Project Background

Bulk power system restoration, recovering electricity service after a partial or complete blackout, is one of the most important resilience capabilities for power grid. However, because restoration activities, such as planning, drilling, etc., are very complex and resource/time-consuming, and large-area blackouts are rare events, restoration, as a major resilience capability, has been receiving significantly less R&D efforts from both industry and academia than it should be. As a result, the modeling, computational methods and decision support tools in power system restoration are still underdeveloped. As new energy components integrated into power system (e.g., renewable energy and storages), many emerging issues in restoration, e.g., crew/utility truck routing during restoration etc., are completely left out. Most decision-support tools, including state-of-the-art commercial tools (e.g., SRN by EPRI), are not taking advantage of the advance in computing technologies and are not computationally effective/efficient for demanding restoration activities. In summary, system restoration is a core resilience capability in power grid; however, due to its complexity and infrequent occurrence, industry and academia are not spending sufficient R&D efforts on restoration, resulting in a significant lack of computing/analytical tools to support system restoration activities. There is an urgent need for DOE and national labs to leverage their mathematical, computing and power engineering expertise to help enhance this resilience capability for U.S. power grid.

Objective:

In this project, we will develop a set of highly efficient mathematical models and computational algorithms (math programming and machine learning) for a number of fundamental optimization tasks in restoration activities, such as controlled islanding, generator restart sequencing, etc. This set of models and algorithms will lay down a computing framework to support most commonly practiced restoration activities. We will also closely interact with industry, understand their emerging needs, clearly define mathematical problem scopes, and develop computational methods. Those emerging needs include, but not limited to, renewable participated restoration, co-optimized crew/utility truck routing with restoration, coordinated transmission and distribution restoration.

Approaches:

This project will take the following approaches. (1) advanced modeling, properly define mathematical problems for decisions in restoration activities. Although there are several standard restoration procedures practiced at different utilities and operators, the decision problems in restoration, in general, are not well defined and can vary from operator to operator. For example, ERCOT needs to send crews to check online and switch status before/during restoration. This is a traveling salesman problem, a classic combinatorial optimization, mixed with the restarting sequencing problem. However, this problem was never properly defined (hence dedicated algorithms investigated for this problem) before this project. Only after properly defining the problem scope and building the mathematical structure, can we start developing computational algorithms. (2) mathematical programming. Math programming includes many modern computing tools, such as mixed-integer programming, dynamic programming, decomposition, etc. Due to the lack of investigation from math programming perspectives, many restoration problems still do not have efficient algorithms. Most of research simply builds a model for some restoration problem and then directly throw the model in to a solver, not looking into solution algorithms. As a result, most of the research papers hardly have reasonable scalability. One example is the generator restart sequencing, which has a clear recursive structure, good for dynamic programming algorithms. However, to the best of the PI’s knowledge, there hasn’t been any study investigating dynamic programming algorithms for generator restart sequencing problem. This project will explore various math programming approaches to address the computational challenges in power system restoration problems. (3) machine learning. ML can be greatly helpful in the following scenarios: (a) physical constraints are extremely complex and a data-driven model can significantly reduce the complexity. For example, description of trajectory constraints requires differential algebraic equations (DAEs), which is complex and computationally challenging. However, the system dynamic behavior could be characterized by a machine learning model, leaving out the complex DAEs. (b) a quick solution with satisfactory quality. In many scenarios where the real situation (e.g., damages and available resources) is very different from what has been planned and drilled, a fast restoration scheduling is needed. Following the standard restoration optimization workflow might take too long in this emergency. A well-trained ML model can quickly generate a satisfactory scheduling, such as reinforce learning, active learning, and other ML models.

The team proposes the following frameworks to address the computational challenges in restoration.

1. Optimization algorithms for co-optimization of system restoration and repair crew routing. We first develop fast heuristics for system restoration. Then we study the general form of the problem with dynamic programming, which is an important technique to understand the problem structure and prepare for more advanced and exact algorithms. We will develop effective mixed-integer programming formulations and computational methods.
2. Novel semi-analytical simulation (SAS) method for dynamic simulation in system restoration. This SAS method utilizes a homomorphic embedding (HE) technique and turns the system of differential-algebraic equations into an equation system with polynomials. HE-based SAS has major advantages over existing dynamic simulation: longer simulation steps, higher precision, and better convergence property. HE-based SAS is especially suitable for dynamic simulation in system restoration because restoration could last for hours and even days and the system is very stressed, causing convergence issues for traditional simulation methods.
3. Fast algorithms for bulk power system restoration. We will propose fast algorithms using better formulation and decomposition algorithms, reducing the restoration problems into subproblems with less complexity. More effective formulation will also be investigated to achieve better computational performance.
4. Machine learning to accelerate solution time of restoration. We will propose machine learning and deep learning techniques, such as imitation and reinforcement learning, to train optimal restoration policy, which will provide the next optimal action given the current system condition. This policy can be used to accelerate solution time of restoration.

Deliverables and Impacts

Deliverables and Impacts

The deliverables in this project will include a number of simulation and optimization tools. An existing restoration tool developed at Argonne, the Electric Grid Resilience Improvement Program (EGRIP), will be enhanced using the results developed in this project. Peer-reviewed journal publications and conference presentations will also be produced.

Public presentations:

• Bahar Cavdar, Qie He, Feng Qiu ​“Power Distribution Network Restoration: Repair Crew Routing”, in preparation
• Sang Ho Shim, Feng Qiu, ​“Service vehicle routing for power system restoration”, to be submitted.
• Sunil Chopra, Feng Qiu, Sang Ho Shim, ​“Parallel computing for transmission system restoration”, to be submitted.
• Rui Yao, Feng Qiu. ​“Extended-Term Simulation for Resilience Analysis Based on Holomorphic Embedding”, IEEE Transactions on Power Systems, under review.
• Yichen Zhang, Hantao Cui, Jianzhe Liu, Feng Qiu, Tianqi Hong, Rui Yao, Fangxing Li, ​“Encoding frequency constraints in preventive unit commitment using deep learning with region-of-interest active sampling,” IEEE Transactions on Power Systems, under review.
• Yichen Zhang, Feng Qiu, Tianqi Hong, Zhaoyu Wang, and Fangxing Li. ​“Hybrid Imitation Learning for Real-Time Service Restoration in Resilient Distribution Systems.” IEEE Transactions on Industrial Informatics, 2021, in press.
• Yichen Zhang, Chen Chen, Guodong Liu, Tianqi Hong, and Feng Qiu. ​“Approximating Trajectory Constraints with Machine Learning - Microgrid Islanding with Frequency Constraints.” IEEE Transactions on Power Systems, 2020, in press.
• Rui Yao, Feng Qiu, ​“Distribution factors for AC power flow”, IEEE Transactions on Power Systems, 2020, in press.
• Bai Cui, Rui Yao, Feng Qiu, ​“Certification and Prediction of Post-Disturbance States in Dynamic Security Assessment”, Electric Power Systems Research, in press.

Team and contact

Argonne National Laboratory

Lab Lead Team Members

Dr. Yichen Zhang
Dr. Sang Ho Shim, Robert Morris University, Visiting Faculty Position

Project PI: Dr. Feng Qiu
Principal Computational Scientist and Group Manager
fqiu@​anl.​gov