Konstantin Turitsyn

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 able to maintain 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.

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 inverters 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.

Local Control of Reactive Power by Distributed Photovoltaic Generators

High penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit may degrade power quality due to voltage sags and swells caused by rapidly varying PV generation during cloud transients coupled with the slow response of existing utility compensation and regulation equipment. 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 a new tool for distribution utilities to minimize the thermal losses in circuit. We suggest a local control scheme that dispatches reactive power from each PV inverter based on local instantaneous measurements of the real and reactive components of the consumed power and the real power generated by the PVs. Using one adjustable parameter per circuit, we balance the requirements on power quality and desire to minimize thermal losses. The performance of the proposed control scheme is evaluated via numerical simulations of realistic rural lines in several generation/consumption scenarios. Simultaneous improvement of both the power quality and the magnitude of losses is observed for all the scenarios, even when the renewable generation in excess of the circuit own load.

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

We consider experimentally the instability and mass transport of 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 quasisteady state. The convective time and velocity scales, finger width, wave number selection, and normalized mass transport are determined for 6000<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.

Information capacity of optical fiber channels with zero average dispersion

We study the statistics of optical data transmission in a noisy nonlinear fiber channel with a weak dispersion management and zero average dispersion. Applying analytical expressions for the output probability density functions both for a nonlinear channel and for a linear channel with additive and multiplicative noise we calculate in a closed form a lower bound estimate on the Shannon capacity for an arbitrary signal-to-noise ratio.

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.

Dynamics of Nearly Spherical Vesicles in an External Flow

Tank-treading, tumbling, and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation enabling us to establish a state of nearly spherical vesicles. For a 2D external flow, the character of the vesicle dynamics is determined by two dimensionless parameters, depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation, whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. A slowdown of vesicle dynamics should be observed in a vicinity of a point separating the transition lines. We show that the slowdown can be described by a power law with two different critical exponents 1/4 and 1/2 corresponding to the slowdown of tumbling and trembling cycles.

Lyapunov Functions Family Approach to Transient Stability Assessment

Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of dynamic security assessment. This paper proposes a novel approach for assessment of transient stability of the system. The approach generalizes the idea of energy methods, and extends the concept of energy function to a more general Lyapunov functions family (LFF) constructed via semidefinite programming techniques. Unlike the traditional energy function and its variations, the constructed Lyapunov functions are proven to be decreasing only in a finite neighborhood of the equilibrium point. However, we show that they can still certify stability of a broader set of initial conditions in comparison to the energy function in the closest-UEP method. Moreover, the certificates of stability can be constructed via a sequence of convex optimization problems that are tractable even for large scale systems. We also propose specific algorithms for adaptation of the Lyapunov functions to specific initial conditions and demonstrate the effectiveness of the approach on a number of IEEE test cases.

Nearly spherical vesicles in an external flow

We theoretically analyze a vesicle with small excess area, which is immersed in an external flow. A dynamical equation for the vesicle evolution is obtained by solving the Stokes equation with suitable boundary conditions imposed on the membrane. The equation has solutions corresponding to different types of motion, such as tank-treading, tumbling and trembling. A phase diagram reflecting the regimes is constructed in terms of two dimensionless parameters that depend on the vesicle excess area, the fluid viscosities, the membrane viscosity and bending modulus, the strength of the flow, and the ratio of the elongational and rotational components of the flow. We investigate the peculiarities of the vesicle dynamics near the tank-treading to tumbling and the tank-treading to trembling transitions, which occur via a saddle-node bifurcation and a Hopf bifurcation, respectively. We examine the slowdown of the vesicle dynamics near the merging point and also predict the existence of a novel dynamic regime, which we call spinning.

Polymer statistics in a random flow with mean shear

We consider the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, to explain how the polymer statistics changes with Weissenberg number, Wi, the product of the polymer relaxation time and the Lyapunov exponent of the flow, λ. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction, having algebraic tails. The PDF of the tumbling time (separating two subsequent flips), r, has a maximum estimated as λ -1 . This PDF shows an exponential tail for large T and a small-r tail determined by the simultaneous statistics of the velocity PDF. Four regimes of Wi are identified for the extension statistics: one below the coil-stretched transition and three above the coil-stretched transition. Emphasis is given to explaining these regimes in terms of the polymer dynamics.