Uncertainty Of Photovoltaic Generation Research Articles

Residential net load interval prediction based on stacking ensemble learning

In response to the high uncertainty associated with residential net load due to the coupling of distributed photovoltaic generation and user demand, this paper proposed a novel cluster-based stacking ensemble learning model for net load interval prediction. Firstly, the k-means algorithm is employed to discover the similarity in user electricity consumption patterns. Then, a RIME optimization algorithm with local enhancement (LRIME) is developed to optimize the parameters and weights of the base learners in stacking ensemble learning. Subsequently, base learners with strong predictive capabilities and significant diversity are chosen as the first-layer predictive models, extreme learning machine (ELM) is utilized as the second-layer predictive model, ultimately resulting in the proposed stacking ensemble learning prediction model. And utilizing the bootstrap method to fit the volatility of point predictions, different prediction intervals are obtained at varying confidence levels, aiming to quantify the integrated uncertainty in photovoltaic generation and load. Testing on the open Ausgrid electricity load data in Australia provided robust validation of the proposed method's effectiveness. In comparison with other outstanding prediction models, the proposed ensemble model can effectively capture the uncertainty in integrating photovoltaic generation and user load.

Quantification of Uncertainty Cost Functions for Controllable Solar Power Modeling

Navigating the secheduling of generation resources of energy in power systems marked by a significant presence of renewable generation involves intricate optimization challenges. The conventional tools for resolving such challenges include programming techniques and heuristic approaches, both contingent upon a precisely articulated target function for optimization. Traditional optimization tools rely on precisely defined target functions, but the evolving landscape of power systems introduces complexity, especially with unpredictable behaviors of renewable sources. The research specifically quantifies penalty costs associated with photovoltaic (PV) generators, employing probabilistic methods for a robust mathematical analysis. The developed analytical model enhances adaptability in economic dispatch problems, considering uncertainty in decision-making. Validation using Monte Carlo simulation emphasizes uncertainty in PV generation and highlights the advantages of the proposed analytic model. The quadratic form of the model aligns coherently with simulation outcomes, contributing significantly to understanding uncertainty quantification in solar power modeling. The research aims to refine controllable solar power models, establish robust uncertainty cost functions, and improve the accuracy of economic dispatch strategies. Ultimately, this work promotes the seamless integration of solar energy into diverse and dynamic energy grids.

Distributionally robust PV planning and curtailment considering cyber attacks on electric vehicle charging under PV/load uncertainties

A manipulated charging behavior of electric vehicles (EVs) due to an adversary along with the uncertain photovoltaic (PV) generation outputs and loads may lead to unstable power distribution system operations with voltage and current violations. To resolve this issue, this paper proposes an optimization framework where the following two types of uncertainties are addressed: (i) the natural uncertainties of PV generation outputs/loads and (ii) artificial uncertainties of load altering attacks (LAAs) on EV charging stations (EVCSs) via the manipulation of EV charging control signals. The proposed framework is formulated as a Wasserstein metric-integrated distributionally robust optimization (DRO)-based Volt/VAR optimization (VVO) problem. The proposed DRO-based VVO framework combined with PV planning and curtailment aims to minimize substation energy and voltage imbalance along with the complete removal of the constraint violations while handling uncertain PV generation outputs/loads and LAAs. To use off-the-shelf optimization solvers, tractable reformulation of the chance constraints of the voltage, current, and curtailed PV real power of the original DRO problem is provided. Numerical examples tested over IEEE 13-bus and 37-bus systems with PV systems and EVCSs show the efficiency of the proposed DRO framework in terms of substation energy, voltage imbalance, and PV planning/curtailment cost under stochastic LAAs.

A Robust Conic Programming Approximation to Design an EMS in Monopolar DC Networks with a High Penetration of PV Plants

This research addresses the problem regarding the efficient operation of photovoltaic (PV) plants in monopolar direct current (DC) distribution networks from a perspective of convex optimization. PV plant operation is formulated as a nonlinear programming (NLP) problem while considering two single-objective functions: the minimization of the expected daily energy losses and the reduction in the expected CO2 emissions at the terminals of conventional generation systems. The NLP model that represents the energy management system (EMS) design is transformed into a convex optimization problem via the second-order cone equivalent of the product between two positive variables. The main contribution of this research is that it considers the uncertain nature of solar generation and expected demand curves through robust convex optimization. Numerical results in the monopolar DC version of the IEEE 33-bus grid demonstrate the effectiveness and robustness of the proposed second-order cone programming model in defining an EMS for a monopolar DC distribution network. A comparative analysis with four different combinatorial optimizers is carried out, i.e., multiverse optimization (MVO), the salp swarm algorithm (SSA), the particle swarm optimizer (PSO), and the crow search algorithm (CSA). All this is achieved while including an iterative convex method (ICM). This analysis shows that the proposed robust model can find the global optimum for two single-objective functions. The daily energy losses are reduced by 44.0082% with respect to the benchmark case, while the CO2 emissions (kg) are reduced by 27.3771%. As for the inclusion of uncertainties, during daily operation, the energy losses increase by 22.8157%, 0.2023%, and 23.7893% with respect to the benchmark case when considering demand uncertainty, PV generation uncertainty, and both. Similarly, CO2 emissions increase by 11.1854%, 0.9102%, and 12.1198% with regard to the benchmark case. All simulations were carried out using the Mosek solver in the Yalmip tool of the MATLAB software.

Dynamic Optimal Power Dispatch in Unbalanced Distribution Networks with Single-Phase Solar PV Units and BESS

Battery energy storage systems (BESSs) are a promising solution for increasing efficiency and flexibility of distribution networks (DNs) with a significant penetration level of photovoltaic (PV) systems. There are various issues related to the optimal operation of DNs with integrated PV systems and BESS that need to be addressed to maximize DN performance. This paper deals with day-ahead optimal active–reactive power dispatching in unbalanced DNs with integrated single-phase PV generation and BESS. The objectives are the minimization of cost for electricity, energy losses in the DN, and voltage unbalance at three-phase load buses by optimal management of active and reactive power flows. To solve this highly constrained non-linear optimization problem, a hybrid particle swarm optimization with sigmoid-based acceleration coefficients (PSOS) and a chaotic gravitational search algorithm (CGSA)called the PSOS-CGSA algorithm is proposed. A scenario-based approach encompassing the Monte Carlo simulation (MCS) method with a simultaneous backward reduction algorithm is used for the probabilistic assessment of the uncertainty of PV generation and power of loads. The effectiveness of the proposed procedure is evaluated through aseries test cases in a modified IEEE 13-bus feeder. The simulation results show that the proposed approach enables a large reduction in daily costs for electricity, as well as a reduction in expected daily energy losses in the DN by 22% compared to the base case without BESS while ensuring that the phase voltage unbalance rate (PVUR) is below the maximum limit of 2% for all three-phase buses in the DN.

PV Inverter Reliability Constrained Volt/Var Control With Power Smoothing via a Convex-Concave Programming Method

Intensive use of photovoltaic (PV) inverter in the volt/var control (VVC) methods in active distribution networks can impair inverter reliability. This article proposes a PV inverter reliability-constrained (PiReCon-) VVC method with a power smoothing scheme under uncertainties. First, considering impacts on inverter reliability, new reliability constraints are developed with a power smoothing factor to constrict inverter apparent power variation. Second, a new VVC optimization model is proposed with the reliability constraints, which minimizes power losses by optimizing both inverter var output and PV curtailment. Uncertainties of PV generation and loads are fully considered and addressed via a stochastic optimization method. Third, this article develops a penalty convex-concave programming method to effectively tackle nonconvexity of the proposed optimization model. The proposed PiReCon-VVC method is tested on a 33-bus distribution network, and simulation results verify its high efficiency in both minimizing the power losses and enhancing the PV inverter reliability.

Economic and Low-Carbon-Oriented Distribution Network Planning Considering the Uncertainties of Photovoltaic Generation and Load Demand to Achieve Their Reliability

The integration of renewable resources with distribution networks (DNs) is an effective way to reduce carbon emissions in energy systems. In this paper, an economic and low-carbon-oriented optimal planning solution for the integration of photovoltaic generation (PV) and an energy storage system (ESS) in DNs is proposed. A convolutional neural network (CNN)-based prediction model is adopted to characterize the uncertainties of PV and load demand in advance. Then, taking the lowest total economic cost, the largest carbon emission reduction, and the highest system power supply reliability as the optimization objectives, the optimal distribution network planning model is constructed. The improved multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the optimization model, and the effectiveness of the proposed solution is confirmed through a comparative case study on the IEEE-33 bus system. Simulation results show that the proposed solution can better maintain the balance between economic cost and carbon emissions in DNs.

A Multi-Timescale Allocation Algorithm of Energy and Power for Demand Response in Smart Grids: A Stackelberg Game Approach

The proliferation of renewable generation brings challenges to the power supply-demand balance. To relieve the power fluctuations caused by photovoltaic (PV) generation variability, a multi-timescale allocation algorithm that considers the allocation of available energy and power is proposed. Contracted demand response energy (CDRE) refers to the regulation energy, which is specified in contracts in advance, that can be used to relieve power fluctuations. First, the capacity of CDRE and available regulation power (RP) provided by load aggregators (LAs) that aggregate different demand response resources (DRRs) are estimated. In hour-timescale, CDRE is allocated to maximize the control economy of all participants, where a sample average approximation-based Stackelberg game is proposed to optimize the behavior of each participant based on considering PV generation uncertainty. In minute-timescale, RP is allocated to smooth the power fluctuations and minimize the power deviations based on the allocated CDRE results. Simulation on a modified IEEE-24 bus system verifies the effectiveness of the proposed algorithm in terms of reducing the power supply-demand imbalance with maximum revenue.

Optimal generation scheduling and operating reserve management for PV generation using RNN-based forecasting models for stand-alone microgrids

Photovoltaic (PV) generation can drop sharply under reductions in solar irradiance due to cloud cover, resulting in adverse impacts on the performance of stand-alone microgrids. In addition, due to the stochastic nature of solar irradiance, it has remained challenging to forecast PV generation accurately. Therefore, a sufficient amount of operating reserve must be allocated for the variability and uncertainty of PV generation. However, excess operating reserve can decrease the economic efficiency of microgrids. This paper proposes an optimal generation scheduling and operating reserve management scheme for stand-alone PV-integrated microgrids, which comprises three core models. First, a two-stage recurrent neural network-based model is proposed for solar irradiance and cloud cover forecasting. Second, the operating reserve required for PV is managed more effectively based on weather conditions. Finally, an optimal generation scheduling model is applied based on the forecasting and operating reserve management models. The proposed scheme is applied to representative case studies to validate its advantages. The forecasting accuracy of the proposed model outperforms a conventional model. Under clear-sky conditions, the operating reserve for PV can be reduced down to 30% of PV output. Subsequently, the optimal operation scheduled by the proposed scheme can produce substantial savings of more than 5.5%.

Mixed Deep Reinforcement Learning Considering Discrete-continuous Hybrid Action Space for Smart Home Energy Management

This paper develops deep reinforcement learning (DRL) algorithms for optimizing the operation of home energy system which consists of photovoltaic (PV) panels, battery energy storage system, and household appliances. Model-free DRL algorithms can efficiently handle the difficulty of energy system modeling and uncertainty of PV generation. However, discrete-continuous hybrid action space of the considered home energy system challenges existing DRL algorithms for either discrete actions or continuous actions. Thus, a mixed deep reinforcement learning (MDRL) algorithm is proposed, which integrates deep Q-learning (DQL) algorithm and deep deterministic policy gradient (DDPG) algorithm. The DQL algorithm deals with discrete actions, while the DDPG algorithm handles continuous actions. The MDRL algorithm learns optimal strategy by trial-and-error interactions with the environment. However, unsafe actions, which violate system constraints, can give rise to great cost. To handle such problem, a safe-MDRL algorithm is further proposed. Simulation studies demonstrate that the proposed MDRL algorithm can efficiently handle the challenge from discrete-continuous hybrid action space for home energy management. The proposed MDRL algorithm reduces the operation cost while maintaining the human thermal comfort by comparing with benchmark algorithms on the test dataset. Moreover, the safe-MDRL algorithm greatly reduces the loss of thermal comfort in the learning stage by the proposed MDRL algorithm.

Comprehensive Analytical Expressions for Assessing and Maximizing Technical Benefits of Photovoltaics to Distribution Systems

The proliferation of photovoltaic (PV) can cause several operational problems in distribution systems. In this paper, comprehensive analytical expressions (CAEs) are proposed for maximizing the technical benefits of multiple PV units to distribution systems considering the uncertainty of PV generation and load profiles. Specifically, the proposed CAEs quantify and optimize the following five vital indices with multiple PV units: 1) active energy losses, 2) reactive losses, 3) voltage deviations, 4) line congestion margin, and 5) voltage stability index. The smart functions of the PV inverter (i.e., reactive power support and active power curtailment) are also incorporated in the CAEs, complying with the revised IEEE 1547:2018 standard. Further, various PV tracking options are considered, including fixed, one-axis, and two-axis trackers. Unlike existing approaches, the CAEs can simultaneously solve the optimal allocation problem of multiple PV units in a direct manner without needing optimization algorithms, iterative processes, or simplifying procedures. The calculated results reveal the high performance of the CAEs in terms of accuracy, flexibility and computational speed while providing further PV planning options. Moreover, CAEs are effectively utilized for two other applications with promising computational performance, i.e., rapid assessment of PV impacts with annual datasets and optimal centralized/decentralized inverter control.

Demand Response for Industrial Micro-Grid Considering Photovoltaic Power Uncertainty and Battery Operational Cost

An intelligent demand response (DR) program is developed for multi-energy industrial micro-grid consisting of manufacturing facilities, photovoltaic (PV) panels, and battery energy storage system (BESS). The proposed DR program tackles the practical challenges of components in the micro-grid including industrial process represented by a discrete manufacturing production model, uncertainty of PV generation, and operational cost of the BESS. The proposed DR program optimizes day-ahead production scheduling for manufacturing facilities and operation regime for the BESS in response to time of use electricity price and probabilistic forecasting of PV power. To capture the uncertainty of PV power, a data-driven PV power probabilistic forecasting model is developed and a copula-based approach is deployed for the sampling of temporally correlated scenarios of PV power over the scheduling horizon from probabilistic forecasts. The multi-energy management optimization problem is formulated as a scenario-based stochastic nonconvex mixed integer nonlinear programming (MINLP). A hybrid optimization method integrating the evolutionary algorithm and the branch-and-bound algorithm for mixed integer liner programming is proposed to solve the nonconvex MINLP. Simulation studies illustrate that the proposed DR program efficiently reduces the operational cost for manufacturing production and releases the stress of the main grid by making full use of flexibility of all the components in the micro-grid.

Short-Term Master-Slave Forecast Method for Distributed Photovoltaic Plants Based on the Spatial Correlation

With the large-scale integration of distributed photovoltaic (DPV) power plants, the uncertainty of photovoltaic generation is intensively influencing the secure operation of power systems. Improving the forecast capability of DPV plants has become an urgent problem to solve. However, most of the DPV plants are not able to make generation forecast on their own due to the constraints of the investment cost, data storage condition, and the influence of microscope environment. Therefore, this paper proposes a master-slave forecast method to predict the power of target plants without forecast ability based on the power of DPV plants with comprehensive forecast system and the spatial correlation between these two kinds of plants. First, a characteristics pattern library of DPV plants is established with K-means clustering algorithm considering the time difference. Next, the pattern most spatially correlated to the target plant is determined through online matching. The corresponding spatial correlation mapping relationship is obtained by numerical fitting using least squares support vector machine (LS-SVM), and the short-term generation forecast for target plants is achieved with the forecast of reference plants and mapping relationship. Simulation results demonstrate that the proposed method could improve the overall forecast accuracy by more than 52% for univariate prediction and by more than 22% for multivariate prediction and obtain short-term generation forecast for DPV or newly built DPV plants with low investment.

Two-Stage Robust Sizing and Operation Co-Optimization for Residential PV–Battery Systems Considering the Uncertainty of PV Generation and Load

This article presents a two-stage adaptive robust optimization (ARO) for optimal sizing and operation of residential solar photovoltaic (PV) systems coupled with battery units. Uncertainties of PV generation and load are modeled by user-defined bounded intervals through polyhedral uncertainty sets. The proposed model determines the optimal size of PV–battery system while minimizing operating costs under the worst-case realization of uncertainties. The ARO model is proposed as a trilevel min–max–min optimization problem. The outer min problem characterizes sizing variables as “here-and-now” decisions to be obtained prior to uncertainty realization. The inner max–min problem, however, determines the operation variables in place of “wait-and-see” decisions to be obtained after uncertainty realization. An iterative decomposition methodology is developed by means of the column-and-constraint technique to recast the trilevel problem into a single-level master problem (the outer min problem) and a bilevel subproblem (the inner max–min problem). The duality theory and the Big-M linearization technique are used to transform the bilevel subproblem into a solvable single-level max problem. The immunization of the model against uncertainties is justified by testing the obtained solutions against 36 500 trial uncertainty scenarios in a postevent analysis. The proposed postevent analysis also determines the optimum robustness level of the ARO model to avoid over/under conservative solutions.

Deep learning architecture for direct probability density prediction of small‐scale solar generation

With the increasing penetration of photovoltaic (PV) systems, the problems posed by the inherent intermittency of small-scale PVs are becoming more severe. To address this issue, it is critical to involve the uncertainty of PV generation in the look-ahead periods in a comprehensive framework. To this end, a direct deep learning architecture for probabilistic forecasting of solar generation is proposed in this paper. An end-to-end deep learning architecture as a novel mixture density network (MDN) is designed based on the combination of a convolutional neural network and a gated recurrent unit. Furthermore, a new loss function and training process based on adversarial training is proposed to enhance the accuracy in direct contracting of the probability density function. Then, several deep and shallow networks are implemented, and the results are compared with the proposed architecture. The effectiveness of the proposed MDN in providing complete statistical information is verified through comparison with Monte Carlo dropout, non-parametric kernel density estimation, and the proposed MDN without adversarial training.

Transactive Real-Time Electric Vehicle Charging Management for Commercial Buildings With PV On-Site Generation

In the future smart grids, it is important for prosumers to manage uncertainties from distributed renewable energy sources such as photovoltaic (PV) generation. As a type of distributed energy resource, electrical vehicles (EVs) are regarded as a promising solution to the problem. In this paper, a transactive real-time EV charging management scheme is proposed for the building energy management system (BEMS) of commercial buildings with PV on-site generation and EV charging services. Instead of direct EV charging control, the proposed EV charging management scheme applies a transactive energy concept-based approach to address real-time EV charging management. With the proposed scheme, the BEMS can schedule its net electricity exchange with the external grid under the uncertainties of PV generation and EV parking and maximize its profit in the real-time operation. Meanwhile, the EV owners need not provide the BEMS with further private information (such as future driving plans) but only their real-time charging requirements and preference setting of the response to the BEMS’s pricing signal in the proposed scheme. As such, the BEMS as a charging service provider only requires the minimal necessary information from EV owners. The EV owners’ charging requirements, preference setting of the response curves and their required reimbursements for the response are respected by the real-time charging management and their contributions to the demand response are reimbursed by the BEMS. Case studies with real world driving data from the Danish National Travel Survey were carried out to verify the proposed framework.

Robust Optimal Allocation of Decentralized Reactive Power Compensation in Three-Phase Four-Wire Low-Voltage Distribution Networks Considering the Uncertainty of Photovoltaic Generation

Due to the unbalanced three-phase loads, the single-phase distributed photovoltaic (PV) integration, the long feeders, and the heavy loads in a three-phase four-wire low voltage distribution network (LVDN), the voltage unbalance factor (VUF), the network loss and the voltage deviation are relatively high. Considering the uncertain fluctuation of the PV output and the load power, a robust optimal allocation of decentralized reactive power compensation (RPC) devices model for a three-phase four-wire LVDN is proposed. In this model, the uncertain variables are described as box uncertain sets, the three-phase simultaneous switching capacity and single-phase independent switching capacity of the RPC devices are taken as decision variables, and the objective is to minimize the total power loss of the LVDN under the extreme scenarios of uncertain variables. The bi-level optimization method is used to transform the robust optimization model with uncertain variables into bi-level deterministic optimization models, which could be solved alternately. The nonlinear programming solver IPOPT in the mature commercial software GAMS is adopted to solve the upper and lower deterministic optimization models to obtain a robust optimal allocation scheme of decentralized RPC devices. Finally, the simulation results for an actual LVDN show that the obtained decentralized RPC scheme can ensure that the voltage deviation and the VUF of each bus satisfied the secure operation requirement no matter how the PV output and load power changed within their own uncertain sets, and the network loss could be effectively reduced.

Probabilistic Optimal Dynamic Planning of Onsite Solar Generation for Residential Energy Hubs

Solar photovoltaic (PV) systems are becoming an indispensable source of energy for residential customers and are contributing to increase the sustainability of energy systems. However, practical methods that can aid customers to make informed decision on installing the PV systems considering their integration with the residential energy system have remained scarce. This paper proposes a probabilistic dynamic planning model for optimizing decisions on installing PV systems for a residential energy hub. In addition to the PV system, residential energy hub integrates combined heat and power (CHP) units and gas boilers to supply the heat and electrical demands. The proposed planning model minimizes the investment cost of PV systems along with the energy cost of energy hub that includes possible PV energy curtailment cost over the planning horizon. The proposed problem also integrates a heat storage system and responsiveness of the heat and electrical demands to the respective gas and electricity prices as additional flexibility to increase the benefits of PV systems for the customers. Two-point estimate method is used to model the uncertainty of PV generation. The proposed method is implemented on a test energy hub for a 10-year planning period to demonstrate features of the proposed method.

Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

The high penetration of photovoltaic (PV) is reshaping the electricity net-load curve and has a significant impact on power system operation and planning. The concept of duck curve is widely used to describe the timing imbalance between peak demand and PV generation. The traditional duck curve is deterministic and only shows a single extreme or typical scenario during a day. Thus, it cannot capture both the probability of that scenario and the uncertainty of PV generation and loads. These weaknesses limit the application of the duck curve on power system planning under high PV penetration. To address this issue, the novel concepts of probabilistic duck curve (PDC) and probabilistic ramp curve (PRC) are proposed to accurately model the uncertainty and variability of electricity net load and ramp under high PV penetration. An efficient method is presented for modeling PDC and PRC using kernel density estimation, copula function, and dependent discrete convolution. Several indices are designed to quantify the characteristics of the PDC and PRC. For the application, we demonstrate how the PDC and PRC will benefit flexible resource planning. Finally, an empirical study on the Qinghai provincial power system of China validates the effectiveness of the presented method. The results of PDC and PRC intuitively illustrate that the ramp demand and the valley of net load face considerable uncertainty under high PV penetration. The results of flexible resource planning indicate that retrofitting coal-fired units has remarkable performance on enhancing the power system flexibility in Qinghai. In average, reducing the minimal output of coal-fired units by 1 MW will increase PV accommodation by over 4 MWh each day.

Energy Management of a Smart Railway Station Considering Regenerative Braking and Stochastic Behaviour of ESS and PV Generation

The smart grid paradigm has provided great opportunities to decrease energy consumption and electricity bills of end users. Among a wide variety of end users, electrical railway systems with their huge installed power capacity should be considered as a vital option in order to avoid wasted energy, provided that an energy management system is utilized. In this study, a mixed-integer linear programming model of a railway station energy management (RSEM) system is formulated by a stochastic approach, aiming to utilize the emerged regenerative braking energy (RBE) during the braking mode in order to supply station loads. Furthermore, the proposed RSEM model is composed of an energy storage system (ESS), RBE utilization, photovoltaic (PV) generation units, and an external grid in this paper. The passengers' impact on RBE as well as the stochastic behaviour of the initial state-of-energy of ESS along with uncertainty of PV generation by the RSEM model are also evaluated. The model is tested under a bunch of case studies formed considering several combinations of the cases that an ESS or PV are available or not and using RBE is possible or not.