Uncertainty In Distributed Systems Research Articles

Stochastic Second-Order Conic Programming for Optimal Sizing of Distributed Generator Units and Electric Vehicle Charging Stations

The increased penetration of electric vehicles (EVs) and distributed generator (DG) units has led to uncertainty in distribution systems. These uncertainties—which have not been adequately considered in the literature—can entail risks in the optimal sizing of EV charging stations (EVCSs) and DG units in active distribution network planning. This paper proposes a method for obtaining the optimal sizing of DG units and EVCSs (considering uncertainty), to achieve exact power system analysis and ensure EV driver satisfaction. To model uncertainties in optimal sizing planning, this study first generates scenarios for each system asset using a probability distribution that considers the asset characteristics. In this step, the wind-turbine (WT), PV, and EVCS are modeled applying the Weibull, exponential, and kernel density estimation (KDE), and scenarios for each asset are generated using random sampling. Then, the k-means clustering is carried out for scenario reduction and the representative scenario abstract. The probability of occurrence for each representative scenario is assigned depending on the number of observations within each cluster. The representative scenarios for each asset are integrated into the scenario for all assets through the joint probability. The integrated scenarios are applied in the optimization problem for optimal sizing of the system asset framework. The optimal sizing of the system assets problem is proposed (to minimize the line loss and voltage deviation) and formulated via stochastic second-order conic programming, to reflect the uncertainty under an AC power flow; this is a convex problem that can be solved in polynomial time. The proposed method is tested on a modified IEEE 15 bus system, and the simulation is performed with various objective functions. The simulation results demonstrate the effectiveness of the proposed method.

Combining model-based and model-free methods for stochastic control of distributed energy resources

Modern distribution systems are experiencing a fast transformation with the growing penetration of distributed energy resources (DERs). Along with the economic and environmental benefits of DERs, challenges arise to address the uncertainties caused by their inherent volatility. If properly coordinated, however, DERs have the potential to provide the controllability that grid operators need. In the paper, we propose a hierarchical control framework that combines the model-based and model-free methods for stochastic DER control in distribution systems. The upper-level scheduler considers a chance-constrained optimal power flow problem (model-based) that schedules DER setpoints to minimize the operational cost and maintain the operating reserve. The lower-level distributed DER controllers absorb real-time disturbances and uncertainties using the extremum seeking control (model-free) to achieve grid objectives. The combination of model-based and model-free methods allows us to take the advantages of both methods to effectively manage the uncertainty in distribution systems. The proposed work is demonstrated on the IEEE 13-node feeder.

Probabilistic State Forecasting and Optimal Voltage Control in Distribution Grids under Uncertainty

Nowadays, the uncertainty in distribution systems rises, notably due to an increasing share of solar panels and electric vehicles whose power production and consumption are characterized by a high volatility. This poses challenges to distribution system operators to ensure stable and secure operation of their grid. Hence, an optimal integration of these distributed energy resources in real-time control schemes inevitably relies on appropriate forecasts of the near-future system state. This paper investigates the short-term probabilistic state prediction of low-voltage grids for operation purposes. The performance of two quantile forecasting algorithms is evaluated for different levels of distributed energy resources penetration and availability of measurements. Quantile forecasts are finally integrated into the framework of an optimization problem that aims at minimizing the costs associated with overvoltages by suitable solar power curtailment. The advantages of quantile forecasts considering different imbalance prices are demonstrated.

Minimisation of voltage fluctuation resulted from renewable energy sources uncertainty in distribution systems

The penetration of renewable energy sources (RESs) in distribution systems faces many issues due to their output uncertainty resulted from climate conditions. The uncertainty impacts on the voltage fluctuations are reduced by using a proposed bi-stage method. At first, the system voltage is controlled by determining the optimal setting of voltage-regulating devices such as voltage regulators, transformer tap changers and static VAR compensator. Then, the dispatchable distributed generation (DDGs) units are accompanied by the voltage regulating devices to achieve more reduction in the voltage fluctuations. In this line, unbalanced backward–forward sweep load flow method is formulated to analyse the unbalanced operation of three-phase distribution systems. The main objectives of the proposed method are to reduce voltage fluctuations to maintain voltage profile within its permissible limits. In addition, the cat swarm optimiser (CSO) is implemented to obtain the optimal planning of voltage regulating devices and DDGs to achieve the lowest uncertainty influence on the voltage fluctuations. The proposed method is applied to a real unbalanced IEEE 34-bus distribution test system. The highest capability of CSO algorithm, i.e. CSO provides the highest reduction on the voltage fluctuations, is proven compared with particle swarm optimisation, harmony search and water cycle algorithms.

Optimal multi objective placement and sizing of multiple DGs and shunt capacitor banks simultaneously considering load uncertainty via MOPSO approach

This study proposes a new application of multi objective particle swarm optimization (MOPSO) with the aim of determining optimal location and size of distributed generations (DGs) and shunt capacitor banks (SCBs) simultaneously with considering load uncertainty in distribution systems. The multi objective optimization includes three objective functions: decreasing active power losses, improving voltage stability for buses and balancing current in system sections. The uncertainty of loads is modeled by using fuzzy data theory. This method uses Pareto optimal solutions to solve the problem with objective functions and constraints. In addition, a fuzzy-based mechanism is employed to extract the best compromised solution among three different objective functions. The proposed method is implemented on IEEE 33 bus radial distribution system (RDS) and an actual realistic 94 bus Portuguese RDS and the results are compared with methods of Strength Pareto Evolutionary Algorithm (SPEA), Non-dominated Sorting Genetic Algorithm (NSGA), Multi-Objective Differential Evolution (MODE) and combination of Imperialist Competitive Algorithm and Genetic Algorithm (ICA/GA). Test results demonstrate that the proposed method is more effective and has higher capability in finding optimum solutions in cases where DG and SCB are located and sized simultaneously in a multi objective optimization.

Distribution systems and productive models: the case of the distribution of a large product variety

The link between productive organisation of the manufacturer and new car distribution is often summarised by the opposition between push and pull systems. However, this view remains incomplete. Indeed, it is not clear how the manufacturer's product policy, for example, plays a part in the general design of his distribution system. The issue of the distribution of an increasing variety of products – an issue that most European manufacturers are facing – is a good example to investigate the links of interdependency between the different elements of a productive model and a distribution system. The main problem of variety as a discriminating product policy (aiming at fulfilling the preferences of consumers in an increasing number of characteristics) is the greatest demand uncertainty and thus risk that the distribution system is now facing. This paper aims at analysing different ways of dealing with this uncertainty in distribution systems. The analysis highlights not only that there is no one-best-way in this field, but also that configurations chosen by producers – and not yet stable – result from several industrial arbitrages on distribution market structure and risk sharing in the value chain.