Scenario Reduction Algorithm Research Articles

Mixed-integer second-order cone programming method for active distribution network

Developing a novel type of power system is an important means of achieving the “dual carbon” goals of achieving peak carbon emissions and carbon neutrality in the near future. Given that the distribution network has access to a wide range of distributed and flexible resources, reasonably controlling large-scale and adjustable resources is a critical factor influencing the safe and stable operation of the active distribution network (ADN). In light of this, the authors of this study propose a mixed-integer second-order cone programming method for an active distribution network by considering the collaboration between distributed, flexible resources. First, Monte Carlo sampling is used to simulate the charging load of electric vehicles (EVs), and the auto regressive moving average (ARMA) and the scenario reduction algorithms (SRA) based on probability distance are used to generate scenarios of the outputs of distributed generation (DG). Second, we establish an economical, low-carbon model to optimize the operation of the active distribution network to reduce its operating costs and carbon emissions by considering the adjustable characteristics of the distributed and flexible resources, such as on-load tap changer (OLTC), devices for reactive power compensation, and EVs and electric energy storage equipment (EES). Then, the proposed model is transformed into a mixed-integer second-order cone programming (SOCP) model with a convex feasible domain by using second-order cone relaxation (SOCR), and is solved by using the CPLEX commercial solver. Finally, we performed an arithmetic analysis on the improved IEEE 33-node power distribution system, the results show that ADN’s day-to-day operating costs were reduced by 47.9% year-on-year, and carbon emissions were reduced by 75.2% year-on-year. The method proposed in this paper has significant effects in reducing the operating cost and carbon emissions of ADNs, as well as reducing the amplitude of ADN node voltages and branch currents.

Optimal stochastic energy management of electrical railway systems considering renewable energy resources' uncertainties and interactions with utility grid

AbstractSeveral studies have been reported for optimal operation of electrical railway systems (ERSs). However, the stochastic energy management of ERSs, including renewable energy resources (RERs), has received less attention. The RERs’ uncertainties might affect the ERSs. On the other hand, the calculation time of the Monte Carlo simulation (MCS)‐based approaches is an essential challenge, which should be solved, particularly in real‐time decisions and recursive optimization problems. Thus, it is crucial to study the ERSs' stochastic behaviors and uncertainties, including RERs. This paper tries to overcome the discussed concerns and challenges by proposing a novel ERS’s optimal stochastic energy management using clustering algorithms. In this paper, the backward scenario reduction algorithm has been used. In addition, regenerative braking energy (RBE) and energy management systems (ESSs) have been studied. Studying the impacts of changes in the number of passengers on the optimized operation of ERSs and investigating the interaction between the utility grid and the ERS are other contributions of this research. The proposed method is applied to an actual test system of Tehran Urban and Suburban Railway Operation Company (TUSROC). Test results are validated by comparing with available MCS‐based methods. Simulation results illustrate the accuracy and computation time advantages of the proposed method. Simulation results illustrate that <0.6% inaccuracy appears in the proposed method, while it would be 500 times faster than MCS‐based ones. The comparative test results show the advantages of the introduced method.

Demand Management for Resilience Enhancement of Integrated Energy Distribution System against Natural Disasters

For energy sustainability, the integrated energy distribution system (IEDS) is an efficient and clean energy system, which is based on the coordinated operation of a power distribution network, a gas distribution network and a district heating system. In this paper, considering the damage of natural disasters to IEDS, a demand management strategy is proposed to improve resilience of IEDS and ensure stable operation, which is divided into three stages. In the first stage, the electricity, natural gas and thermal energy are co-optimized in the simulating fault state to develop the importance ranking of transmission lines and gas pipelines. In the second stage, the natural disasters are classified as surface natural disasters and geological natural disasters. According to the types of natural disasters, the demand management strategy includes semi-emergency demand management scheme and full-emergency demand management scheme in the electrical resilience mode and the integrated resilience mode, respectively. In the third stage, the non-sequential Monte-Carlo simulation and scenario reduction algorithm are applied to describe potential natural disaster scenarios. According to the importance ranking of transmission lines and gas pipelines, a demand management strategy is formulated. Finally, the proposed strategy is applied on an IEEE 33-bus power system and a 19-node natural gas system. Its effectiveness is verified by numerical case studies.

Risk and resilience-based optimal post-disruption restoration for critical infrastructures under uncertainty

Post-disruption restoration of critical infrastructures (CIs) often faces uncertainties associated with the required repair tasks and the related transportation network. However, such challenges are often overlooked in most studies on the improvement of CI resilience. In this paper, two-stage risk-averse and risk-neutral stochastic optimization models are proposed to schedule repair activities for a disrupted CI network with the objective of maximizing system resilience. Both models are developed based on a scenario-based optimization technique that accounts for the uncertainties of the repair time and the travel time spent on the underlying transportation network. Given the large number of uncertainty realizations associated with post-disruption restoration tasks, an improved fast forward algorithm based on a wait-and-see solution methodology is provided to reduce the number of chosen scenarios, which results in the desired probabilistic performance metrics. To assess the risks associated with post-disruption scheduling plans, a conditional value-at-risk (CVaR) metric is incorporated into the optimization models through a scenario reduction algorithm. The proposed restoration framework is applied to the French RTE electric power network with a DC power flow procedure, and the results demonstrate the added value of using the stochastic optimization models incorporating the travel times related to repair activities. It is essential that risk-averse decision-making under uncertainty largely impacts the optimum schedule and the expected resilience, especially in the worst-case scenarios.

Data Driven Stochastic Energy Management for Isolated Microgrids Based on Generative Adversarial Networks Considering Reactive Power Capabilities of Distributed Energy Resources and Reactive Power Costs

This paper proposes a two-stage stochastic energy management (EM) in an isolated microgrid (MG) to decide for the day-ahead optimal dispatch. The dispatch aims to effectively manage the MG power sources, including intermittent renewable energy sources (RESs), battery energy storage systems (BESSs), and diesel generators such that the expected operation costs, reactive power costs, spinning reserve, and load shedding are minimized. The Generative Adversarial Networks (GANs) is utilized in this paper as a data driven scenario generation method to model the uncertainties in the output power of the RESs to be used in the stochastic programming formulation. Then, the fast forward scenario reduction algorithm is used to reduce the number of scenarios with the help of SCENRED/GAMS software. Usually, fuel consumption costs of diesel generators are considered to be dependent on active power generation only. However, neglecting the related reactive power costs might result in increased operation costs and deviations in the dispatches from the optimal solutions. Hence, this paper co-optimizes the costs related to both active and reactive powers of diesel generators. In addition, this study considers the reactive power capability of inverter-interfaced distributed energy resources (DERs). Moreover, the detailed models for the different resources are presented, especially for diesel generators where the actual capability curves are used instead of the widely used box constraints. The problem is formulated as a nonlinear programming problem in the General Algebraic Modeling System (GAMS) software and is solved by the CONOPT solver.

Stochastic optimization model for coordinated operation of natural gas and electricity networks

Renewable energy sources will anticipate significantly in the future energy system paradigm due to their low cost of operation and low pollution. Considering the renewable generation (e.g., wind) intermittency, flexible gas-fired power plants will continue to play their essential role as the main linkage of natural gas and electricity networks, and hence coordinated operation of these networks is beneficial. Furthermore, uncertainty is always found in gas demand prediction, electricity demand prediction, and output power of wind generation. Therefore, in this paper, a two-stage stochastic model for operation of natural gas and electricity networks is implemented. In order to model uncertainty in these networks, Monte Carlo simulation is applied to generate scenarios representing the uncertain parameters. Afterwards, a scenario reduction algorithm based on distances between the scenarios is applied. Stochastic and deterministic models for natural gas and electricity networks are optimized and compared considering integrated and iterative operation strategies. Furthermore, the value of flexibility options (i.e., electricity storage systems) in dealing with uncertainty is quantified. A case study is presented based on a high pressure 15-node gas system and the IEEE 24-bus reliability test system to validate the applicability of the proposed approach. The results demonstrate that applying the stochastic model of gas and electricity networks as well as considering integrated operation strategy in the presence of flexibility provides different benefits (e.g., 14% cost savings) and enhances the system reliability in the case of contingency.

Optimal probabilistic scenario‐based operation and scheduling of prosumer microgrids considering uncertainties of renewable energy sources

AbstractUncertainties of renewable energy sources (RESs) such as wind turbine (WT) and photovoltaic (PV) units are one of the considerable challenges of prosumer microgrids (PMGs) for the optimal day‐ahead operation. In this study, a new probabilistic scenario‐based method of optimal scheduling and operation of PMGs is developed. In this regard, different scenarios are generated using Monte Carlo Simulations (MCS). Furthermore, k‐means, k‐medoids, and differential evolution algorithms (DEA) are deployed to cluster the scenarios in the proposed method. A realistic commercial PMG in Iran is selected to apply the introduced method. The validity of the developed probabilistic optimization method for PMG operation is examined by comparing the results under various scenario reduction algorithms and MCS ones. The comparison of the obtained results and those of other existing deterministic methods highlights the advantages of the presented method. Furthermore, the sensitivity analyses are carried out to investigate the robustness of the developed method against the increase in the system uncertainty level. According to the test results, it is concluded that the k‐medoids algorithm has the best performance in comparison with the k‐means and the DEA‐based clustering under various conditions.

Statistical Machine Learning Model for Stochastic Optimal Planning of Distribution Networks Considering a Dynamic Correlation and Dimension Reduction

Distributed generation and reactive power resource allocation will affect the economy and security of distribution networks. Deterministic scenario planning cannot solve the problem of network uncertainties, which are introduced by intermittent renewable generators and a variable demand for electricity. However, stochastic programming becomes a problem of great complexity when there is a large number of scenarios to be analyzed and when the computational burden has an adverse effect on the programming solution. In this paper, statistical machine learning theories are proposed to quickly solve the optimal planning for capacitors. Various technologies are used: Markov chains and copula functions are formulated to capture the variability and correlation of weather; consumption behavior probability is involved in the weather-sensitive load model; nearest neighbor theory and nonnegative matrix decomposition are combined to reduce the dimensions and scenario scale of stochastic variables; the stochastic response surface is used to calculate the probabilistic power flow; and probabilistic inequality theory is introduced to directly estimate the objective and constraint functions of the stochastic programming model. The effectiveness and efficiency of the proposed method are verified by comparing the method with the scenario reduction algorithm and the Monte Carlo method in a 33-bus distribution system.

Evaluation of scenario reduction algorithms with nested distance

Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times. Such problems need the representation of stochastic processes, which are usually approximated by scenario trees. In this article, we implement seven scenario reduction algorithms: three based on random extraction, named Random, and four based on specific distance measures, named Distance-based. Three of the latter are well known in literature while the fourth is a new approach, namely nodal clustering. We compare all the algorithms in terms of computational cost and information cost. The computational cost is measured by the time needed for the reduction, while the information cost is measured by the nested distance between the original and the reduced tree. Moreover, we also formulate and solve a multistage stochastic portfolio selection problem to measure the distance between the optimal solutions and between the optimal objective values of the original and the reduced tree.

On adaptation cost and tractability in robust adaptive radiation therapy optimization.

In this paper, a framework for online robust adaptive radiation therapy (ART) is discussed and evaluated. The purpose of the presented approach to ART is to: (a) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (b) address adaptation cost, and (c) address computational tractability. A novel framework for online robust ART using the concept of Bayesian inference and scenario reduction is introduced and evaluated in a series of simulated cases on a one-dimensional phantom geometry. The initial robust plan is generated from a robust optimization problem based on either expected-value or worst-case optimization approach using the a priori hypothesis of the probability distribution governing the interfractional geometric variations. Throughout the course of treatment, the simulated interfractional variations are evaluated in terms of their likelihood with respect to the a priori hypothesis of their distribution and violation of user-specified tolerance limits by the accumulated dose. If an adaptation is considered, the a posteriori distribution is computed from the actual variations using Bayesian inference. Then, the adapted plan is optimized to better suit the actual interfractional variations of the individual case. This adapted plan is used until the next adaptation is triggered. To address adaptation cost, the proposed framework provides an option for increased adaptation frequency. Computational tractability in robust planning and ART is addressed by an approximation algorithm to reduce the size of the optimization problem. According to the simulations, the proposed framework may improve target coverage compared to the corresponding nonadaptive robust approach. In particular, Bayesian inference may be useful to individualize plans to the actual interfractional variations. Concerning adaptation cost, the results indicate that mathematical methods like Bayesian inference may have a greater impact on improving individual treatment quality than increased adaptation frequency. In addition, the simulations suggest that the concept of scenario reduction may be useful to address computational tractability in ART and robust planning in general. The simulations indicate that the adapted plans may improve target coverage and OAR protection at manageable adaptation and computational cost within the novel framework. In particular, adaptive strategies using Bayesian inference appear to perform best among all strategies. This proof-of-concept study provides insights into the mathematical aspects of robustness, tractability, and ART, which are a useful guide for further development of frameworks for online robust ART.

Non-Network Solution Coordinated Voltage Stability Enhancement With STATCOM and UVLS for Wind-Penetrated Power System

This paper proposes an effect orientated approach to enhance the short-term voltage stability for wind-penetrated power systems. The low system stability with high uncertain renewable energy is addressed by coordination of network and non-network solutions, i.e., STATCOM placement and UVLS respectively in this paper. The proposed model considers the uncertainties of power systems, including operating points load dynamics and multiple contingencies. Unlike other methods that try to minimize the cost, the proposed method aims to maximize the voltage stability enhancement with a fixed cost. The high computing burden is alleviated by a net flow-based scenario reduction algorithm. Compared with the conventional approaches, this paper has three major contributions: 1) Device placement is coordinated with demand response. 2) Operating points and type 4 wind turbines are considered. 3) An effect maximizing DP algorithm with a robust scenario reduction method is applied. The effectiveness and efficiency of the proposed method is demonstrated on the New England 39-bus test system.

Capacity Scheduling of Energy Storage and Conventional Generation for Frequency Regulation Based on CPS1

This paper proposes and evaluates a systematic method of scheduling energy storage and conventional generation capacities in a day-ahead frequency regulation market, based on compliance to control performance standard 1 (CPS1), during each hour of the following day. The salient feature of this method is the development of two simple piecewise linear curves that represent the relationship between first, conventional generation and energy storage power capacities, and second, energy storage power and energy capacities, to satisfy CPS1 compliance in the presence of stochastic load variations. These curves are then modeled inside a mixed integer linear program to solve for resource allocations by minimizing total capacity cost. As such, the formulation avoids complex algorithms that are otherwise required to model frequency dynamics inside the optimization problem. To reduce computation time, a scenario reduction algorithm is used to obtain a small set of scenarios to represent the stochastic load. The proposed method is evaluated using comprehensive dynamic simulations of the two-area IEEE reliability test system implemented in PSS/E. The results prove that the proposed method is effective for scheduling capacities to meet CPS1 compliance with minimum cost.

Long-term cross-border electricity trading model under the background of Global Energy Interconnection

Environmental problems caused by traditional power production and the unbalanced distribution of energy resources and demand limit the development of sustainable societies. A feasible method to optimize the resource allocation has been proposed, and it involves cross-border and cross-regional electricity transactions. However, the uncertainty of renewable energy and the specific features of the cross-border electricity market are key issues which need to be considered in the trading mechanism design. Based on this, this paper sets up a long-term cross-border electricity trading model considering the uncertainty of renewable energy. First, annual transactions are matched according to the declared data of bidders with consideration of cross-border interconnection development benefits, potential benefit risks, and transmission costs. Second, for annual contract decomposition, the model uses the minimum generation cost function with a penalty item for power shortages to allocate electricity to each month. Additionally, the scenario reduction algorithm is combined with the unit commitment to construct a stochastic generation plan. Finally, a case study of the numerical results for the multinational electricity market in northeast Asia is used to show that the proposed trading model is feasible for cross-border electricity trading with high penetration of renewable energy.

Risk‐constrained energy management of PV integrated smart energy hub in the presence of demand response program and compressed air energy storage

Multi-carrier energy systems create new challenges as well as opportunities in future energy systems. One of these challenges is the interaction among different energy hubs' facilities and various operational parameters on the scheduling of the energy hub systems. This paper deals with the problem of optimal scheduling of smart residential energy hub (SREH) considering the different uncertain parameters. The effect of the market prices, demands and solar radiation uncertainties on the SREH scheduling problem is characterised through a risk-constrained two-stage stochastic programming model. The objective of the proposed scheduling problem is to determine the least-cost 24 h operation of the facilities that would cover the cooling, thermal and electrical demands. The Monte Carlo simulation method is applied to model the inaccuracies of solar radiation, energy demands, and electricity market prices. Additionally, a proper scenario-reduction algorithm is employed to reduce the number of scenarios and simulation burden. The proposed approach evaluates the impacts of different values of risk aversion parameter and the utility of the demand response program on the optimal solution of the proposed PV integrated SREH scheduling. Finally, an illustrative example is provided to confirm the efficiency and the applicability of the proposed approach.

CVaR-constrained scheduling strategy for smart multi carrier energy hub considering demand response and compressed air energy storage

Coupling different energy infrastructures, i.e. the concept of energy hub (EH), is an efficient approach to the optimal operation of both electrical and natural gas systems. This paper optimizes the risk-constrained scheduling of a wind-integrated smart multi-carrier energy hub (SMEH) and evaluates its operation in combination with compressed air energy storage (CAES) system, an electrical demand response (EDR) program, and a thermal demand response (TDR) program. The proposed SMEH consists of combined heat and power (CHP) units, a CAES system, a thermal storage system, boiler units, and an electrical heat pump (EHP) system. The penetration of wind power generation and application of the CAES system make a dependable condition to the optimal scheduling of the SMEH. The wind turbine generation and electrical and thermal demands are modeled as a scenario-based stochastic problem using the Monte Carlo simulation method. A proper scenario-reduction algorithm is also used to reduce the computational burden. Moreover, the conditional value-at-risk (CVaR) algorithm is merged with the proposed model to propitiate the risk of the high costs relevant to worst scenarios as a proper risk evaluation method. Finally, the proposed system is applied to a studied case to demonstrate the applicability and appropriateness of the proposed method.

Spatial Risk Analysis of Power Systems Resilience During Extreme Events

The increased frequency of extreme events in recent years highlights the emerging need for the development of methods that could contribute to the mitigation of the impact of such events on critical infrastructures, as well as boost their resilience against them. This article proposes an online spatial risk analysis capable of providing an indication of the evolving risk of power systems regions subject to extreme events. A Severity Risk Index (SRI) with the support of real-time monitoring assesses the impact of the extreme events on the power system resilience, with application to the effect of windstorms on transmission networks. The index considers the spatial and temporal evolution of the extreme event, system operating conditions, and the degraded system performance during the event. SRI is based on probabilistic risk by condensing the probability and impact of possible failure scenarios while the event is spatially moving across a power system. Due to the large number of possible failures during an extreme event, a scenario generation and reduction algorithm is applied in order to reduce the computation time. SRI provides the operator with a probabilistic assessment that could lead to effective resilience-based decisions for risk mitigation. The IEEE 24-bus Reliability Test System has been used to demonstrate the effectiveness of the proposed online risk analysis, which was embedded in a sequential Monte Carlo simulation for capturing the spatiotemporal effects of extreme events and evaluating the effectiveness of the proposed method.

Optimal Distribution System Operation for Enhancing Resilience Against Wildfires

Natural disasters can cause significant damage to power grids. During summer, in countries with high temperatures, distribution systems passing through forested areas are prone to wildfires. This paper proposes a stochastic programming approach for increasing resiliency of a distribution system exposed to an approaching wildfire. Dynamic line rating of the overhead lines is considered in order to model the impact of the wildfire on conductor temperature and flowing current. The uncertainties associated with solar radiation, wind speed, and wind direction that affect the progression of the wildfire and the production of stochastic distributed generators are taken into account. A scenario reduction algorithm is applied to reduce the number of scenarios in a tractable size and subsequently the computational burden. The proposed model is transformed to a mixed-integer problem with quadratic constraints, which provides effective solution to the operation of a distribution system against an approaching wildfire. A modified IEEE 33-bus distribution system is used to illustrate the applicability of the proposed approach.

An efficient uncertainty representation for the design of sustainable energy generation systems

Process sustainability is one of the major concerns in the process systems engineering area. Addressing this concept inevitably requires a multi-objective analysis to evaluate the social and environmental impacts in addition to the usual economic performance objective. Furthermore, the final sustainability of the proposed solutions very often depends on uncertain conditions, especially in the very frequent case that renewable resources are considered in order to enhance environmental sustainability: these resources are usually affected by unpredictable variations in their quality/quantity availability. But the approaches presented for solving multi-objective problems under uncertainty are limited by the amount of scenarios required to represent the unknown conditions. Here it is presented a solution strategy that combines a scenario reduction algorithm within the framework of a multi-objective formulation. Such a strategy is able to produce a fast and robust multi-objective optimization (MOO) while considering uncertainty in the raw material conditions (more precisely quality and availability). The solutions forming the resulting set of Pareto solutions are sorted hierarchically using the Elimination and Choice Expressing Reality IV (ELECTRE IV) method, which identifies the ones showing better overall performance considering the uncertain parameters space.

Application of Scenario Tree Reduction Via Quadratic Process to Medium-Term Hydrothermal Scheduling Problem

In systems with hydraulic predominance, the medium-term hydrothermal scheduling problem (MTHS) is usually modeled as a stochastic programming model where the objective is to obtain an optimal operation policy over a planning horizon. Inflows follow a stochastic process that is approximated by a multistage scenario tree and a multistage stochastic programming model is employed to compute the generation policy. The difficulty in solving the MTHS depends on the size of the scenario tree. To obtain a small but representative scenario tree, we employ the scenario reduction algorithm of Kovacevic and Pichler with quadratic process distances defined by appropriate metrics exploiting relevant features of the problem. Numerical assessments of the MTHS problem, using a reduced hydrothermal configuration extracted from the Brazilian system, show that reduced trees obtained by eliminating 80% scenarios provide approximate solutions to the problem with less than 1% accuracy errors and CPU time reduction of around 90%.

Scenario Reduction With Submodular Optimization

Stochastic programming methods have been proven to deal effectively with the uncertainty and variability of renewable generation resources. However, the quality of the solution that they provide (as measured by cost and reliability metrics) depends on the accuracy and the number of scenarios used to model this uncertainty and variability. Scenario reduction techniques are used to manage the computational burden by selecting representative scenarios. The common drawback of existing scenario reduction techniques is that the number of representative scenarios is a user-defined parameter. We propose a scenario reduction algorithm based on submodular function optimization to endogenously optimize the number of scenarios as well as rank these scenarios. This algorithm is compared, both qualitatively and quantitatively, with the state-of-the-art fast forward selection algorithm.