Method for determining customer contribution to harmonic variations in a large power network
A method for identifying the source of harmonic emission and for determining its contribution to the harmonic distortion at different points on a large power supply grid is presented in this paper. The proposed method is based on vector analysis of the harmonic currents, measured synchronously at multiple points on the electrical grid. This approach allows real time locating of the responsible customer (harmonic cause) for a given harmonic current disturbance and determining its contribution to the harmonic voltage and current variations at all measured points (harmonic effect). A physical model, representing a power network supplying three non-linear loads, has been used to illustrate the performances of this method. The presented method can be used to analyze the harmonic current and voltage variations in a large power network in real time, thus assisting the electrical power utility to rapidly identify the harmonic causes and their effect and to better understand different problems associated with the harmonics.
Managing the responsibility for harmonic distortion in power networks
A method to manage the responsibility for harmonic distortion is presented in this paper. The method can determine the contributions to harmonic distortion at the point of common coupling between a customer and a utility. The proposed approach is based on network representation with the Norton equivalent circuits where customer and utility sides are represented with the reference impedance and an equivalent harmonic source. Resistance is introduced as the customer side reference impedance. With this approach any customer deviation from the ideal resistance can be penalized, for example, according to an incentive based scheme. The resistance value is calculated directly from the measurement data. The presented method allows real-time harmonic contribution determination without knowing the actual harmonic customer impedances and enables the evaluation and diagnostic for harmonic distortion also in resonance conditions that cause an amplification of harmonics.
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.