Parallel Power System Restoration Research Articles

Parallel Power System Restoration

After a blackout event, power system restoration is an essential activity for grid resilience; operators restart generators, re-establish transmission paths, and restore loads. With a goal of restoring electric service in the shortest time, the core decisions in restoration planning are to partition the grid into subnetworks, each of which has an initial power source for black-start (called sectionalization problem), and then restart all generators in each network (called generator startup sequencing (GSS) problem) as soon as possible. Due to their complexity, the sectionalization and GSS problems are usually solved separately, often resulting in a suboptimal solution. Our paper develops models and computational methods to solve the two problems simultaneously. We first study the computational complexity of the GSS problem and develop an efficient integer linear programming formulation. We then integrate the GSS problem with the sectionalization problem and develop an integer linear programming formulation for the parallel power system restoration (PPSR) problem to find exact optimal solutions. To solve larger systems, we then develop bounding approaches that find good upper and lower bounds efficiently. Finally, to address computational challenges for very large power grids, we develop a randomized approach to find a high-quality feasible solution quickly. Our computational experiments demonstrate that the proposed approaches are able to find good solutions for PPSR in up to 2,000-bus systems. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This research was supported by the Visiting Faculty Program of Argonne National Laboratory and the U.S. Department of Energy Advanced Grid Modeling Program [Grant DE-OE0000875].

Propagation-Based Network Partitioning Strategies for Parallel Power System Restoration With Variable Renewable Generation Resources

Grid resiliency is defined as the ability to prepare for and adapt to changing conditions and withstand and recover rapidly from disruptions. Following large-scale disruptions of the power grid such as a complete blackout, parallel power system restoration accelerates the recovery process by allowing for simultaneous restoration in each island through network partitioning, thus enhancing grid resiliency. However, existing network partitioning strategies have not sufficiently considered variable renewable resources yet, and may not be flexible or computationally efficient to accommodate additional requirements from the evolving bulk power grid. To bridge these gaps, this study proposes a propagation-based optimization approach for power grid network partitioning. The requirements of blackstart resources, power balancing, synchrocheck relays for ties lines, and increased ramp rate requirements due to variable renewable resources are modeled in the constraints. Through propagation on the physical connectivity of grid assets, the network partitioning issue is formulated as a mixed integer linear programming (MILP) problem. The linearity ensures highly computational performance and optimality of the solutions from the proposed approach to identify the cutset edge possibilities for bulk power grid applications. Graph reduction strategies are proposed to further improve the computational performance for online or nearly online applications. Case studies based on two IEEE benchmark systems show that the proposed MILP model is able to determine the optimal cutset for network partitioning in approximately 0.28 seconds, and the proposed network reduction strategy is able to further improve the computational performance by approximately 9%.

An Improved Label Propagation Algorithm-Based Method to Develop Sectionalizing Strategies for Parallel Power System Restoration

The first task of parallel power system restoration is to sectionalize the blackout system into multiple subsystems. This paper applies the complex network community discovery theory into this sectionalizing problem and proposes an improved label propagation algorithm-based sectionalizing method considering the system topology and operation before blackouts. Firstly, each blackstart (BS) unit bus is marked with a different subsystem label. A label propagation matrix is calculated based on the active power of branches before the blackout. Then, to avoid the label oscillation, a novel label impact strategy considering the influence of the bus label itself is developed to improve the label propagation matrix. The buses' labels propagate to neighboring buses as the improved label propagation matrix until they do not change. The initial sectionalizing strategy is obtained through classifying the buses with the same label in the same subsystem. Finally, the sectionalizing constraints are used to evaluate the feasibility of the initial strategy. For the initial strategy that does not satisfy the constraints, a refining method to minimize the absolute value of active power exchange among subsystems is proposed to determine the final sectionalizing strategy based on it. Case studies on IEEE 39-bus and IEEE 118-bus test systems verify the effectiveness of the proposed method. The results indicate that the proposed method has advantages in creating strongly connected subsystems.

Parallel power system restoration planning using heuristic initialization and discrete evolutionary programming

This paper proposes a sectionalizing planning for parallel power system restoration after a complete system blackout. Parallel restoration is conducted in order to reduce the total restoration process time. Physical and operation knowledge of the system, operating personnel experience, and computer simulation are combined in this planning to improve the system restoration and serve as a guidance for system operators/planners. Sectionalizing planning is obtained using discrete evolutionary programming optimization method assisted by heuristic initialization and graph theory approach. Set of transmission lines that should not be restored during parallel restoration process (cut set) is determined in order to sectionalize the system into subsystems or islands. Each island with almost similar restoration time is set as an objective function so as to speed up the resynchronization of the islands. Restoration operation and constraints (black start generator availability, load-generation balance and maintaining acceptable voltage magnitude within each island) is also taken into account in the course of this planning. The method is validated using the IEEE 39-bus and 118-bus system. Promising results in terms of restoration time was compared to other methods reported in the literature.

Controlled Islanding with Special Consideration of Parallel Power System Restoration Constraints

Las islas controladas intencionales (ICI, siglas en inglés) pueden evitar apagones de gran extensión mediante la división del sistema eléctrico en islas después de una perturbación severa. No obstante, eventos posteriores a la creación de estas islas podrían conducir a inestabilidades que pueden resultar en apagones dentro de una o más islas. Por lo tanto, garantizar que estas se puedan restaurar en el caso de apagones locales es fundamental, sin embargo, esto no se ha abordado en la literatura. Para llenar este vacío, este artículo propone un método de ICI que considera junto a sus restricciones típicas, la restauración en paralelo del sistema de potencia (PPSR, siglas en inglés). Se considera la mínima interrupción del flujo de potencia garantizando la coherencia de generadores, pero se amplía para incluir al menos una unidad de arranque autógeno dentro de cada isla y para excluir distintas líneas de las posibles soluciones. El método cuantifica la generación de energía activa y reactiva disponible dentro de cada isla para determinar la máxima demanda que puede ser incrementada. Utilizando el método propuesto, el proceso derestauración puede facilitarse y acelerarse. Para demostrar la eficacia del método propuesto en la determinación de una solución de islas considerando PPSR, fueron realizadas simulaciones en dos sistemas de la IEEE con diferentes topologías y tamaños.

Network partitioning strategy for parallel power system restoration

Parallel restoration is an efficient way to speed up the restoration process after a wide-area outage or a complete blackout of a power system. To implement efficient parallel restoration, an appropriate network partitioning method is necessary. Given this background, a two-step network partitioning strategy for parallel power system restoration is presented. In order to minimise the restoration time of generating units, a grouping model for non-black-start units is developed first. Based on the graph theory, a power network partitioning model is presented with the objectives of minimising the number of the interconnected lines and maximising the electrical distance of the interconnected lines among different restoration subsystems. The well-established AMPL/CPLEX is employed to solve the developed optimisation models. Finally, the IEEE New England 10-unit 39-bus system and a part of Zhejiang provincial power system in China are employed to illustrate the feasibility and effectiveness of the developed models.

Sectionalising methodology for parallel system restoration based on graph theory

Parallel power system restoration (PPSR) restores isolated sections (islands) of the network in parallel, thus the overall restoration process is accelerated. These islands are defined during the preparation stage of PPSR as part of a sectionalising strategy (SS). During this process, it is important that the operators only use updated post-blackout system information. This study proposes a new methodology based on the ‘cut-set’ matrix defined in graph theory, which can identify a shortlist of suitable SSs that satisfy the critical PPSR constraints in a few minutes. This short list of SSs, not identified in previous works, can be presented to the operators to help them select a restoration plan that is tailored to the specific changes in topology and asset availability that the blackout has caused. The methodology is illustrated using the IEEE 9-bus system, and validated using the IEEE 118-bus and the Polish 3375-bus system to demonstrate the efficiency of the new approach for large-scale networks. Multiple case studies are developed to demonstrate the adaptability of the methodology to different system conditions, for example, the unavailability of assets. In every case, the methodology quickly identified a number of SSs that create suitable islands for parallel restoration.

Sectionalizing strategies for minimizing outage durations of critical loads in parallel power system restoration with bi-level programming

Fast restoration of critical loads and non-black-start generators can significantly reduce the economic losses caused by power system blackouts. In a parallel power system restoration scenario, the sectionalization of restoration subsystems plays a very important role in determining the pickup of critical loads before synchronization. Most existing research mainly focuses on the startup of non-black-start generators. The restoration of critical loads, especially the loads with cold load characteristics, has not yet been addressed in optimizing the subsystem divisions. As a result, sectionalized restoration subsystems cannot achieve the best coordination between the pickup of loads and the ramping of generators. In order to generate sectionalizing strategies considering the pickup of critical loads in parallel power system restoration scenarios, an optimization model considering power system constraints, the characteristics of the cold load pickup and the features of generator startup is proposed in this paper. A bi-level programming approach is employed to solve the proposed sectionalizing model. In the upper level the optimal sectionalizing problem for the restoration subsystems is addressed, while in the lower level the objective is to minimize the outage durations of critical loads. The proposed sectionalizing model has been validated by the New-England 39-bus system and the IEEE 118-bus system. Further comparisons with some existing methods are carried out as well.

Determination of sectionalising strategies for parallel power system restoration: A spectral clustering-based methodology

Parallel power system restoration (PPSR) accelerates the restoration of a system in complete blackout by restoring isolated sections (islands) of the network in parallel. These islands are defined during the preparation stage of PPSR using a sectionalising strategy that considers system information collected after the blackout and must satisfy multiple PPSR constraints. This paper introduces a methodology based on spectral clustering that, in contrast to existing approaches, uses the physical and inherent properties of the network to determine a suitable solution. An undirected edge-weighted graph is initially constructed based on the electrical distance between buses, and constraints related to transmission line availability and cranking groups are included by modifying the edge-weights of the graph and using a subspace projection. This graph is then used to define islands that have strong internal connections but weak external connections, whilst satisfying the following constraints: blackstart availability, load-generation balance, voltage stability and the ability to monitor synchronisation between adjacent islands. Simulation results for the Institute of Electrical and Electronic Engineers (IEEE) 39- and IEEE 118-bus test systems demonstrate the ability of the methodology to define a strategy that creates strongly connected islands. Additionally, they indicate that the new approach determines solutions that have larger ratios between the inter-cluster electrical distance and the intra-cluster electrical distance for larger systems.

Closure to Discussion of “OBDD-Based Sectionalizing Strategies for Parallel Power System Restoration”

It is necessary to explain the definition of “path”, “solution”, and “strategy” in the paper. A “path” is the line in the OBDD connection diagram from xι to the terminal node “1”. Each “path” could be related to multiple “solutions”. A “solution” is the full combination of all binary parameters in the OBDD. The “strategy”, which is the final result of the paper, is the boundaries that will split the entire original system into two or more subsystems so that parallel restoration can be carried out within the subsystems.

Discussion on “OBDD-Based Sectionalizing Strategies for Parallel Power System Restoration”

The paper is a discussion on the work of C. Wang et al. (2011). The paper argues the incorrect results from the simulation study presented in the above work.

Discussion on "OBDD-Based Sectionalizing Strategies for Parallel Power System Restoration"

Discussion on "OBDD-Based Sectionalizing Strategies for Parallel Power System Restoration"