Efficient parallel power grid analysis via additive Schwarz method

Electric power has become an essential part of daily life: we plug our electronic devices in, switch our lights on, and expect to have power. As the availability of power is usually taken for granted in modern societies, we mostly feel annoyed at its absence and perceive the importance of power during outages which have severe effects on the public order. Blackouts have had disastrous consequences for many countries and they continue to occur frequently. Such examples demonstrate the necessity for careful analysis and planning of power grids, to ultimately increase the reliability of power grids. The power grids have evolved due to economic, environmental and human-caused factors. In addition to the contingency analysis, nowadays, the operation and planning of power grids are facing many other challenges (such as demand growth, targeted attacks, cascading failures, and renewable energy integration). Thus, many questions arise, including: which buses (nodes) to connect with a new line (link)? What are the impacts of malicious attacks on power grids? How may an initial failure result in a cascade of failures? How to prepare for the integration of renewable energy? Answering such questions requires developing new concepts and tools for analysing and planning of power grids. Power grids are one of the largest and the most complex man-made systems on earth. The complex nature of power grids and its underlying structure make it possible to analyse power grids relying on network science. The applications of network science on power grids have shown the promising potential to capture the interdependencies between components and to understand the collective emergent behaviour of complex power grids. This thesis is motivated by the increasing need of reliable power grids and the merits of network science on the investigation of power grids. In this context, relying on network science, we model and analyse the power grid and its near-future challenges in terms of line removals/additions, malicious attacks, cascading failures, and renewable integration.

The bulk hydropower transmission via trans-provincial and trans-regional power networks in China provides great operational flexibility to dispatch power resources between multiple power grids. This is very beneficial to alleviate the tremendous peak load pressure of most provincial power grids. This study places the focus on peak operations of cascaded hydropower plants serving multiple provinces under a regional connected AC/DC network. The objective is to respond to peak loads of multiple provincial power grids simultaneously. A two-stage search method is developed for this problem. In the first stage, a load reconstruction strategy is proposed to combine multiple load curves of power grids into a total load curve. The purpose is to deal with different load features in load magnitudes, peaks and valleys. A mutative-scale optimization method is then used to determine the generation schedules of hydropower plants. In the second stage, an exterior point search method is established to allocate the generation among multiple receiving power grids. This method produces an initial solution using the load shedding algorithm, and further improves it by iteratively coordinating the generation among different power grids. The proposed method was implemented to the operations of cascaded hydropower plants on Xin-Fu River and another on Hongshui River. The optimization results in two cases satisfied the peak demands of receiving provincial power grids. Moreover, the maximum load difference between peak and valley decreased 12.67% and 11.32% in Shanghai Power Grid (SHPG) and Zhejiang Power Grid (ZJPG), exceeding by 4.85% and 6.72% those of the current operational method, respectively. The advantage of the proposed method in alleviating peak-shaving pressure is demonstrated.

With the development of power electronic devices, the research of Flexible AC Transmission System (FACTS) in regulating line power flow and improving static voltage stability is more in-depth. This paper discusses the static voltage stability of power grid with new energy taking into account the distributed static series compensator (DSSC), and evaluates the power flow control efficiency of DSSC from the aspect of system static voltage stability. First, the equivalent circuit and working principle of DSSC are analyzed, and the power flow equations are obtained based on the equivalent power injection model of DSSC; Secondly, based on the power flow calculation equation, the efficiency evaluation index that can reflect the static voltage stability of the system is proposed, and the impact of new energy with different capacities on the static voltage stability is calculated and analyzed; Finally, the proposed method is verified by the simulation analysis of IEEE-24 bus system and actual power grid: the proposed method is fast and simple, and has certain engineering application value.

The global power grid is undergoing a major transformation as a result of the growing utilization of renewable energy sources (RESs). The incorporation of these RESs is leading to a decline in the use of conventional synchronous generators and an increase in the use of inverter-based RESs. This shift is causing a decrease in the grid's inertia, presenting substantial difficulties for grid operators to maintain frequency stability. The purpose of this study is to examine the impact of declining inertia on the frequency behavior of the grid, as RESs become more prevalent. In order to measure the impact, this study utilizes eigenvalue analysis of power grids to assess the sensitivity of grid frequency and rate of change of frequency (RoCoF) characteristics, as well as the lowest frequency, to variations in grid inertia resulting from changes in RES penetration. Moreover, we have introduced indices that quantify the impact of RES penetration on the grid frequency behaviour in comparison to a grid without RES. To showcase the proposed approach, this research presents case studies using the modified IEEE 39 bus test system, which demonstrate the ability to assess the impact of a high RESs penetration on grid frequency characteristics.

As the size and complexity of current VLSI circuits grows, faster power grid simulation is becoming more and more desirable. In this article, we present a parallel iterative method for static VLSI power grid simulation. In the proposed enlarged-partition-based preconditioned conjugate gradient (EPPCG) power grid solver, the power grid is divided into disjoint partitions that are subsequently enlarged to obtain accurate solution within each partition. The global solution obtained by solving enlarged partition problems concurrently acts as a highly effective parallel preconditioner. The combination of effective preconditioning and efficient parallelization helps achieve very high performance. The experiments show that our parallel implementation can achieve significant speed improvement [61X--142X] over a state-of-the-art direct solver.

Large VLSI on-chip power delivery networks (PDN) are challenging to analyze due to sheer network complexity. In this paper, three power grid solvers developed in our group: a direct solver using Cholesky decomposition, a GPU-based multigrid preconditioning solver, and a partitioning-based solver using spatial locality, are reviewed. Following the requirements of TAU 2011 Power Grid Simulation Contest, single-threaded versions of these solvers are implemented and their performances are evaluated in terms of runtime, memory, maximum error and average error. The experimental results show that for the published IBM power grid benchmarks, the direct solver has the best overall performance among the three.

An effective three-stage hybrid optimization method for source-network-load power generation of cascade hydropower reservoirs serving multiple interconnected power grids

Network topology and resilience analysis of South Korean power grid

The study of static voltage stability is actually based on asymptotic stability, which is affected by the operation state of the power grid. In this paper, the voltage stability margin index is deduced, and the stability margin of the existing power grid under different actual working conditions is analyzed based on the proposed index. the leading factors and the worst system conditions are determined by practical experience. The correctness of the proposed method is verified by the simulation analysis of the actual provincial power grid.

Dynamic load model is of great value in analysis and simulation of power grid, while the composition of load has an important influence on the characteristic and accuracy of load model. There is mass of load equipment in power grid, so it is usually necessary to classify the load equipment according to their different characteristic first, then establish a suitable load model separately, and synthesize them into a composite model according to their proportion. Only the power value of load can be measured when power grid operates in a normal and steady state, and their dynamic response characteristics are unknown. Therefore, it is difficult to obtain sufficient information for load classification. However, frequency characteristics of load are distinguished and easy to obtain, so it is useful for load classification indirectly. Firstly, several elector-magnetism models of typical load are established, and their harmonic curves and frequency characteristic are simulated and analyzed separately. Then, cluster analysis is carried out to obtain the typical characteristics and the membership degree which can represent the contents of load overall. Finally, a classification method combined with Neural Network is adopted, and the computation speed is also improved.

As VLSI techniques are getting more and more advanced, the size of the power grid network increases dramatically. Therefore, the power grid analysis becomes a challenging task during the design procedure. This work utilizes the macromodeling technique [1] and enhances the Orthogonal Matching Pursuit (OMP) based method [2] to develop an effective and robust incremental analysis method for the power grid network, MA-OMP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> . Given a power grid network, MA-OMP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> not only can deal with the change of its element values but also can handle the modification of its topology. The experimental results show that MA-OMP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> can be an order of magnitude faster than the OMP-based method [2] which can only deal with the change of element values of the power grid. The experimental results also demonstrate that MA-OMP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> can accurately and efficiently handle the modified topology of the power grid network.

Iterative linear equation solvers depend on high quality preconditioners to achieve fast convergence. For sparse symmetric systems arising from large power grid analysis problems, however, preconditioners generated by traditional incomplete Cholesky factorizations are usually of low quality, resulting in slow convergence. On the other hand, although preconditioners generated by random walks are quite effective to reduce the number of iterations, it takes considerable amount of time to compute them in a stochastic manner. In this paper, we propose a new preconditioning technique for power grid analysis, named deterministic random walk, that combines the advantages of the above two approaches. Our proposed algorithm computes the preconditioners in a deterministic manner to reduce computation time, while achieving similar quality as stochastic random walk preconditioning by modifying fill-ins to compensate dropped entries. We have proved that for such compensation scheme, our algorithm will not fail for certain matrix orderings, which otherwise cannot be guaranteed by traditional incomplete factorizations. We demonstrate that by incorporating our proposed preconditioner, a conjugate gradient solver is able to outperform a state-of-the-art algebraic multigrid preconditioned solver on public IBM power grid benchmarks for DC power grid analysis, while potentially remaining very efficient for transient analysis.

Power grid analysis is a challenging problem for modern integrated circuits. For 3-D systems fabricated using stacked tiers with TSVs, traditional power grid analysis methods for planar (2-D) circuits do not demonstrate the same performance. An efficient IR drop analysis method for 3-D large-scale circuits, called 3-D voltage propagation method, is proposed in this paper. This method is compared with another widely used power grid analysis method, with preconditioned conjugated gradients. Simulation results demonstrate that the proposed method is more efficient for the IR drop analysis of large size 3-D power grids. Speedups between 10× to 20× over the preconditioned conjugated gradients method are shown.

Effective assessment of power grid investment efficiency is crucial for optimizing resource allocation and improving operational performance. However, existing evaluation methods typically fail to account for two critical factors: inherent uncertainties in input–output data and temporal delays in investment returns. To address these limitations, this study introduces an integrated evaluation framework combining robust optimization techniques for uncertain variables with a time-lag Data Envelopment Analysis (DEA) approach to capture the multi-period dynamics and ensure resilience against external shocks and data perturbations. An empirical analysis conducted on panel data from 31 provincial power grid enterprises in China (2015–2023) reveals significant regional disparities in efficiency, particularly between coastal and resource-rich provinces. The findings highlight that excluding time-lag effects leads to systematic underestimation of efficiency and employing robust optimization yields more resilient efficiency scores amidst data uncertainties. The study contributes methodologically by advancing DEA frameworks to better reflect the complexities of power grid investments and empirically provides valuable insights for policymakers seeking to enhance investment strategies and achieve sustainable development goals.

New techniques and approaches are constantly being introduced to analyze and enhance the transient stability of renewable energy-source-dominated power systems. This review article extensively discusses recent papers that have proposed novel and innovative techniques for analyzing and enhancing the renewable source-dominated power system’s transient stability. The inherent low-inertia characteristics of renewable energy sources combined with fast-acting power electronic devices pose new challenges in power systems. Different stability concerns exist for grid-following and subsequent grid-forming converter/inverter connections to power grids; hence, distinct solutions for enhancing the transient stability have been devised for each. Moreover, the fundamental concepts and characteristics of converter/inverter topologies are briefly discussed in this study. Recent discussions and reviews of analysis and enhancement techniques in transient stability could lead to new ways to solve problems in power systems that rely primarily on renewable energy sources.