arXiv subjects

Konstantin Turitsyn

Publications and source records attributed to Konstantin Turitsyn.

At least 37 records · Page 2Linked to original sources

arXiv2018

Micro Water-Energy Nexus: Optimal Demand-Side Management and Quasi-Convex Hull Relaxation

This paper investigates the water network's potential ability to provide demand response services to the power grid under the framework of a distribution-level water-energy nexus (micro-WEN). In particular, the hidden controllability of water loads, such as irrigation systems, was closely studied to improve the flexibility of electrical grids. A optimization model is developed for the demand-side management (DSM) of micro-WEN, and the simulation results assert that grid flexibility indeed benefits from controllable water loads. Although the proposed optimal DSM model is an intractable mixed-integer nonlinear programming (MINLP) problem, quasi-convex hull techniques were developed to relax the MINLP into a mixed-integer convex programming (MICP) problem. The numerical study shows that the quasi-convex hull relaxation is tight and that the resulting MICP problem is computationally efficient.

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arXiv2018

Using Effective Generator Impedance for Forced Oscillation Source Location

Locating the sources of forced low-frequency oscillations in power systems is an important problem. A number of proposed methods demonstrate their practical usefulness, but many of them rely on strong modeling assumptions and provide poor performance in certain cases for reasons still not well understood. This paper proposes a systematic method for locating the source of a forced oscillation by considering a generator's response to fluctuations of its terminal voltages and currents. It is shown that a generator can be represented as an effective admittance matrix with respect to low-frequency oscillations, and an explicit form for this matrix, for various generator models, is derived. Furthermore, it is shown that a source generator, in addition to its effective admittance, is characterized by the presence of an effective current source thus giving a natural qualitative distinction between source and nonsource generators. Detailed descriptions are given of a source detection procedure based on this developed representation, and the method's effectiveness is confirmed by simulations on the recommended testbeds (eg. WECC 179-bus system). This method is free of strong modeling assumptions and is also shown to be robust in the presence of measurement noise and generator parameter uncertainty.

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arXiv2018

Convexity of Solvability Set of Power Distribution Networks

The solvability set of a power network - the set of all power injection vectors for which the corresponding Power Flow equations admit a solution - is central to power systems stability and security, as well as to the tightness of Optimal Power Flow relaxations. Whenever the solvability set is convex, this allows for substantial simplifications of various optimization and risk assessment algorithms. In this paper we focus on the solvability set of power distribution networks and prove convexity of the full solvability set (real and reactive powers) for tree homogeneous networks with the same r/x ratio for all elements. We also show this result can not be improved: once the network is not homogeneous, the convexity is immediately lost. It is nevertheless the case that if the network is almost homogeneous, a substantial practically-important part of the solvability set is still convex. Finally, we prove convexity of real solvability set (only real powers) for any tree network as well as for purely resistive networks with arbitrary topology.

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arXiv2018

Stability of DC Networks with Generic Load Models

DC grids are prone to small-signal instabilities due to the presence of tightly controlled loads trying to keep the power consumption constant over range of terminal voltage variations. Th, so-called, constant power load (CPL) represents a classical example of this destabilizing behavior acting as an incremental negative resistance. Real-life DC loads represented by controlled power converters exhibit the CPL behavior over a finite frequency range. There exist a number of methods for stability certification of DC grids which are primarily concerned with the source-load interaction and do not explicitly account for the influence of network. In the present manuscript, we develop a method for stability assessment of arbitrary DC grids by introducing the Augmented Power Dissipation and showing that it's positive definiteness is a sufficient condition for stability. We present an explicit expression for this quantity through load and network impedances and show how it could be directly used for stability certification of networks with arbitrary configuration.

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arXiv2017

A Stability-constrained Optimization Framework for Lur'e Systems with Applications in Power Grids

For many nonlinear control systems, the chosen equilibrium determines both the steady-state efficiency and the dynamic performance. This paper addresses the issue of obtaining an optimal equilibrium in terms of some steady-state operation criteria for a Lur'e-type system and such an equilibrium can also guarantee a sufficiently large stability region in the dynamic domain such that the system can tolerate some given disturbance. For this purpose, a set of computationally tractable algebraic constraints, which can properly represent the stability certificate under the optimization framework, are proposed. The existing methods formulate the dynamic performance under the optimization framework by discretizing the differential-algebraic equations, which are computationally intractable for large-scale Lur'e systems like power grids. Dissimilarly, the introduced approach first constructs the stability region based on quadratic Lyapunov functions. Then, a novel method is proposed to project the stability region onto the feasible domain of the optimization problem such that the stability certificate can be incorporated into the optimization framework easily. In the transient stability-constrained optimal power flow (TSCOPF) problem of power systems, researchers look for a steady-state operating point with the minimum generation costs that can maintain system stability under some given transient disturbances. The proposed approach is applied to develop a scalable TSCOPF framework for power systems. The TSCOPF model is tested on the IEEE 118-Bus power system.

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arXiv2017

Modeling A Micro-Nexus of Water and Energy for Smart Villages/Cities/Buildings

This paper introduces a micro-nexus of water and energy which can be considered as one of the physical infrastructures of the future building/city/village systems. For the electricity side, an alternating current (AC) power flow model integrated with battery energy storage and renewable generation is adopted. The nonlinear hydraulic characteristics in pipe networks is also considered in the proposed micro water-energy nexus (WEN) model. Integer variables are involved to represent the on/off state of pumps. Base on the proposed nexus model, a co-optimization framework of water and energy networks is developed. The overall co-optimization model is a mixed-integer nonlinear programming problem which is tested on a waterenergy nexus which consists of the IEEE 13-bus distribution system and a 8-node water distribution network. The simulation results demonstrate that the cost-efficiency of the co-optimization framework is higher than optimizing two systems independently.

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arXiv2017

Transient stability guarantees for ad hoc dc microgrids

Ad hoc electrical networks are formed by connecting power sources and loads without planning the interconnection structure (topology) in advance. They are designed to be installed and operated by individual communities---without central oversight---and as a result are well-suited to addressing the lack of electricity access in rural and developing areas. However, ad hoc networks are not widely used, and a major technical challenge impeding their development (and deployment) is the difficulty of certifying network stability without a priori knowledge of the topology. We develop conditions on individual power sources and loads such that a microgrid comprised of many units will be stable. We use Brayton-Moser potential theory to develop design constraints on individual microgrid components that certify transient stability---guaranteeing that the system will return to a suitable equilibrium after load switching events. Our central result is that stability can be ensured by installing a parallel capacitor at each constant power load, and we derive an expression for the required capacitance.

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arXiv2017

Inverse Stability Problem and Applications to Renewables Integration

In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range of operating points would be essential to assuring their reliable operation, and possibly allow higher integration of renewable resources. This letter introduces a non-traditional way to think about the stability assessment problem of power systems. Instead of estimating the set of initial states leading to a given operating condition, we characterize the set of operating conditions that a power grid converges to from a given initial state under changes in power injections and lines. We term this problem as "inverse stability", a problem which is rarely addressed in the control and systems literature, and hence, poorly understood. Exploiting quadratic approximations of the system's energy function, we introduce an estimate of the inverse stability region. Also, we briefly describe three important applications of the inverse stability notion: (i) robust stability assessment of power systems w.r.t. different renewable generation levels, (ii) stability-constrained optimal power flow (sOPF), and (iii) stability-guaranteed corrective action design.

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arXiv2017

PMU-Based Estimation of Dynamic State Jacobian Matrix and Dynamic System State Matrix in Ambient Conditions

In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix and the dynamic system state matrix in near real-time utilizing statistical properties extracted from PMU measurements. The proposed method can be used to detect and identify network topology changes that have not been reflected in an assumed network model. Additionally, an application of the estimated system state matrix in online dynamic stability monitoring is presented.

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arXiv2017

Dynamic Polytopic Template Approach to Robust Transient Stability Assessment

Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable assessment of transient stability. Conventional approaches such as time-domain simulations and direct energy methods are computationally expensive to take account of uncertainties. This paper proposes a reachability analysis approach that computes bounds of the possible trajectories from uncertain initial conditions. The eigenvalue decomposition is used to construct a polytopic template with a scalable number of hyperplanes that is guaranteed to converge near the equilibrium. The proposed algorithm bounds the possible states at a given time with a polytopic template and solves the evolution of the polytope over time. The problem is solved with linear programming relaxation based on outer-approximations of nonlinear functions, which is scalable for large scale systems. We demonstrate our method on IEEE test cases to certify the stability and bound the state trajectories.

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arXiv2017

Solvability regions of affinely parameterized quadratic equations

Quadratic systems of equations appear in several applications. The results in this paper are motivated by quadratic systems of equations that describe equilibrium behavior of physical infrastructure networks like the power and gas grids. The quadratic systems in infrastructure networks are parameterized- the parameters can represent uncertainty (estimation error in resistance/inductance of a power transmission line, for example)or controllable decision variables (power outputs of generators,for example). It is then of interest to understand conditions on the parameters under which the quadratic system is guaranteed to have a solution within a specified set (for example, bounds on voltages and flows in a power grid). Given nominal values of the parameters at which the quadratic system has a solution and the Jacobian of the quadratic system at the solution i snon-singular, we develop a general framework to construct convex regions around the nominal value such that the system is guaranteed to have a solution within a given distance of the nominal solution. We show that several results from recen tliterature can be recovered as special cases of our framework,and demonstrate our approach on several benchmark power systems.

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arXiv2017

PMU-Based Estimation of Dynamic State Jacobian Matrix

In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network topology. A numerical example is given to show that the proposed method is able to provide good estimation for the dynamic state Jacobian matrix and is superior to the model-based method under undetectable network topology change. The proposed method may also help identify big discrepancy in the assumed network model.

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arXiv2017

Contraction Analysis of Nonlinear DAE Systems

This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium, by establishing the relation between the contraction rates of the original systems and the corresponding virtual extended systems. We show that for a contracting DAE system, the reduced system always contracts faster than the extended ones; furthermore, there always exists an extension with contraction rate arbitrarily close to that of the original system. The proposed construction technique is illustrated with a power system example in the context of transient stability assessment.

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arXiv2017

Structural Emergency Control Paradigm

Power grids normally operate at some stable operating condition where power supply and demand are balanced. In response to emergency situations, load shedding is a prevailing approach where local protective devices are activated to cut a suitable amount of load to quickly rebalance the supply demand and hopefully stabilize the system. This traditional emergency control results in interrupted service with severe economic damage to customers. Also, such control is usually less effective due to the lack of coordination among protective devices. In this paper, we propose a novel structural emergency control to render post-fault dynamics from the critical/emergency fault-cleared state to the stable equilibrium point. This is a new control paradigm that does not rely on any continuous measurement or load shedding, as in the classical setup. Instead, the grid is made stable by discretely relocating the equilibrium point and its stability region such that the system is consecutively attracted from the fault-cleared state back to the original equilibrium point. The proposed control is designed by solving linear and convex optimization problems, making it possibly scalable to large-scale power grids. Finally, this emergency control scheme can be implemented by exploiting transmission facilities available on the existing grids.

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arXiv2016

High-Fidelity Model Order Reduction for Microgrids Stability Assessment

Proper modeling of inverter-based microgrids is crucial for accurate assessment of stability boundaries. It has been recently realized that the stability conditions for such microgrids are significantly different from those known for large- scale power systems. While detailed models are available, they are both computationally expensive and can not provide the insight into the instability mechanisms and factors. In this paper, a computationally efficient and accurate reduced-order model is proposed for modeling the inverter-based microgrids. The main factors affecting microgrid stability are analyzed using the developed reduced-order model and are shown to be unique for the microgrid-based network, which has no direct analogy to large-scale power systems. Particularly, it has been discovered that the stability limits for the conventional droop-based system (omega - P/V - Q) are determined by the ratio of inverter rating to network capacity, leading to a smaller stability region for microgrids with shorter lines. The theoretical derivation has been provided to verify the above investigation based on both the simplified and generalized network configurations. More impor- tantly, the proposed reduced-order model not only maintains the modeling accuracy but also enhances the computation efficiency. Finally, the results are verified with the detailed model via both frequency and time domain analyses.

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arXiv2016

Stability and Control of Ad Hoc DC Microgrids

Ad hoc electrical networks are formed by connecting power sources and loads without pre-determining the network topology. These systems are well-suited to addressing the lack of electricity in rural areas because they can be assembled and modified by non-expert users without central oversight. There are two core aspects to ad hoc system design: 1) designing source and load units such that the microgrid formed from the arbitrary interconnection of many units is always stable and 2) developing control strategies to autonomously manage the microgrid (i.e., perform power dispatch and voltage regulation) in a decentralized manner and under large uncertainty. To address these challenges we apply a number of nonlinear control techniques---including Brayton-Moser potential theory and primal-dual dynamics---to obtain conditions under which an ad hoc dc microgrid will have a suitable and asymptotically stable equilibrium point. Further, we propose a new decentralized control scheme that coordinates many sources to achieve a specified power dispatch from each. A simulated comparison to previous research is included.

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arXiv2016

A Framework for Robust Assessment of Power Grid Stability and Resiliency

Security assessment of large-scale, strongly nonlinear power grids containing thousands to millions of interacting components is a computationally expensive task. Targeting at reducing the computational cost, this paper introduces a framework for constructing a robust assessment toolbox that can provide mathematically rigorous certificates for the grids' stability in the presence of variations in power injections, and for the grids' ability to withstand a bunch sources of faults. By this toolbox we can "off-line" screen a wide range of contingencies or power injection profiles, without reassessing the system stability on a regular basis. In particular, we formulate and solve two novel robust stability and resiliency assessment problems of power grids subject to the uncertainty in equilibrium points and uncertainty in fault-on dynamics. Furthermore, we bring in the quadratic Lyapunov functions approach to transient stability assessment, offering real-time construction of stability/resiliency certificates and real-time stability assessment. The effectiveness of the proposed techniques is numerically illustrated on a number of IEEE test cases.

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arXiv2016

Distributed Frequency Control in Power Grids Under Limited Communication

In this paper, we analyze the impact of communication failures on the performance of optimal distributed frequency control. We consider a consensus-based control scheme, and show that it does not converge to the optimal solution when the communication network is disconnected. We propose a new control scheme that uses the dynamics of power grid to replicate the information not received from the communication network, and prove that it achieves the optimal solution under any single communication link failure. In addition, we show that this control improves cost under multiple communication link failures. Next, we analyze the impact of discrete-time communication on the performance of distributed frequency control. In particular, we will show that the convergence time increases as the time interval between two messages increases. We propose a new algorithm that uses the dynamics of the power grid, and show through simulation that it improves the convergence time of the control scheme significantly.

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