An application of interval analysis and optimization to electric energy markets

In this paper, we address the issue of quantifying model uncertainties in a deregulated power market. We are interested in a worst-case analysis of effects of network parameter uncertainties on optimization problems that are solved on the level of an independent system operator (ISO). The focus is on linear programming (LP) formulations because of their practical relevance. After briefly reviewing applications of different interval analysis tools (interval matrix inversion and various contractors and solvers for systems of interval equations), we propose two tailored algorithms. In the first (basic LP approach), we propose another solver for a system of linear interval equations, while in the second (power system-customized LP approach), we use features of the power system model to reduce the width of the interval solution. The interval-based results are compared with a deterministic robust noninterval matrix inversion-based solution of a model of the benchmark 68-node New England/New York interconnected power system. Presented analyzes demonstrate that even small parameter variations can have significant impact on optimization.     

Model abstraction and inclusion principle: a comparison

This paper discusses connections between the inclusion principle and model abstraction in large-scale hierarchical control systems. It also provides conditions for implementation of controllability and observability in linear continuous-time dynamic systems satisfying either aggregation or restriction conditions, as well as for observability implementation in linear continuous-time dynamic systems satisfying conditions for abstraction     

Water electrolysis and pressure drop behaviour in a three-dimensional electrode

Water electrolysis from acidified solution was used as a model system to investigate the net contribution of hydrogen bubbles to the pressure drop increase in a three-dimensional electrode. A bed of silvered glass beads in both fixed and fluidized state was used, assuming an unchanging particle surface during the experiments. Pressure drop behaviour with time was measured for different experimental conditions and presented relative to the pressure drop determined for a bubble free bed. Parameters, such as current density, electrolyte velocity and particle size, greatly influence the relative pressure drop behaviour in the three-dimensional electrode. A sudden increase in the pressure drop occurs with the appearance of a gas phase in the bed, reaching a constant value (plateau) after a certain time; this plateau corresponds to steady state conditions. The pressure drop increases with increasing current density. This increase is in the range 40-150% relative to the bubble free electrolyte flow through the bed. Electrolyte flow-rate also strongly influences the pressure drop in the hydrogen evolving fixed bed electrode. It was observed that the relative pressure drop decreases with increasing electrolyte velocity. At higher flow rates, peaks occur on the pressure drop-time curves, indicating the existence of channeling inside the bed in which spouting occurs. The time to reach the pressure drop plateau decreases with increasing electrolyte velocity as do the time intervals corresponding to maximum pressure drop values. At the minimum fluidization velocity the peaks disappear and the relative pressure drop decreases with time, tending to approach a constant value. For hydrogen evolution in the fluidized bed, the pressure drop is lower than that measured in the absence of gas, and reason for this decrease being the gas hold-up in the bed.     

Modelling of time-dependent performance criteria in a three-dimensional cell system during batch recirculation copper recovery

A three-dimensional electrode cell with cross-flow of current and electrolyte is modelled for galvanostatic and pseudopotentiostatic operation. The model is based on the electrodeposition of copper from acidified copper sulphate solution onto copper particles, with an initial concentration ensuring a diffusion-controlled process and operating in a batch recycle mode. Plug flow through the cell and perfect mixing of the electrolyte in the reservoir are assumed. Based on the model, the behaviour of reacting ion concentration, current efficiency, cell voltage, specific energy consumption and process time on selected independent variables is analysed for both galvanostatic and pseudopotentiostatic modes of operation. From the results presented it is possible to identify the optimal values of parameters for copper electrowinning.List of symbols a specific surface area (m^–1) - A cross-sectional area (mu²) - a _a Tafel constant for anode overpotential (V) - a _II Tofel constant for hydrogen evolution overpotential (V) - b _a Tafel coefficient for anode overpotential (V decade^–1) - b _H Tafel coefficient for hydrogen evolution overpotential (V decade^–1) - C _e concentration at the electrode surface (m) - C _L cell outlet concentration (m) - C ₀ cell inlet concentration (m) - C ₀ ⁰ initial cell inlet concentration att = 0 (m) - d _p particle diameter (m) - e, e _p current efficiency and pump efficiency, respectively - E specific energy consumption (Wh mol^–1) - E solution phase potential drop through the cathode (V) - F Faraday number (C mol^–1) - h interelectrode distance (m) - i, i _L current density and limiting current density, respectively (A m^–2) - I, I _L current and limiting current, respectively (A) - I _H partial current for hydrogen evolution (A) - k _L mass transfer coefficient (m s^–1) - L bed height (m) - l bed depth (m) - M molecular weight (g mol^–1) - N power per unit of electrode area (W m^–2) - n exponent in Equation 19 - P pressure drop in the cell (N m^–2) - Q electrolyte flow rate (m³ h^–1) - R Universal gas constant (J mol^–1 K^–1) - r _e electrochemical reaction rate (mol m^–2 h^–1) - t _c critical time for operating current to reach instantaneous limiting current (s) - t _p process time to reach specified degree of conversion (s) - T temperature (K) - u electrolyte velocity (m s^–1) - U total cell voltage (V) - U ₀ reversible decomposition potential (V) - U _ohm ohmic voltage drop between anode and threedimensional cathode (V) - V volume of electrolyte (m³) - z number of transferred electrons Greek letters ratio of the operating and limiting currents - _{A, a} anodic activation overpotential (V) - _{c, e} cathodic concentration overpotential (V) - bed voidage - _H void fraction of hydrogen bubbles in cathode - constant (Equation 2) - ₀ electrolyte conductivity (ohm^–1 m^–1) - v electrolyte kinematic viscosity (m² s^–1) - _d diaphragm voltage drop (V) - _H voltage drop due to hydrogen bubble containing electrolyte in cathode (V) - electrolyte density (kg m^–3) - _p particle density (kg M^–3) - reservoir residence time (s)     

Dissipativity-based adaptive and robust control of UPS

In this paper, we investigate the output voltage control for a three-phase uninterruptible power supply (UPS) using controllers based on ideas of dissipativity. To provide balanced sinusoidal output voltages, even in the presence of nonlinear and unbalanced loads, we first derive a dissipativity-based controller using a frequency-domain representation of system dynamics. Adaptive refinements have been added to the controller to cope with parametric uncertainties. Second, based on the first adaptive controller, we propose a controller which turns out to have the proportional-plus-integral-type structure on rotating-frame variables, but with a special design of gain matrices. A sufficient condition in terms of the design parameters is presented for this controller that guarantees stability of the desired equilibrium and robustness against parameter uncertainties. Finally, simulation and experimental results on a three-phase prototype show effectiveness and advantages of the proposed approach     

SAR imaging of moving targets using polynomial Fourier transform

The polynomial Fourier transform (FT) is employed as a tool for the SAR imaging of moving targets. An efficient algorithm is proposed that can be used for radar images containing both moving and stationary targets. The proposed algorithm can be used in the form of the second-order polynomial FT, but it can also be extended to higher-order and order-adaptive polynomial FT forms.     

Optimized error protection of scalable image bit streams [advances in joint source-channel coding for images]

This article focuses on FEC for scalable image coders. For various channel models, we survey recent progress made in system design and discuss efficient source-channel bit allocation techniques, with emphasis on unequal error protection. This article considered JSCC (joint source-channel coding) at the application layer only. Recent research has studied cross-layer optimization where JSCC is applied to both the application layer and the physical layer. The basic task here is to minimize the average distortion by allocating available power, subcarriers, and bandwidth among users at the physical layer and source-channel symbols at the application layer subject to a total resource constraint. Most of the JSCC systems covered in this article can be readily extended to transmit scalable compressed bit streams of video sequences and 3-D meshes. Due to the stringent delay constraints in video communications and the fact that MPEG is currently exploring a scalable video coding standard, fast JSCC algorithms are expected to play a bigger role and bring more performance gains. This article is also expected to stimulate further research efforts into JSCC and more importantly, prompt the industry to adopt some of these JSCC algorithms in their system designs, thus closing the cycle from algorithm development to implementation.