Planetscope. However, the detection of distributed PV systems showed limitations particularly when dealing with small solar PV installations (less than 45 pixels) due to Sentinel-2’s coarse spatial resolution.

Five-dimensional assessment of China's centralized and distributed photovoltaic potential: From solar irradiation to CO2 mitigation

Owing to China's escalating demand for renewable energy and carbon emissions reduction, and given its prominent position as one of the fastest-growing nations in photovoltaic (PV) development, a comprehensive assessment of the potential of both centralized and distributed photovoltaic systems in China is crucial. However, current research on PV potential assessment presents several challenges. Therefore, this study presents a five-dimensional assessment model, encompassing geographical, technical, economic, CO2 mitigation, and realizable potential, to systematically map China's centralized photovoltaic (CPV) and distributed photovoltaic (DPV) potential. The findings underscore the vast PV potential across the country, with areas of 3.11 million km2 and 252.72 thousand km2 deemed suitable for CPV and DPV development, respectively. This corresponds to a technical potential of 416,383.27 and 28,261.53 TWh/yr for CPV and DPV, respectively. Furthermore, this study explored the economic potential of CPV and DPV, revealing that the generation costs of both CPV and DPV in China are in proximity to the feed-in tariffs. With technological advancements and economies of scale, a broader PV potential is projected to be economically feasible by 2030. Full implementation of the current economic potential can yield an annual CO2 mitigation of 54.20 and 8.39 gigatonnes (Gt) using CPV and DPV, respectively. Notably, China's PV potential exhibits distinct regional heterogeneity, with CPV potential concentrated primarily in the western region and DPV potential distributed predominantly across the eastern provinces. This study identified the most resource-intensive areas in the western region of Inner Mongolia for CPV and in the coastal regions of Guangdong and Shandong provinces for DPV. Considering policy imperatives and the development status, China's PV sector holds tremendous potential to significantly contribute to carbon reduction targets. Based on the findings, policy recommendations are proposed, emphasizing the imperative of jointly developing CPV and DPV systems, as well as implementing phased and planned growth strategies for PV growth.

Distributed photovoltaic power output prediction based on satellite cloud map video frames

To address the challenge of predicting distributed photovoltaic (PV) power output for improved system integration and stability, this study proposes a novel method. Given the expanding scale of distributed PV systems and their economic constraints, accurate power output prediction becomes pivotal. Conventional prediction methods are hindered by the lack of meteorological stations at most distributed PV stations. In response, we present a dynamic convolutional generative adversarial network (DC-GAN) approach coupled with satellite cloud map video frames. By extracting shading features from satellite cloud images and utilizing DC-GAN, our method forecasts short-term cloud shading effects on future radiation. We further integrate radiation data from centralized PV stations, spatial correlations of distributed PV stations, and cloud shading characteristics. This information is used to construct a predictive model combining Convolutional Neural Networks (CNN) and Long short-term memory (LSTM), enhancing prediction accuracy. Comparative experiments confirm the superiority of our proposed method over traditional approaches, substantiating its effectiveness and practicality. Our method achieves notable accuracy improvements, establishing its value in predicting distributed PV power output. This research’s findings offer a valuable contribution to the field of renewable energy integration. In numerical assessments, our method demonstrates a significant increase in prediction accuracy, outperforming conventional techniques by 3.3%. This underscores the practical relevance and efficiency of our proposed approach in enhancing distributed PV power output prediction.

Impact of wheeling photovoltaic system on distribution low voltage feeder

Renewable energy generation (REG) has been the main concern for policymakers, governments, industries, researchers, and other energy agencies in leaser fossil fuel and polluted environments. Nowadays, distributed photovoltaic (DPV) integration is a vital substitute for installing new substation feeders. DPV is used to reduce distribution loading. Thus, it can be analyzed as an optimization problem addressing multiple objectives. This optimization can help select the technology, siting, and sizing of DPV. This work studies automatic voltage regulator (AVR) and capacitor bank placement to mitigate the DPV penetration effect in the distribution low voltage feeder. A domestic distribution load of Irbid-Jordan is selected to perform this study. Based on the downstream 0.4 kV data, a feeder profile is monitored as live data via multichannel meters. The operating characteristic of the DPV system, such as losses, voltage profile, variation in voltage, and reliability, depend on the sizing and siting of the DPV. The size and siting of DPV are optimized using iterative techniques. The size of the DPV varies from 10 kW to 100 kW, and its location varies from 100 m to 1000 m. Different scenarios are simulated before and after PV penetration, installing an AVR and a low-voltage capacitor bank. Results show that an optimum installation is at a 7 kW rating and 700 m far from the main feeder with a loss reduction is (8167 kWh, 25.96%, 571.7 JD). A maximum permissible generation curve is obtained for this wheeling system. Thus, the optimum installation of DPV reduces the system losses and enhances the system's reliability and voltage profile. The system is modeled and studied via CYME software.

Short-Term Net Load Forecasting for Regions with Distributed Photovoltaic Systems Based on Feature Reconstruction

Short-term load forecasting is the guarantee for the safe, stable, and economical operation of power systems. Deep learning methods have been proven effective in obtaining accurate forecasting results. However, in recent years, the large-scale integration of distributed photovoltaic systems (DPVS) has caused changes in load curve fluctuations. Current deep learning models generally train with historical load series and load-related meteorological data series as input features, which limits the model’s ability to recognize the load fluctuations caused by DPVS. In order to further improve the accuracy of load forecasting models, this paper proposes an input feature reconstruction method based on the maximum information coefficient (MIC). Firstly, the load curves with DPVS are classified by Gaussian mixture model (GMM) clustering. Then, considering the coupling relationship between the load and input features at different times, the load data and input features are reordered. Finally, the MIC between different features and loads at different times is calculated to select the relevant features at those different times and construct new input features. The case analysis shows that the feature reconstruction strategy proposed in this paper effectively improves the prediction performance of deep neural networks.

A regional solar forecasting approach using generative adversarial networks with solar irradiance maps

The intermittent and stochastic nature of solar resource hinders the integration of solar energy into modern power system. Solar forecasting has become an important tool for better photovoltaic (PV) power integration, effective market design, and reliable grid operation. Nevertheless, most existing solar forecasting methods are dedicated to improving forecasting accuracy at site-level (e.g. for individual PV power plants) regardless of the impacts caused by the accumulated penetration of distributed PV systems. To tackle with this issue, this article proposes a novel generative approach for regional solar forecasting considering an entire geographical region of a flexible spatial scale. Specifically, we create solar irradiance maps (SIMs) for solar forecasting for the first time by using spatial Kriging interpolation with satellite-derived solar irradiance data. The sequential SIMs provide a comprehensive view of how solar intensity varies over time and are further used as the inputs for a multi-scale generative adversarial network (GAN) to predict the next-step SIMs. The generated SIM frames can be further transformed into PV power output through a irradiance-to-power model. A case study is conducted in a 24 × 24 km area of Brisbane to validate the proposed method by predicting of both solar irradiance and the output of behind-the-meter (BTM) PV systems at unobserved locations. The approach demonstrates comparable accuracy in terms of solar irradiance forecasting and better predictions in PV power generation compared to the conventional forecasting models with a highest average forecasting skill of 10.93±2.35% for all BTM PV systems. Thus, it can be potentially used to assist solar energy assessment and power system control in a highly-penetrated region.

Cloud-edge collaborated dust deposition degree monitoring for distributed photovoltaic systems

After installation, the long-term efficient operation dominates the profitability of photovoltaic (PV) generation systems. Unlike large-scale PV plants, distributed PV systems are relatively dispersed, and belong to different owners, whose main obstacle for maximizing the profit is the lack of professional maintenance. This paper therefore proposes a cloud-edge collaborated dust deposition degree monitoring scheme for distributed PV systems without employing additional equipment, sensors or meteorological data, which just assumes the operational and historical data of all distributed PV systems in the same area to give the guidance whether the distributed PV system needs cleaning. In implementation, temporal and interactive models are established based on the operation characteristics of distributed PV systems, whose overall classification accuracy could reach more than 98%. In addition, in order to improve the adaptivity of monitoring scheme, this paper proposes a data-based random grouping method, which avoids the model mismatch caused by the addition or withdrawal of PV arrays. Finally, experimental verifications are carried out to prove the effectiveness of the presented scheme.© 2017 Elsevier Inc. All rights reserved.

GIScience can facilitate the development of solar cities for energy transition

The energy transition is increasingly being discussed and implemented to cope with the growing environmental crisis. However, great challenges remain for effectively harvesting and utilizing solar energy in cities related to time and location-dependant supply and demand, which needs more accurate forecasting- and an in-depth understanding of the electricity production and dynamic balancing of the flexible energy supplies concerning the electricity market. To tackle this problem, this article discusses the development of solar cities over the past few decades and proposes a refined and enriched concept of a sustainable solar city with six integrated modules, namely, land surface solar irradiation, three-dimensional (3D) urban surfaces, spatiotemporal solar distribution on 3D urban surfaces, solar photovoltaic (PV) planning, solar PV penetration into different urban systems, and the consequent socio-economic and environmental impacts. In this context, Geographical Information Science (GIScience) demonstrates its potent capability in building the conceptualized solar city with a dynamic balance between power supply and demand over time and space, which includes the production of multi-sourced spatiotemporal big data, the development of spatiotemporal data modelling, analysing and optimization, and geo-visualization. To facilitate the development of such a solar city, this article from the GIScience perspective discusses the achievements and challenges of (i) the development of spatiotemporal big data used for solar farming, (ii) the estimation of solar PV potential on 3D urban surfaces, (iii) the penetration of distributed PV systems in digital cities that contains the effects of urban morphology on solar accessibility, optimization of PV systems for dynamic balancing between supply and demand, and PV penetration represented by the solar charging of urban mobility, and (iv) the interaction between PV systems and urban thermal environment. We suggest that GIScience is the foundation, while further development of GIS models is required to achieve the proposed sustainable solar city.

Distribution network expansion planning considering a distributed hydrogen-thermal storage system based on photovoltaic development of the Whole County of China

The large-scale access of a substantial proportion of the distributed photovoltaic (PV) power sources has introduced considerable source-side randomness and volatility to the distribution network in the development of PV power generation in the whole county of China. This paper proposes a cooling-heat-electric multi-energy coupled power distribution network expansion bi-level planning model to reduce the influence of uncertainty and improve the PV consumption rate (PVCR). It is based on the distributed hydrogen-thermal storage system (DHTSS) in a high-proportion PV scenario. First, an irradiation-load-temperature multi-grid joint scenario generation model is constructed based on each meteorological cluster to effectively describe the uncertainty of PV power generation and multi-energy consumption. Subsequently, a refined distributed PV system physical model chain is constructed to address the low accuracy of the traditional PV output model in the high PV output (HPVO) scenarios. Lastly, considering the power supply reliability objective of the low-probability with high-load (LPHL) scenarios, a multi-objective bi-level expansion planning model of the distribution network is constructed to accurately determine the capacity of each equipment in DHTSS, the distribution lines, and low-voltage transformers to be expanded in the distribution network.

Adaptive power system frequency support from distributed photovoltaic systems

The integration of converter-based renewable energy resources in a power system leads to reduced inertia, creating a multitude of challenges relating to stability and reliability. On the positive side, the faster response of converter-based renewable energy resources to frequency disturbances, compared to the conventional synchronous-based generators, reduces the required minimum level of inertia in future low-inertia power systems. Accordingly, grid support from distributed photovoltaic (DPV) systems is one of the emerging solutions to overcome the challenges of these systems. This paper demonstrates how adaptive power system frequency support, which modifies the dynamic of frequency support in DPV systems according to the available level of power system inertia, improves overall system operation. In this way, for lower values of power system inertia, a higher amount of power reserve is maintained across DPV systems. Additionally, a faster frequency–Watt response is implemented to provide a larger amount of grid support under frequency disturbances. Simulation results on a composite load model of distribution feeder show that applying for adaptive frequency support from DPV systems improves the frequency nadir during under-frequency events. Experimental results show the effectiveness of the proposed approach in providing a faster dynamic response and higher amount of power support from DPV systems under low inertia conditions.

ACGL-TR: A deep learning model for spatio-temporal short-term irradiance forecast

With the vigorous development of renewable energy, the installed capacity of photovoltaic (PV) power plants continuously expands. For distributed PV systems, spatio-temporal short-term solar irradiance forecasting can give forecasts for multiple sites simultaneously and help improve the generation of the PV power. However, it is difficult to explore appropriate spatio-temporal relationship for high-dimensional and long-historical data. Thus, an Attention Graph Convolution Long short term memory neural network with Tensor Regression (AGCL-TR) is proposed. Firstly, the adaptive adjacent matrices, which represents the relationship among PV sites, are obtained directly from the encoded feature of the history meteorological data of multiple PV sites by self-attention mechanism. Secondly, graph feature along with original data are handled by AGCL to obtain spatio-temporal feature. Thirdly, a TR network is used to decode the higher-order spatio-temporal feature into next step irradiance forecasts for each PV site. The proposed method is validated on an open access dataset, the National Solar Radiation Database (NSRDB), with eight sites randomly selected in Nevada, North America. The experiment demonstrates that the proposed method outperforms the existing spatio-temporal prediction methods in each site, with an improvement of RMSE of 11.9%–19.8%. The proposed method can effectively extract and preserve the spatio-temporal features of high-dimensional data, which can improve the prediction performance in distributed PV systems.

Centralized controlling of distributed PV systems using cloud and IoT technologies

Usage of electrical energy obtained from renewable sources is rapidly increasing. Distributed solar systems will be widely used. The photovoltaic (PV) systems can be used to produce active and reactive power or to compensate reactive power. This paper proposes a solution for monitoring and management of distributed PV systems from the integrated center. The main parts of the system are a cloud infrastructure at the Data Center and Internet of Things (IoT) devices at distributed sites. Also, networks that are used for communication between main parts are an important piece of the proposed solution. While IoT devices continuously send information about electrical parameters of the system and environmental conditions, the inverter, as a part of the PV system, can be controlled by influencing the Maximum Power Point Tracking (MPPT) algorithm operation and inverter functionality.

Distributed Nodal Voltage Regulation Method for Low-Voltage Distribution Networks by Sharing PV System Reactive Power

With the intensive integration of photovoltaic (PV) sources into the low-voltage distribution networks (LVDN), the nodal voltage limit violations and fluctuation problem cause concerns on the safety operation of a power system. The intermittent, stochastic, and fluctuating characteristics of PV output power leads to the frequent and fast fluctuation of nodal voltages. To address the voltage limit violation and fluctuation problem, this paper proposes a distributed nodal voltage regulation method based on photovoltaic reactive power and on-load tap changer transformers (OLTC). Using the local Q/V (Volt/Var) feedback controller derived from the grid sensitivity matrix, the voltage magnitude information is adopted to adjust the output of PV systems. Moreover, in order to share the burden of voltage regulation among distributed PV systems, a weighted distributed reactive power sharing algorithm is designed to achieve the voltage regulation according to the rated reactive power. Theoretical analysis is provided to show the convergence of the proposed algorithm. Additionally, the coordination strategy for distributed PV systems and OLTC is provided to reduce the reactive power outputs of PV systems. Five simulation case studies are designed to show the effectiveness of the proposed voltage regulation strategy, where the voltage regulation and proportional reactive power sharing can be achieved simultaneously.

Flexible Active Power Control of Distributed Photovoltaic Systems With Integrated Battery Using Series Converter Configurations

Flexible active power control (FAPC) is becoming mandatory for PV systems, which is to limit/reserve the PV power below certain constraints as commanded, including the power ramp-rate control (PRRC), power limiting control (PLC), and power reserve control (PRC). In practice, energy storage (ES) such as batteries can be adopted to reduce the PV energy discarding in such cases. On the other hand, concerning the system overall cost, single-stage series power converter configurations are becoming attractive. Such configurations bring more flexibilities by integrating PV systems and batteries. However, the implementation of FAPC functions in series power converter configurations has not been systematically investigated. To fill this gap, the PRRC, PLC, and PRC strategies for series-PV-battery systems are developed in this article. With the proposed strategies, the power ramp-rate/limiting/reserve constraints are maintained by the coordinated control of individual converters. The reserved power is then distributed among all converters depending on the available power of individual PV converters, battery power, and state-of-charge (SoC) conditions. Experimental tests performed on a 1.6-kW system have validated the effectiveness of the proposed solution.

Power Loss Analysis and Suggestions for Efficiency Improvement of Roof Distributed Photovoltaic System

With the gradual depletion of traditional fossil energy and the increasingly prominent environmental problems caused by it, China has proposed carbon peaking and carbon neutrality goals to promote the transformation of the energy structure. Solar energy is one of the important renewable energy sources, and roof-distributed photovoltaic power generation technology has a broad market prospect. Given the efficiency analysis of the roof-distributed photovoltaic power generation system, this paper first establishes an analysis model of the roof-distributed photovoltaic power generation system, analyzes the factors affecting the power loss of each link in detail, and further clarifies the distribution characteristics of the power loss of the system through simulation. Finally, some suggestions are put forward for the efficiency promotion of the roof-distributed photovoltaic power generation system.