Fundamentals of electricity

Electricity is found in two common forms:

AC (Alternating current)

DC (Direct current)

Marine AC voltage levels are roughly defined as LV (Low Voltage) and HV (High Voltage ≥ 1000 V) with frequency of 50-60 Hz.

Figure 1. Current forms

 

An electrical circuit has the following three basic components irrespective of its electrical energy form:

Voltage (volts) – Voltmeter

Ampere (amps) – Ampere meter

Resistance (ohms) – Ohmmeter

Voltage – electric potential difference, electric pressure or electric tension (symbol as V or U) is the difference in electric potential energy between two points per unit electric charge.

 

Figure 2. Voltage

Current measured in amps [A].

An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas (plasma).

 

Figure 3. Current

 

Resistance is the ohm [Ω].

The electrical resistance of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor.

 

Figure 4. Resistance

 

The electrical circuit.

A circuit is defined as a path taken by an electric current. A current flows through a circuit if a source of electrical energy such as a battery or generator is connected, and the circuit is continuous or conducting along its complete length. The figure below (fig. 5) represents a simple circuit in which a current flows. It shows a source, from which energy is transmitted in the current, the conducting path or cable along which the current flows and the ‘load’. The load is the point where energy is released or work is to be done by the flowing current [1].

Figure 5. Electrical circuit

 

Ohm’s law.

The relationships stated above, are summarized by the first law of an electrical circuit, which is called Ohm’s law and is expressed thus: the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. This can be written as:

 

or

 or

Other forms are:

When using the Ohm’s law formula, it is essential to pay due regard to the magnitudes of the units used. Reference should be made to the appropriate table of conversions. Example 1.1. An e.m.f. of 6 V is applied across a 300Ω resistor. Find the current which will flow

 

 

Series and parallel circuits.

Study of the electrical circuit shows that in its simplest form it may be built up as a series circuit or a parallel circuit. Resistance is considered to be concentrated in a resistor, or in more than 1 resistor; while connecting leads are assumed to have negligible resistance, unless a definite resistance value for these is stated. Similarly, the cell, battery or generator is assumed to have no resistance unless otherwise stated. Figure circuits shows a series circuit. Only one current path is possible and the same current passes through all the resistors. The current is thus common for such a circuit but the applied potential drops progressively as current flows along the circuit [1].

Figure shows a parallel circuit. Here the main current is made up of 3 branch currents, but the applied potential difference (P.D). is the same or common for all 3 branches. At any junction point there is no current accumulation, i.e. the total current entering a point is the same as the total current leaving the point. Simple laws based on voltage conditions for the series circuit and current conditions for the parallel circuit allow the solution of problems for such simple circuits, and also those of more complicated series–parallel arrangements or electrical networks [1].

Kirchhoff’s law

(1)               VOLTAGE LAW. The sum of the potential or voltage drops taken round a circuit must equal to the applied P.D. Thus, for figure Parallel circuits:

 

 

(2) CURRENT LAW. The current flowing away from a junction point in a circuit must equal the current flowing into that point. Thus for figure Series circuits:

 

 

The above laws help deduce simple formulae for series and parallel circuits in terms of the equivalent resistances of the circuits.

THE SERIES CIRCUIT. For figure Series circuits, let I amperes be the common current flowing round a circuit. Then from Ohm’s law, the voltage dropped across resistor R1 is V1 volts = IR1. Similarly, the voltage dropped across R2 is V2 = IR2 etc. If R is taken as the equivalent resistance of the whole circuit, then as V is the applied voltage and it will be dropped over this equivalent resistance, we can write V = IR [1].

Using Kirchhoff ’s voltage law then

 

 

or

 

 

THE PARALLEL CIRCUIT. For figure Parallel circuits, let V volts be the common voltage applied to all the parallel branches and with a total main current of I amperes. Voltage V would also cause a current of I amperes through an equivalent circuit of resistance R ohms [1].

Thus I = V/R and using Kirchhoff ’s current law then

 

But for branch 1

And similarly for branch 2  etc.

Thus  can be written as:

 

 

 

Note. The reciprocal of resistance is often referred to as Conductance, symbolized by G = 1/R

The unit is the Siemens; the symbol S appended to the numerical value [1].

So for a parallel circuit  etc.

 

Power.

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit.

Figure 9. Electric power

 

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit.

In DC circuits, power (watts) is simply a product of voltage and current:

P = U x I (Watt)

I= P/V (Ampere)

U=P/I (Voltage)

In AC circuits, power is divided on:

- Apparent Power is the product of voltage and ampere, i.e., [VA] or [kVA]. Apparent power is total power supplied to a circuit inclusive of the true and reactive power.

 

S= V x A = [VA]

 

- Real Power, True Power or Active Power is the power that can be converted into work is measured in [kW].

 

P= VA x cosφ = [Watts]

 

- Reactive Power. If the circuit is of an inductive or capacitive type, then the reactive component consumes power and cannot be converted into work and is denoted by the units [VAR].

 

Q= VA x sinφ =[VAR]

 

Relationship Between Powers

 

Figure 10. Power triangle

Power Factor (PF or Cos φ)

Power factor of an AC electrical power system is defined as the ratio of the real power flowing to the load to the apparent power in the circuit, and is a dimensionless number in the closed interval of −1 to 1.

cosφ = P / S = [Watts / VA]

 

P.F. = (𝐓𝐫𝐮𝐞 𝐏𝐨𝐰𝐞𝐫)/(𝐀𝐩𝐩𝐚𝐫𝐞𝐧𝐭 𝐏𝐨𝐰𝐞𝐫) 𝑾𝒂𝒕𝒕𝒔/𝒌𝑽𝑨

 

Figure 11. Power factor

 

Single-Phase AC Power System

In the figure current (I) lags voltage (U) by an angle φ.

P= U x I x cos φ = Watt

I=P / (U x cos φ)= Amps

 

Figure 12. Single phase AC power system

 

Three-Phase AC Power System

P= √3 x U x I x cos ɸ = Watts

I=P / (√3 x U x cos ɸ) = Amps

Figure 13. Three-phase AC power connection

 

For Delta-connected system

V line =V phase

I line = √3 x I phase

Figure 14. Delta connection

 

For Star-connected system

V line =√3 x V phase

I line = I phase

Figure 15. Star connection

 

Figure 16. Terminals Star/Delta connections

Electrical Machines (Generators and Electric Motors)

Two categories of large AC machines

The two types of AC machines differ on how their torque is generated.

The definition of Large machines is shown below: