scholarly journals Probabilistic Optimal Power Flow Using Linear Fuzzy Relation

2021 ◽  
Author(s):  
Inderdeep S. Arneja
Keyword(s):  
Power Systems ◽  
Stochastic Models ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Hessian Matrix ◽  
Optimal Solution ◽  
Fuzzy Relation ◽  
Monte Carlo Simulation Technique ◽  
Optimal Power

Optimal Power Flow (OPF) is a very important tool for planning and analysis of power systems. In the recent times, uncertain renewable energy is being integrated into power systems in a large scale. Appropriate modeling of renewables in optimal power flow requires using stochastic models. Using stochastic models of renewables in optimal power flow is numerically and algorithmically challenging due to the complexity of stochastic models and nonlinear nature of bus power balance equations. Hitherto, Monte Carlo simulation technique and Cumulant technique have been proposed, but they are not computationally viable for large systems. In this thesis, we propose the use of linear fuzzy relation technique to relate stochastic models of dependent variables of optimal power flow formulation in terms of control variables that include power output of renewables. This fuzzy relation uses Hessian matrix of the LaGrangian of the optimal power flow formulation at optimal solution point. The technique is tested on a six bus system and results are reported. One can intuitively see that this technique can be easily extended to larger systems.

scholarly journals Probabilistic Optimal Power Flow Using Linear Fuzzy Relation

2021 ◽  
Author(s):  
Inderdeep S. Arneja
Keyword(s):  
Power Systems ◽  
Stochastic Models ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Hessian Matrix ◽  
Optimal Solution ◽  
Fuzzy Relation ◽  
Monte Carlo Simulation Technique ◽  
Optimal Power

Optimal Power Flow (OPF) is a very important tool for planning and analysis of power systems. In the recent times, uncertain renewable energy is being integrated into power systems in a large scale. Appropriate modeling of renewables in optimal power flow requires using stochastic models. Using stochastic models of renewables in optimal power flow is numerically and algorithmically challenging due to the complexity of stochastic models and nonlinear nature of bus power balance equations. Hitherto, Monte Carlo simulation technique and Cumulant technique have been proposed, but they are not computationally viable for large systems. In this thesis, we propose the use of linear fuzzy relation technique to relate stochastic models of dependent variables of optimal power flow formulation in terms of control variables that include power output of renewables. This fuzzy relation uses Hessian matrix of the LaGrangian of the optimal power flow formulation at optimal solution point. The technique is tested on a six bus system and results are reported. One can intuitively see that this technique can be easily extended to larger systems.

scholarly journals Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

2020 ◽  
Vol 34 (01) ◽  
pp. 630-637 ◽  
Author(s):  
Ferdinando Fioretto ◽  
Terrence W.K. Mak ◽  
Pascal Van Hentenryck
Keyword(s):  
Deep Learning ◽  
Power Systems ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Renewable Energy Sources ◽  
Electrical Power ◽  
Practical Applications ◽  
Fundamental Building Block ◽  
Optimal Power

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the similar states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic medium-sized power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of the widely adopted linear DC approximation by at least two orders of magnitude.

scholarly journals TSO-DSO Coordination Schemes to Facilitate Distributed Resources Integration

2021 ◽  
Author(s):  
Fatemeh Najibi ◽  
Dimitra Apostolopoulou ◽  
Eduardo Alonso
Keyword(s):  
Power Systems ◽  
Power Flow ◽  
Distribution Systems ◽  
Optimal Power Flow ◽  
Optimal Solution ◽  
Distributed Resources ◽  
Optimal Power ◽  
Conflicting Objectives ◽  
Marginal Prices ◽  
Transmission And Distribution

The incorporation of renewable energy into power systems poses serious challenges to the transmission and distribution power system operators (TSOs and DSOs). To fully leverage these resources there is a need for a new market design with improved coordination between TSOs and DSOs. In this paper we propose two coordination schemes between TSOs and DSOs: one centralised and another decentralised that facilitate the integration of distributed based generation; minimise operational cost; relieve congestion; and promote a sustainable system. To this end, we approximate the power equations with linearised equations so that the resulting optimal power flows (OPFs) in both the TSO and DSO become convex optimisation problems. In the resulting decentralised scheme, the TSO and DSO collaborate to optimally allocate all resources in the system. In particular, we propose an iterative bi-level optimisation technique where the upper level is the TSO that solves its own OPF and determines the locational marginal prices at substations. We demonstrate numerically that the algorithm converges to a near optimal solution. We study the interaction of TSOs and DSOs and the existence of any conflicting objectives with the centralised scheme. More specifically, we approximate the Pareto front of the multi-objective optimal power flow problem where the entire system, i.e., transmission and distribution systems, is modelled. The proposed ideas are illustrated through a five bus transmission system connected with distribution systems, represented by the IEEE 33 and 69 bus feeders.

scholarly journals An Expeditious Methodology to Assess the Effects of Intermittent Generation on Power Systems

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1135
Author(s):  
Gracita Rosas ◽  
Elizete Lourenço ◽  
Djalma Falcão ◽  
Thelma Fernandes
Keyword(s):  
Power Systems ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Solution ◽  
Active Power ◽  
Circuit Breakers ◽  
Optimal Power ◽  
Flow Through ◽  
Nodal Voltage ◽  
Triangular Model

This paper proposes an expeditious methodology that provides hourly assessments of the effect of intermittent wind and solar power generation on the electrical quantities characterizing power systems. Currents are measured via circuit breakers to confirm the correct sizing of devices based on their rated currents. Nodal voltage magnitudes are assessed for compliance with limits imposed by regulatory authorities, whereas the active power produced by hydroelectrical generators is assessed for reserve energy. The proposed methodology leverages a fuzzy extended deterministic optimal power flow that uses in power balance equations the average hourly values of active power generated by wind and solar sources as well as hourly energy load. The power grid is modeled at the substation level to directly obtain power flow through circuit breakers. Uncertainties in power system electrical quantities are assessed for an optimal solution using a Taylor series associated with deviations from the average values of the active power produced by the wind and solar sources. These deviations are represented using a fuzzy triangular model reflecting the approximations of the probability density functions of these powers. The methodology takes into account a subjective investigation that focuses on the qualitative characteristic of these energy sources’ behaviors.

scholarly journals TSO-DSO Coordination Schemes to Facilitate Distributed Resources Integration

2021 ◽  
Vol 13 (14) ◽  
pp. 7832
Author(s):  
Fatemeh Najibi ◽  
Dimitra Apostolopoulou ◽  
Eduardo Alonso
Keyword(s):  
Power Systems ◽  
Power Flow ◽  
Distribution Systems ◽  
Optimal Power Flow ◽  
Optimal Solution ◽  
Distributed Resources ◽  
Optimal Power ◽  
Conflicting Objectives ◽  
Marginal Prices ◽  
Transmission And Distribution

The incorporation of renewable energy into power systems poses serious challenges to the transmission and distribution power system operators (TSOs and DSOs). To fully leverage these resources there is a need for a new market design with improved coordination between TSOs and DSOs. In this paper we propose two coordination schemes between TSOs and DSOs: one centralised and another decentralised that facilitate the integration of distributed based generation; minimise operational cost; relieve congestion; and promote a sustainable system. In order to achieve this, we approximate the power equations with linearised equations so that the resulting optimal power flows (OPFs) in both the TSO and DSO become convex optimisation problems. In the resulting decentralised scheme, the TSO and DSO collaborate to optimally allocate all resources in the system. In particular, we propose an iterative bi-level optimisation technique where the upper level is the TSO that solves its own OPF and determines the locational marginal prices at substations. We demonstrate numerically that the algorithm converges to a near optimal solution. We study the interaction of TSOs and DSOs and the existence of any conflicting objectives with the centralised scheme. More specifically, we approximate the Pareto front of the multi-objective optimal power flow problem where the entire system, i.e., transmission and distribution systems, is modelled. The proposed ideas are illustrated through a five bus transmission system connected with distribution systems, represented by the IEEE 33 and 69 bus feeders.

Sign in / Sign up

Export Citation Format

Share Document