A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

DISTRIBUTED APPROACH FOR SOLVING OPTIMAL POWER FLOW PROBLEMS IN THREE-PHASE UNBALANCED DISTRIBUTION NETWORK

The objective of this report is to study distributed (decentralized) three phase optimal power flow (OPF) problem in unbalanced power distribution networks. A full three phase representation of the distribution networks is considered to account for the highly unbalance state of the distribution networks. All distribution network’s series/shunt components, and load types/combinations had been modeled on commercial version of General Algebraic Modeling System (GAMS), the high-level modeling system for mathematical programming and optimization. The OPF problem has been successfully implemented and solved in a centralized approach and distributed approach, where the objective is to minimize the active power losses in the entire system. The study was implemented on the IEEE-37 Node Test Feeder. A detailed discussion of all problem sides and aspects starting from the basics has been provided in this study. Full simulation results have been provided at the end of the report.

Fast response static var generator for improving the power system performance of an electric arc furnace (EAF)

Cascaded multilevel inverters-based Static Var Generators (SVGs) are FACTS equipment introduced for active and reactive power flow control. They eliminate the need for zigzag transformers and give a fast response. However, with regard to their application for flicker reduction in using Electric Arc Furnace (EAF), the existing multilevel inverter-based SVGs suffer from the following disadvantages. (1) To control the reactive power, an off-line calculation of Modulation Index (MI) is required to adjust the SVG output voltage. This slows down the transient response to the changes of reactive power; and (2) Random active power exchange may cause unbalance to the voltage of the d.c. link (HBI) capacitor when the reactive power control is done by adjusting the power angle d alone. To resolve these problems, a mathematical model of 11-level cascaded SVG, was developed. A new control strategy involving both MI (modulation index) and power angle (d) is proposed. A selected harmonics elimination method (SHEM) is taken for switching pattern calculations. To shorten the response time and simplify the controls system, feed forward neural networks are used for on-line computation of the switching patterns instead of using look-up tables. The proposed controller updates the MI and switching patterns once each line-cycle according to the sampled reactive power Qs. Meanwhile, the remainder reactive power (compensated by the MI) and the reactive power variations during the line-cycle will be continuously compensated by adjusting the power angles, d. The scheme senses both variables MI and d, and takes action through the inverter switching angle, qi. As a result, the proposed SVG is expected to give a faster and more accurate response than present designs allow. In support of the proposal there is a mathematical model for reactive powered distribution and a sensitivity matrix for voltage regulation assessment, MATLAB simulation results are provided to validate the proposed schemes. The performance with non-linear time varying loads is analysed and refers to a general review of flicker, of methods for measuring flickers due to arc furnace and means for mitigation.

Two way power flow using GTO thyristors

Two-way power flow is nothing new and has been in practical use using line commutated converters for at least 50 years. With these types of converters, reversal of power flow can be achieved by increasing the firing angle of the devices beyond 90 degrees thus producing a negative DC voltage. Line commutated converters have several known disadvantages including: the direct current cannot be reversed, the power factor decreases when the firing angle increases and the harmonics are high on the line current. To tackle the above problems a forced commutated converter can be used. The power factor can be unity and the harmonics can be reduced. Many researchers have used PWM with different control techniques to serve the above purposes. In each converter arm, they used a forced commutated device with an antiparallel diode. Under the rectification mode of operation the current path is preponderantly through the diodes and under the inverter operation the current flows preponderantly through the forced commutated devices. Although their results were encouraging and gave a unity power factor with nearly sinusoidal current, the main disadvantage was that there were difficulties in controlling the power factor when the system is needed to operate at lagging or leading power factor. In this work, a new idea was introduced by connecting two GTOs antiparallel instead of a diode and a GTO. A single phase system using two GTO converters which are connected in series was built. One converter operates as a rectifier and the other converter operates as an inverter. In the case of the inversion mode and in each inverter arm one GTO is operated as a diode simply by switching it always on and the other antiparallel GTO is operated as a normal device to carry the inverter current. In case of the rectification mode, in each arm one GTO is always off and the other GTP is operated as a controlled device. The main advantage is that the system can be operated at lagging or leading power factor.

The steady state performance of converter type reactive power compensators

As a source or sink of reactive power, compensators can be made from a voltage sourced inverter circuit with the a.c. terminals of the inverter connected to the system through an inductive link and with a capacitor connected across the d.c. terminals. Theoretical calculations on linearised models of the compensators have shown that the parameters characterising the performance are the reduced firing angle and the resonance ratio. The resonance ratio is the ratio of the natural frequency of oscillation of the energy storage components in the circuit to the system frequency. The reduced firing angle of the inverter divided by the damping coefficient, β, where β is half the R to X ratio of the link between the inverter and the system. The theoretical results have been verified by computer simulation and experiment. There is a narrow range of values for the resonance ratio below which there is no appreciable improvement in performance, despite an increase in the cost of the energy storage components, and above which the performance of the equipment is poor with the current being dominated by harmonics. The harmonic performance of the equipment is improved by using multiple inverters and phase shifting transformers to increase the pulse number. The optimum value of the resonance ratio increases pulse number, indicating a reduction in the energy storage components needed at high pulse numbers. The reactive power output from the compensator varies linearly with the reduced firing angle while the losses vary as the square of it.

System operational costs reduction with non-conventional reactive power sources

Wind energy installations are increasing in power systems worldwide and wind generation capacity tends to be located some distance from load centers. A conflict may arise at times of high wind generation when it becomes necessary to curtail wind energy in order to maintain conventional generators on-line for the provision of voltage control support at load centers. Using the island of Ireland as a case study and presenting commercially available reactive power support devices as possible solutions to the voltage control problems in urban areas, this paper explores the reduction in total generation costs resulting from the relaxation of the operational constraints requiring conventional generators to be kept on-line near load centers for reactive power support. The paper shows that by 2020 there will be possible savings of 87€m per annum and a reduction in wind curtailment of more than a percentage point if measures are taken to relax these constraints.

Integrated Optimal Power Flow for Distribution Networks in Local and Urban Scales

This paper develops an integrated optimal power flow (OPF) tool for distribution networks in two spatial scales. In the local scale, the distribution network, the natural gas network, and the heat system are coordinated as a microgrid. In the urban scale, the impact of natural gas network is considered as constraints for the distribution network operation. The proposed approach incorporates unbalance three-phase electrical systems, natural gas systems, and combined cooling, heating, and power systems. The interactions among the above three energy systems are described by energy hub model combined with components capacity constraints. In order to efficiently accommodate the nonlinear constraint optimization problem, particle swarm optimization algorithm is employed to set the control variables in the OPF problem. Numerical studies indicate that by using the OPF method, the distribution network can be economically operated. Also, the tie-line power can be effectively managed.

Analysis of Transmission System Adequacy Considering the Constrained Fuzzy Power Flow

Power flow calculations are one of the most important tools for power system planning and operation. The need to account for uncertainties when performing power flow studies led, among others methods, to the development of the fuzzy power flow (FPF). This kind of models is especially interesting when a scarcity of information exists, which is a common situation in liberalized power systems (where generation and commercialization of electricity are market activities). In this framework, the symmetric/constrained fuzzy power flow (SFPF/CFPF) was proposed in order to avoid some of the problems of the original FPF model. The SFPF/CFPF models are suitable to quantify the adequacy of transmission network to satisfy “reasonable demands for the transmission of electricity” as defined, for instance, in the European Directive 2009/72/EC. In this work it is illustrated how the SFPF/CFPF may be used to evaluate the impact on the adequacy of a transmission system originated by specific investments on new network elements

Constrained fuzzy power flow models with correlation between nodal injections

This paper extends the symmetric/constrained fuzzy powerflow models by including the potential correlations between nodal injections. Therefore, the extension of the model allows the specification of fuzzy generation and load values and of potential correlations between nodal injections. The enhanced version of the symmetric/constrained fuzzy powerflow model is applied to the 30-bus IEEE test system. The results prove the importance of the inclusion of data correlations in the analysis of transmission system adequacy.

Probabilistic Security Constrained Fuzzy Power Flow Models

In restructured power systems, generation and commercialization activities became market activities, while transmission and distribution activities continue as regulated monopolies. As a result, the adequacy of transmission network should be evaluated independent of generation system. After introducing the constrained fuzzy power flow (CFPF) as a suitable tool to quantify the adequacy of transmission network to satisfy 'reasonable demands for the transmission of electricity' (as stated, for instance, at European Directive 2009/72/EC), the aim is now showing how this approach can be used in conjunction with probabilistic criteria in security analysis. In classical security analysis models of power systems are considered the composite system (generation plus transmission). The state of system components is usually modeled with probabilities and loads (and generation) are modeled by crisp numbers, probability distributions or fuzzy numbers. In the case of CFPF the component’s failure of the transmission network have been investigated. In this framework, probabilistic methods are used for failures modeling of the transmission system components and possibility models are used to deal with 'reasonable demands'. The enhanced version of the CFPF model is applied to an illustrative case.

Power flow forecasting and smart charging for electric vehicle charging systems with photovoltaic integration

An essential role in the global energy transition is attributed to Electric Vehicles (EVs) the energy for EV traction can be generated by renewable energy sources (RES), also at a local level through distributed power plants, such as photovoltaic (PV) systems. However, EV integration with electrical systems might not be straightforward. The intermittent RES, combined with the high and uncontrolled aggregate EV charging, require an evolution toward new planning and paradigms of energy systems. In this context, this work aims to provide a practical solution for EV charging integration in electrical systems with RES. A method for predicting the power required by an EV fleet at the charging hub (CH) is developed in this thesis. The proposed forecasting method considers the main parameters on which charging demand depends. The results of the EV charging forecasting method are deeply analyzed under different scenarios. To reduce the EV load intermittency, methods for managing the charging power of EVs are proposed. The main target was to provide Charging Management Systems (CMS) that modulate EV charging to optimize specific performance indicators such as system self-consumption, peak load reduction, and PV exploitation. Controlling the EV charging power to achieve specific optimization goals is also known as Smart Charging (SC). The proposed techniques are applied to real-world scenarios demonstrating performance improvements in using SC strategies. A viable alternative to maximize integration with intermittent RES generation is the integration of energy storage. Battery Energy Storage Systems (BESS) may be a buffer between peak load and RES production. A sizing algorithm for PV+BESS integration in EV charging hubs is provided. The sizing optimization aims to optimize the system's energy and economic performance. The results provide an overview of the optimal size that the PV+BESS plant should have to improve whole system performance in different scenarios.

The influence of high cable penetration in distribution networks on earth fault currents and the operation of relay protection.

Recent Storms in Nordic countries were a reason of long power outages in huge territories. After these disasters distribution networks' operators faced with a problem how to provide adequate quality of supply in such situation. The decision of utilization cable lines rather than overhead lines were made, which brings new features to distribution networks. The main idea of this work is a complex analysis of medium voltage distribution networks with long cable lines. High value of cable’s specific capacitance and length of lines determine such problems as: high values of earth fault currents, excessive amount of reactive power flow from distribution to transmission network, possibility of a high voltage level at the receiving end of cable feeders. However the core tasks was to estimate functional ability of the earth fault protection and the possibility to utilize simplified formulas for operating setting calculations in this network. In order to provide justify solution or evaluation of mentioned above problems corresponding calculations were made and in order to analyze behavior of relay protection principles PSCAD model of the examined network have been created. Evaluation of the voltage rise in the end of a cable line have educed absence of a dangerous increase in a voltage level, while excessive value of reactive power can be a reason of final penalty according to the Finish regulations. It was proved and calculated that for this networks compensation of earth fault currents should be implemented. In PSCAD models of the electrical grid with isolated neutral, central compensation and hybrid compensation were created. For the network with hybrid compensation methodology which allows to select number and rated power of distributed arc suppression coils have been offered. Based on the obtained results from experiments it was determined that in order to guarantee selective and reliable operation of the relay protection should be utilized hybrid compensation with connection of high-ohmic resistor. Directional and admittance based relay protection were tested under these conditions and advantageous of the novel protection were revealed. However, for electrical grids with extensive cabling necessity of a complex approach to the relay protection were explained and illustrated. Thus, in order to organize reliable earth fault protection is recommended to utilize both intermittent and conventional relay protection with operational settings calculated by the use of simplified formulas.

Fluxo de potência ótimo reativo via método da função lagrangiana barreira modificada

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)