Basic Electrical Theory Review Learning Objectives – At the end of this presentation, students will be able to: - Define terminology with respect to basic electrical theory. - Identify series and parallel circuits and describe the differences between the two. - Define the fundamental laws of electricity, to include: o Ohms Law. o Kirchhoff’s Voltage Law. o Kirchhoff’s Current Law. - Discuss the different types of power in AC circuits. - Discuss power factor and how it is affected by circuit components. - Discuss dissipation factor. - Discuss the power triangle and what components of the power system are represented by the power triangle. - Discuss power factor correction. Electrical Terminology a) Conductors – Materials with electrons that are loosely bound to their atoms, or materials that permit motion of a large number of electrons. i) Examples: (1) Copper (2) Silver (3) Gold b) Insulators (or Non-conductors) – Materials with electrons that are tightly bound to their atoms and require large amounts of energy to free them from the influence of the nucleus. i) Examples: (1) Rubber (2) Plastic (3) Glass (4) Dry wood c) Resistors – Made of materials that conduct electricity, but offer opposition to current flow. i) Examples: (1) Carbon (2) Silicon (3) Germanium (4) Lead d) Voltage – The basic unit of measurement for potential difference, or electromotive force, is the volt (V). Voltage is the force that pushes current through electrical circuits. i) A volt is defined as that amount of force required to “push” one ampere of current through one ohm of resistance. e) Current – The rate of flow of electrical current. Electrons in the outer shell of a copper atom move easily from one atom to the next. Free electrons randomly drift from one atom to another. When a difference in potential, or a voltage, is applied to a copper wire, the direction of movement of electrons can be controlled. As the difference of potential increases, more of Basic Electrical Theory Review f) the electrons moving randomly will take a more directional path through the wire. The movement or flow of these electrons is called current. The basic unit of measurement for current is the ampere, or amp (I). i) An amp is defined as the unit of measurement of the rate of electron current flow, or current, in an electrical conductor. ii) Electric current flow is classified as either Direct Current (DC) or Alternating Current (AC). (1) Direct current flows in the same direction continuously. (2) Alternating current regularly reverses direction. Resistance – Opposition to current flow. Resistance, measured in ohms, is represented by (R). i) An ohm is that amount of resistance that will limit the current in a conductor to one amp with one volt applied and is represented by (ο). g) Ground – An electrical ground is the reference point in an electrical circuit from which voltages are measured, a common return path for electric current, or a direct physical connection to Earth. Basic Electrical Theory Review h) Capacitor – A component consisting of one or more pairs of conductors separated by an insulator, used to store and electric charge. (Click here for video.) i) Capacitance is the ability of a component to store an electric charge and is measured in units of Farads. i) Inductor – A component that consists of a loop, or loops of wire, that stores energy in the form of a magnetic field. (Click here for video.) i) Inductance is the property of an electric conductor that causes a voltage to be generated by a change in the current flowing through the conductor. j) Reactance – The part of total resistance that appears in AC circuits only. Like resistance, reactance is measured in ohms and is represented by (X). There are two types of reactance in an AC circuit: inductive reactance (XL), and capacitive reactance (XC). i) Inductive Reactance (XL) is the opposition to the change in current in an AC circuit due to the effect of inductors. An inductor, which consists of a loop, or loops of wire, is a component that stores energy in the form of a magnetic field. Inductors will cause a component of the total current within an AC circuit to lag the voltage by 90°. When the voltage begins to change in the circuit, the current does not immediately change, due to the inductors ability to oppose the change in current. Inductors have no effect on a DC circuit. (1) The equation for inductive reactance is πL = 2πππΏ where: (a) π = pi (3.14159…) (b) f = system frequency (c) L = Inductance in Henries (typically millihenries) Basic Electrical Theory Review ii) Capacitive Reactance (XC) is the opposition of the change in voltage in an AC circuit due to the effect of capacitors. A capacitor, which consists of one or more pairs of conductors separated by an insulator, is a component that stores energy in the form of an electric field. Capacitors will cause a component of the total current within an AC circuit to lead the voltage by 90°. When the voltage is removed from the circuit and there is still a path for current flow, the capacitor will discharge through the components in that path. Capacitors act as an open in a DC circuit. (1) The equation for capacitive reactance is πc = 1 2πππΆ where: (a) π = pi (3.14159…) (b) f = system frequency (c) C = Capacitance in Farads (typically micro- or picofarads) iii) Capacitive and inductive loads are polar opposites, will have opposite electrical effects on the circuit, and can cancel each other in certain circuit designs. k) Impedance – The total opposition to current flow in an AC circuit due to the effects of resistive, inductive, and capacitive elements. Impedance is measured in ohms and is represented by (Z). l) Impedance Angle (or Phase Angle) – A measure of the phase shift between voltage and current in an AC circuit due to the effects of inductors or capacitors, or both. Impedance angle is represented by (∠ο±ο©. i) A purely resistive circuit has an impedance angle of 0°. Resistive components do not cause a phase shift between voltage and current and the current is said to be in phase with the system voltage. ii) A purely inductive circuit has an impedance angle of 90°. The inductive components will cause the current in the AC circuit to lag the voltage by 90°. iii) A purely capacitive circuit has an impedance angle of -90°. The capacitive components will cause the current in the AC circuit to lead the voltage by 90°. Basic Electrical Theory Review Series vs. Parallel Circuits a) A series circuit provides only one path for current to flow back to the source through the entire circuit. All elements in the circuit are arranged in a “chain”. i) Adding resistances in a series circuit. (1) Total resistance in a series circuit is equal to the sum total of all the resistances in the circuit. (2) π Total = π 1 + π 2 + π 3 … + π n ii) Adding impedances in an AC series circuit is the same as adding resistances in series. Series RLC circuit example: iii) πTotal = πR + πXL + πXC b) A parallel circuit provides more than one path for current to flow back to the source. Each parallel path is sometimes called a “branch” or “leg”. Total resistance in a parallel circuit is calculated in a much different way. i) Adding resistances in a parallel circuit. (1) 1 π T 1 1 1 1 = π +π +π + …+π 1 2 3 n ii) Adding impedances in an AC parallel circuit is the same as adding resistances in parallel. Parallel RLC circuit example: iii) 1 πTotal 1 1 1 =π +π +π XL XC Basic Electrical Theory Review Fundamental Laws of Electricity a) Ohm’s Law – States the relationships between voltage, current, and resistance: current is directly proportional to voltage and inversely proportional to resistance. Accordingly: i) π Current is equal to voltage divided by the resistance, or πΌ = π ii) Voltage is equal to the current multiplied by the resistance, or π = πΌπ π iii) Resistance is equal to voltage divided by current, or π = πΌ . b) Kirchhoff’s Voltage Law – States that the sum of all voltage drops and rises in a closed loop equals zero. c) Kirchhoff’s Current Law – States that the sum of all currents entering a node equals the sum of the currents leaving the node. Basic Electrical Theory Review Power in AC circuits a) The basic definition of power in electrical circuits is: the rate, per unit time, at which electrical energy is transferred by an electric circuit. i) The basic power equation: (1) π = (π)(πΌ) ii) From the basic power equation, we can derive two additional equations by looking at Ohm’s Law: π a. πΌ = π b. π = πΌπ c. π = π πΌ iii) So, if π = πΌπ , and we make this substitution in our basic power equation, then: π = (π)(πΌ) = (πΌπ )(πΌ), or π = (πΌ)2(π ). π iv) Similarly, if πΌ = π , and we make another substitution in our basic power equation, π then: π = (π)(πΌ) = (π) (π ), or π = (π)2 . (π ) b) True Power (P) – The rate at which work is performed or energy is transferred, measured in watts (W, KW, or MW), and is a measure of the amount of current that is in phase with the system voltage. True power is represented by (P). i) Basic equations: (1) π = (π)(πΌ)πππ π (2) π = (πΌ)2(π)πππ π (3) π = (π)2 πππ π (π) ii) Three phase equations: (1) π = 3(π)(πΌ)πππ π (2) π = 3(πΌ)2(π)πππ π (3) π = 3 (π)2 πππ π (π) c) Apparent Power (S) – The product of the RMS current and the RMS voltage measured in voltamps (VA, KVA, or MVA). Apparent power does not account for the difference in phase angle between the voltage and the current due to the reactive components of the circuit. Apparent power is represented by (S). i) Basic equations: (1) π = (π)(πΌ) (2) π = (πΌ)2(π) (3) π = (π)2 (π) ii) Three phase equations: (1) π = 3(π)(πΌ) (2) π = 3(πΌ)2(π) (3) π = 3 (π)2 (π) Basic Electrical Theory Review d) Reactive Power (Q) – The power in an AC circuit that performs no real work, measured in voltamps reactive (VAR, KVAR, or MVAR). It is a measure of the amount of current that is out of phase with the system voltage and determines whether the system is operates at a leading or lagging power factor. Reactive power is the energy that is stored in the magnetic fields of inductors and the electric fields of capacitors. Reactive power is represented by (Q). i) Basic equations: (1) π = (π)(πΌ)π πππ (2) π = (πΌ)2(π)π πππ (3) π = (π)2 π πππ (π) ii) Three phase equations: (1) π = 3(π)(πΌ)π πππ (2) π = 3(πΌ)2(π)π πππ (3) π = 3 (π)2 π πππ (π) e) Power Factor – The ratio of true power to apparent power, represented by (pf). The difference between the two is caused by the inductive and capacitive reactance in the circuit and represents power that does no useful work. Power factor is equal to the cosine of the phase angle between system voltage and the total current. i) Equation: ππ = πππ π, where ο± represents the phase angle ii) A leading power factor is a result of how capacitive components affect the system and cause the current to lead the system voltage. iii) A lagging power factor is a result of how inductive components affect the system and cause the current to lag the system voltage. f) Dissipation Factor – The ratio of true power to reactive power, represented by (df). Dissipation factor is equal to the tangent of the delta between 90° and the phase angle. i) Equation: ππ = π‘ππβ Basic Electrical Theory Review The Power Triangle a) The Power Triangle is the representation of a right-angle triangle showing the relationship between true power, reactive power, and apparent power. It can be used to analyze how adding or removing reactive loading from a system can change the system power factor. b) The legs of the power triangle represent the quantity of true power, reactive power, and apparent power that is present in the system. The relationship between true power and apparent power can also be seen. This is known as the phase angle and is represented on the triangle by ο±. This phase angle is what determines the system power factor. c) Example: d) It is important to note that the phase angle represented on the power triangle is actually a measure of the impedance angle. The impedance angle is merely the opposite of the current angle. i) Remember that values of voltage, current, and impedance in an AC circuit have both a magnitude and a direction. These values are represented by: (1) Voltage (VΡ²): V∠ (2) Current (IΡ²): I∠ (3) Impedance (ZΡ²): Z∠ ii) Using Ohm’s Law as it applies to AC circuits: π∠∅ (1) πΌ∠∅ = π∠∅ ο Ρ²I = Ρ²V − Ρ²Z ο Since Ρ²V is assumed to be 0°, then Ρ²I = −Ρ²Z. iii) With this, we can see that a positive phase angle on the power triangle represents a lagging power factor and, vice versa, a negative phase angle on the power triangle represents a leading power factor. Basic Electrical Theory Review Power Factor Correction a) Inductive and capacitive reactance can be added to the system to correct the system power factor. This is done by simply adding inductors or capacitors to the system. Facilities often add capacitors to their systems to correct for a low power factor. b) A low power factor can be detrimental for various reasons. Examples: i) A low power factor can mean increased utility bills. When there is more apparent power on a system than true power, the utility must supply the excess reactive current (current that does no real work) in addition to the working current (true power). This increases cost for the consumer. ii) Low power factor is a sign of inefficiency that can result in higher maintenance costs when equipment breaks. c) Power factor can be corrected relatively easily. i) Capacitor banks can be added to the system to add capacitive reactance to the system to cancel a portion of the inductive reactance. ii) Example: If system power factor is too low (i.e. there is a large amount of inductive reactance on the system), capacitive reactance can be added. This can be easily seen by analyzing the power triangle below. Let’s assume that the total reactive load on the system is due to inductive reactance, represented by the first triangle. The second triangle represents adding a load that is more capacitive. NOTE: Remember that capacitive and inductive loads are polar opposites that have opposite electrical effects on the circuit and will cancel each other in certain circuit designs. iii) When these two power triangles are added together, there is a smaller amount of reactive loading (KVAR) on the system (the added capacitive reactance “cancels out” some of the inductive reactance), which changes the amount of apparent power (KVA) that needs to be supplied. This, in turn, changes the phase angle and the power factor has been corrected to a new higher value. d) Synchronous motors, which can be operated at a leading power factor, can also be added to the system. By operating at a leading power factor, the motor has the effect of a large capacitor on the system. This is further discussed at the end of the module. Basic Electrical Theory Review Power Factor Testing a) One practical example of how we can use the method above is when performing power factor testing. So, what is power factor testing? i) An AC test that applies a voltage to an electrical insulating system and measures the leakage current. ii) Power factor testing is used to evaluate the integrity of an electrical insulating system. b) Every insulating system should be viewed as a capacitor. Remember that a capacitor is a component consisting of a pair of conductors separated by an insulator, or dielectric. When discussing power factor testing, we can consider one conductor of the capacitor as the current carrying conductor. The other conductor would be considered ground, which could be the frame of a circuit breaker or the tank of a transformer. The dielectric is the insulation. c) An ideal capacitor, or an ideal insulating system, would be a totally reactive circuit, meaning that there is no resistive component. In reality, there will be some small amount of resistive current flow through every insulating system due to moisture, impurities, etc. This current would be on a very small scale, but it would still be present. If there was no resistive component, the power factor would be 0.00% and we would have a perfect insulating system. If this were the case, the power triangle for this insulating system would be a vertical line. However, there is no such thing as a perfect insulator, so the power triangle for the system would be slightly different. d) Every insulating system will have a reactive and a resistive component and it is the amount of resistive (or loss) current that we are testing for. The testing equipment (e.g. the Doble M4000) cannot distinguish the difference between reactive and resistive currents, so how do we separate the two? i) Power factor test sets use the principal of “zero reactance” to measure power factor. This means that the reactive component of current (due to the capacitive effect of the insulation) is cancelled out by introducing a value of inductance into the system. The test unit basically cancels out the capacitive reactance of the insulating system. ii) There is a transformer inside of the unit that introduces the inductive reactance. It will automatically determine how much inductive reactance to insert into the system to make the total reactive current equal zero. The test set can calculate the capacitance of the test specimen by knowing how much inductance was added. iii) Once all the reactive power is eliminated, the only thing left is the resistive power (leakage current, or watts loss). This is calculated by simply multiplying the remaining resistive current by the test voltage. Basic Electrical Theory Review Power Factor Correction and the Synchronous Motor a) Basic requirements to produce motor action (i.e. to produce a force on a winding): i) Current carrying conductor ii) Magnetic field b) Synchronous motor construction and operation. (Click here for video.) i) Stator windings, along with amortisseur windings are placed around the rotor, or armature windings. ii) Stator windings are stationary and are fed with a rotating 3 phase AC input which creates a rotating magnetic field around the rotor. The speed at which this magnetic field rotates is called synchronous speed. iii) The amortisseur windings basically function as an AC induction motor within the synchronous motor. Voltage is induced into the amortisseur windings from the rotating magnetic flux produced by the stator windings. Current flows through the amortisseur windings and the rotor begins to spin. iv) The rotor, or armature winding, is supplied with a DC signal which produces a magnetic field around the rotor. When the rotor reaches a pre-determined speed, the DC excitation is applied to the rotor windings and the motor comes up to synchronous speed. c) Power Factor Correction i) To help correct a poor system power factor, a synchronous motor can be made to operate at a leading power factor. (1) Once the motor is spinning at synchronous speed, the field poles on the rotor are in line with the rotating magnetic poles of the stator. (2) At a motor unity power factor, all the magnetizing current of the rotor is supplied by the external DC source. (3) If the external DC source is strengthened, then the rotor field current will attempt to increase the system voltage by supplying magnetizing current to the stator windings to increase their magnetic flux. This causes the motor to operate at a leading power factor because it is supplying part of the AC magnetizing current and, essentially, providing VAR’S back to the system. (4) Consequently, the opposite happens if the rotor field current is weakened and the motor operates at a lagging power factor, utilizing VAR’s from the system.
