Long Solution Times or Low Solution Quality: On Trade-Offs in Choosing a Power Flow Formulation for the Optimal Power Shut-Off Problem

The Optimal Power Shutoff (OPS) problem is an optimization problem that makes power line de-energization decisions in order to reduce the risk of igniting a wildfire, while minimizing the load shed of customers. This problem, with DC linear power flow equations, has been used in many studies in recent years. However, using linear approximations for power flow when making decisions on the network topology is known to cause challenges with AC feasibility of the resulting network, as studied in the related contexts of optimal transmission switching or grid restoration planning. This paper explores the accuracy of the DC OPS formulation and the ability to recover an AC-feasible power flow solution after de-energization decisions are made. We also extend the OPS problem to include variants with the AC, Second-Order-Cone, and Network-Flow power flow equations, and compare them to the DC approximation with respect to solution quality and time. The results highlight that the DC approximation overestimates the amount of load that can be served, leading to poor de-energization decisions. The AC and SOC-based formulations are better, but prohibitively slow to solve for even modestly sized networks thus demonstrating the need for new solution methods with better trade-offs between computational time and solution quality

Optimal operation of DC networks to support power system outage management

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The penetration of dc networks for different applications in power systems is increasing. This paper presents a novel methodology for security-constrained optimal power flow (SCOPF) operation of a power system, such as a smart grid or a supergrid, with an embedded dc network. The methodology demonstrates that dc networks can be operated to provide support to ac systems, increasing its security of supply and resilience in case of outages, while reducing operational costs. Moreover, the outage management support can be achieved via a preventive SCOPF – i.e. the combined network stays N-1 secure after outages without need for further control action – or via a corrective SCOPF, by using the fast controls of the ac-dc converters to react to the contingencies. The methodology relies on the construction of a binary outage matrix and optimizes only the control variables of the ac and dc networks. It was successfully tested in system with 12 buses and in the IEEE30 network with 35 buses. Operational savings of up to 1% and 0.52% were obtained for the first and second networks, respectively, while network violations for the N-1 contingency scenarios were completely eliminated in the first and reduced by 70% in the former.Postprint (author's final draft

MILP formulation for controlled islanding of power networks

This paper presents a flexible optimization approach to the problem of intentionally forming islands in a power network. A mixed integer linear programming (MILP) formulation is given for the problem of deciding simultaneously on the boundaries of the islands and adjustments to generators, so as to minimize the expected load shed while ensuring no system constraints are violated. The solution of this problem is, within each island, balanced in load and generation and satisfies steady-state DC power flow equations and operating limits. Numerical tests on test networks up to 300 buses show the method is computationally efficient. A subsequent AC optimal load shedding optimization on the islanded network model provides a solution that satisfies AC power flow. Time-domain simulations using second-order models of system dynamics show that if penalties were included in the MILP to discourage disconnecting lines and generators with large flows or outputs, the actions of network splitting and load shedding did not lead to a loss of stability

On the Efficiency in Electrical Networks with AC and DC Operation Technologies: A Comparative Study at the Distribution Stage

This research deals with the efficiency comparison between AC and DC distribution networks that can provide electricity to rural and urban areas from the point of view of grid energy losses and greenhouse gas emissions impact. Configurations for medium-and low-voltage networks are analyzed via optimal power flow analysis by adding voltage regulation and devices capabilities sources in the mathematical formulation. Renewable energy resources such as wind and photovoltaic are considered using typical daily generation curves. Batteries are formulated with a linear representation taking into account operative bounds suggested by manufacturers. Numerical results in two electrical networks with 0.24 kV and 12.66 kV (with radial and meshed configurations) are performed with constant power loads at all the nodes. These simulations confirm that power distribution with DC technology is more efficient regarding energy losses, voltage profiles and greenhouse emissions than its AC counterpart. All the numerical results are tested in the General Algebraic Modeling System widely known as GAMS.Fil: Montoya Giraldo, Oscar Danilo. Universidad Tecnológica de Bolívar; Colombia. Universidad Distrital Francisco José de Caldas; ColombiaFil: Serra, Federico Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Luis; ArgentinaFil: de Angelo, Cristian Hernan. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Instituto de Investigaciones en Tecnologías Energéticas y Materiales Avanzados. - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Tecnologías Energéticas y Materiales Avanzados; Argentin

Steady-State Analysis and Optimal Power Routing of Standalone Unbalanced Hybrid AC/DC Microgrids

The concept of ac microgrids was introduced to integrate distributed generators (DGs) and loads within one entity that can operate autonomously or connected to a utility grid. Furthermore, dc microgrids have received increasing attention as a potential solution to deliver power from DGs to modern dc loads with reduced conversion stages. Moreover, hybrid ac/dc microgrids have been introduced as a paradigm combining the benefits of the two types of microgrids by interconnecting them through interlinking converters (ICs). Steady-state analysis is essential for planning and operation studies of electrical power systems. However, conventional analysis approaches cannot be applied to hybrid ac/dc microgrids due to their distinctive features, such as droop characteristics, lack of a slack bus, and coupling between the ac and dc variables. Additionally, the unbalanced nature of ac microgrids adds to the complexity of modeling and analysis in such networks. Therefore, this thesis is focused on developing steady-state modeling and analysis framework for standalone unbalanced hybrid ac/dc microgrids. First, a steady-state analysis tool for unbalanced hybrid ac/dc microgrids is developed. The ac subgrid's components are modeled in phase coordinates. Furthermore, the dc subgrid's components are modeled and the coupling between the ac and dc variables is formulated. The models of the various system elements are incorporated into a unified power flow formulation, which is solved using a Newton-Trust Region (NTR) method. The developed power flow algorithm is verified through comparisons with time-domain simulations of test microgrids. The analysis tool is used to analyze a larger hybrid ac/dc microgrid through case studies. The case studies shed light on some challenges of these microgrids, namely, imposed limitations on microgrid loadability due to unbalanced ac subgrid's loading, effect of IC settings on microgrid operation, and trade-off between proportional loading of the ac and dc subgrids and proportional power-transfer sharing among ICs. Second, based on the identified microgrid loadability limitation of unbalanced microgrids, a novel adaptive power routing (APR) scheme is proposed to maximize the microgrid loadability. The proposed scheme allows independent control of active and reactive powers flowing through IC phases, so that power can be routed among the ac subgrid's phases. The DPR scheme is integrated into an optimal power flow (OPF) formulation with the objective of minimizing load shedding. A supervisory controller is proposed to solve the OPF problem by adjusting the DG and IC settings. Several case studies are conducted to show the ineffectiveness of conventional supervisory controllers in resolving the loadability issue, and to verify the success of the proposed controller in solving the problem. Third, a power flow approach based on sequence component analysis of the ac microgrid's elements is adopted for faster convergence and improved modeling accuracy as compared to conventional approaches in phase coordinates. This approach breaks down the system model into positive-, negative-, and zero-sequence subsystems that can be solved in parallel for enhanced performance. The positive-sequence power flow is solved using a Newton-Raphson (NR) method, while the negative- and zero-sequence voltages are obtained by solving linear complex equations. The approach is verified through comparisons with time-domain simulations. In addition, the algorithm is utilized to investigate the operation of droop-controlled DGs in larger-scale isochronous unbalanced ac microgrids, and to examine its limit-enforcement abilities at the same time. The algorithm demonstrates significant improvements in terms of accuracy and convergence time when compared against the conventional NTR-based approach in phase coordinates. Finally, the power flow approach developed in the third part is extended to include the IC's and dc subgrid's models so that it can be applied to hybrid ac/dc microgrids. A power flow algorithm is proposed to solve the ac and dc power flows independently in a sequential manner, while maintaining the correlation between the two. The algorithm is verified through comparisons with time-domain models of test hybrid microgrids. Case studies are introduced to test the algorithm's effectiveness in enforcing the DG and IC limits in the power flow solution under various conditions. The algorithm also shows enhanced accuracy and solution speed with respect to the tool developed in the first stage

INTELLIGENT OPTIMIZATION OF INTERLINE POWER FLOW CONTROLLER IN TRANSMISSION SYSTEM

Flexible AC Transmission system (FACTS) controllers are widely accepted worldwide to provide benefits in increasing power transfer capability and maximizeing the use of the existing transmission networks. A new generation of FACTS controllers, particularly the Interline Power Flow Controller (IPFC) based on voltage source converter (VSC) provides fast power flow control flexibility. The IPFC with its unique capability of power flow management is significantly extended to control power flows of multi-lines or a sub network. Generally IPFC employs two or more VSCs connected together with DC links and each converter provides series compensation for the selected line of the transmission system. Optimal power flow is an important factor in power system operation, planning and control. In this thesis, the mathematical model of IPFC together with the modified Newton-Raphson method for power flow is used to derive the optimal parameters (the magnitude and voltage angles) of VSCs of IPFC. The optimal parameters are derived to minimize the transmission line losses using three intelligent optimization techniques, namely Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA). The proposed methods are applied using MATLAB 7.6 and tested on IEEE 14-bus and 30-bus bench mark power systems. The optimal parameters of IPFC, the voltage profile and the transmission line losses of the bench mark power systems are derived from the simulations. The simulation results obtained with PSO technique are compared with those obtained by other two optimization techniques. The thesis also covers the basic principles and operation of IPFC, the modified Newton-Raphson power flow method and an overview of the three intelligent optimization techniques used in this thesis. The results prove the efficacy of the three intelligent methods for the optimization of IPFC parameters and minimization of transmission line losses

Computational Complexity of Electrical Power System Problems

The study of the computational complexity of real-world applications, although theoretical, can provide many pragmatic outcomes. For example, demonstrating that some types of algorithms cannot exist to solve the problem; the creation of challenging benchmark examples; and new insights into the underling structure and properties of the problem. In this thesis, we study the computational complexity of several important problems in the application of electrical power systems. Knowledge of the current state of the power system is important for power network operators. This helps, for example, to predict if the network is trending towards an undesirable state of operation, or if a power line is working at its operational limits. The state of a power system is determined by the demand, the generation and the bus voltage magnitudes and phase angles. The demand of loads can be reliably estimated via forecasts, historic records and/or measurements and the operators of generators report the generation values. Given generation and demand values, the voltage magnitudes and phase angles can be computed. This is what is called the Power Flow problem. Cost for generating power often varies from generator to generator. In the Optimal Power Flow problem, the aim is to find the cheapest generation dispatch, such that the forecast demand can be satisfied. Disasters, such as storms or floods, and operator errors have to potential to destroy parts of the network. This can make it impossible to satisfy all the demand. In the Maximum Power Flow problem, the aim is to find a generation dispatch that can satisfy as much demand as possible. In this thesis, we provide the proofs that the Maximum Power Flow, Optimal Power Flow and the Power Flow problem are NP-hard for: radial networks in the Alternating Current power flow model and planar networks in the Linear AC Approximation (DC) power flow model with line switching. Furthermore, we show that there does not exist a polynomial approximation algorithm for the Optimal Power Flow problem in any of these settings. We also study the complexity of the Lossless-Sin AC Approximation power flow model, showing that the Maximum Power Flow and Optimal Power Flow problem are strongly NP-hard for planar networks

Advanced Modeling, Design, and Control of ac-dc Microgrids

An interconnected dc grid that comprises resistive and constant-power loads (CPLs) that is fed by Photovoltaic (PV) units is studied first. All the sources and CPLs are connected to the grid via dc-dc buck converters. Nonlinear behavior of PV units in addition to the effect of the negative-resistance CPLs can destabilize the dc grid. A decentralized nonlinear model and control are proposed where an adaptive output-feedback controller is employed to stabilize the dc grid with assured stability through Lyapunov stability method while each converter employs only local measurements. Adaptive Neural Networks (NNs) are utilized to overcome the unknown dynamics of the dc-dc converters at Distributed Energy Resources (DERs) and CPLs and those of the interconnected network imposed on the converters. Additionally, the use of the output feedback control makes possible the utilization of other measured signals, in case of loss of main signal, at the converter location and creates measurement redundancy that improves reliability of the dc network. The switching between measurement signals of different types are performed through using the NNs without the need to further tuning. Then, in a small-scale ac grid, PV-based Distributed Generation (DG) units, including dc/dc converters and inverters, are controlled such that mimic a synchronous generator behavior. While other control schemes such as Synchronverters are used to control the inverter frequency and power at a fixed dc link voltage, the proposed approach considers both the dc-link voltage and the inverter ac voltage and frequency regulation. The dc-link capacitor stores kinetic energy similar to the rotor of a synchronous generator, providing inertia and contributes to the system stability. Additionally, a reduced Unified Power Flow Controller (UPFC) structure is proposed to enhance transient stability of small-scale micro grids. The reduced UPFC model exploits dc link of the DG unit to generate appropriate series voltage and inject it to the power line to enhance transient stability. It employs optimal control to ensure that the stability of the system is realized through minimum cost for the system. A neural network is used to approximate the cost function based on the weighted residual method