arXiv subjects

Konstantin Turitsyn

Publications and source records attributed to Konstantin Turitsyn.

At least 19 recordsLinked to original sources

arXiv2021

Network Topology Invariant Stability Certificates for DC Microgrids with Arbitrary Load Dynamics

DC microgrids are prone to small-signal instabilities due to the presence of tightly regulated loads. This paper develops a decentralized stability certificate which is capable of certifying the small-signal stability of an islanded DC network containing such loads. Utilizing a novel homotopy approach, the proposed standards ensure that no system eigenmodes are able to cross into the unstable right half plane for a continuous range of controller gain levels. The resulting "standards" can be applied to variety of grid components which meet the specified, but non-unique, criteria. These standards thus take a step towards offering plug-and-play operability of DC microgrids. The proposed theorems are explicitly illustrated and numerically validated on multiple DC microgrid test-cases containing both buck and boost converter dynamics.

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arXiv2021

Robust Model Predictive Control for Nonlinear Systems Using Convex Restriction

We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set. By viewing the system as a fixed point of an operator acting over trajectories, we propose a convex condition on control actions that guarantee safety against the uncertainty set. The proposed condition guarantees that all realizations of the state trajectories satisfy safety constraints. Our algorithm solves a sequence of convex quadratic constrained optimization problems of size n*N, where n is the number of states, and N is the prediction horizon in the model predictive control problem. Compared to existing methods, our approach solves convex problems while guaranteeing that all realizations of uncertainty set do not violate safety constraints. Moreover, we consider the implicit time-discretization of system dynamics to increase the prediction horizon and enhance computational accuracy. Numerical simulations for vehicle navigation demonstrate the effectiveness of our approach.

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arXiv2021

Robust AC Optimal Power Flow with Robust Convex Restriction

Electric power grids regularly experience uncertain fluctuations from load demands and renewables, which poses a risk of violating operational limits designed to safeguard the system. In this paper, we consider the robust AC OPF problem that minimizes the generation cost while requiring a certain level of system security in the presence of uncertainty. The robust AC OPF problem requires that the system satisfy operational limits for all uncertainty realizations within a specified uncertainty set. Guaranteeing robustness is particularly challenging due to the non-convex, nonlinear AC power flow equations, which may not always have a solution. In this work, we extend a previously developed convex restriction to a robust convex restriction, which is a convex inner approximation of the non-convex feasible region of the AC OPF problem that accounts for uncertainty in the power injections. We then use the robust convex restriction in an algorithm that obtains robust solutions to AC OPF problems by solving a sequence of convex optimization problems. We demonstrate our algorithm and its ability to control robustness versus operating cost trade-offs using PGLib test cases.

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arXiv2020

Data-driven control of micro-climate in buildings: an event-triggered reinforcement learning approach

Smart buildings have great potential for shaping an energy-efficient, sustainable, and more economic future for our planet as buildings account for approximately 40% of the global energy consumption. Future of the smart buildings lies in using sensory data for adaptive decision making and control that is currently gloomed by the key challenge of learning a good control policy in a short period of time in an online and continuing fashion. To tackle this challenge, an event-triggered -- as opposed to classic time-triggered -- paradigm, is proposed in which learning and control decisions are made when events occur and enough information is collected. Events are characterized by certain design conditions and they occur when the conditions are met, for instance, when a certain state threshold is reached. By systematically adjusting the time of learning and control decisions, the proposed framework can potentially reduce the variance in learning, and consequently, improve the control process. We formulate the micro-climate control problem based on semi-Markov decision processes that allow for variable-time state transitions and decision making. Using extended policy gradient theorems and temporal difference methods in a reinforcement learning set-up, we propose two learning algorithms for event-triggered control of micro-climate in buildings. We show the efficacy of our proposed approach via designing a smart learning thermostat that simultaneously optimizes energy consumption and occupants' comfort in a test building.

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arXiv2020

Feasible Path Identification in Optimal Power Flow with Sequential Convex Restriction

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is not always clear that there exists a feasible path to reach the desired operating point. Transitioning between operating points while avoiding constraint violations can be challenging since the feasible space of the OPF problem is nonconvex and potentially disconnected. To address this problem, we propose an algorithm that computes a provably feasible path from an initial operating point to a desired operating point. Given an initial feasible point, the algorithm solves a sequence of convex quadratically constrained optimization problems over conservative convex inner approximations of the OPF feasible space. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to improve the operating point locally. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations.

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arXiv2020

A Passivity Interpretation of Energy-Based Forced Oscillation Source Location Methods

This paper develops a systematic framework for analyzing how low frequency forced oscillations propagate in electric power systems. Using this framework, the paper shows how to mathematically justify the so-called Dissipating Energy Flow (DEF) forced oscillation source location technique. The DEF's specific deficiencies are pinpointed, and its underlying energy function is analyzed via incremental passivity theory. This analysis is then used to prove that there exists no passivity transformation (i.e. quadratic energy function) which can simultaneously render all components of a lossy classical power system passive. The paper goes on to develop a simulation-free algorithm for predicting the performance of the DEF method in a generalized power system, and it analyzes the passivity of three non-classical load and generation components. The proposed propagation framework and performance algorithm are both tested and illustrated on the IEEE 39-bus New England system and the WECC 179-bus system.

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arXiv2019

Sequential Convex Restriction and its Applications in Robust Optimization

This paper presents a convex sufficient condition for solving a system of nonlinear equations under parametric changes and proposes a sequential convex optimization method for solving robust optimization problems with nonlinear equality constraints. By bounding the nonlinearity with concave envelopes and using Brouwer's fixed point theorem, the sufficient condition is expressed in terms of closed-form convex inequality constraints. We extend the result to provide a convex sufficient condition for feasibility under bounded uncertainty. Using these conditions, a non-convex optimization problem can be solved as a sequence of convex optimization problems, with feasibility and robustness guarantees. We present a detailed analysis of the performance and complexity of the proposed condition. The examples in polynomial optimization and nonlinear network are provided to illustrate the proposed method.

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arXiv2019

Convex Restriction of Power Flow Feasibility Sets

The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the convex restriction provides a sufficient condition for power flow feasibility and is particularly useful for problems involving uncertainty in the power generation and demand. In this paper, we present a general framework of constructing convex restriction of an algebraic set defined by equality and inequality constraints and apply the framework to power flow feasibility problem. The procedure results in convex quadratic constraints that provide a sufficiently large region for practical operation of the grid.

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arXiv2019

Mathematical Models for Optimization of Grid-Integrated Energy Storage Systems

Energy storage has been proven to yield positive effects on planning, operation and control of electric grids. It has become a crucial task to properly model the energy storage systems (ESS) under the framework of grid optimization on transmission and distribution networks including microgrids. This paper presents a review on mathematical models and test cases of ESSs used for grid optimization studies, where the network constraints of power systems are included. The existing ESS models are mainly classified into two categories; linear and nonlinear models. The two main categories are further divided into several subcategories respectively; such as mixed integer linear and convex nonlinear subcategories. Based on the review and discussions, this paper aims at providing suggestions for choosing proper ESS models for specific grid optimization studies considering the chosen power network model.

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arXiv2018

Robustness against Disturbances in Power Systems under Frequency Constraints

The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulation-based assessment of the system robustness against uncertain and stochastic disturbances is extremely time-consuming. In this paper, we develop an alternative approach, which has its roots in the input-output stability analysis for Lur'e systems. Our approach consists of a mathematically rigorous characterization of the external disturbances that the power system is transiently stable and the frequency constraints are not violated. The derived certificate is efficiently constructed via convex optimization and is shown to be non-conservative for different IEEE test cases.

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arXiv2018

A Framework for Robust Steady-State Voltage Stability of Distribution Systems

Power injection uncertainties in distribution power grids, which are mostly induced by aggressive introduction of intermittent renewable sources, may drive the system away from normal operating regimes and potentially lead to the loss of long-term voltage stability (LTVS). Naturally, there is an ever increasing need for a tool for assessing the LTVS of a distribution system. This paper presents a fast and reliable tool for constructing \emph{inner approximations} of LTVS regions in multidimensional injection space such that every point in our constructed region is guaranteed to be solvable. Numerical simulations demonstrate that our approach outperforms all existing inner approximation methods in most cases. Furthermore, the constructed regions are shown to cover substantial fractions of the true voltage stability region. The paper will later discuss a number of important applications of the proposed technique, including fast screening for viable injection changes, constructing an effective solvability index and rigorously certified loadability limits.

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arXiv2018

Constructing Convex Inner Approximations of Steady-State Security Regions

We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to $1354$ buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases.

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arXiv2018

Contraction and Robustness of Continuous Time Primal-Dual Dynamics

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work focuses on continuous, possibly non-autonomous PD dynamics arising in a network context, in distributed optimization, or in systems with multiple time-scales. We show that the PD algorithm is indeed strictly contracting in specific metrics and analyze its robustness establishing stability and performance guarantees for different approximate PD systems. We derive estimates for the performance of multiple time-scale multi-layer optimization systems, and illustrate our results on a primal-dual representation of the Automatic Generation Control of power systems.

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arXiv2018

A Sufficient Condition for Small-Signal Stability and Construction of Robust Stability Region

The small-signal stability is an integral part of the power system security analysis. The introduction of renewable source related uncertainties is making the stability assessment difficult as the equilibrium point is varying rapidly. This paper focuses on the Differential Algebraic Equation (DAE) formulation of power systems and bridges the gap between the conventional reduced system and the original one using logarithmic norm. We propose a sufficient condition for stability using Bilinear Matrix Inequality and its inner approximation as Linear Matrix Inequality. Another contribution is the construction of robust stability regions in state-space in contrast to most existing approaches trying same in the parameter space. Performance evaluation of the sufficiency condition and its inner approximation has been given with the necessary and sufficient condition for a small-scale test case. The paper provides a necessary base to develop tractable construction techniques for the robust stability region of power systems.

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arXiv2018

Using Passivity Theory to Interpret the Dissipating Energy Flow Method

Despite wide-scale deployment of phasor measurement unit technology, locating the sources of low frequency forced oscillations in power systems is still an open research topic. The dissipating energy flow method is one source location technique which has performed remarkably well in both simulation and real time application at ISO New England. The method has several deficiencies, though, which are still poorly understood. This paper borrows the concepts of passivity and positive realness from the controls literature in order to interpret the dissipating energy flow method, pinpoint the reasons for its deficiencies, and set up a framework for improving the method. The theorems presented in this paper are then tested via simulation on a simple infinite bus power system model.

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arXiv2018

Stability-constrained Optimization for Nonlinear Systems based on Convex Lyapunov Functions

This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to certain disturbances. Existing solution approaches to analogous DAE-constrained problems are based on discretization of DAE system into a large set of nonlinear algebraic equations representing the time-marching schemes. These approaches are not scalable to large size models. The proposed framework, based on LaSalle's invariance principle, uses convex Lyapunov functions to develop a novel stability certificate which consists of a limited number of algebraic constraints. We develop specific algorithms for two major types of nonlinearities, namely Lur'e, and quasi-polynomial systems. Quadratic and convex-sum-of-square Lyapunov functions are constructed for the Lur'e-type and quasi-polynomial systems respectively. A numerical experiment is performed on a 3-generator power network to obtain a solution for transient-stability-constrained optimal power flow.

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arXiv2018

A Bayesian Approach to Forced Oscillation Source Location Given Uncertain Generator Parameters

Since forced oscillations are exogenous to dynamic power system models, the models by themselves cannot predict when or where a forced oscillation will occur. Locating the sources of these oscillations, therefore, is a challenging problem which requires analytical methods capable of using real time power system data to trace an observed oscillation back to its source. The difficulty of this problem is exacerbated by the fact that the parameters associated with a given power system model can range from slightly uncertain to entirely unknown. In this paper, a Bayesian framework, via a two-stage Maximum A Posteriori optimization routine, is employed in order to locate the most probable source of a forced oscillation given an uncertain prior model. The approach leverages an equivalent circuit representation of the system in the frequency domain and employs a numerical procedure which makes the problem suitable for real time application. The derived framework lends itself to successful performance in the presence of PMU measurement noise, high generator parameter uncertainty, and multiple forced oscillations occurring simultaneously. The approach is tested on a 4-bus system with a single forced oscillation source and on the WECC 179-bus system with multiple oscillation sources.

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arXiv2018

A Robustness Measure of Transient Stability under Operational Constraints in Power Systems

The aggressive integration of distributed renewable sources is changing the dynamics of the electric power grid in an unexpected manner. As a result, maintaining conventional performance specifications, such as transient stability, may not be sufficient to ensure its reliable operation in stressed conditions. In this paper, we introduce a novel criteria in transient stability with consideration of operational constraints over frequency deviation and angular separation. In addition, we provide a robustness measure of the region of attraction, which can quantify the ability of the post-fault system to remain synchronized even under disturbances. To assess this new stability specification, we adopt the notion of Input-to-State Stability (ISS) to the context of power systems and introduce a new class of convex Lyapunov functions, which will result in tractable convex-optimization-based stability certificates. As a result, we are able to quantify the level of disturbance a power system can withstand while maintaining its safe operation. We illustrate the introduced stability specification and certificate on the IEEE 9 bus system.

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