Scenario Tree Research Articles

Allocation and sizing of reactive power compensators considering PV power and load demand uncertainty using beetle-antenna grey wolf optimization

AbstractDistributed photovoltaic (PV) systems play an important role in supplying many recent microgrids. The absence of reactive power support for these small-scale PV plants increases total microgrid losses and voltage-instability threats. Reactive power compensations (RPCs) should be integrated to enhance both microgrid losses and voltage profiles. RPC planning is a non-linear, complicated problem. In this paper, a combined RPC allocation and sizing algorithm is proposed. The RPC-integrating buses are selected using a new adaptive approach of loss sensitivity analysis. In the sizing process, the uncertainties in PV power and load demand are modelled using proper probability density functions. Three simulation techniques for handling uncertainties are compared to define the accurate and fast accurate method as follows: Monte Carlo simulation (MCS), scenario tree construction and reduction method, and point estimation method (PEM). The load flow equations are solved using the forward–backward sweep method. RPCs are optimally sized using the beetle-antenna-based strategy with grey wolf optimization (BGWO) to overcome the local minima problem that appeared in the other pre-proposed methods. Results have been compared using particle swarm optimization and conventional GWO. The proposed model is verified using the IEEE 33 radial bus system. The expected power loss has been reduced by 22% and 31% using compensation of 26% and 44%, respectively. The results obtained prove that the BGWO optimal power flow and PEM to handle the uncertainty can significantly reduce the computation time with sufficient accuracy. Under the study conditions, PEM reduces the computation time to 4 minutes compared with 4 hours for MCS, with only a 3% error compared with MCS as an uncertainty benchmark method.

Handling Type-I and Type-II endogenous uncertainties in simultaneous production planning and condition-based maintenance optimization in continuous production

This work proposes a novel stochastic programming formulation that can handle Type-I and Type-II endogenous uncertainties with the goal of simultaneously optimize production planning and condition-based maintenance of continuous production plants. A degradation model that is able to predict the Remaining Useful Life of the equipment is embedded into the optimization problem and we consider this prediction to be uncertain. Each scenario of the stochastic program represents an uncertain realization of the predicted Remaining Useful Life and has a certain probability of realization. These probabilities can be altered by the decision maker, thus rendering some predictions more likely than the others by acting on the utilization of the plant (Type-I endogenous uncertainty). The maintenance activities recover the health of the equipment and the decisions on maintenance make some scenarios not realize any more and, therefore, modify the structure of the scenario-tree (Type-II endogenous uncertainty). We present two different modelling approaches for this novel class of stochastic programs based on superstructure scenario trees and on conditional non-anticipativity constraints. For a simple generic example, we analyse the influence of the modelling approach on the computational time that is needed to solve the resulting MINLP problem with the global solver BARON. We also investigate several branching priority strategies to reduce the computational effort for this class of problems. We demonstrate the advantages that can be achieved using the proposed formulation compared to the deterministic counterpart.This work sets the ground for modelling and solving simultaneous production planning and condition-based maintenance problems. To deal with larger-scale industrial problems, additional work is required to develop custom solution techniques to reduce the computational burden.

Multi-Stage NMPC for a MAV based Collision Free Navigation Under Varying Communication Delays

Time delays in communication networks are one of the main concerns in deploying robots with computation boards on the edge. This article proposes a multi-stage Nonlinear Model Predictive Control (NMPC) that is capable of handling varying network-induced time delays for establishing a control framework being able to guarantee collision-free Micro Aerial Vehicles (MAVs) navigation. This study introduces a novel approach that considers different sampling times by a tree of discretization scenarios contrary to the existing typical multi-stage NMPC where system uncertainties are modeled by a tree of scenarios. Additionally, the proposed method considers adaptive weights for the multi-stage NMPC scenarios based on the probability of time delays in the communication link. As a result of the multi-stage NMPC, the obtained optimal control action is valid for multiple sampling times. Finally, the overall effectiveness of the proposed novel control framework is demonstrated in various tests and different simulation environments.

Stochastic unit commitment for power systems with offshore wind farms towards frequency resiliency

AbstractTo enhance the resilience of transmission systems with offshore wind farms before the advent of typhoons, a proactive unit commitment scheme is proposed. A novel scenario tree is proposed to quantify the uncertain impacts of typhoons on offshore wind farms, transmission lines, and system states, where the inertia support from offshore wind farms and random system state are in‐cooperated. The frequency security constraint is captured by a multi‐variative piece‐wise linear function, where the frequency nadir are simulated under varying inertia and disturbance combinations. The unit commitment problem is formulated as a two‐stage stochastic optimisation problem with nonlinear recourse. This problem is solved by a multi‐cuts Benders decomposition algorithm with finite iteration convergence property. Simulations are conducted on a modified IEEE‐RTS 79 test system with offshore wind farms. Results verify the effectiveness of the proposed model regarding the load shedding and frequency nadir enhancement.

Technical Note—Risk-Averse Regret Minimization in Multistage Stochastic Programs

Regret minimization has gained popularity in a wide range of decision-making problems under uncertainty because of its capacity to identify more opportunistic solutions than worst-case value optimization. Unfortunately, the rigidity of current worst-case regret models and scarcity of tractable solution methods have been serious obstacles in multistage applications. In “Risk-Averse Regret Minimization in Multistage Stochastic Programs,” M. Poursoltani, E. Delage, and A. Georghiou consider a multistage stochastic programming setting with a discrete scenario tree. They introduce the notion of the Δ-regret model, which bridges between the ex ante and ex post regret minimization paradigms that are currently used in the regret minimization literature for single-stage problems. The notion of Δ-regret minimization is investigated for the first time both theoretically and numerically in order to better understand its behavior under a set of popular risk measures.

Scenario-dominance to multi-stage stochastic lot-sizing and knapsack problems

This paper presents strong scenario dominance cuts for effectively solving the multi-stage stochastic mixed-integer programs (M-SMIPs), specifically focusing on the two most well-known M-SMIPs: stochastic capacitated multi-item lot-sizing (S-MCLSP) and the stochastic dynamic multi-dimensional knapsack (S-MKP) problems. Scenario dominance is characterized by a partial ordering of scenarios based on the pairwise comparisons of random variable realizations in a scenario tree of a stochastic program. In this paper, we study the implications of scenario-dominance relations and inferences obtained by solving scenario sub-problems to drive new strong cutting planes to solve S-MCLSP and S-MKP instances faster. Computational experiments demonstrate that our strong scenario dominance cuts can significantly reduce the solution time for such M-SMIP problems with an average of 0.06% deviation from the optimal solution. The results with up to 81 random variables for S-MKP show that strong dominance cuts improve the state-of-the-art solver solution of two hours by 0.13% in five minutes. The proposed framework can also be applied to other scenario-based optimization problems.

Two-region Perimeter Control Based on Risk-averse Model Predictive Control

The perimeter control is effective in alleviating traffic congestion. However, previous studies about perimeter control based on macroscopic fundamental diagram didn't consider the influences of the system uncertainty even though this uncertainty may lead to significant congestion. This paper presents a two-region perimeter control method based on a risk-averse model predictive control considering uncertainty. The advantage of this paper is that we design a risk index for uncertainty and design a controller which takes the risk index as an optimization objective. A scenario tree is used to model the uncertainty of the two-region dynamic equations. Average value at risk mapping is employed to calculate the systematic risk due to uncertainty. Then, the optimization objective of a multi-stage risk is used in MPC based on the scenario tree. Finally, the multi-stage risk is formulated as a solvable form. Simulation results show that the proposed perimeter control method reduces the total travel time of the two-region road network with uncertainty and significantly reduces traffic congestion compared to stochastic model predictive control method.

A framework for assessing confidence in freedom from infection in animal disease control programmes.

In the Surveillance Tool for Outcome-based Comparison of FREEdom from infection (STOC free) project (https://www.stocfree.eu), a data collection tool was constructed to facilitate standardised collection of input data, and a model was developed to allow a standardised and harmonised comparison of the outputs of different control programmes (CPs) for cattle diseases. The STOC free model can be used to evaluate the probability of freedom from infection for herds in CPs and to determine whether these CPs comply with the European Union's pre-defined output-based standards. Bovine viral diarrhoea virus (BVDV) was chosen as the case disease for this project because of the diversity in CPs in the six participating countries. Detailed BVDV CP and risk factor information was collected using the data collection tool. For inclusion of the data in the STOC free model, key aspects and default values were quantified. A Bayesian hidden Markov model was deemed appropriate, and a model was developed for BVDV CPs. The model was tested and validated using real BVDV CP data from partner countries, and corresponding computer code was made publicly available. The STOC free model focuses on herd-level data, although that animal-level data can be included after aggregation to herd level. The STOC free model is applicable to diseases that are endemic, given that it needs the presence of some infection to estimate parameters and enable convergence. In countries where infection-free status has been achieved, a scenario tree model could be a better suited tool. Further work is recommended to generalise the STOC free model to other diseases.

A Hybrid Neural Network Approach for Adaptive Scenario-Based Model Predictive Control in the LPV Framework

This paper presents a hybrid neural network (NN) approach for adaptive scenario-based model predictive control (SMPC) design of nonlinear systems in the linear parametervarying (LPV) framework. In particular, a deterministic artificial neural network (ANN)-based LPV model is learned from data as the nominal model. Then, a Bayesian NN (BNN) is used to describe the mismatch between the plant and the LPV-ANN model. Adaptive scenarios are generated online based on the BNN model to reduce the conservativeness of scenario generation. Moreover, a probabilistic safety certificate is incorporated into the scenario generation by ensuring that the trajectories of scenarios contain the trajectory of the system and that all the scenarios satisfy the constraints with a high probability. Furthermore, conditions for the recursive feasibility of the SMPC are given. Experiments on the closed-loop simulations of a two-tank system demonstrate that the proposed approach can better model the behaviors of nonlinear systems than sole ANN/BNN models can, and the SMPC based on the hybrid NN (HyNN) model can improve the control performance compared to the SMPC with a fixed scenario tree.

Scenario reduction and scenario tree generation for stochastic programming using Sinkhorn distance

Scenario-based stochastic programming is a widely used method for optimization under uncertainty. The solution quality of this approach is dependent on the approximation of the underlying uncertainty distribution. Therefore, the optimal generation of scenarios (or scenario trees) is a pertinent research objective in stochastic programming. In this work, we approach the scenario reduction and scenario tree generation problem through the perspective of optimal transport, specifically entropy-regularized optimal transport. The availability of an iterative procedure to compute the optimal entropy-regularized transport plan between support sets, using the Sinkhorn–Knopp algorithm in lieu of conventional linear programming-based optimal transport, is found to decrease solution time appreciably, with a decrease in memory burden as well. We present algorithms for optimal scenario reduction and multistage scenario tree generation, and illustrate their use through two case studies. We show that the proposed approach generates high-quality scenarios whose use in stochastic programming offers solutions with good accuracy.

Learning‐based adaptive‐scenario‐tree model predictive control with improved probabilistic safety using robust Bayesian neural networks

SummaryScenario‐based model predictive control (MPC) methods can mitigate the conservativeness inherent to open‐loop robust MPC. Yet, the scenarios are often generated offline based on worst‐case uncertainty descriptions obtained a priori, which can in turn limit the improvements in the robust control performance. To this end, this paper presents a learning‐based, adaptive‐scenario‐tree model predictive control approach for uncertain nonlinear systems with time‐varying and/or hard‐to‐model dynamics. Bayesian neural networks (BNNs) are used to learn a state‐ and input‐dependent description of model uncertainty, namely the mismatch between a nominal (physics‐based or data‐driven) model of a system and its actual dynamics. We first present a new approach for training robust BNNs (RBNNs) using probabilistic Lipschitz bounds to provide a less conservative uncertainty quantification. Then, we present an approach to evaluate the credible intervals of RBNN predictions and determine the number of samples required for estimating the credible intervals given a credible level. The performance of RBNNs is evaluated with respect to that of standard BNNs and Gaussian process (GP) as a basis of comparison. The RBNN description of plant‐model mismatch with verified accurate credible intervals is employed to generate adaptive scenarios online for scenario‐based MPC (sMPC). The proposed sMPC approach with adaptive scenario tree can improve the robust control performance with respect to sMPC with a fixed, worst‐case scenario tree and with respect to an adaptive‐scenario‐based MPC (asMPC) using GP regression on a cold atmospheric plasma system. Furthermore, closed‐loop simulation results illustrate that robust model uncertainty learning via RBNNs can enhance the probability of constraint satisfaction of asMPC.

Modeling the impact of surveillance activities combined with physical distancing interventions on COVID-19 epidemics at a local level.

Physical distancing and contact tracing are two key components in controlling the COVID-19 epidemics. Understanding their interaction at local level is important for policymakers. We propose a flexible modeling framework to assess the effect of combining contact tracing with different physical distancing strategies. Using scenario tree analyses, we compute the probability of COVID-19 detection using passive surveillance, with and without contact tracing, in metropolitan Barcelona. The estimates of detection probability and the frequency of daily social contacts are fitted into an age-structured susceptible-exposed-infectious-recovered compartmental model to simulate the epidemics considering different physical distancing scenarios over a period of 26 weeks. With the original Wuhan strain, the probability of detecting an infected individual without implementing physical distancing would have been 0.465, 0.515, 0.617, and 0.665 in designated age groups (0-14, 15-49, 50-64, and >65), respectively. As the physical distancing measures were reinforced and the disease circulation decreased, the interaction between the two interventions resulted in a reduction of the detection probabilities; however, despite this reduction, active contact tracing and isolation remained an effective supplement to physical distancing. If we relied solely on passive surveillance for diagnosing COVID-19, the model required a minimal 50% (95% credible interval, 39-69%) reduction of daily social contacts to keep the infected population under 5%, as compared to the 36% (95% credible interval, 22-56%) reduction with contact tracing systems. The simulation with the B.1.1.7 and B.1.167.2 strains shows similar results. Our simulations showed that a functioning contact tracing program would reduce the need for physical distancing and mitigate the COVID-19 epidemics.

Epidemiologic and import risk analysis of Peste des petits ruminants between 2010 and 2018 in India

BackgroundPeste des petits ruminants (PPR) is a serious disease that affects goats, sheep and other small ruminants. As one of the earliest and most serious countries, PPR has seriously threatened India's animal husbandry economy.ResultsIn this study, the spatiotemporal characteristics of the PPR in India outbreaks were analyzed. Between 2010 and 2018, the epidemic in India broke out all over the country in a cluster distribution. Epidemic clusters in northern and southern India are at higher risk, and the outbreak time of PPR has significant seasonality. The results of the analysis of the development and transmission of PPR under the natural infection conditions showed that the PPR outbreak in India reached a peak within 15 days. Finally, the quantitative risk analysis results based on scenario tree show showed that the average probability of infecting PPRV in live sheep exported from India was 1.45 × 10–4.ConclusionsThis study analyzed the prevalence of PPR in India. The analysis of transmission dynamics on the development of the epidemic provides a reference for the prevention and control of the epidemic. At the same time, it provides risk analysis and suggestions on trade measures for the trading countries of India.

The Development of a Cross-Border Energy Trade Cooperation Model of Interconnected Virtual Power Plants Using Bilateral Contracts

By coordinating the operation of regionally interconnected virtual power plants (VPPs), the growing penetration problem of renewable energy sources (RESs) into the power system can be addressed. This study presents an interactive trading cooperation model of regionally interconnected VPPs using bilateral contracts. The proposed model maximizes overall electricity market social welfare (SW) (i.e., maximization of consumer benefits while minimizing energy costs). The focus of the proposed approach is to design and develop a parallel energy exchange cooperation model of interconnected VPPs, ensuring the operational efficiency and reliability of interconnected power systems over the planning horizon. Given that adjacent VPPs may have differences in their energy generation and usage patterns, a scenario tree method is used to model the uncertainties associated with solar irradiation and load demand. A case study of two interconnected VPPs is used, the operational scenario is designed, and the corresponding computational model is developed. The results highlight that the proposed approach gives VPPs the option to utilize their internal network’s maximum capacity. As a result, there will be less reliance on the main grid for interconnected VPPs, and an improvement in key performance indicators, including the cost of the VPPs systems and renewable power variations.

Value function gradient learning for large-scale multistage stochastic programming problems

A stagewise decomposition algorithm called “value function gradient learning” (VFGL) is proposed for large-scale multistage stochastic convex programs. VFGL finds the parameter values that best fit the gradient of the value function within a given parametric family. Widely used decomposition algorithms for multistage stochastic programming, such as stochastic dual dynamic programming (SDDP), approximate the value function by adding linear subgradient cuts at each iteration. Although this approach has been successful for linear problems, nonlinear problems may suffer from the increasing size of each subproblem as the iteration proceeds. On the other hand, VFGL has a fixed number of parameters; thus, the size of the subproblems remains constant throughout the iteration. Furthermore, VFGL can learn the parameters by means of stochastic gradient descent, which means that it can be easil0y parallelized and does not require a scenario tree approximation of the underlying uncertainties. VFGL was compared with a deterministic equivalent formulation of the multistage stochastic programming problem and SDDP approaches for three illustrative examples: production planning, hydrothermal generation, and the lifetime financial planning problem. Numerical examples show that VFGL generates high-quality solutions and is computationally efficient.

A stochastic dual dynamic integer programming based approach for remanufacturing planning under uncertainty

ABSTRACT We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent the uncertain information structure. We introduce a new dynamic programming formulation that relies on a partial nested decomposition of the scenario tree. We then propose a new approximate stochastic dual dynamic integer programming algorithm based on this partial decomposition. Our numerical results show that the proposed solution approach is able to provide near-optimal solutions for large-size instances with a reasonable computational effort.

Assessing the export trade risk of bluetongue virus serotypes 4 and 8 in France.

Bluetongue (BT) causes an economic loss of $3 billion every year in the world. After two serious occurrences of BT (bluetongue virus [BTV] occurrence in 2006 and 2015), France has been controlling for decades, but it has not been eradicated. As the largest live cattle export market in the world, France is also one of the major exporters of breeding animals and genetic materials in the world. The biosafety of its exported cattle and products has always been a concern. The scenario tree quantitative model was used to analyze the risk of BTV release from French exported live cattle and bovine semen. The results showed that with the increase in vaccination coverage rates, the risk decreased. If the vaccine coverage is 0%, the areas with the highest average risk probability of BTV-4 and BTV-8 release from exported live cattle were Haute-Savoie and Puy-de-Dôme, and the risk was 2.96 × 10-4 and 4.25 × 10-4 , respectively. When the vaccine coverage was 90%, the risk probability of BTV-4 and BTV-8 release from exported live cattle was 2.96 × 10-5 and 4.24 × 10-5 , respectively. The average probability of BTV-8 release from bovine semen was 1.09 × 10-10 . Sensitivity analysis showed that the probability of false negative polymerase chain reaction (PCR) test and the probability of BT infection in the bull breeding station had an impact on the model. The identification of high-risk areas and the discovery of key control measures provide a reference for decision makers to assess the risk of French exports of live cattle and bovine semen.

Data-driven scenario generation for two-stage stochastic programming

Optimisation under uncertainty has always been a focal point within the Process Systems Engineering (PSE) research agenda. In particular, the efficient manipulation of large amount of data for the uncertain parameters constitutes a crucial condition for effectively tackling stochastic programming problems. In this context, this work proposes a new data-driven Mixed-Integer Linear Programming (MILP) model for the Distribution & Moment Matching Problem (DMP). For cases with multiple uncertain parameters a copula-based simulation of initial scenarios is employed as preliminary step. Moreover, the integration of clustering methods and DMP in the proposed model is shown to enhance computational performance. Finally, we compare the proposed approach with state-of-the-art scenario generation methodologies. Through a number of case studies we highlight the benefits regarding the quality of the generated scenario trees by evaluating the corresponding obtained stochastic solutions.

Solving stochastic hydro unit commitment using benders decomposition and modified stochastic dual dynamic programming

This paper proposes a stochastic hydro unit commitment (SHUC) model for a price-taker hydropower producer in a liberalized market. The objective is to maximize the total revenue of the hydropower producer, including the immediate revenue, future revenue (i.e., opportunity cost), and startup and shutdown cost. The market price uncertainty is taken into account through the scenario tree. The solution of the model is a challenging task due to its non-convex and high-dimensional characteristics. A solution method based on the Benders Decomposition (BD) and Modified Stochastic Dual Dynamic Programming (MSDDP) is proposed to solve the problem efficiently. Firstly, the BD is applied to decompose the original problem into a Benders master problem representing the hydro unit commitment and a Benders subproblem representing the optimal operation of the hydropower plants. The Benders subproblem, which contains a large number of integer variables, is further decomposed by the period and solved by the MSDDP proposed in this paper. Finally, we verify the effectiveness of the SHUC model and the performance of the proposed solution method in case studies.

A Hybrid Framework for Real-Time Dispatching of Airline Unit Load Devices under Demand Variations

This study is devoted to a new research topic in real-time airline operations, the redispatching of unit load devices (ULDs) under demand variations. We develop a new hybrid framework to solve the problem of ULD redispatch following the time-sequence decision-making required by airlines. The hybrid framework is developed by integrating techniques including the probability distribution technique to simulate different types of operational demand, the adjustable number of stages which is needed to meet the requirements of a decision-making process following a time sequence and the time pressure characteristic of real operations, and the scenario tree and probability rule approaches which are aimed and representing all possible demand scenarios for a stage, while the network flow technique is applied to represent the movement and location of ULDs at each airport over time and is used for the development of the associated mathematical model and the simulation. We performed a simulation of 2,000 cases based on different operational days and types of operational demand. The results show that this hybrid framework is able to achieve stability and also a small variability of both ULD operating costs and solution times, which could allow the airline to save on ULD operating costs, under demand variations in real-time operations.