Claudio R. Fuerte-Esquivel

Advanced SVC models for Newton-Raphson load flow and Newton optimal power flow studies

Advanced load flow models for the static VAr compensator (SVC) are presented in this paper. The models are incorporated into existing load flow (LF) and optimal power flow (OPF) Newton algorithms. Unlike SVC models available in open literature the new models depart from the generator representation of the SVC and are based instead on the variable shunt susceptance concept. In particular, a SVC model which uses the firing angle as the state variable provides key information for cases when the load flow solution is used to initialize other power system applications, e.g., harmonic analysis. The SVC state variables are combined with the nodal voltage magnitudes and angles of the network in a single frame-of-reference for a unified, iterative solution through Newton methods. Both algorithms, the LF and the OPF exhibit very strong convergence characteristics, regardless of network size and the number of controllable devices. Results are presented which demonstrate the prowess of the new SVC models.

A thyristor controlled series compensator model for the power flow solution of practical power networks

A new and comprehensive load flow model for the thyristor controlled series compensator (TCSC) is presented in this paper. In this model the state variable is the TCSCs firing angle, which is combined with the nodal voltage magnitudes and angles of the entire network in a single frame-of-reference for a unified iterative solution through a Newton-Raphson method. Unlike TCSC models available in the open literature, this model takes account of the loop current that exists in the TCSC under both partial and full conduction operating modes. Also, the model takes proper care of the resonant points exhibited by the TCSC fundamental frequency impedance. The Newton-Raphson algorithm exhibits quadratic or near-quadratic convergence characteristics, regardless of the size of the network and the number of TCSC devices.

Modeling of VSC-Based HVDC Systems for a Newton-Raphson OPF Algorithm

The paper presents the model of a voltage source converter -high voltage direct current (VSC-HVDC) suitable for optimal power flow (OPF) solutions using Newtons algorithm. The VSC-HVDCs ability to provide independent control of the converters ac voltage magnitudes and phase angles relative to the system voltage, which allows the use of separate active and reactive power control loops for system regulation, is well represented by the model. In this new development in Newton OPF, the VSC-HVDC system equations are incorporated directly into the matrix W for a unified optimal solution in a single frame-of-reference. The multipliers method is used to handle all inequality constraints of variables, leading to highly efficient OPF solutions of constrained power networks. The solution approach does not require structural changes in the linearised system of equations during the iterative process using Newtons method. The effectiveness of the VSC-HVDC model and its proposed implementation in Newton OPF is demonstrated by means of two sample systems.

A Unified Gas and Power Flow Analysis in Natural Gas and Electricity Coupled Networks

The restructuring of energy markets has increased the concern about the existing interdependency between the primary energy supply and electricity networks, which are analyzed traditionally as independent systems. The aim of this paper is focused on an integrated formulation for the steady-state analysis of electricity and natural gas coupled systems considering the effect of temperature in the natural gas system operation and a distributed slack node technique in the electricity network. A general approach is described to execute a single gas and power flow analysis in a unified framework based on the Newton-Raphson formulation. The applicability of the proposed approach is demonstrated by analyzing the Belgian gas network combined with the IEEE-14 test system and a 15-node natural gas network integrated with the IEEE-118 test system.

Global Transient Stability-Constrained Optimal Power Flow Using an OMIB Reference Trajectory

This paper presents a new approach to transient stability control using global transient stability-constrained optimal power flow (TSC-OPF) methods. Its novelty consists in using the single machine equivalent (SIME) method to perform (and improve) two main important functions of global TSC-OPF approaches: first, SIME is used to efficiently perform the power system transient stability analysis; second, SIME determines a stable one machine infinite bus equivalent rotor angular trajectory that is used as the reference stability constraint, at one specific integration step. In this way, the stability constraint is adjusted by SIME, at each iteration of the TSC-OPF method, in order to accurately reflect power system dynamic behavior. The prowess and main characteristics of the proposed approach are shown by numerical examples.

A New Practical Approach to Transient Stability-Constrained Optimal Power Flow

This paper presents a new, significantly improved, approach to formulate a global transient stability-constrained optimal power flow (TSC-OPF), where the sets of dynamic and transient stability constraints to be considered in the optimization process are reduced to one single stability constraint. This constraint is derived from dynamic information provided by the SIngle Machine Equivalent (SIME) method and is only expressed in terms of steady-state variables, which allows us to diminish the length of the time-domain simulation to be included into the global TSC-OPF to a single (initial) time step. In this way, the size of the resulting optimization problem is reduced to one very similar to that of a conventional OPF, overcoming the main drawback of global TSC-OPF techniques (its huge dimension) while maintaining its accuracy and improving its practical application to real power networks. Effectiveness of the proposal is demonstrated by numerical examples on the WSCC three-machine, nine-bus system and the Mexican 46-machine, 190-bus system.

Neural-Network Security-Boundary Constrained Optimal Power Flow

This paper proposes a new approach to model stability and security constraints in optimal power flow (OPF) problems based on a neural network (NN) representation of the system security boundary (SB). The novelty of this proposal is that a closed form, differentiable function derived from the systems SB is used to represent security constraints in an OPF model. The procedure involves two main steps: First, an NN representation of the SB is obtained based on back-propagation neural network (BPNN) training. Second, a differentiable mapping function extracted from the BPNN is used to directly incorporate this function as a constraint in the OPF model. This approach ensures that the operating points resulting from the OPF solution process are within a feasible and secure region, whose limits are better represented using the proposed technique compared to typical security-constrained OPF models. The effectiveness and feasibility of the proposed approach is demonstrated through the implementation, as well as testing and comparison using the IEEE two-area and 118-bus benchmark systems, of an optimal dispatch technique that guarantees system security in the context of competitive electricity markets.

A Robust Optimization Approach for the Interdependency Analysis of Integrated Energy Systems Considering Wind Power Uncertainty

As power generation plants which use wind energy are increasingly integrated into existing electric power systems, it becomes important to evaluate how the wind power uncertainties affect the power systems operation as well as its interdependency with those infrastructures utilized to transport the various forms of primary energy that is converted into electric energy. This paper proposes a robust optimization model for analyzing the interdependency between natural gas, coal and electricity infrastructures considering their operation constraints and wind power uncertainties. The optimization model obtains an uncertainty-immunized solution in a unified framework based on the balance of nodal energy flows, which remains feasible and nearly optimal for all values of uncertain data. Case studies are presented to verify the effectiveness of the proposed solution for a multi-energy system composed by the IEEE-118 test system coupled to a 15-nodes natural gas network and a 4-nodes coal distribution system as well as for the real life Belgian natural gas and electricity infrastructures.

Advanced transformer control modeling in an optimal power flow using Newton's method

This paper reports on advanced transformer modeling facilities suitable for large-scale optimal power flow studies. The new transformer models are developed from first principles and incorporated into an existing Newton-based optimal power flow computer program for highly robust iterative solutions. A three-winding transformer model with tap ratios in all three windings is shown to be a general case for existing two-winding transformer models and the classic load tap-changing and phase-shifting transformer models. The newly developed transformer models add a great deal to software flexibility and are amenable to more realistic electric energy studies. This is partly due to the transformer models being fitted with complex tap changers in each winding and a nonlinear representation of the magnetizing branch. The three-winding transformer model interfaces easily with reactive power plant models, e.g., static VAr compensators.

Solution of Power Flow With Automatic Load-Frequency Control Devices Including Wind Farms

This paper proposes the integration of steady-state models of several types of wind generators into a power flow algorithm with automatic load-frequency control. Since the system frequency deviation is considered a state variable to be computed by the power flow solution, this formulation helps identify the operating point of wind generators after the action of the primary frequency control when power imbalances have occurred. The mathematical formulation of fixed-speed wind generators is presented based on the steady-state representation of the induction generator. Furthermore, as variable-speed wind generators keep gaining prominence in power systems, their potential contribution to frequency support is also analyzed herein. These models are formulated within the power flow approach by using a unified single frame of reference and the Newton-Raphson algorithm. The proposed approach is then applied to the analysis of a three-machine, eight-bus system and the IEEE-14 bus test system.