Modelling of a transmission line is done to analyse its performance and characteristics. The gathered information vis simulating the model can be used to reduce losses or to compensate these losses. Moreover, it gives more insight into the working of transmission lines and helps to find a way to improve the overall transmission efficiency with minimum cost.
Performance modelling Performance modelling is the abstraction of a real system into a simplified representation to enable the prediction of performance. The creation of a model can provide insight into how a proposed or actual system will or does work. This can, however, point towards different things to people belonging to different fields of work.
Performance modelling has many benefits, which includes: Relatively inexpensive prediction of future performance. A clearer understanding of a system's performance characteristics. Additionally it may include, a mechanism for risk management and reduction with design support for future projects. A model will often be created specifically so that it can be interpreted by a software tool that simulates the system's behaviour, based on the information contained in the performance model. Such tools provide further insight into the system's behaviour and can be used to identify bottlenecks or hot spots where the design is inadequate. Solutions to the problems identified might involve the provision of more physical resources or change in the structure of the design.
Performance modelling is found helpful, in case of: Estimating the performance of a new system. Estimating the impact on the performance of an existing system when a new system is interacting with it. Estimating the impact of a change of workload or input on an existing system.
Overview
Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation and is different from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The interconnected network which facilitates this movement is known as a transmission line. A transmission line is a set of electrical conductors carrying an electrical signal from one place to another. Coaxial cable and twisted pair cable are examples. The transmission line is capable of transmitting electrical power from one place to another. In many electric circuits, the length of the wires connecting the components can, for the most part, be ignored. That is, the voltage on the wire at a given time can be assumed to be the same at all points. However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to or less than the length of the wire. So far transmission lines are categorized and defined in many ways. Few approaches to modelling have also being done by different methods. Most of them are mathematical and assumed circuit-based models.
Transmission can be of two types : HVDC Transmission (High Voltage Direct Current transmission) HVAC Transmission (High Voltage Alternating Current Transmission)
HVDC transmission
High-voltage direct current (HVDC) is used to transmit large amounts of power over long distances or for interconnections between asynchronous grids. When electrical energy is to be transmitted over very long distances, the power lost in AC transmission becomes appreciable and it is less expensive to use direct current instead of alternating current.Stephen W. Fardo & Dale R. Patrick, Electrical Power Systems Technology, Third Edition, Taylor & Francis Ltd., USA, 2008, , Chapter 8 Power Distribution Fundamentals For a very long transmission line, these lower losses (and reduced construction cost of a DC line) can offset the additional cost of the required converter stations at each end.In DC transmission line, the mercury arc rectifier converts the alternating current into the DC. The DC transmission line transmits the bulk power over long distance. At the consumer ends the thyratron converts the DC into the AC.
HVAC transmission The AC transmission line is used for transmitting the bulk of the power generation end to the consumer end. The power is generated in the generating station. The transmission line transmits the power from generation to the consumer end. High-voltage power transmission allows for lesser resistive losses over long distances in the wiring. This efficiency of high voltage transmission allows for the transmission of a larger proportion of the generated power to the substations and in turn to the loads, translating to operational cost savings. The power is transmitted from one end to another with the help of step-up and step down transformer. Most transmission lines are high-voltage three-phase alternating current (AC), although single phase AC is sometimes used in railway electrification systems. Electricity is transmitted at high voltages (115 kV or above) to reduce the energy loss which occurs in long-distance transmission.
Power is usually transmitted through overhead power lines. Underground power transmission has a significantly higher installation cost and greater operational limitations, but reduced maintenance costs. Underground transmission is sometimes used in urban areas or environmentally sensitive locations.
Terminologies Lossless line
The lossless line approximation is the least accurate model; it is often used on short lines when the inductance of the line is much greater than its resistance. For this approximation, the voltage and current are identical at the sending and receiving ends.
The characteristic impedance is purely real, which means resistive for that impedance, and it is often called surge impedance for a lossless line. When a lossless line is terminated by surge impedance, there is no voltage drop. Though the phase angles of voltage and current are rotated, the magnitudes of voltage and current remain constant along the length of the line. For load > SIL, the voltage will drop from sending end and the line will "consume" VARs. For load < SIL, the voltage will increase from sending end, and the line will generate VARs.
Power factor
In electrical engineering, the power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the instantaneous product of the two. A negative power factor occurs when the device (which is normally the load) generates power, which then flows back towards the source.
Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the average product of current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power(pf ≤0.5).
In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase energy loss in the distribution system and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.
Surge impedance
The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. Alternatively and equivalently it can be defined as the input impedance of a transmission line when its length is infinite. Characteristic impedance is determined by the geometry and materials of the transmission line and, for a uniform line, is not dependent on its length. The SI unit of characteristic impedance is Ohm (Ώ)
Surge impedance determines the loading capability of the line and reflection coefficient of the current or voltage propagating waves.
Where,
Z0 = Characteristic Impedance of the Line L = Inductance per unit length of the Line C = Capacitance per unit length of the Line
Line parameters The transmission line has mainly four parameters, resistance, inductance, and capacitance and shunt conductance. These parameters are uniformly distributed along the line. Hence, it is also called the distributed parameter of the transmission line.
Ferranti Effect
In electrical engineering, the Ferranti effect is the increase in voltage occurring at the receiving end of a very long (> 200 km) AC electric power transmission line, relative to the voltage at the sending end, when the load is very small, or no load is connected. It can be stated as a factor, or as a percent increase:.J. F. Wilson, Ferranti and the British Electrical Industry, 1864-1930, Manchester University Press, 1988 page 44
The capacitive line charging current produces a voltage drop across the line inductance that is in-phase with the sending-end voltage, assuming negligible line resistance. Therefore, both line inductance and capacitance are responsible for this phenomenon. This can be analysed by considering the line as a transmission line where the source impedance is lower than the load impedance (unterminated). The effect is similar to an electrically short version of the quarter-wave impedance transformer, but with smaller voltage transformation.
The Ferranti effect is more pronounced the longer the line and the higher the voltage applied.Line-Charging Current Interruption by HV and EHV Circuit Breakers, Carl-Ejnar Sölver, Ph. D. and Sérgio de A. Morais, M. Sc. The relative voltage rise is proportional to the square of the line length and the square of frequency.A Knowledge Base for Switching Surge Transients, A. I. Ibrahim and H. W. Dommel
The Ferranti effect is much more pronounced in underground cables, even in short lengths, because of their high capacitance per unit length, and lower electrical impedance.
Corona discharge A corona discharge is an electrical discharge brought on by the ionization of a fluid such as air surrounding a conductor that is electrically charged. Spontaneous corona discharges occur naturally in high-voltage systems unless care is taken to limit the electric field strength. A corona will occur when the strength of the electric field (potential gradient) around a conductor is high enough to form a conductive region, but not high enough to cause electrical breakdown or arcing to nearby objects. It is often seen as a bluish (or another colour) glow in the air adjacent to pointed metal conductors carrying high voltages and emits light by the same property as a gas discharge lamp.
In many high voltage applications, the corona is an unwanted side effect. Corona discharge from high voltage electric power transmission lines constitutes an economically significant waste of energy. Corona discharges are suppressed by improved insulation, corona rings, and making high voltage electrodes in smooth rounded shapes.
ABCD parameters A, B, C, D are the constants also known as the transmission parameters or chain parameters. These parameters are used for the analysis of an electrical network. It is also used for determining the performance of input, output voltage and current of the transmission network.
Propagation constant