Norberto Garcia

Parallel power flow solutions using a biconjugate gradient algorithm and a Newton method: A GPU-based approach

A new approach to solve the power flow problem based on graphic processing units is presented in this paper. A Newton method is implemented to solve the set of nonlinear equations of the power flow formulation. A parallel kernel for the biconjugate gradient method allows solving the voltage corrections on a graphic processing card. While the evaluation of the Jacobian matrix is carried out on the CPU of the host PC, the most demanding task of the iterative biconjugate gradient method for the solution of a linear system is performed on the GPU. Furthermore, a row-indexed sparse storage scheme implemented in the host PC and on the device graphic card allows providing efficient solutions in terms of storage and computational effort. A test case based on the IEEE-118 node system is solved to show the accuracy and efficiency of power flow solutions computed on the graphic processing unit.

Unbalanced three-phase power flow studies of distribution systems with plug-in electric vehicles

A three-phase power flow analysis of a distribution system with plug-in electric vehicular fleets is proposed in this paper. The plug-in electric vehicle based on a voltage controlled representation is incorporated into a power flow formulation suitable for radial and unbalance distribution network. The PEV model comprises a voltage source converted (VSC) and a battery pack. While active power is regulated at the storage device according to the charging and discharging status of battery, the voltage magnitude at the point of common coupling is regulated by the VSC. Furthermore, a comprehensive VSC-based PEV equivalent model that accurately reflects the behavior of a distributed vehicular fleet is proposed in this work to carry-out efficient steady-state analyses. The impact of a plug-in vehicular fleet in the voltage unbalance of the IEEE 13-node test feeder is analyzed, where each PEV is modeled as a Tesla Roadster EV with a lithium-ion battery pack.

Fast convergence to the steady-state operating point of a VFT park using the limit cycle method and a reduced order model

In this paper, a new and efficient VFT park model suitable for stability and dynamic analyses of asynchronous links is presented. This model allows the simulation of multi-unit VFTs operated in parallel in order to increase the power transfer between two electric power systems. The backbone of the VFT model relies on a reduced order model of a wound-rotor induction machine. The computation of the steady-state operating point is achieved with the limit cycle method based on a Newton method and the Poincaré map. This approach is particularly useful for the fast determination of the steady-state operating point of the variable frequency transformer because of the inherently large inertia of its rotary machine, which may cause a prolonged transient response after a system disturbance. The computation of the steady-state operating point with the limit cycle method paves the way to carry-out efficient stability studies. The steady-state operating point of a VFT park consisting of five 100 MW VFT units is computed for its energization, step power transfer and fault scenarios.

Transmission line model with frequency dependency and propagation effects: A model order reduction and state-space approach

A new and comprehensive transmission line model for the study of power systems electro-magnetic transients based on a highly effective model order reduction, is presented in this paper. The model takes the form of a state-space representation and differs fundamentally from the well-known family of transmission line model based on the wave-travelling concept. The core principles of the model order reduction procedure are the application of singular approximations, balancing-free square-roots and the computation of projection matrices. Grammian factors in combination with a Cholesky factorization are applied to the solution of the Lyapunov equations and, hence, to the calculation of the projection matrices. Commensurate with state-of-the-art transmission line models for the study of electromagnetic transients, the new model includes full frequency dependency, propagation effects and geometric imbalances.While its frequency dependency characteristic is modelled using a set of parallel RL branches, the long-line effects are incorporated by discretizing its distributed parameters with respect to the line distance. Newtonpsilas method is used to fit the set of parallel RL branches and Singular Value Decomposition is employed to solve cases where the Jacobian becomes ill-conditioned. The effectiveness of the proposed transmission line model is demonstrated using a non-transposed version of the Jaguara-Taquaril three-phase transmission line system.

Comprehensive Wind Park Model Including a Reduced Order Model for an Induction Generator and a STATCOM for Reactive Compensation

In this paper, a comprehensive time domain model for a wind park, suitable for stability analysis, is presented. The wind generator is modeled with a reduced order model for an asynchronous machine, whilst the wind turbine model takes into account the dimension of the turbine, the rotor blade and blade pitch angle. Each wind generator incorporates a STATCOM (STAtic COMpensator) controller in order to provide reactive power compensation needed by the induction generators. The dynamic behavior of a 50MW wind park is reported for different operating scenarios.

Power flow solution of power networks with photovoltaic generation and a battery energy storage system

This paper addresses the computation of the power flow solution of power networks with photovoltaic (PV) generation and energy storage devices. The PV model implemented in this work provides the steady state solution taking into account meteorological conditions. This model is validated with field measurements recorded at a PV installation consisting of monocrystalline solar PV panels. A battery storage system (BESS) based on a lithium-ion battery storage device is used to balance power generation of the PV renewable source. Furthermore, the power flow analysis is carried out for a 5-node benchmark power system using PSS/E software package. Results indicate that the active and reactive power losses can be reduced approximately to 60% of the base case when a PV system is connected to the power grid. However, the voltage deviation index and the loading of the transmission line connected to the point of common coupling increase up to 60%. In contrast, simulation results show that the operation of a BESS helps to reduce power losses and line loading in about 30% and 40%, respectively, while the voltage deviation increases in only 20% with respect to the base case.

Voltage unbalance analysis of distribution systems using a three-phase power flow ans a Genetic Algorithm for PEV fleets scheduling

A powerful blend based on a three-phase distribution power flow method and a Genetic Algorithm for plug-in electric vehicular fleets scheduling is proposed in this paper. The Genetic Algorithm optimizes the number of charging and discharging plug-in electric vehicles in order to efficiently manage voltage unbalances and power losses. The plug-in electric vehicle based on a voltage controlled representation is incorporated into a power flow formulation suitable for radial and unbalance distribution network. The PEV model comprises a voltage source converted (VSC) and a battery pack. While active power is regulated at the storage device according to the charging and discharging status of battery, the voltage magnitude at the point of common coupling is regulated by the VSC. Furthermore, a comprehensive VSC-based PEV equivalent model that accurately reflects the behavior of a distributed vehicular fleet is proposed in this work to carry-out efficient steady-state analyses. The impact of a plug-in vehicular fleet in the voltage unbalance of the IEEE 13-node test feeder is optimized with a multiobjective genetic algorithm, where each PEV is modeled as a Tesla Roadster EV with a lithium-ion battery pack.

Steady-state solution of a VFT park using the limit cycle method and a reduced order model

A VFT park model suitable for stability analyses of asynchronous links is presented in this work. This model allows the simulation of multi-unit VFTs operated in parallel in order to increase the power transfer between two electric power systems. The backbone of the VFT model relies on a reduced order model of a wound-rotor induction machine. The VFT control system includes power and speed regulators in order to provide a smooth dynamic operation. The computation of the steady-state operating point is achieved with the limit cycle method based on a Newton method and the Poincaré map. This approach is particularly useful for the fast determination of the steady-state operating point of the variable frequency transformer because of the inherently large inertia of its rotary machine, which may cause a prolonged transient response after a system disturbance. The computation of the steady-state operating point with an acceleration procedure based on the limit cycle method paves the way to carry-out efficient stability studies. The steady-state operating point of a VFT park consisting of three 100 MW VFT units is computed for different operating scenarios.

GPU-accelerated Poincaré map method for harmonic-oriented analyses of power systems

A parallel Poincaré map method based on graphic processing units (GPU), suitable for harmonic-oriented studies, is presented in this paper. It relies on a Newton method and a transition matrix computed by columns on the GPU. A parallel kernel for the Trapezoidal Rule integration routine allows solving the set of ordinary differential equations, whilst sparse matrices involved in the Trapezoidal Rule are stored at the GPU using a Compressed Sparse Row (CSR) format. Direct and iterative solvers based on LU decomposition and Krylov subspace methods are used to solve system of equations arising from the Newton-Raphson algorithm. Results in terms of convergence to the periodic steady-state and speedup factors of order 7 confirm that this novel GPU-based approach is an efficient parallel version of the Poincaré map method. An advanced memory optimization approach based on pinned memory and asynchronous transfers provides further computational savings of the order of 20%.

Periodic steady-state solutions of nonlinear circuits based on a differentiation matrix

A discrete time-domain method suitable to compute stable, periodic steady-state solutions of nonlinear systems is presented in this paper. This approach applies a discrete-time representation of the differentiation operator, which estimates the exact derivative of a trigonometric polynomial. The set of ordinary differential equations that represents the dynamic behavior of the nonlinear problem is transformed into a nonlinear algebraic formulation and solved with a Newton algorithm. Furthermore, a direct method for solving sparse systems is incorporated in the Newton method to improve its efficiency in both storage and time. Two test cases based on the Duffing circuit and a power supply illustrate the applicability and effectiveness of this method to determine periodic steady-state solutions. Comparative results are reported with the proposal presented in this work and the well-known finite-difference method.