Scenario-based Stochastic Optimization Research Articles

Scenario-based stochastic optimization on the variability of solar and wind for component sizing of integrated energy systems

The inherent intermittency and variability of renewable energy sources present significant challenges to the optimal design and implementation of integrated energy systems (IES). This paper introduces a novel stochastic optimization model that integrates advanced scenario generation and clustering algorithm for renewable energy sources within a multi-objective, bi-level optimization framework. Specifically, the clearness index is employed to represent the stochastic distribution of solar radiation intensity by beta distribution, while wind speed uncertainty is modeled seasonally using the Weibull distribution. Monte Carlo sampling with synchronous back substitution is applied for scenario generation and reduction of solar radiation and wind speed. To address the multi-objective evaluation, the analytic hierarchy process is utilized, and the joint optimization is achieved by combining a region contraction algorithm with stochastic programming. The proposed methodology is validated on an IES featuring various heating devices, incorporating uncertainties in both wind and solar energy. The results indicate that the absorption heat pump-based scheme achieves superior energy-saving performance, achieving an energy rate of 0.4724. Additionally, the compression heat pump-based scheme exhibits excellent economic efficiency and environmental sustainability, with a cost of energy of 0.3639 and a renewable fraction of 0.5536.

Optimizing the bidding strategy and assessing profitability of over-install renewable plants equipped with battery energy storage systems

The over-installation of renewable energy sources (RES) can enhance the profits of RES producers by increasing the total exporting energy; however, RES power curtailments must be applied under over-production of RES plants to ensure their contracted maximum export capacity limits. Battery energy storage systems (BESSs) can be used to reduce the RES curtailments and therefore enhance the profits of producers. This work develops a bidding strategy as a scenario-based stochastic optimization scheme to maximize the expected profits of producers in electricity markets considering battery degradation and maximum export capacity constraints. Using the proposed scheme, a financial analysis is performed to assess the profitability for over-installing hybrid RES plants by calculating the net present value and internal rate of return of the project under different BESS costs. Simulation results, using real data from a wind and photovoltaic plant, demonstrate the effectiveness of the proposed stochastic scheme in enhancing the profit of producers compared to the corresponding deterministic scheme. The performed financial analysis, using the net present value metric, indicates that a maximum over-installation of 150%–170% and 160%–180% for the wind and photovoltaic plant, respectively, is profitable, while the usage of a BESS is profitable when its cost is under 200,000 €/MWh.

Dynamic pricing strategy for electric vehicle charging stations to distribute the congestion and maximize the revenue

Electric vehicle (EV) charging station (CS) congestion is highly dependent on the EV owner’s behavior and their selected CS as charging choice. A fixed pricing strategy causes some CSs to be congested with EVs waiting in line to charge, while there are some other CSs with available electric plugs, which adversely affects both charging station operator (CSO) revenue and EV users’ welfare. To solve this problem, this paper presents a dynamic pricing strategy aimed at conducting EVs from congested CSs to the uncongested ones through controlling the charging prices of CSs at different times. The problem is formulated as a scenario-based stochastic optimization with the objective of maximizing overall revenue of the CSO. Moreover, an attraction function model is developed to quantify the charging choice of the EV owners by considering the effective parameters of CSs in EV charging choice decisions. QGIS software is used in this work to formulate a realistic modeling for CS locations and EV routes to calculate the distances from EVs to CSs. Three scenarios are designed to evaluate the performance of the proposed framework and to compare the results with the fixed pricing approach. The results indicate that the proposed dynamic pricing strategy mitigates the congestion of CSs while facilitating an increased number of charged EVs up to 48% as well as increasing the overall revenue of the CSO.

Energy management system based on economic Flexi-reliable operation for the smart distribution network including integrated energy system of hydrogen storage and renewable sources

This paper presents the energy management of smart distribution network including integrated system of hydrogen storage and renewable sources. Objective is to assess economic, operation, flexibility, and reliability goals of the distribution system operator. Objective function minimizes costs of operation, reliability, energy losses, and network flexibility. Scheme is constrained by AC optimal power flow equations, network reliability limitation, and integrated system model. Scheme utilizes scenario-based stochastic optimization to model of uncertainties, such as load, parameters of renewable resources, energy prices, and the availability of network equipment. Novelty is modeling and performance evaluation of the proposed integrated system as a type of flexibility resource in the operation of distribution systems proportional to the economic, operation, flexibility, and reliability objectives of the network operator. Numerical results demonstrate energy management capabilities of the discussed integrated energy system, which contribute to enhancing economic and technical conditions of distribution network. The inclusion of hydrogen storage in the renewable integrated energy system has been found to enhance the economic viability, operational efficiency, and reliability of the distribution network by around 46.8%, 41%–53%, and 95%, respectively, when compared to network power flow. Aforementioned integrated system demonstrates 100% flexibility through the utilization of hydrogen storage.

Probabilistic spatiotemporal scenario generation method for dynamic optimal power flow in distribution networks

Due to the intricate intertwining of spatiotemporal characteristics and the substantial computational complexity caused by high dimensionality, the simultaneous consideration of both spatial and temporal correlations is a non-trivial problem in power system scheduling with variable renewable energy sources. This paper proposes a novel probabilistic spatiotemporal scenario generation (PSTSG) method for the dynamic optimal power flow problem in distribution networks, which generates probabilistic scenarios considering the spatial and temporal correlations among random variables simultaneously. First, static scenarios are generated by Latin hypercube sampling, and the probability of each static scenario is determined by copula-importance sampling theory, which is proposed to ensure the static scenarios yield the same probabilistic characteristics as the random variables. Next, a probability-based scenario reduction technique is implemented to retain effective scenarios and lower the computational burden. Then, multiple linear regression generalizes the static scenarios into dynamic ones with the same probabilities. Finally, a spatiotemporal scenario-based stochastic optimization is proposed for the dynamic optimal power flow problem, which considers uncertainties in variable renewable energy generation and aims to balance the output of controllable generators, renewable energy curtailment, and load shedding. Numerical simulations in a modified IEEE 33-node distribution network show that the proposed approach outperforms the existing methods that do not simultaneously consider spatial and temporal correlations in terms of computational efficiency and accuracy, proving that the proposed PSTSG method can efficiently capture the spatial and temporal correlation so as to make the optimal scheduling decision.

A hybrid heuristic-reinforcement learning-based real-time control model for residential behind-the-meter PV-battery systems

The behind-the-meter (BTM) energy management problem has recently attracted a lot of attention due to the increase in the number of residential photovoltaic (PV)-battery energy storage systems (BESSs). In this work, the use of deep reinforcement learning (DRL) combined with a novel heuristic model for real-time control of home batteries is investigated. The control problem is formulated as a finite Markov Decision Process with discrete time steps, where a proximal policy optimization (PPO) algorithm is employed to train the DRL agent with discrete action space. The agent is trained using real-world measured data to learn the policy for sequential charge/discharge tasks, aiming to minimize daily electricity costs. The battery power is calculated using an innovative heuristic model considering the agent's decision and the battery's available capacity, ensuring demand-supply balance through PV self-consumption and load demand shifting. The performance of the model is evaluated by comparing it to four RL agents and two benchmark models based on rule-based and scenario-based stochastic optimization strategies. The results confirm that the presented model outperforms its counterparts, offering €80.38 savings on electricity bills over 46 days of the test data set. This figure exceeds the savings of the rule-based and stochastic models by €15.64 and €19.38, respectively.

A low-carbon economic dispatch for integrated energy systems with CCUS considering multi-time-scale allocation of carbon allowance

The carbon allowance trading mechanism provides an economic basis to facilitate emission reductions for market participants. As a compliance mechanism, allowance-based emission control demands emitter to surrender the same amount of carbon allowances as it emits during the accounting period, the duration of which is often set to one year by the administrators. This requires emitters to determine the upper limit of annual emissions and allocate it to each day based on the current carbon price to minimize their overall operating costs over the longer carbon accounting period. This paper proposes a low-carbon economic dispatch for IES with CCUS considering multi-time-scale allocation of carbon allowance. In the upper level, a scenario-based stochastic optimization is adopted to decide the annual allowance and complete the allocation from year to month and then from month to day. The lower level is a Wasserstein ambiguity set-based two-stage distributionally robust optimization (TSDRO) model to find the optimal dispatch strategy of each day. The uncertainty from the long-term available renewable energy resources and user demands and from the short-term forecasting errors is both considered. Simulation results show that the proposed model can realize reasonable carbon allocation and decrease the annual operation costs.

Flexible and sustainable scheduling of electric power grids: A dynamic line and transformer rating based approach under uncertainty condition

Integration of renewable and sustainable energies into the electric power grids has affected planning and operation problems of the power system. Voltage and congestion as well as uncertainty issues are some challenges regarding this integration. Dynamic line and transformer ratings, known as DLR and DTR, are kinds of smart-grid technologies that can help alleviation of above-mentioned problems and perform a flexible scheduling for the power system. In this paper, the DLR and DTR have been simultaneously incorporated in optimal power flow (OPF) problem in wind-energy-integrated power systems considering the presence of uncertainties. The aim is to perform an optimal day-ahead scheduling of thermal and wind power units where the uncertainty of DLR and DTR as well as that of wind power generation are considered. The uncertainty scenarios are generated by Monte-Carlo method where k-means clustering algorithm is employed to reduce the number of scenarios within a scenario-based stochastic optimization. As the AC power flow and dynamic rating relations have non-convex nature, they have been convexified in order to formulate the optimization problem as a mixed-integer quadratically-constrained programming (MIQCP). The proposed approach is applied to IEEE-24-bus system in different experiments in GAMS environment. The simulations demonstrate efficiency of the conducted approach in reducing operating costs, minimizing load shedding cost, and maximum scheduling of wind power units as sustainable and clean energy resources.

Optimal planning of hybrid energy storage systems using curtailed renewable energy through deep reinforcement learning

Energy management systems are becoming increasingly important to utilize the continuously growing curtailed renewable energy. Promising energy storage systems, such as batteries and green hydrogen, should be employed to maximize the efficiency of energy stakeholders. However, optimal decision-making, i.e., planning the leveraging between different strategies, is confronted with the complexity and uncertainties of large-scale problems. A sophisticated deep reinforcement learning methodology with a policy-based algorithm is proposed to achieve real-time optimal energy storage systems planning under the curtailed renewable energy uncertainty. A quantitative performance comparison proved that the deep reinforcement learning agent outperforms the scenario-based stochastic optimization algorithm, even with a wide action and observation space. A robust performance, with maximizing net profit and a stable system, confirmed the uncertainty rejection capability of the deep reinforcement learning under a large uncertainty of the curtailed renewable energy. Action mapping was performed to visually assess the action the deep reinforcement learning agent took according to the state. The corresponding results confirmed that the deep reinforcement learning agent learns how the deterministic solution performs and demonstrates more than 90% profit accuracy compared to the solution.

Day-Ahead Distributionally Robust Optimization-Based Scheduling for Distribution Systems With Electric Vehicles

In this paper, a day-ahead optimal scheduling strategy for the DSO based on EV aggregation is proposed. Generally, the uncertain parameters of EVs, i.e., arrival and departure times as well as the charging demands, can be effectively modeled by a Gaussian mixture model (GMM) with historical charging records. The empirical data of net load error, i.e., mean values and covariance, can be obtained from historical data, while the explicit probability distribution function may not be fully known. Therefore, a distributionally robust optimization (DRO) model is formulated for the DSO to characterize the net load uncertainty. Then, an EV aggregation-based reservation capacity prearrangement method is proposed to specifically address the net load error. Next, with the reservation capacity from EVs, the DRO model is convexified by transforming into two subproblems with deterministic forms. Finally, simulation and comparison tests are conducted on the 33-bus distribution network to demonstrate that the proposed approach achieves a tradeoff between economic performance and computation efficiency compared with the scenario-based stochastic optimization method and achieves a tradeoff between operation costs and system reliability compared with the chance constraint method.

Three-stage coordinated operation of steel plant-based multi-energy microgrids considering carbon reduction

Steel production is one of the most energy-intensive industries on demand side. Highly distributed energy resource-penetrated multi-energy microgrids (MEMGs) with combined heat and power (CHP) units can supply both electricity and heat while the by-product coal gases during manufacturing can be reused for onsite power supply. However, there is a lack of coordination between steel production and MEMG operation, and the steelmaking process is not fully modelled. Thus, this paper proposes a three-stage coordinated operation method for steel plant-based MEMGs, aiming to minimize the total operating cost. In this method, the steel production is scheduled weekly-ahead to meet the production demand considering carbon emission reduction. Then, the CHP commitment and day-ahead energy transaction are optimized in a day-ahead stage, while the dispatchable device output and intraday energy transaction are determined hourly-ahead based on uncertainty realizations. Accordingly, the steel production is modelled as continuous and discontinuous processes in parallel or series. To tackle the uncertainty of renewable generation, a scenario-based stochastic optimization method is utilized. Moreover, different carbon prices are applied to investigate their effects on steel production. The results show that the proposed method can decrease the operating cost by 14.33% and 1.45% compared with the other two conventional methods.

Utilizing Aggregated Distributed Renewable Energy Sources With Control Coordination for Resilient Distribution System Restoration

Due to the energy transition process, distribution systems will feature a high penetration of distributed renewable energy sources (RESs). The multiple distributed generation can provide emergency power supply to critical loads against blackouts caused by natural disasters and malicious attacks. However, the uncertainty of RESs, the control mode variation of RESs together with energy storage systems (ESSs), and the interaction among distribution system operator (DSO) and RESs add increasing difficulties to load restoration decisions. This paper applies the coordination control strategy to enable RESs to regulate the frequency and voltage during restoration process. Then, distributed energy resource management systems (DERMSs) and its aggregation characteristic are studied in load restoration. Finally, a two-step scenario-based stochastic optimization with the DSO-DERMS interaction framework is formulated to utilize RESs for resilient distribution systems. At last, the proposed critical load restoration optimization method is validated on a modified IEEE 37 and 123 node test feeder to verify the effectiveness.

Multi-source coordinated stochastic restoration for SOP in distribution networks with a two-stage algorithm

After suffering from a grid blackout, distributed energy resources (DERs), such as local renewable energy and controllable distributed generators and energy storage can be used to restore loads enhancing the system’s resilience. In this study, a multi-source coordinated load restoration strategy was investigated for a distribution network with soft open points (SOPs). Here, the flexible regulation ability of the SOPs is fully utilized to improve the load restoration level while mitigating voltage deviations. Owing to the uncertainty, a scenario-based stochastic optimization approach was employed, and the load restoration problem was formulated as a mixed-integer nonlinear programming model. A computationally efficient solution algorithm was developed for the model using convex relaxation and linearization methods. The algorithm is organized into a two-stage structure, in which the energy storage system is dispatched in the first stage by solving a relaxed convex problem. In the second stage, an integer programming problem is calculated to acquire the outputs of both SOPs and power resources. A numerical test was conducted on both IEEE 33-bus and IEEE 123-bus systems to validate the effectiveness of the proposed strategy.

Design and optimization of an entirely hybrid renewable energy system (WT/PV/BW/HS/TES/EVPL) to supply electrical and thermal loads with considering uncertainties in generation and consumption

Renewable energy resources have gotten considerable attention in recent years owing to significant advancements in power electronics technologies, decreased cost of utilizing renewable resources, and increasing concerns about environmental pollutants, particularly in stand-alone applications. Utilizing entirely renewable resources to meet demand has numerous advantages, including lower energy prices, energy price stability, local accessibility, etc. The capability to apply a modified combination of the gray wolf optimization algorithm and the sine–cosine algorithm is evaluated to minimize the levelized cost of energy and the total annualized net present cost (comprising investment, replacement, decommissioning, and operation & maintenance costs) of the proposed system while complying with system constraints and demand requirements. The optimal power planning of a stand-alone hybrid entirely renewable system comprising wind turbines, PV systems, bio-waste units, and storage devices to supply electrical and thermal loads simultaneously was investigated in this paper. A parking lot for electric vehicles is also considered in non-smart and smart charging strategies. In addition, a redefined scenario-based stochastic optimization is utilized to consider uncertainties in electrical and thermal loads, EVs' parameters, and renewable energy resources. The proposed approach is implemented on a small system in Espoo, Finland. The results confirm its efficiency for economically and uninterrupted supplying electrical and thermal demands simultaneously in a stand-alone hybrid system with entirely renewable resources.

Economic scheduling of mobile energy storage in distribution networks based on equivalent reconfiguration method

Compared with traditional stationary energy storage system(SESS), mobile energy storage system(MESS) has power transfer ability in both spatial and temporal dimensions. Thus, it can provide greater flexibility in power system auxiliary services. To simplify and clarify the optimal scheduling problem, a novel “virtual switch” indicator is defined to describe the scheduling of MESS and an equivalent reconfiguration method is proposed by analogy with distribution network reconfiguration. Based on the method proposed, the dynamic economic scheduling of MESS in distribution networks(DNs) can be formulated as a scenario-based stochastic optimization problem, where the uncertainties of traffic flow and renewable energy output are considered by generating scenarios using Monte Carlo simulation. The objective function is to maximize the profit of distribution network operator. The time and cost of MESS scheduling are transformed into those of virtual switch switching in distribution network reconfiguration. Therefore, the operation scheduling problem of a MESS is equivalent to a distribution network reconfiguration problem with a SESS and several virtual switches. In this way, a grid-traffic network coupling problem is simplified to a pure distribution network problem, which provides a novel way to solve the MESS scheduling problems. Finally, simulation results on the IEEE 33-bus distribution system and simple traffic network verify the validity and feasibility of the method proposed.

Multi-objective risk-constrained optimal performance of hydrogen-based multi energy systems for future sustainable societies

Hydrogen is one of the leading energy sources under special consideration due to its sustainability and technological development. The main concept of integrated energy system is applied in this article. The goal is to maintain a coordination between hydrogen cycle where hydrogen is produced and converted with renewable energy (RE). Three energy storage for charging/discharging hydrogen, hot and cold water are employed enhance the energy efficiency. The demand-side energy system could rely on this combination that enables the increase in wind and solar energy utilization and uses it to generate hydrogen in future smart cities. This paper uses a scenario-based stochastic optimization to model the associated uncertainties. The epsilon-constraint and max-min fuzzy methods are used as multi-objective approach to satisfy environmental and economic goals, simultaneously. To analyze the associated risk imposed by multiple uncertain parameters, the downside risk constraint (DRC) is implemented to render several risk-averse strategies to the decision-maker based on various constraint level. The results show that the final solution in risk neutral strategy satisfies both emission and operation costs. The ultimate associated risk in conservative strategy will tend to zero at the 4.2% operation cost increment and 3% emission reduction.

Scenario-Based Stochastic Optimization for Energy and Flexibility Dispatch of a Microgrid

Energy storage is one of the most important components of microgrids with non-dispatchable generators and can offer both energy and flexibility services when the microgrid operates in grid-connected mode. This paper proposes a scenario-based stochastic optimization model that can be used to determine the energy and flexibility dispatch of a residential microgrid with solar and stationary battery systems. The objective of the model is to minimize the expected energy and peak power cost as well as the battery aging cost, while maximizing the expected revenue from flexibility. The formulated stochastic optimization problem is solved in rolling horizon with the uncertainty model being dynamically updated to consider the most recent forecast profiles for solar power and electricity demand. The benefits of the proposed approach were demonstrated by simulating the daily operation of a real building. The results showed that the estimated flexibility was successfully dispatched yielding an economic value of at least 7% of the operation cost of the building microgrid. The model can be used by flexibility providers to assess their flexibility and design a bidding strategy as well as by system operators to design incentives for flexibility providers.

Optimal design of low-carbon energy systems towards sustainable cities under climate change scenarios

The design of low-carbon energy systems towards sustainable cities requires correctly quantifying uncertainties in future climate variations, since they affect both energy demand of urban cities and energy system performance. However, quantifying climate uncertainties is challenging due to the stochastic and unpredictable nature of future climate events. This paper develops a novel and general framework to quantify climate uncertainties for urban energy system design using scenario-based stochastic optimization. Climate models are coupled with building performance simulation to generate scenarios for uncertainty quantification and energy system optimization. We apply this optimization framework to US cities for demonstration. We find that climate uncertainties in renewable generation and energy demand can lead to significant performance differences in urban energy systems. Neglecting climate uncertainties results in an optimistic energy system; however, it is unable to provide stable power supply to urban cities. Moreover, we observe that maintaining a certain degree of grid integration is beneficial for urban energy systems and can alleviate the economic burden of urban cities. Finally, we provide some valuable insights on urban energy systems for system designer and policymakers. The designers should fully consider uncertainties associated with various climate events during system design and deploy proper backup systems in case of contingency. The policymakers should thoroughly account for climate uncertainties and their resulting costs when stipulating energy policies for promoting low-carbon energy systems. Both designers and policymakers need to cooperate together and coordinate their actions on urban energy systems towards sustainable cities.

Stochastic medical tourism problem with variable residence time considering gravity function

Medical tourism is a recent term in healthcare logistics referring to travel of patients to receive health services and spending leisure time in a destination country. This transferring of patients leads to access high-quality health services which are cheaper than the original country of patients. During this travel, passengers who are the patients from another country, have this opportunity for complimentary entertainment packages (e.g., pleasure tours) in the aftercare period. As far as we know, the term of medical tourism is rarely studied in healthcare logistics and such services are highly important for developing countries. Such facts motivate us to develop a practical optimization model for the Medical Tour Centers (MTCs) for allocation of patients to hospitals in proper time and creation of memorable aftercare time for them. In this regard, the main aim of the proposed model is to maximize the total profit of MTCs through optimal allocation of patients to hospitals while considering an aftercare tour for the passengers. To make the proposed model more realistic, the optimal residence time in attractive places is simulated by a time-dependent gravity function. To address the uncertainty of medical tourism problem, a scenario-based two-stage stochastic optimization approach is extended to encounter different sources of uncertainty existing in surgical success, medical time, restoration restrictions, and the attraction of tourist places. Another novelty of this work is to propose an innovative hybrid meta-heuristic for large-scale instances, which is a combination of Progressive Hedging Algorithm (PHA) and Genetic Algorithm (GA). The model is analyzed by different test problems for small, medium, and large-scale instances where the hybrid meta-heuristic algorithm could solve them with an average gap of 3.4% in comparison with the commercial solver. The results revealed the importance of tourist opinion and public preferences in medical and pleasure tours, respectively, to improve the economic growth in this sector in developing countries.

Dynamic MGs-based load restoration for resilient urban power distribution systems considering intermittent RESs and droop control

The large amount of small-scale distributed generation can provide emergency power supply to critical loads during blackouts and help build resilient urban power distribution systems. However, the uncertainty from intermittent renewable energy sources (RESs) and loads complicates the modeling and challenges the operation of resilient distribution systems. This paper first proposes a novel offline probabilistic modeling and online updating method to characterize the time-varying uncertainty of multiple RESs power outputs and loads. Then, a scenario-based stochastic optimization model is proposed for load restoration, which incorporates the new concept of dynamic microgrids (MGs) and also takes into account the effects of droop control and frequency regulation. The case study to the modified 37 and 123 node test feeders shows that the restoration with droop control and frequency regulation could simultaneously consider the importance and frequency requirement of loads, and the proposed uncertainty modeling and updating method as well as the dynamic MGs could increase the overall system resilience, where the served ratio of critical loads would be particularly improved. All of these factors should be considered in real applications for a more realistic and feasible decision of load restoration strategy.