Linear/Quadratic Programming-Based Optimal Power Flow using Linear Power Flow and Absolute Loss Approximations

This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear power flow approximation and consider a convex reformulation of the power losses in the form of absolute value functions. We show four ways how to incorporate this approximation into LP/QP based OPF problems. In a comprehensive case study the usefulness of our OPF methods is analyzed and compared with an existing OPF relaxation and approximation method. As a result, the errors on voltage magnitudes and angles are reasonable, while obtaining near-optimal results for typical scenarios. We find that our methods reduce significantly the computational complexity compared to the nonlinear AC-OPF making them a good choice for planning purposes

Transmission Network Reduction Method using Nonlinear Optimization

This paper presents a new method to determine the susceptances of a reduced transmission network representation by using nonlinear optimization. We use Power Transfer Distribution Factors (PTDFs) to convert the original grid into a reduced version, from which we determine the susceptances. From our case studies we find that considering a reduced injection-independent evaluated PTDF matrix is the best approximation and is by far better than an injection-dependent evaluated PTDF matrix over a given set of arbitrarily-chosen power injection scenarios. We also compare our nonlinear approach with existing methods from literature in terms of the approximation error and computation time. On average, we find that our approach reduces the mean error of the power flow deviations between the original power system and its reduced version, while achieving higher but reasonable computation times

Supervisory hybrid model predictive control for voltage stability of power networks

International audienceEmergency voltage control problems in electric power networks have stimulated the interest for the implementation of online optimal control techniques. Briefly stated, voltage instability stems from the attempt of load dynamics to restore power consumption beyond the capability of the transmission and generation system. Typically, this situation occurs after the outage of one or more components in the network, such that the system cannot satisfy the load demand with the given inputs at a physically sustainable voltage profile. For a particular network, a supervisory control strategy based on model predictive control is proposed, which provides at discrete time steps inputs and set-points to lower-layer primary controllers based on the predicted behavior of a model featuring hybrid dynamics of the loads and the generation system

Transmission Network Reduction Method using Nonlinear Optimization

This paper presents a new method to determine the susceptances of a reduced transmission network representation by using nonlinear optimization. We use Power Transfer Distribution Factors (PTDFs) to convert the original grid into a reduced version, from which we determine the susceptances. From our case studies we find that considering a reduced injection-independent evaluated PTDF matrix is the best approximation and is by far better than an injection-dependent evaluated PTDF matrix over a given set of arbitrarily-chosen power injection scenarios. We also compare our nonlinear approach with existing methods from literature in terms of the approximation error and computation time. On average, we find that our approach reduces the mean error of the power flow deviations between the original power system and its reduced version

Sector Coupling: SGEN Project

This study aimed at making a step in quantitatively analyzing the future energy system as a whole, i.e. considering all demand sectors and all potential energy carriers. The objective of the performed analysis has been to identify the potential individual role of each of the various energy carriers, as well as the way that they might complement each other towards an economic and efficient CO2-free energy system. The problem has been addressed by formulating and solving an optimization problem that explicitly models each of the considered energy carriers and the various generation, storage, energy carrier conversion, and demand technologies. The problem, which models an entire year in hourly resolution (i.e. it considers, in a sequential manner, 8760 time-steps), is optimizing the "operation" of the entire energy system, i.e. it dispatches for every hour all the dispatchable technologies (and curtails excess available generation), subject to the cross-country network constraints and the technology technical limits, with the objective to satisfy the final demand for energy carriers (demand curtailment is possible, but it is avoided except if otherwise, the problem is not feasible) at the minimum total cost. The performed analysis concluded with the following findings: 1. Huge investments in electricity generation technologies are needed in order to maintain energy adequacy (measured annually) if a pathway is followed where fossil fuels are eliminated from the heating and transport sectors. 2. Even with extremely high wind and solar penetration levels, reliably satisfying the final demand requires the presence of very high levels of installed peak power generation capacity and/or very aggressive demand-side flexibility schemes 3. Energy storage has a high value in the future energy system, at all time scales (from diurnal to seasonal). Hydrogen storage, in specific, is a great enabler for higher utilization of wind and solar. 4. It is questionable whether satisfaction of the end demand by means of hydrogen (instead of electrifying) brings value from the overall energy system perspective. 5. Switzerland just relying on the rest of Europe acting as a buffer (via electricity imports and exports) entails risks, because the moments when Switzerland will have an energy supply deficit (due to no solar availability) highly correlate with when the rest of Europe faces the same challenge

Nexus-e: eMark Module Documentation

Policy changes in the energy sector result in wide-ranging implications throughout the entire energy system and influence all sectors of the economy. Due partly to the high complexity of combining separate models, few attempts have been undertaken to model the interactions between the components of the energy-economic system. The Nexus-e Integrated Energy Systems Modeling Platform aims to fill this gap by providing an interdisciplinary framework of modules that are linked through well-defined interfaces to holistically analyze and understand the impacts of future developments in the energy system. This platform combines bottom-up and top-down energy modeling approaches to represent a much broader scope of the energy-economic system than traditional stand-alone modeling approaches. In Phase 1 of this project, the objective is to develop a novel tool for the analysis of the Swiss electricity system. This study illustrates the capabilities of Nexus-e in answering the crucial questions of how centralized and distributed flexibility technologies could be deployed in the Swiss electricity system and how they would impact the traditional operation of the system. The aim of the analysis is not policy advice, as some critical developments like the European net-zero emissions goal are not yet included in the scenarios, but rather to illustrate the unique capabilities of the Nexus-e modeling framework. To answer these questions, consistent technical representations of a wide spectrum of current and novel energy supply, demand, and storage technologies are needed as well as a thorough economic evaluation of different investment incentives and the impact investments have on the wider economy. Moreover, these aspects need to be combined with modeling of the long- and short-term electricity market structures and electricity networks. This report illustrates the capabilities of the Nexus-e platform. The Nexus-e Platform consists of five interlinked modules: 1. General Equilibrium Module for Electricity (GemEl): a computable general equilibrium (CGE) module of the Swiss economy, 2. Centralized Investments Module (CentIv): a grid-constrained capacity expansion planning module considering system flexibility requirements, 3. Distributed Investments Module (DistIv): a generation expansion planning module of distributed energy resources, 4. Electricity Market Module (eMark): a market-based dispatch module for determining generator production schedules and electricity market prices, 5. Network Security and Expansion Module (Cascades): a power system security assessment and transmission system expansion planning module. This report provides the description and documentation for the eMark module, which is utilized in the Nexus-e framework to provide a market-based dispatch of generators that better reflects the actual procedures currently used to clear the energy and reserve markets as well as the timing of the various market products and the coupling of market zones