Electric Power – Part 1 – SI Units & History
Preamble
The concept of power in electrical power systems is an important topic for power systems engineers. Everyone remembers the equation for power as a product of voltage and current (P = V x I) taught in high school physics and in the introductory courses on electric circuits. This equation is valid for direct current (DC) systems and it is only valid for alternating current (AC) systems with resistances. However, AC systems have resistances, inductances and capacitances.
AC power is ‘complex’ – literally! The concept of ‘reactive power’ eludes most power system engineers. Many power systems students (and consequently power systems engineers) fail to make the required transition from the equation for DC power to AC power. I have seen technical presentations which try to explain the concept of reactive power as the ‘froth’ in a glass of beer!
This series of blogs aims to provide a good understanding of electric power concepts along with equations and practical examples. Hopefully, we can now drink the beer without thinking about ‘reactive’ power!
Unit of power
Energy is the capacity to do ‘Work’. In other words, ‘Work done’ is the ‘Energy spent’ or ‘Energy generated’. For example, ‘work’ is said to be done when a person carries a given mass, say 50 kg, up a ladder.
The ‘power’ is defined as the ‘Rate of Energy’. The ‘power’ is determined by how fast the person can climb the ladder. A more ‘powerful’ person can climb the ladder faster or can carry more mass in the same time.
A popular unit of measurement for mechanical power is ‘horsepower (hp)’. In the late 1760s, James Watt, the Scottish inventor of the steam engine, coined this term. In fact, Watt’s steam engine was an improved version of Thomas Newcomen’s steam engine, which was in commercial use since 1712. But James Watt was a clever salesman. He marketed the product by claiming that his steam engine had enough power to replace 10 cart-pulling horses! His business soared! Watt’s steam engine relaced Newcomen’s engine completely by 1804.
James Watt based his calculation on the basis that a ‘regular’ horse can carry 330 pounds of coal up a mine shaft in 1 minute. Based on this, 1 horsepower (hp) corresponds to 33,000 ft-lb per minute! This unit of power has survived the centuries and is still popular.
The unit of electrical power is a ‘watt’. It is named to honour James Watt. It has been a tradition in electrical science to name the units in honour of famous physicists and inventors. For example, the unit of voltage (volt) is named after Alessandro Volta, the Italian physicist and chemist who invented the battery. Hence, Volta is effectively the inventor of electric power!
The unit of electric power (watt) is also used in SI units as the unit of power for mechanical and thermal energy. The horsepower (hp) as a unit of power may become extinct in future, but ‘Watt’ will continue to live on!
Unit of energy
The unit of energy in electricity in SI units is a ‘joule’. Since power is defined as the rate of energy, 1 joule per second (J/s) is equal to the power of 1 watt. In other words, 1 joule of energy is equal to 1 watt-second (W-s). As in the case of power, the joule is now used in SI units as the unit of energy for mechanical and thermal energy.
The unit of electric energy is named in honour of James Joule – an English physicist and a brewer! He conducted experiments using a paddle wheel and calorimeter to prove that heat and mechanical work are both forms of energy. His technical paper presented at a conference in 1843 led to the development of thermodynamics.
He also conducted experiments which led to the development of refrigerators. In fact, the cooling of gas when it is allowed to expand freely is called the Joule-Thomson effect.
James Joule also experimented with the amount of heat generated by electric current when it is passed through a conductor (resistance). It is known as Joule’s first law or Joule-Lenz’s law. It states that the heat generated by an electrical conductor is proportional to the product of its resistance and the square of the current. We can write this relationship in equation form as below, by appropriate choice of units.
P = I2 R
The electrical units of current, resistance and power have been chosen so that a current of 1 ampere flowing in a resistance of 1 ohm produces a heat of 1 watt (1 joule per second). This equation relates electrical energy to thermal energy.
Before 2019, one ampere was defined as the current which produces a force of 2×10-7 newton between conductors per metre length of parallel conductors which are 1 metre away from each other. This definition of ‘ampere’ relates electrical energy to mechanical energy. However, since 2019, the definition of 1 ampere has been redefined as the motion of charge across a surface at the rate of 1 coulomb per second.
1 joule is a small value in practice. It is approximately the amount of energy required to lift an apple to a height of one metre! Hence, more practical values of energy units, such as of kilo-joules (kJ), mega-joules (MJ) and kilo-watt-hour (kwh) are used in practice.
Even though the definition of ‘ampere’ has changed, the above discussion provides an insight into how electrical energy is related to mechanical and thermal energy.
A brief history of units
The units used for the measurement of parameters such as length, mass, heat etc. evolved independently based on specific requirements of applications. For example, the measurement of distance was originally based on the ‘foot’, literally! The popular term, the ‘pound’ evolved from the weight of grains – 7200 grains to be precise! In fact, the symbol ‘lb’ for pound is derived from the Latin term ‘Libra’ – ‘scale’ or ‘balance’. The evolution of these units dates back to Roman times!
The popular ‘foot-pound-second (FPS)’ system was developed by the British and the Americans. It is also called the ‘Imperial’ system.
The ‘cm-gram-second (CGS)’ system was developed by the French and the Europeans. The CGS system is also referred to as the ‘Metric’ system. The metric system has units based on multiples of ‘10’, making its usage much simpler in practice.
Fortunately, the system of units used for electrical parameters are the same in both the FPS and CGS systems.
After the development of economical and efficient electric motors, electricity became popular for applications in mechanical and thermal systems. This provided a strong incentive for the development of a system of units that can be used across the board for all types of energy. This is especially useful for energy conversion calculations. This was the main motivation for the development of SI units. This will make the energy conversion calculations for equipment design simpler and more versatile.
