Oleg O. Khamisov’s research while affiliated with Skolkovo Institute of Science and Technology and other places

In this paper virtual synchronous generation (VSG) approach is investigated in application to low- and zero-inertia grids operated by grid-forming (GFM) inverters. The key idea here is to introduce dynamic inertia and damping constants in order to keep power gird stable during different types of faults, islanding or large power balance oscillations. In order to achieve such robustness, we introduce frequency and phase angle shift functions to VSG along with dynamics virtual generator parameters. The stability of such approach is theoretically proven and theoretical results are supported by detailed case studies in RTDS (Real-Time Digital Simulator) NovaCor 1.0 with GFM inverters dynamics simulated with 1-3 microseconds timestep using two-level universal inverter model. Case studies include all aforementioned types of faults and demonstrate increased power grid robustness and survivability in comparison with traditional synchronous generation of comparable size.

We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if they were distributed. We demonstrate that for the proposed distributed method: (i) communications are significantly less time-consuming than oracle calls, (ii) its convergence rate is equivalent to the convergence of Newton’s method concerning oracle calls, and (iii) for the cases when oracle calls are more expensive than communication between agents, the transition from a centralized to a distributed paradigm does not significantly affect computational time. The proposed method is applicable when the objective function is twice differentiable and constraints are differentiable, which holds for a wide range of machine learning methods and optimization setups.

In this paper we propose a novel distributed continuous-time algorithm aimed to solve optimization problems with cost function being a sum of local strictly convex multidimensional functions associated to individual agents. Additionally, the problems can have coupled equality and inequality constraints. We prove global asymptotic convergence of the algorithm for a connected graph topology. In order to investigate its practical implementation, we analyze convergence when Euler method is applied to represent discrete-time communication. Finally, we support our results with numerical experiments of the developed approach application for power balancing in New England power system.

This study investigates the application of the maximum Lyapunov exponent in combination with k-means clustering to identify short-term voltage instability in multi-machine power grids. The authors explored the complex regulatory challenges that arise with the integration of renewable energy sources, particularly during short-term voltage instability episodes. The critical role of the maximum Lyapunov exponent in mitigating these risks and bolstering grid resilience was emphasized. This research involved detailed modeling of transient processes within the grid, followed by an in-depth analysis of the resulting data. By integrating maximum Lyapunov exponent with clustering method, this study introduces an automated approach to labeling voltage measurement sets, effectively differentiating between transient regimes, such as short-term voltage instability, normal operational modes, and faults. Extensive numerical experiments conducted using PSCAD simulation software demonstrate the effectiveness of the proposed approach in providing a comprehensive monitoring solution for transient regimes and significantly enhancing stability of the power system with renewable energy sources.

Frequency control is one of the key aspects connected with usage of power electronic devices. On the one hand, replacement of synchronous generation with power electronic interfaces removes kinetic energy of rotor’s rotating mass, making system dynamics more volatile. On the other hand, fast response to control signals calls for a shift control paradigm. In this work a bang-bang primary frequency control is proposed. Its effectiveness is supported by both theoretical results and detailed numerical experiments.

The ever-growing trend of Converter-Interfaced Generation (CIG) integration in electrical power grids has led to a tremendous concern about systems' inertia, stability, and frequency regulation effectiveness. During contingencies, like the loss of a large generator, the primary frequency control is deployed to compensate for the frequency drop. However, as CIG penetration grows, traditional primary frequency control becomes less effective in mitigating significant post-contingency frequency deviations. To address this problem, we introduce a novel control framework that fully utilizes the proportional primary frequency control concept manifested in the contingency-aware control discontinuity. The proposed framework collects information about the disturbance and redistributes control gains according to the pre-calculated optimal strategy employing dynamic properties of both synchronous generation and CIG. It incorporates a novel frequency security assessment using frequency majorant functions, providing a conservative low boundary estimate of the frequency nadir. Numerical studies demonstrate that this proposed control strategy reduces nadir deviation by 49% and shortens the transient period by 30%. Furthermore, we illustrate the optimization of droop control gains considering CIG characteristics, such as location and inertia, to enhance system stability by allowing CIGs to perform primary frequency control functions from synchronous generators.

Modern power systems are now in continuous process of massive changes. Increased penetration of distributed generation, usage of energy storage and controllable demand require introduction of a new control paradigm that does not rely on massive information exchange required by centralized approaches. Distributed algorithms can rely only on limited information from neighbours to obtain an optimal solution for various optimization problems, such as optimal power flow, unit commitment etc. As a generalization of these problems we consider the problem of decentralized minimization of the smooth and convex partially separable function $f = \sum_{k=1}^l f^k(x^k,\tilde x)$ under the coupled $\sum_{k=1}^l (A^k x^k - b^k) \leq 0$ and the shared $\tilde{A} \tilde{x} - \tilde{b} \leq 0$ affine constraints, where the information about $A^k$ and $b^k$ is only available for the k-th node of the computational network. One way to handle the coupled constraints in a distributed manner is to rewrite them in a distributed-friendly form using the Laplace matrix of the communication graph and auxiliary variables (Khamisov, CDC, 2017). Instead of using this method we reformulate the constrained optimization problem as a saddle point problem (SPP) and utilize the consensus constraint technique to make it distributed-friendly. Then we provide a complexity analysis for state-of-the-art SPP solving algorithms applied to this SPP.