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# Transmission Line Parameters And Its Losses Pdf

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## Predictive Models of Current, Voltage, and Power Losses on Electric Transmission Lines

Bamigbola, M. Ali, K. A modern and civilized society is so much dependent on the use of electrical energy because it has been the most powerful vehicle for facilitating economic, industrial, and social developments.

Electrical energy produced at power stations is transmitted to load centres from where it is distributed to its consumers through the use of transmission lines run from one place to another. As a result of the physical properties of the transmission medium, some of the transmitted power is lost to the surroundings. The overall effect of power losses on the system is a reduction in the quantity of power available to the consumers.

An accurate knowledge of transmission losses is hinged on the ability to correctly predict the available current and voltage along transmission lines. Therefore, mathematical physics expressions depicting the evolution of current and voltage on a typical transmission line were formulated, and derived therefrom were models to predict available current and voltage, respectively, at any point on the transmission line.

The predictive models evolved as explicit expressions of the space variable and they are in close agreement with empirical data and reality. The importance of electric power in today's world cannot be overemphasized for it is the key energy source for industrial, commercial, and domestic activities [ 1 ].

Its availability in the right quantity is essential to the advancement of civilization. Electrical energy is generated at power stations which are usually situated far away from load centers. As such, an extensive network of conductors between the power stations and the consumers is required. This network of conductors may be divided into two main components, called the transmission system and the distribution system. The transmission system is to deliver bulk power from power stations to load centers and large industrial consumers while the distribution system is to deliver power from substations to various consumers.

The efficiency of the transmission component of the electric power system is known to be hampered by a number of problems, especially in third-world countries. The major problems identified in [ 2 ] include application of inappropriate technology, inadequacy of materials, equipment, and man power.

From the physics of electric power transmission, when a conductor is subjected to electric power or voltage , electric current flows in the medium. Resistance to the flow produces heat thermal energy which is dissipated to the surroundings. This power loss is referred to as ohmic loss [ 3 ]. Furthermore, if the applied voltage exceeds a critical level, another type of power loss, called the corona effect [ 4 ], occurs.

The power losses accumulate as the induced current flows and the corona effect propagate along the transmission lines. The power losses could take off a sizeable portion of the transmitted power since transmission lines usually span a long distance, sometimes several hundred kilometers [ 5 ]. Therefore, an accurate knowledge of power losses on transmission lines will be useful in planning for the supply of sufficient quantity of power needed in an electrical network.

One way of mitigating losses in the process of transmitting electric power is to apply some strategies to reduce the losses. Ramesh et al. Rugthaicharoencheep and Sirisumrannukul [ 7 ] employed the use of feeder reconfiguration for loss reduction in distribution system with distributed generators by Tabu Search. Sinsuphun et al. Recently, the classical optimization technique was applied to formulate the optimal strategy that reduces the transmission power losses to the barest minimum [ 9 ]. The strategy is to transmit electric power at very low current with high operating voltage close to the critical disruptive voltage and the spacing between the transmission lines not less than the value of where and are radiuses of the transmission medium and the phase voltage, respectively.

In the process, the evolution of current and voltage on the transmission line is studied and models to predict both current and voltage were constructed.

In the end, the desired model for predicting power losses along transmission lines were formulated by reframing the power loss function as a mathematical physics problem. This strategy led to the exclusion of all the transmission parameters from the model. In the next section, we derive the equations that characterise the evolution of electric current and voltage on a typical transmission line.

In Section 3 , a predictive model of the power losses incurred at different locations on the transmission line is obtained. An analysis of the models is conducted and discussed in Section 4 , while the paper is concluded in Section 5. In this section, we derive the expressions which voltage and current must satisfy on uniform transmission lines. A real transmission line will have some series resistance associated with power losses in the conductor [ 10 ].

There may also be some shunt conductance if the insulating material holding two conductors has some leakage current. Therefore, resistance and conductance are responsible for power losses on transmission lines [ 11 ]. To this end, we formulate a model for a lossy transmission line where the effect of the series resistance and shunt conductance is taken care of on the transmission lines. Herein, we are interested in determining the extent to which voltage and current outputs differ from their input values over an elemental portion of the transmission line.

As such, we consider an equivalent circuit of a transmission line of length containing resistance and conductance as shown in Figure 1. The circuit illustrates how power both voltage and current flow through the transmission medium is considered positioned along the space variable [ 12 ], pp.

Applying the Kirchoff voltage law [ 13 ] on the equivalent circuit of the transmission line, we have which on simplification, dividing through by and taking limits as tends to zero, is simplified to and from which we have Using the Kirchoff current law [ 13 ], which also on simplification, dividing through by and taking limits as tends to zero, is simplified to which is further simplified to since is independent of. Differentiating 6 with respect to again results in Substituting 6 into 3 and 2 into 7 yields Equations 8 and 9 are mathematical physics expressions that characterise the power flow along the transmission lines.

Solving power voltage flow equation 8 which is subject to the boundary conditions, where is the initial voltage, results in The equivalent solution to 9 for current flow along the transmission line is where denotes the initial current in the circuit.

With the aid of the last two equations, the quantity of current and voltage at any point on the transmission line can be discerned. The main reason for losses on transmission lines is the resistance of the conductor against the flow of current [ 14 ]. As a result, heat is produced in the conductor and this increases the temperature of the conductor. The value of the ohmic power loss [ 15 ] is given as where denotes current along the conductor and represents resistance of the conductor.

The formation of corona on transmission lines is associated with loss of power too, which will have some effect on the efficiency of the transmission line [ 16 ]. Corona discharge has to do with emission of ions from the surface of the transmission medium [ 17 ].

The corona power loss for a fair weather condition [ 18 , 19 ] has the value where represents the frequency of transmission, denotes the air density factor, is radius of the conductor, represents the space between the transmission lines, is the operating voltage, and denotes the disruptive voltage.

The total losses on a transmission line is then given as That is, The power losses are therefore given by. It would have sufficed to substitute and from 11 and 12 into 17 so as to obtain an expression for the transmission losses but the transmission parameters , , , and would have remained as undetermined factors.

As such, it is more desirable to rewrite 17 implicitly in terms of the space variable. Thus from 17 , On integrating and utilising 2 — 9 , 18 is simplified to. Solving 19 together with the requisite boundary conditions where denotes the transmitted power. The solution to the transmission power losses model is obtained as where. Perusal of the results presented in Tables 1 and 2 confirms consistency in reduction of the numerical solutions returned, and so the results are in line with reality.

On the other hand the results in Table 3 show close agreement with those in Table 2. Hence, the predictions are in line with reality and empirical data. The evolution of current and voltage on high tension transmission lines as well as the power losses when modelled evolved as second order ordinary differential equations.

With appropriate boundary conditions, the solutions obtained are prescribed in closed forms. Allotting values to the input factors, numerical values were obtained for the requisite factors—current, voltage, and power losses.

Based on the above observations, the models can be used to predict requisite electrical measures along typical transmission lines.

With these measures, electric transmission-related activities can be planned with a view to enhancing efficiency of the electric power system. The equations describing the evolution of current and voltage along transmission lines have been utilised to fashion tools to predict requisite electrical measures such as current, voltage, and power losses. The evolution of current and voltage on transmission lines is a process that can aid the determination of current and voltage as a function of the space variable on transmission lines.

Fashioning the power loss function as a mathematical physics expression led to the formulation of a predictive model for power losses explicitly in terms of the space variable only. The authors declare that there is no conflict of interests regarding the publication of this paper.

Bamigbola et al. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Journal overview. Special Issues.

Bamigbola, 1 M. Academic Editor: Aderemi Oluyinka Adewumi. Received 02 Jan Accepted 01 Feb Published 05 Mar Abstract A modern and civilized society is so much dependent on the use of electrical energy because it has been the most powerful vehicle for facilitating economic, industrial, and social developments. Introduction The importance of electric power in today's world cannot be overemphasized for it is the key energy source for industrial, commercial, and domestic activities [ 1 ].

Power Flow on Transmission Lines In this section, we derive the expressions which voltage and current must satisfy on uniform transmission lines. Model Formulation Herein, we are interested in determining the extent to which voltage and current outputs differ from their input values over an elemental portion of the transmission line. Figure 1. Length of line km Current A Voltage kV 10 Table 1. Table 2. Table 3. References O. Okoro and E. View at: Google Scholar A.

Kenneth and A. View at: Google Scholar T. Smed, G. Andersson, G. Sheble, and L. Sakhavati, M.

## Predictive Models of Current, Voltage, and Power Losses on Electric Transmission Lines

Premium Membership. Learn from experienced power engineers. Like all other power system systems, no matter how carefully the system is designed, losses are present and must be modeled before an accurate representation of the system response can be calculated. Due to the size of the area that the power system serves, the majority of the system components are dedicated to power transmission. The focus of this paper is to describe the losses that occur in the transmission system, present component models, and investigate ways to reduce these losses.

KEYWORDS Transmission Line, Losses, Energy, Electricity, Distribution Line, Table Resistive loss values using sample parameters and the formulas.

## Transmission Lines

Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant , to an electrical substation. The interconnected lines which facilitate this movement are known as a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The combined transmission and distribution network is part of electricity delivery , known as the " power grid " in North America , or just "the grid". Efficient transmission involves reducing the currents by stepping up the voltage prior to transmission, and stepping it down at a substation at the far end.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Shield wire loss reduction for double circuit transmission lines Abstract: A significant loss reduction property in a particular phasing arrangement for vertical double circuit transmission lines is discussed. This conductor arrangement is sometimes referred to as low-reactance phasing, where the conductors of the two circuits, from top to bottom, are arranged in reverse order.

Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant , to an electrical substation. The interconnected lines which facilitate this movement are known as a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution.

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A transmission line is used for the transmission of electrical power from generating substation to the various distribution units. It transmits the wave of voltage and current from one end to another. The transmission line is made up of a conductor having a uniform cross-section along the line.

Bamigbola, M. Ali, K. A modern and civilized society is so much dependent on the use of electrical energy because it has been the most powerful vehicle for facilitating economic, industrial, and social developments.

ing the transmission-line parameters (i.e., the circuit elements). Consider a very long section of a transmission line, such Although all lines have losses, they.

#### Resistive (Skin) Loss

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. To investigate the frequency shift phenomenon by inserting graphene, a generalized lossy transmission-line model and the related electrical parameter-extraction theory are proposed in this paper. Three kinds of graphene-based transmission lines with attenuation phenomenon including microstrip line, double-side parallel strip line and uniplanar coplanar waveguide are analyzed under the common conditions where different chemical potentials are loaded on graphene.

Transmission lines in a power system network are used for transferring power from generating station to the neighboring utility grid substation under all environmental conditions. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Transmission Line Parameters and Analysis. Authors Authors and affiliations Md.

According to the Department of Energy, California lost about The former occurs because of the non-zero resistance found wire's metal. Corona loss is an ionization of the air that occurs when the electric fields around a conductor exceed a specific value.

A transmission line is a wire with a uniform goemetry along its length. Some of the discussion involved losses on power transmission lines. The transmission line losses per transferred energy unit would then be lower for sctl because the losses are fixed.

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Distribution Sector considered as the weakest link in the entire power sector. There are two types of transmission and distribution losses:. Technical Losses 2. Non-Technical Losses Commercial Losses. The technical losses are due to energy dissipated in the conductors, equipment used for transmission line, transformer, sub- transmission line and distribution line and magnetic losses in transformers.

Performance modelling is the abstraction of a real system into a simplified representation to enable the prediction of performance. This can, however, point towards different things to people belonging to different fields of work. 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.

Шифровалка исчезла. ГЛАВА 57 В туалетных комнатах шифровалки не было окон, и Сьюзан Флетчер оказалась в полной темноте. Она замерла, стараясь успокоиться и чувствуя, как растущая паника сковывает ее тело. Душераздирающий крик, раздавшийся из вентиляционной шахты, все еще звучал в ее ушах.

ГЛАВА 97 Фонтейн стремительно вбежал в комнату для заседаний. Бринкерхофф и Мидж последовали за. - Смотрите! - сдавленным голосом сказала Мидж, махнув рукой в сторону окна.

По вашему приказу, директор, - говорил он, - мы провели в Севилье два дня, выслеживая мистера Энсея Танкадо. - Расскажите, как он погиб, - нетерпеливо сказал Фонтейн. Смит сообщил: - Мы вели наблюдение из мини-автобуса с расстояния метров в пятьдесят. Вначале все шло гладко.

Неудачный выбор места, - прокомментировал Смит.  - Халохот думал, что поблизости никого. Халохот какое-то время наблюдал за происходящим, потом скрылся за деревьями, по-видимому, выжидая. - Сейчас произойдет передача, - предупредил Смит.

- Вы не видели девушку. Пожилой уборщик наклонился и выключил мотор. - Eh. - Una nina? - повторил Беккер.  - Pelo rojo, azul, y bianco.

Он всегда питал слабость к Мидж Милкен. Умница, да к тому же единственная женщина, не упускавшая случая с ним пококетничать.  - Как твои дела. - Не жалуюсь.

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