arXiv subjects

Konstantin Turitsyn

Publications and source records attributed to Konstantin Turitsyn.

67 records · Page 4Linked to original sources

arXiv2014

Voltage multi-stability in distribution grids with power flow reversal

High levels of penetration of distributed generation and aggressive reactive power compensation with modern power electronics may result in the reversal of active and reactive power flows in future distribution grids. The voltage stability of these operating conditions may be very different from the more traditional power consumption regime. We study the stability characteristics of distribution networks with reversed power flow. After introducing a universal algebraic approach to characterize all the solutions of the power flow equations, we show that new solutions appear in the reversed power flow regime even in the simplest three bus systems. We show that the some of these solutions are stable and the system may exhibit a phenomenon of multistability, where multiple stable equilibria co-exist at the given set of parameters, and the system may converge to an undesirable equilibrium after a disturbance. These predictions are validated with dynamic simulations of two different systems. Under certain conditions the new states are viable and may be characterized by relatively high voltages. Possible approaches towards reactive power/voltage regulation as well as permissible distributed generation capacity in future power systems are proposed and discussed in the end of the paper.

nlin.CD↗

arXiv2014

Critical slowing-down as indicator of approach to the loss of stability

We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations of the system state vector are driven by random variations of loads and intermittent renewable generation. In the vicinity of collapse the power system experiences so-called phenomenon of critical slowing-down characterized by slowing and simultaneous amplification of the system state vector fluctuations. In generic case of a co-dimension 1 bifurcation corresponding to the threshold of instability it is possible to extract a single mode of the system state vector responsible for this phenomenon. We characterize stochastic fluctuations of the system state vector using the formal perturbative expansion over the lowest (real) eigenvalue of the system power flow Jacobian and verify the resulting expressions for correlation functions of the state vector by direct numerical simulations. We conclude that the onset of critical slowing-down is a good marker of approach to the threshold of global instability. It can be straightforwardly detected from the analysis of single-node autostructure and autocorrelation functions of system state variables and thus does not require full observability of the grid.

physics.soc-ph↗

arXiv2012

Random load fluctuations and collapse probability of a power system operating near codimension 1 saddle-node bifurcation

For a power system operating in the vicinity of the power transfer limit of its transmission system, effect of stochastic fluctuations of power loads can become critical as a sufficiently strong such fluctuation may activate voltage instability and lead to a large scale collapse of the system. Considering the effect of these stochastic fluctuations near a codimension 1 saddle-node bifurcation, we explicitly calculate the autocorrelation function of the state vector and show how its behavior explains the phenomenon of critical slowing-down often observed for power systems on the threshold of blackout. We also estimate the collapse probability/mean clearing time for the power system and construct a new indicator function signaling the proximity to a large scale collapse. The new indicator function is easy to estimate in real time using PMU data feeds as well as SCADA information about fluctuations of power load on the nodes of the power grid. We discuss control strategies leading to the minimization of the collapse probability.

physics.soc-ph↗

arXiv2012

DistFlow ODE: Modeling, Analyzing and Controlling Long Distribution Feeder

We consider a linear feeder connecting multiple distributed loads and generators to the sub-station. Voltage is controlled directly at the sub-station, however, voltage down the line shifts up or down, in particular depending on if the feeder operates in the power export regime or power import regime. Starting from this finite element description of the feeder, assuming that the consumption/generation is distributed heterogeneously along the feeder, and following the asymptotic homogenization approach, we derive simple low-parametric ODE model of the feeder. We also explain how the homogeneous ODE modeling is generalized to account for other distributed effects, e.g. for inverter based and voltage dependent control of reactive power. The resulting system of the DistFlow-ODEs, relating homogenized voltage to flows of real and reactive power along the lines, admits computationally efficient analysis in terms of the minimal number of the feeder line "media" parameters, such as the ratio of the inductance-to-resistance densities. Exploring the space of the media and control parameters allows us to test and juxtapose different measures of the system performance, in particular expressed in terms of the voltage drop along the feeder, power import/export from the feeder line as the whole, power losses within the feeder, and critical (with respect to possible voltage collapse) length of the feeder. Our most surprising funding relates to performance of a feeder rich on PhotoVoltaic (PV) systems during a sunny day. We observe that if the feeder is sufficiently long the DistFlow-ODEs may have multiple stable solutions. The multiplicity may mean troubles for successful recovery of the feeder after a very short, few periods long, fault at the head of the line.

math.OC↗

arXiv2011

Controlled Tripping of Overheated Lines Mitigates Power Outages

We study the evolution of fast blackout cascades in the model of the Polish (transmission) power grid (2700 nodes and 3504 transmission lines). The cascade is initiated by a sufficiently severe initial contingency tripping. It propagates via sequential trippings of many more overheated lines, islanding loads and generators and eventually arriving at a fixed point with the surviving part of the system being power-flow-balanced and the rest of the system being outaged. Utilizing an improved form of the quasi-static model for cascade propagation introduced in our earlier study (Statistical Classification of Cascading Failures in Power Grids, IEEE PES GM 2011), we analyze how the severity of the cascade depends on the order of tripping overheated lines. Our main observation is that the order of tripping has a tremendous effect on the size of the resulting outage. Finding the "best" tripping, defined as causing the least damage, constitutes a difficult dynamical optimization problem, whose solution is most likely computationally infeasible. Instead, here we study performance of a number of natural heuristics, resolving the next switching decision based on the current state of the grid. Overall, we conclude that controlled intentional tripping is advantageous in the situation of a fast developing extreme emergency, as it provides significant mitigation of the resulting damage.

physics.soc-ph↗

arXiv2011

Smart Finite State Devices: A Modeling Framework for Demand Response Technologies

We introduce and analyze Markov Decision Process (MDP) machines to model individual devices which are expected to participate in future demand-response markets on distribution grids. We differentiate devices into the following four types: (a) optional loads that can be shed, e.g. light dimming; (b) deferrable loads that can be delayed, e.g. dishwashers; (c) controllable loads with inertia, e.g. thermostatically-controlled loads, whose task is to maintain an auxiliary characteristic (temperature) within pre-defined margins; and (d) storage devices that can alternate between charging and generating. Our analysis of the devices seeks to find their optimal price-taking control strategy under a given stochastic model of the distribution market.

eess.SY↗

arXiv2010

Statistical Classification of Cascading Failures in Power Grids

We introduce a new microscopic model of the outages in transmission power grids. This model accounts for the automatic response of the grid to load fluctuations that take place on the scale of minutes, when the optimum power flow adjustments and load shedding controls are unavailable. We describe extreme events, initiated by load fluctuations, which cause cascading failures of loads, generators and lines. Our model is quasi-static in the causal, discrete time and sequential resolution of individual failures. The model, in its simplest realization based on the Directed Current description of the power flow problem, is tested on three standard IEEE systems consisting of 30, 39 and 118 buses. Our statistical analysis suggests a straightforward classification of cascading and islanding phases in terms of the ratios between average number of removed loads, generators and links. The analysis also demonstrates sensitivity to variations in line capacities. Future research challenges in modeling and control of cascading outages over real-world power networks are discussed.

physics.soc-ph↗

arXiv2010

Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry

We consider experimentally the instability and mass transport of a porous-medium flow in a Hele-Shaw geometry. In an initially stable configuration, a lighter fluid (water) is located over a heavier fluid (propylene glycol). The fluids mix via diffusion with some regions of the resulting mixture being heavier than either pure fluid. Density-driven convection occurs with downward penetrating dense fingers that transport mass much more effectively than diffusion alone. We investigate the initial instability and the quasi steady state. The convective time and velocity scales, finger width, wave number selection, and normalized mass transport are determined for 6,000<Ra<90,000. The results have important implications for determining the time scales and rates of dissolution trapping of carbon dioxide in brine aquifers proposed as possible geologic repositories for sequestering carbon dioxide.

physics.flu-dyn↗

arXiv2010

Options for Control of Reactive Power by Distributed Photovoltaic Generators

High penetration levels of distributed photovoltaic(PV) generation on an electrical distribution circuit present several challenges and opportunities for distribution utilities. Rapidly varying irradiance conditions may cause voltage sags and swells that cannot be compensated by slowly responding utility equipment resulting in a degradation of power quality. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g. by minimizing thermal losses. We discuss and compare via simulation various design options for control systems to manage the reactive power generated by these inverters. An important design decision that weighs on the speed and quality of communication required is whether the control should be centralized or distributed (i.e. local). In general, we find that local control schemes are capable for maintaining voltage within acceptable bounds. We consider the benefits of choosing different local variables on which to control and how the control system can be continuously tuned between robust voltage control, suitable for daytime operation when circuit conditions can change rapidly, and loss minimization better suited for nighttime operation.

math-ph↗

arXiv2010

Non-Equilibrium Statistical Physics of Currents in Queuing Networks

We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition rates between nodes. For such systems, we ask the question ``What is the most likely way for large currents to accumulate over time in a network ?'', where time is large compared to the system correlation time scale. We identify two interesting regimes. In the first regime, in which the accumulation of currents over time exceeds the expected value by a small to moderate amount (moderate large deviation), we find that the large-deviation distribution of currents is universal (independent of the interaction details), and there is no long-time and averaged over time accumulation of particles (condensation) at any nodes. In the second regime, in which the accumulation of currents over time exceeds the expected value by a large amount (severe large deviation), we find that the large-deviation current distribution is sensitive to interaction details, and there is a long-time accumulation of particles (condensation) at some nodes. The transition between the two regimes can be described as a dynamical second order phase transition. We illustrate these ideas using the simple, yet non-trivial, example of a single node with feedback.

cond-mat.stat-mech↗

arXiv2010

Robust Broadcast-Communication Control of Electric Vehicle Charging

The anticipated increase in the number of plug-in electric vehicles (EV) will put additional strain on electrical distribution circuits. Many control schemes have been proposed to control EV charging. Here, we develop control algorithms based on randomized EV charging start times and simple one-way broadcast communication allowing for a time delay between communication events. Using arguments from queuing theory and statistical analysis, we seek to maximize the utilization of excess distribution circuit capacity while keeping the probability of a circuit overload negligible.

math.OC↗

arXiv2009

Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration

We show how distributed control of reactive power can serve to regulate voltage and minimize resistive losses in a distribution circuit that includes a significant level of photovoltaic (PV) generation. To demonstrate the technique, we consider a radial distribution circuit with a single branch consisting of sequentially-arranged residential-scale loads that consume both real and reactive power. In parallel, some loads also have PV generation capability. We postulate that the inverters associated with each PV system are also capable of limited reactive power generation or consumption, and we seek to find the optimal dispatch of each inverter's reactive power to both maintain the voltage within an acceptable range and minimize the resistive losses over the entire circuit. We assume the complex impedance of the distribution circuit links and the instantaneous load and PV generation at each load are known. We compare the results of the optimal dispatch with a suboptimal local scheme that does not require any communication. On our model distribution circuit, we illustrate the feasibility of high levels of PV penetration and a significant (20% or higher) reduction in losses.

math.OC↗

arXiv2007

Stochastic suspensions of heavy particles

Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical and statistical properties. Substantial progress followed from the study of suspensions in model flows which, although much simpler, reproduce most of the important mechanisms observed in real turbulence. This paper presents recent developments made on the relative motion of a pair of particles suspended in time-uncorrelated and spatially self-similar Gaussian flows. This review is complemented by new results. By introducing a time-dependent Stokes number, it is demonstrated that inertial particle relative dispersion recovers asymptotically Richardson's diffusion associated to simple tracers. A perturbative (homogeneization) technique is used in the small-Stokes-number asymptotics and leads to interpreting first-order corrections to tracer dynamics in terms of an effective drift. This expansion implies that the correlation dimension deficit behaves linearly as a function of the Stokes number. The validity and the accuracy of this prediction is confirmed by numerical simulations.

nlin.CD↗