Any system that deals with electrical energy on its way between energy sources and loads can be considered to be an electrical energy system. These systems vary greatly in size and complexity. For instance, consider a supply system of a computer, large data center, or power system of a country. All these systems include some sort of power conversion to generate electrical energy, power transmission, and distribution. In all cases, some kind of power transformation is also included either to convert between direct current (DC) and alternating current (AC) systems or to adapt electric supply voltage to the load’s requirements.

All electrical energy systems are characterized by the voltage waveform, rated voltage, power levels, and the number of lines or phases in the case of AC systems. Based on the voltage waveform, electrical energy systems can be divided in two main categories, AC systems and DC systems. AC systems transport and distribute energy using alternating voltages and currents while DC systems use direct currents and voltages for the same purpose. Another classification of low voltage (less than 600 V), medium voltage (600 V–69 kV), high voltage (69–230 kV), and extra-high voltage systems (more than 230 kV) can be done based on the voltage ratings of the system [1]. AC systems exist at all voltage levels. DC systems, on the other hand, are more common at extra-high and low voltage levels. AC systems can be further divided to single-phase and polyphase systems depending on the number of phases used for power transmission. Among polyphase systems, the three-phase system is most commonly used.

Another classification of electrical energy systems can be based on their purpose. Assuming that the electrical energy goes through a chain of systems on its path from sources to the loads, it is possible to identify system groups that have common or similar purposes. At the beginning and end of this chain, we generally have some types of energy conversion systems. These devices convert mechanical, thermal, chemical, or some other form of energy into electrical energy or vice versa. They are usually considered to be sources or loads, depending on whether they produce or consume electrical energy. In between we have transmission and distribution systems, which may include a number of electrical energy conversion (transformation) systems. The main purpose of transmission systems is to transport electrical energy in the most efficient manner. Distribution systems distribute electrical energy among loads and make sure that the form of the electrical energy fits the load requirements. Electrical energy conversion (transformation) systems are usually part of transmission and distribution systems. They change the form of electrical energy by modifying either the voltage levels, voltage waveforms, or the number of phases in the case of polyphase systems.

As an example, consider a large utility grid system. In this type of system, the end points are sources and loads. On the source side, we have energy conversion systems in the form of large power plants, converting the energy from fossil, renewable, or nuclear energy sources into electrical energy. These systems are highly complicated and may include several energy conversion stages. However, output is in most cases at the terminals of a medium voltage three-phase generator, which is an electromechanical energy conversion system on its own. In a large power system, generators are usually far from loads. As a consequence, medium voltage three-phase power from the generators first goes to the transmission system, which transports the energy over long distances. Before it is transported, electrical energy is transformed into a form that is suitable for low loss transportation over large distances, usually high voltage AC or DC. From the transmission system, the high voltage electrical energy is transferred to a distribution system where it is converted into low and medium voltage levels and distributed among loads.

In electrical energy systems, energy and power terms are easily defined by looking at the simple circuit shown in Figure 1.1. The equations for instantaneous electrical power (p) and energy (E) drawn by the load during a time period of ∆t are given in (1.1) and (1.2) [2].

In the case where the voltage does not change over time (DC supply case) and the load is constant, the current and power are also constant, while the integral in (1.2) is reduced to $E=vi∆t$. These values are simple to calculate and are very informative.

If it is assumed that the supply voltage is an alternating waveform (AC supply), the equation for power (1.1) becomes a value that changes in time while the energy equation (1.2) becomes a bit more complicated to calculate. The simplicity of the DC case no longer exists. To make things similarly informative for the AC systems, the concepts of root main square (RMS) values, active power (P), reactive power (Q), and apparent power (S) have been introduced. Assuming that voltage and current in the system can be described by Equations (1.3) and (1.4), RMS values are defined by Equations (1.5) and (1.6), active power is given by Equation (1.7), reactive power by Equation (1.8), and apparent power by Equation (1.9) [3].

If the consumer notation convention is assumed, which states that the load draws positive active power, the source will draw negative active power (or produce positive power). Active power is given in watts (W) and describes how fast energy is converted from electrical into some other form (e.g., thermal in the case of a resistive load). Reactive power, on the other hand, characterizes the ability of reactive loads (capacitors and inductors) to return the energy stored in them back to the source. It actually describes the rate at which the energy circulates between sources and reactive loads.

Parameter cos(θ) is defined as the system power factor. The load that has a power factor with positive angle θ is called lagging and by convention draws reactive power. In practice the inductive loads have current lagging behind the voltage waveform. The angle θ is positive in this case if expressed with Equation (1.4), which means that the inductor draws positive reactive power. A load that has a power factor with negative angle θ is called leading and draws negative reactive power (or supplies positive reactive power). These loads are mostly capacitive. Reactive power is usually expressed in volt-amperes-reactive (VAr).

In AC systems, all instantaneous values have an alternating nature. As a result, instantaneous power and energy also have alternating components. Active power is used to quantify the energy producing component of power and the rate at which energy flows, on average, in one direction and is converted into another form by the load. It can be proved that Equation (1.7) represents the average value of the instantaneous power expressed in Equation (1.1) for current and voltage waveforms given in Equations (1.3) and (1.4). Consequently, the useful amount of energy drawn by the load during the time period ∆t can be expressed as an integral of active power, given by Equation (1.10). If the power factor remains constant, Equation (1.10) is reduced to (1.11), which is simple to calculate and is very informative.

It should be also noted that reactive power only circulates between sources and loads and is not converted into other energy forms (at least not in a useful manner), which means that it does not contribute to useful energy consumption by load. However, it increases losses in the transmission systems as the energy is moved back and forth between generators and loads. For this reason, reactive power must be taken into account and is equally as important as active power in large distribution systems.

For the three-phase system exemplified in Figure 1.2, voltage and current waveform expressions are given by Equations (1.12) and (1.13). In this case, power and energy equations are similar to a single-phase system. The difference is that there are three power carrying lines and three times more power can be transferred with the same voltage and current ratings. The expression for active and reactive power and energy consumed by the load during a time interval of ∆t is given by Equations (1.14-1.16) [3].

For the sake of simplicity, Equations (1.12-1.16) are given in terms of rated phase to neutral RMS voltage (V_rms). In power systems engineering, it is more common to express multiphase voltages in terms of phase-to-phase rated voltage (V_rmsll). The relationship between phase-to-phase and phase-to-neutral voltages in a symmetric three-phase system is described by Equation (1.17). Using this equation, it is easy to express energy and power in three-phase systems in terms of line-to-line voltages. This task is left to the reader as an exercise.

Another important point is related to the measurement units used for power systems calculations. Instead of joule (J) for energy, which is essentially watt-second, units like watt-hour (Wh) or the prefixed units kilowatt-hour (kWh), megawatt-hour (MWh), or terrawatt-hour (TWh) are commonly used. For volt and ampere units, due to the high amplitudes, prefixes kilo (k) and mega (M) are also commonly used, for example, kA, MV.

One of the main benefits of AC systems is easy voltage transformation. Relatively simple and robust transformers can be used for this purpose. The ability to transform voltage level is very important for the electrical energy distribution systems and it should be noted that DC voltage transformation was not an easy task in the late nineteenth century. Voltage transformation enables high voltage transmission, which reduces conduction losses. For the same amount of transmitted power, the conduction losses are reduced with the square of the voltage used for transmission. Another important benefit of easy voltage transformation is the ability to regulate voltage at load centers and to keep it nearly constant with, again, relatively simple and robust multiple tap transformers.

The use of three-phase systems and Tesla’s rotating magnetic field is another advantage of AC systems. Three-phase transmission additionally reduces losses in the system while the principle of the rotating magnetic field enables easy electromechanical energy conversion with the help of robust high power synchronous generators and induction machines.

Nowadays DC and AC systems are intertwined at many levels. DC systems are more common for lower voltages while AC systems still dominate large-scale power distribution and power transmission. In recent decades, DC systems have become more popular mainly as a consequence of development of digital systems and power electronics converters. Some types of energy sources such as solar photovoltaic (PV) and fuel cells, which are becoming increasingly popular, also require a DC interface. Another field where high voltage DC systems have made significant progress is long distance energy transmission where AC systems can have stability issues.

If we limit ourselves to engineering science, one of the most important goals is to find an efficient, clean, and convenient way to convert the energy available in nature into a form that we can easily use. For electrical engineers, the most usable form of energy is electrical.

Arguably, the most common form of energy in nature is thermal; every object that has a temperature higher than its surroundings can be considered as a source of thermal energy. A device that converts electrical into thermal energy can be a simple resistor. The conversion process from thermal directly into electrical is a bit more complicated and requires the use of a special type of device called a thermoelectric energy converter based on Peltier and Seebeck effects. It should be noted that thermal energy can be converted into a mechanical form (steam pressure), which can be used for electromechanical energy conversion. This is in fact the most common way of energy conversion from thermal into electrical in two steps: thermal–mechanical–electrical.

Mechanical energy is also very common in everyday life. Wind, for example, carries large amounts of mechanical (kinetic) energy. Large accumulation lakes of hydropower systems also hold tremendous amounts of mechanical (potential) energy. This energy can be converted into electrical energy with the help of electromechanical energy conversion systems. Most of these systems, usually referred to as electrical generators, convert rotational kinetic energy into electrical energy. As a consequence, electromechanical energy conversion systems usually require devices that convert other mechanical energy types into rotational energy. These devices are called prime movers and are usually in the form of a turbine system.

Solar (light or electromagnetic radiation) energy can be considered as another form of energy commonly used to produce electricity. PV systems convert sunlight directly into electrical energy. These systems are becoming increasingly popular as they produce clean energy with very little environmental impact. The technology is still relatively expensive and new but is the focus of many researchers and is constantly developing.

Chemical energy is used by all life forms and is the earliest form of energy used by humankind. Most of the substances that hold chemical energy can be used for creating fire that gives off thermal energy (coal and wood burn very well). In fact, fire can be seen as a self-sustaining energy conversion process that converts chemical into thermal energy. Most of the modern power conversion systems still convert chemical energy into thermal and then thermal energy into electrical. Large coal power plants, for example, burn coal in order to heat the steam and then use the pressure of the heated steam for electromechanical energy conversion. Systems that perform direct conversion of chemical energy into electrical energy are called electrochemical energy conversion systems. The most common electrochemical energy conversion system is a common battery. These systems require special energy storage chemicals and specialized energy conversion structures, which are one of the most popular research areas today.

Nuclear energy can be considered as another form of energy, which comes directly from nuclear reactions at an atomic level inside a nuclear fuel. There are two forms of nuclear reactions, nuclear fusion and nuclear fission. Nuclear fission is a nuclear reaction where the atom of an element breaks apart into two smaller atoms. Nuclear fusion is the reaction where two smaller atoms form a larger one. In both cases, a part of the mass of the initial atoms is converted to energy. These reactions produce high-energy particles and intense heat. The produced heat can be used for the generation of electrical energy. All nuclear power plants are currently based on nuclear fission. Nuclear fusion is still in its early stages and a feasible fusion reactor with a positive net energy balance still does not exist. Research efforts are under way and some predictions state that fusion power generation could become a reality by 2030.

Thermodynamics describes a system as a whole and does not take individual particles or even parts of the system into account. A thermodynamic system is described with aggregate properties such as temperature, energy, pressure, and work. The relations between these properties in a thermodynamic system are governed by the laws of thermodynamics.

A production of free positive and negative charged particles in the crystal is still not enough to create a useful macroscopic potential difference. If there is no other influence, electrons and holes will be created randomly and will be recombined after they lose the energy acquired from the photons in thermal interactions with the atoms in the crystal. In order to create a useful potential difference, we need a barrier that will separate holes and electrons. A large PN junction similar to the one found in common semiconductor diodes can be used for this purpose.

A PN junction with its space charge region electric field serves as a barrier that will separate holes and electrons and create a useful potential difference across the junction. As soon as the generated electron (hole) enters the space charge region, the field accelerates it toward the N(P) side of the panel. Once the electrons reach the N region and the holes reach the P region, it is not likely that they will be recombined as a majority carrier, so we have a buildup of charges, as shown in Figure 1.3. The charge buildup creates a field (E_pv) and a useful potential difference across the panel terminals. Note that when the panel is not lit, charge buildup due to the diffusion of carriers on the electrode–panel junction, which is not explicitly shown in Figure 1.3, cancels out the field of the PN junction space charge so there is no useful net potential difference on the panel terminals.

In practice, silicon is most commonly used for PV energy conversion. Single-crystal ingots or polycrystalline silicon rods are cut into plates (usually several centimeters in diameter and about 0.5-mm thick). P-type silicon is used as a base and the other side is doped to create an N-type layer across the entire surface, creating one large PN junction [7]. Metal electrodes are then applied to both surfaces, which are then used to connect the plates in series and create panels as shown in Figure 1.4.

The simplest model of a PV cell can be represented with a circuit shown in Figure 1.5. When the cell is unloaded, the voltage across its terminal can be expressed by Equation (1.20), where k represents the Boltzmann constant, q is the charge of the electron in coulombs, T is the absolute temperature of the panel in degrees Kelvin, I₀ is reverse saturation current of the PN junction, and I_sc is the so-called short circuit current of the cell. Both I₀ and I_sc depend on the manufacturing parameters of the cell, while I_sc also depends on the incoming light irradiance [2].

The chemical processes involved in the energy conversion can be reversible or irreversible. Devices that use irreversible processes are usually called nonrechargeable. For these devices, the electrolyte reacts with electrodes, creates an electric current flow and usually is chemically changed into by-products that cannot be reused in the cell. As an example, we can look at a hydrogen fuel cell. The cell uses the hydrogen gas as a fuel, special polymer electrolyte membrane, and atmosphere oxygen to create electricity. The by-product of the reaction is water, as shown in Figure 1.6. There is no way to separate water into oxygen and hydrogen for possible reuse by this fuel cell, which means that the reaction is irreversible and the device is not rechargeable. This particular reaction produces about 1 V across the electrodes and must be stacked to achieve higher voltages [8,9].

Reversible processes are used in devices such as rechargeable and flow batteries. These devices have two distinct operation cycles, charge and discharge, which are characterized by different chemical reactions and different electrical properties. During the discharge cycle, the electrolyte is transformed in order to release the energy from the chemical bonds and generate electrical energy. For the charge cycle, electrical energy flows into the device and transforms the electrolyte back into its original state, storing the electrical energy back into chemical bonds.

One example of a rechargeable electrochemical energy conversion device is the common lead–acid battery. The battery uses lead and lead dioxide plates submerged in a water solution of sulfuric acid as shown in Figure 1.7. Plates react with the solution and produce potential difference; the reaction is shown in Equation (1.21). The lead plate reacts with the water solution of sulfuric acid and forms lead sulfate. The reaction releases positive hydrogen atoms into the solution and two electrons into the plate making it negative. Lead dioxide plate also reacts with the water solution of sulfuric acid and also creates lead sulfate but it needs three hydrogen atoms and one electron for the reaction; the electron comes from the plate leaving it positive. The reaction produces the potential difference of about 2.1 V and it varies with the level of charge. The cells are usually stacked to achieve the voltage range of about 12–14 V.

It should be noted that the reactions are completely reversible if the opposite current flow is applied to the battery terminals [2,10].

It is worth mentioning that Peltier and Thomson effects are also linked to thermoelectric phenomena. The Peltier effect is opposite to the Seebeck effect. If we replace the load in Figure 1.8 with a voltage source, we can force the flow of thermal energy from the cold plate to the hot plate. This makes Peltier plates effective as cooling devices. The Thomson effect is similar to the Seebeck effect but explains the voltage gradient present across a single conductor experiencing a thermal gradient [11,12].

An electromechanical energy conversion system usually has three subsystems, electrical, mechanical, and a system of electromagnetic fields, which is used to couple mechanical forces and electric currents. The basic coupling principle is described by Lorentz force law, which gives the force on a particle carrying an electric change moving in an electromagnetic field, given by Equation (1.23).

$\overrightarrow{F}$ is the vector of the force acting on the charged particle, q is the electric charge of the particle, $\overrightarrow{E}$ is the electric field vector, $\overrightarrow{v}$ is the speed of the particle, and $\overrightarrow{B}$ is the magnetic induction vector. If we have multiple charged particles flowing in the wire in the stationary magnetic field, the forces acting on the short wire segment (actually on the electric charges in it) can be calculated using Equation 1.24, which is derived from Equation (1.23).

Consider an example shown in Figure 1.9. The force vector $d\overrightarrow{F}$, given in Equation (1.24), acts on the very short straight wire segment $\overrightarrow{dl}$ in the magnetic field $\overrightarrow{B}$ along the current carrying conductor c with the current magnitude i [13].

Wire segment vector $\overrightarrow{dl}$ has a magnitude equal to the length of a segment and a direction equal to the direction of the current in the wire segment. Equation (1.24) can be integrated to calculate forces on the entire wire.

For systems such as electric machines, where the magnetic field is not stationary and system geometry is not simple, it is not an easy task to calculate the forces acting in the system using Equations (1.23) and (1.24). In these cases, we can apply basic thermodynamic principles; we can turn to Equation (1.18) to evaluate the system behavior. We can separate any electromechanical conversion system into three subsystems, electrical, mechanical, and the system of coupling fields. We can now apply the first law of thermodynamic and Equation (1.18) on all three subsystems and treat them as if they are linked through their inputs and outputs.

Assuming that our system converts mechanical energy into electrical energy, for the mechanical subsystem the energy balance can be written in a form described by Equation (1.25). Mechanical work at the system input E_{m_input} increases the mechanical subsystem energy E_{m_sys} (e.g., kinetic energy of the moving parts) and creates useful work of mechanical forces E_{m_work}. Useful work of mechanical forces is converted to mechanical losses E_{m_losses} and to energy of the generated coupling fields E_{f_in}, as shown in Equation (1.26). Energy invested in the coupling fields E_{f_in} splits again into a couple of parts (1.27). Some of invested energy is stored in the coupling field energy E_{f_sys}. Energy denoted as E_{f_work} in Equation (1.27) splits between the losses in the field energy E_{f_losses} (e.g., electromagnetic radiation, iron core losses, dielectric losses, etc.) and the energy that is transferred to the induced electromotive force E_{e_in} as shown in Equation (1.28). Energy invested into induced electromotive forces E_{e_in} again splits into energy of the system E_{e_sys} (energy of the fields other than coupling fields), losses E_{e_losses}, and useful work E_{e_work} as given by Equations (1.29) and (1.30). Energy E_{e_work} is the actual electrical energy that is delivered from the energy conversion system and energy E_{e_losses} accounts for the losses in the electrical conductors of the system.

We can usually express all variables in Equations (1.25), (1.27), and (1.29) in terms of values that are known for a particular electromechanical system. Note that all the parameters in these equations are aggregate properties of the system and not related to geometry and detail field distributions in the actual machine. If we can determine system losses from the Equations (1.26), (1.28), and (1.30), we can easily link the mechanical input work and electrical energy output as described by Equation (1.31) and Figure 1.10. The machine power balance can be obtained by performing a time derivative of Equation (1.31) [14].

Examples of chemical energy storage systems include batteries, flow batteries, and fuel cells. Mechanical (kinetic and potential) energy storage systems include pumped storage hydropower, flywheels, and pressurized gas storage systems. Thermal energy can be stored as a molten salt and is also mainly used for large-scale systems. Magnetic energy can be stored in superconducting magnetic storage systems, which is still a relatively new and expensive technology [2].

System efficiency is usually denoted with the Greek letter eta (η). It is always less than one for practical systems, or less than 100% if expressed in percentage. The first law of thermodynamics excludes the possibility of a system that has efficiency greater than one. Furthermore, as a consequence of the second law of thermodynamics, for any practical system, there is always some amount of energy that is converted to other forms (other than useful form). This makes the efficiency of any practical system less than one. An extreme case of a system with 100% efficiency is theoretical and cannot be found in nature [5,6].

Consider an example of a rotating machine with electrical energy as an input and generated mechanical work at its shaft as useful output. Besides mechanical work, the machine performs other things. It radiates thermal energy, generates mechanical vibrations, creates electromagnetic interference, moves air around, etc. All of these effects require some amount of invested energy, which can be considered as a loss in the system. The ideal machine that converts all electrical energy into mechanical work at 100% efficiency would have to work at the ambient temperature; it would be completely silent, and would not radiate any electromagnetic signature, which is clearly impossible.

Fossil energy resources are obtained from dead plant and animal deposits created over the long history of the planet. These resources are vast, but limited, and are not renewable. Until recently fossil fuels have provided for the majority of humanity’s energy demands. These resources mainly include coal, oil, and natural gas.

Renewable energy resources are forms of energy that are naturally replenished on our planet. Examples of traditional renewable resources are hydropower and biomass (e.g., plant fuels such as wood traditionally have been used throughout history, mostly for heating). Modern renewable resources include wind, wave, tidal, solar, and geothermal. Some forms of fuels created from biomass (plants and animals) also fall under this category.

Deposits of certain radioactive elements in Earth’s crust can be classified as nuclear energy resources. These resources are used as fuel for nuclear fission-based power plants. The amount of these rare radioactive elements is limited on our planet and cannot be replenished. Over the years, there has been some research on fusion power but it is still not proven to be a feasible energy resource. This form of energy conversion aims to harvest the energy from sustained fusion of hydrogen atoms into helium [15].