# Power transmission lines voltage and current relationship

### The Physics of Everyday Stuff - Transmission Lines

High-voltage direct current (HVDC) is used to transmit For a very long transmission line, these lower losses. All modern countries are crisscrossed with high-voltage transmission lines, which What are the advantages of alternating current (AC) versus direct current. Electronics Tutorial about the Relationship between Voltage Current and Resistance in house and industrial power and lighting as well as power transmission. To continue with this line of thought, in all circuit diagrams and schematics, the.

The volt is therefore defined by saying that if a charge of 1 C moves across a potential drop of 1 V it picks up energy 1 J: Electric power is the rate at which energy is transported. Since current is the rate of transport of charge, electric power is given by the above expression, but using current I instead of charge Q: For example, you may see written on your hair dryer that it draws 10 A current on the hot setting from a standard US V outlet. That's about as high a power as home appliances go, and this is not too far from tripping a 15 A circuit breaker, standard in modern US houses.

For very high power appliances, like a clothes washer or dryer, you may need a special outlet and dedicated circuit breaker. Another handy version of the power formula replaces voltage V with resistance and current: This is done with high-voltage transmission lines, and the question is: It certainly has a negative safety aspect, since a low voltage line wouldn't be harmful you can put your hands on a 12 V car battery, for example, you won't even feel it; but make sure you don't put metal across the terminals, you'll get a huge current and a nasty spark!

Electric energy is transported across the countryside with high-voltage lines because the line losses are much smaller than with low-voltage lines. All wires currently used have some resistance the development of high-temperature superconductors will probably change this some day.

Let's call the total resistance of the transmission line leading from a power station to your local substation R.

The reason is simply that you want the smallest amount of current that you can use to deliver the power P. Again, this is because power is proportional to current but line loss is proportional to current squared. It also reroutes power to other transmission lines that serve local markets.

This is the PacifiCorp Hale Substation, Orem, UtahUSA Engineers design transmission networks to transport the energy as efficiently as feasible, while at the same time taking into account economic factors, network safety and redundancy. These networks use components such as power lines, cables, circuit breakersswitches and transformers. The transmission network is usually administered on a regional basis by an entity such as a regional transmission organization or transmission system operator.

Transmission efficiency is greatly improved by devices that increase the voltage and thereby proportionately reduce the currentin the line conductors, thus allowing power to be transmitted with acceptable losses.

The reduced current flowing through the line reduces the heating losses in the conductors.

According to Joule's Lawenergy losses are directly proportional to the square of the current. Thus, reducing the current by a factor of two will lower the energy lost to conductor resistance by a factor of four for any given size of conductor. The optimum size of a conductor for a given voltage and current can be estimated by Kelvin's law for conductor sizewhich states that the size is at its optimum when the annual cost of energy wasted in the resistance is equal to the annual capital charges of providing the conductor.

At times of lower interest rates, Kelvin's law indicates that thicker wires are optimal; while, when metals are expensive, thinner conductors are indicated: The increase in voltage is achieved in AC circuits by using a step-up transformer. HVDC systems require relatively costly conversion equipment which may be economically justified for particular projects such as submarine cables and longer distance high capacity point-to-point transmission.

HVDC is necessary for the import and export of energy between grid systems that are not synchronized with each other. A transmission grid is a network of power stationstransmission lines, and substations. Energy is usually transmitted within a grid with three-phase AC. Single-phase AC is used only for distribution to end users since it is not usable for large polyphase induction motors.

Higher order phase systems require more than three wires, but deliver little or no benefit. The synchronous grids of the European Union The price of electric power station capacity is high, and electric demand is variable, so it is often cheaper to import some portion of the needed power than to generate it locally. Because loads are often regionally correlated hot weather in the Southwest portion of the US might cause many people to use air conditionerselectric power often comes from distant sources.

Because of the economic benefits of load sharing between regions, wide area transmission grids now span countries and even continents. The web of interconnections between power producers and consumers should enable power to flow, even if some links are inoperative.

## Electric power transmission

The unvarying or slowly varying over many hours portion of the electric demand is known as the base load and is generally served by large facilities which are more efficient due to economies of scale with fixed costs for fuel and operation. Such facilities are nuclear, coal-fired or hydroelectric, while other energy sources such as concentrated solar thermal and geothermal power have the potential to provide base load power.

Renewable energy sources, such as solar photovoltaics, wind, wave, and tidal, are, due to their intermittency, not considered as supplying "base load" but will still add power to the grid. The remaining or 'peak' power demand, is supplied by peaking power plantswhich are typically smaller, faster-responding, and higher cost sources, such as combined cycle or combustion turbine plants fueled by natural gas.

Hydro and wind sources cannot be moved closer to populous cities, and solar costs are lowest in remote areas where local power needs are minimal. Connection costs alone can determine whether any particular renewable alternative is economically sensible.

Costs can be prohibitive for transmission lines, but various proposals for massive infrastructure investment in high capacity, very long distance super grid transmission networks could be recovered with modest usage fees. Grid input[ edit ] At the power stationsthe power is produced at a relatively low voltage between about 2.

For example, the Western System has two primary interchange voltages: Losses[ edit ] Transmitting electricity at high voltage reduces the fraction of energy lost to resistancewhich varies depending on the specific conductors, the current flowing, and the length of the transmission line.

Measures to reduce corona losses include conductors having larger diameters; often hollow to save weight, [24] or bundles of two or more conductors.

Factors that affect the resistance, and thus loss, of conductors used in transmission and distribution lines include temperature, spiraling, and the skin effect. The resistance of a conductor increases with its temperature. Temperature changes in electric power lines can have a significant effect on power losses in the line.

Spiraling, which refers to the way stranded conductors spiral about the center, also contributes to increases in conductor resistance. The skin effect causes the effective resistance of a conductor to increase at higher alternating current frequencies.

Transmission and distribution losses in the USA were estimated at 6. We can use a stub to introduce an impedance into a circuit instead of using capacitors, inductors, and resistors. Stubs with open-circuit and short-circuit terminations are often used in radio-frequency matching networks. In the figure below, we derive the impedance at the near end in terms of L, ZL, and the characteristics impedance of the line, ZT.

In our derivation, we represent voltages, currents, and phase shifts with complex exponentials. Transmission Line Stub Impedance. The numerator represents the sum of the forward and reflected voltages at the near end, while the denominator represents the difference between the forward and reflected currents at the near end.

The following table gives some example stub impedances for various stub lengths and load impedances. The stub length, L, is in units of wavelength.

### Transmission Line Analysis

The characteristic impedance, ZT, we assume is resistive. The load impedance, ZL, has a real and imaginary part. We calculate the real and imaginary parts of the reflection coefficient, Gamma. We calculate the real and imaginary parts of the reflection coefficient R. We obtained our table with our stub impedance calculation spreadsheet, available here.

We use "1e10" as an open-circuit load. And "inf" result means an open circuit stub impedance. Conclusion Our discusion answers the most important questions about the behavior of transmission lines.

We show that it is the attenuation of higher frequencies by the skin effect that causes the degradation of voltage transitions on long transmission lines, not the dispersion of higher frequencies. Indeed, the dispersion alone would cause the opposite effect: The amplitude of the 1-GHz signal, however, will be attenuated by a factor of six hundred by the time it gets to the other end, while the 1-kHz signal will arrive at almost the same amplitude as it entered.

The late-arrival of the low-frequency component of a signal gives rise to settling times of order microseconds at the far end of hundred-meter cables. The attenuation of higher frequencies is dominated by the skin effect, which serves to increase the effective resistance of the transmission line in proportion to the square root of the frequency. Once we get above MHz, the surface polish of the conductor begins to limit the performance of a cable, which explains why the best high-frequency coaxial cables use polished silver conductors.

Because an imperfectly-terminated transmission line causes power to be reflected back to the source, the impedance seen looking into such a line is not equal to the characteristic impedance of the line, but some function of the reflection coefficient at the far end, and the length of the line.