Batched Second-Order Adjoint Sensitivity for Reduced Space Methods

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic differentiation (AutoDiff) backend that targets highly parallel architectures by extracting the second-order information in batch. When the nonlinear equations are associated to a reduced space optimization problem, we leverage the parallel reverse-mode accumulation in a batched adjoint-adjoint algorithm to compute efficiently the reduced Hessian of the problem. We apply the method to extract the reduced Hessian associated to the balance equations of a power network, and show on the largest instances that a parallel GPU implementation is 30 times faster than a sequential CPU reference based on UMFPACK.Comment: SIAM-PP2

Study Of Reactive Power Compensation Using STATCOM

The study of shunt connected FACTS devices is a connected field with the problem of reactive power compensation and better mitigation of transmission related problems in today’s world. In this paper we study the shunt operation of FACTS controller, the STATCOM, and how it helps in the better utilization of a network operating under normal conditions. First we carry out a literature review of many papers related to FACTS and STATCOM, along with reactive power control. Then we look at the various devices being used for both series and shunt compensation. The study of STATCOM and its principles of operation and control, including phase angle control and PWM techniques, are carried out. We also delve into the load flow equations which are necessary for any power system solution and carry out a comprehensive study of the Newton Raphson method of load flow. Apart from this, we also carry out a study of the transient stability of power systems, and how it is useful in determining the behavior of the system under a fault. As an example, a six bus system is studied using the load flow equations and solving them. First this is done without the STATCOM and then the STATCOM is implemented and the characteristics of the rotor angle graph along with faults at various buses are seen. In this thesis, it is tried to show the application of STATCOM to a bus system and its effect on the voltage and angle of the buses. Next the graphs depicting the implemented STATCOM bus are analyzed and it is shown that the plots of the rotor angles show a changed characteristic under the influence of the STATCOM

A Variable-Structure Variable-Order Simulation Paradigm for Power Electronic Circuits

Solid-state power converters are used in a rapidly growing number of applications including variable-speed motor drives for hybrid electric vehicles and industrial applications, battery energy storage systems, and for interfacing renewable energy sources and controlling power flow in electric power systems. The desire for higher power densities and improved efficiencies necessitates the accurate prediction of switching transients and losses that, historically, have been categorized as conduction and switching losses. In the vast majority of analyses, the power semiconductors (diodes, transistors) are represented using simplified or empirical models. Conduction losses are calculated as the product of circuit-dependent currents and on-state voltage drops. Switching losses are estimated using approximate voltage-current waveforms with empirically derived turn-on and turn-off times

Circuit simulation using distributed waveform relaxation techniques

Simulation plays an important role in the design of integrated circuits. Due to high costs and large delays involved in their fabrication, simulation is commonly used to verify functionality and to predict performance before fabrication. This thesis describes analysis, implementation and performance evaluation of a distributed memory parallel waveform relaxation technique for the electrical circuit simulation of MOS VLSI circuits. The waveform relaxation technique exhibits inherent parallelism due to the partitioning of a circuit into a number of sub-circuits. These subcircuits can be concurrently simulated on parallel processors. Different forms of parallelism in the direct method and the waveform relaxation technique are studied. An analysis of single queue and distributed queue approaches to implement parallel waveform relaxation on distributed memory machines is performed and their performance implications are studied. The distributed queue approach selected for exploiting the coarse grain parallelism across sub-circuits is described. Parallel waveform relaxation programs based on Gauss-Seidel and Gauss-Jacobi techniques are implemented using a network of eight Transputers. Static and dynamic load balancing strategies are studied. A dynamic load balancing algorithm is developed and implemented. Results of parallel implementation are analyzed to identify sources of bottlenecks. This thesis has demonstrated the applicability of a low cost distributed memory multi-computer system for simulation of MOS VLSI circuits. Speed-up measurements prove that a five times improvement in the speed of calculations can be achieved using a full window parallel Gauss-Jacobi waveform relaxation algorithm. Analysis of overheads shows that load imbalance is the major source of overhead and that the fraction of the computation which must be performed sequentially is very low. Communication overhead depends on the nature of the parallel architecture and the design of communication mechanisms. The run-time environment (parallel processing framework) developed in this research exploits features of the Transputer architecture to reduce the effect of the communication overhead by effectively overlapping computation with communications, and running communications processes at a higher priority. This research will contribute to the development of low cost, high performance workstations for computer-aided design and analysis of VLSI circuits

dPV: An End-to-End Differentiable Solar-Cell Simulator

We introduce dPV, an end-to-end differentiable photovoltaic (PV) cell simulator based on the drift-diffusion model and Beer-Lambert law for optical absorption. dPV is programmed in Python using JAX, an automatic differentiation (AD) library for scientific computing. Using AD coupled with the implicit function theorem, dPV computes the power conversion efficiency (PCE) of an input PV design as well as the derivative of the PCE with respect to any input parameters, all within comparable time of solving the forward problem. We show an example of perovskite solar-cell optimization and multi-parameter discovery, and compare results with random search and finite differences. The simulator can be integrated with optimization algorithms and neural networks, opening up possibilities for data-efficient optimization and parameter discovery

Efficient method for detection of periodic orbits in chaotic maps and flows

An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp. 4733-4736] with a modified semi-implicit Euler iterative scheme and seeding with periodic orbits of neighbouring periods, has been shown to be highly efficient when applied to low-dimensional system. The difficulty in applying the algorithm to higher dimensional systems is mainly due to the fact that the number of stabilising transformations grows extremely fast with increasing system dimension. In this thesis, we construct stabilising transformations based on the knowledge of the stability matrices of already detected periodic orbits (used as seeds). The advantage of our approach is in a substantial reduction of the number of transformations, which increases the efficiency of the detection algorithm, especially in the case of high-dimensional systems. The performance of the new approach is illustrated by its application to the four-dimensional kicked double rotor map, a six-dimensional system of three coupled H\'enon maps and to the Kuramoto-Sivashinsky system in the weakly turbulent regime.Comment: PhD thesis, 119 pages. Due to restrictions on the size of files uploaded, some of the figures are of rather poor quality. If necessary a quality copy may be obtained (approximately 1MB in pdf) by emailing me at [email protected]

BATTPOWER Toolbox: Memory-Efficient and High-Performance Multi-Period AC Optimal Power Flow Solver

With the introduction of massive renewable energy sources and storage devices, the traditional process of grid operation must be improved in order to be safe, reliable, fast responsive and cost efficient, and in this regard power flow solvers are indispensable. In this paper, we introduce an Interior Point-based (IP) Multi-Period AC Optimal Power Flow (MPOPF) solver for the integration of Stationary Energy Storage Systems (SESS) and Electric Vehicles (EV). The primary methodology is based on: 1) analytic and exact calculation of partial differential equations of the Lagrangian sub-problem, and 2) exploiting the sparse structure and pattern of the coefficient matrix of Newton-Raphson approach in the IP algorithm. Extensive results of the application of proposed methods on several benchmark test systems are presented and elaborated, where the advantages and disadvantages of different existing algorithms for the solution of MPOPF, from the standpoint of computational efficiency, are brought forward. We compare the computational performance of the proposed Schur-Complement algorithm with a direct sparse LU solver. The comparison is performed for two different applicational purposes: SESS and EV. The results suggest the substantial computational performance of Schur-Complement algorithm in comparison with that of a direct LU solver when the number of storage devices and optimisation horizon increase for both cases of SESS and EV. Also, some situations where computational performance is inferior are discussed.Comment: 24 pages, 15 figures, Accepted for publication in IEEE Transactions on Power System