Benha University Faculty of Engineering Shoubra Electrical Power
Benha University Faculty of Engineering Shoubra Electrical Power Engineering Dept.
References: [1] J. B. Gupta, "Switchgear & Protection", S. K. KATARIA & SONS, Delhi, 2006. [2] M L Anand, "A Textbook of Electrical Power", VIKAS Publishing House PVT LTD, New Delhi, 1998. [3] Les Hewitson, Mark Brown and Ben Ramesh, "Practical Power Systems Protection ", Elsevier, 2004. [4] Anthony J. Pansini, "Guide to electrical power distribution systems", sixth edition, by The Fairmont Press, 2005. [5] Christophe Prévé, "Protection of electrical networks", ISTE Ltd, 2006. [6] M S Naidu and V Kamaraju, "High Voltage Engineering", Mc. Graw- Hill, Second Edition, 1996. [7] Kuffel E. and Zaengl W. , "High Voltage Engineering Fundamentals", Pergamon Press, Oxford, England, 1984. [8] V. K. Mehata and Rohit Mehata, "Principles of Power Systems", S. Chand & Company Ltd. , New Delhi-110055, 2004. [9] J. Duncan Glover, Mulukutla S. Sarma & Thomas J. Overbye, "Power System -Analysis and Design", Fourth edition, Thomson, 2008. [10] Ebtisam Saied, Reda Morsi, Electrical power engineering text book, Shoubra faculty of engineering, Benha University, LCMS
Contents Chapter 6: Fundamentals of Power Systems Chapter 7: D. C Power Transmission System Chapter 8: D. C Power Distribution Chapter 9: A. C Power Distribution Chapter 10: Interconnections of Power Systems
Chapter 1: Fundamentals of Power Systems The three basic elements of electrical engineering are resistor, inductor and capacitor, the resistor consumes ohmic or dissipative energy whereas the inductor and capacitor store in the positive half cycle and give away in the negative half cycle of supply the magnetic field and electric field energies respectively.
Continue The ohmic form of energy is dissipated into heat whenever a current flows in a resistive medium, if I is the current flowing for a period of t seconds through a resistance of R ohms, the heat dissipated will be watt sec.
Continue in case of an inductor the energy is stored in the form of magnetic field, for a coil of L henries and a current of I amperes flowing, the energy stored is given by the The Energy is stored between the metallic plates of the capacitor in the form of electric field and is given by where C is the capacitance and V is the voltage across the plates
Single-phase transmissions. We shall start with power transmission using circuits and assume in all our analysis that the source is a perfect sinusoidal with fundamental frequency component only. let us consider an inductive circuit and let the instantaneous voltage be (1. 1)
Continue Then the current will be Where Φ is the angle by which the current lags the voltage (fig. 1. 1) the instantaneous power is given by (1. 2)
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Continue Equation (1. 2) can be rewritten as (1. 3) We have decomposed the instantaneous power into two components
Continue (i) The component P marked i pulsates around the same average power VI cos Φ, but never goes negative as the factor can at the most become zero but it will never go negative. We define this average power as the real power p which physically means the useful power being transmitted.
Continue (ii) The component marked ii contains the term sin Φ , which is negative for capacitive circuit and is positive for inductive circuit, this component pulsates and has zero as its average value, this component is known as reactive power as it travels back and forth on the line without doing any useful work.
Continue (1. 3) both P and Q have the same dimensions of watts but to emphasis the fact that Q represents a nonactive power, it is measured in terms of voltamperes reactive i. e. VAR. The term Q requires more attention because of the interesting property of sin Φ, which is -ve for capacitive circuits and is +ve for inductive circuits, this means a capacitor is a generator of positive reactive var, a concept which is usually adopted by power system engineers, so it is better to consider a capacitor supplying a lagging current rather than taking a leading current (fig. 1. 3).
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Continue Consider a circuit in which an inductive load is shunted by a capacitor. If Q is the total reactive power requirement of the load and Q' is the re active power that the capacitor can generate, the net reactive power to be transmitted over the line will be (Q — Q') this is the basic concept of synchronous phase modifiers for controlling the voltage of the system, the phase modifier controls the flow of reactive power by suitable excitation and hence the voltage is controlled. The phase modifier is basically
Continue a synchronous machine working as a capacitor when overexcited and as an inductor when under excited. It is interesting to consider the case when a capacitor and an inductor of the same reactive power requirement are connected in parallel (fig. 1. 4).
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Continue The currents are equal in magnitude and, therefore, the power requirement is same. The line power will, therefore, be zero. physically this means that the energy travels back and forth between the capacitor and the inductor, in one half cycle at a particular moment the capacitor is fully charged and the coil has no energy stored. Half a voltage cycle later the coil stores maximum energy and the capacitor is fully discharged.
Continue The following example illustrates the relationship between the reactive power and the electric field energy stored by the capacitor. consider an RC circuit (fig. 1. 5).
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Continue Now this can related with the electric energy stored by the capacitor. The energy stored by the capacitor
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Continue From this it is clear that the rate of change of electric field energy is a harmonically varying quantity with a frequency double the supply frequency and has a peak value equal to Q. In an R-L circuit the magnetic field energy and reactive power in a coil are similarly related.
The 3 -phase transmission Assuming that the system is balanced which means that the three-phase voltages and currents are balanced, these quantities can be expressed mathematically as follows:
Continue The total power transmitted equals the sum of the individual powers in each phase.
Continue This shows that the total instantaneous 3 -phase power is constant and is equal to three times the real power phase i. e. p = 3 p, where P is the power phase. In case of single phase transmission we noted that the instantaneous power expression contained both the real and reactive power expression but here in case of 3 -phase we find that the Instantaneous power is constant; this does not mean that the reactive power is of no importance in a 3 -phase system.
Continue For a 3 -phase system the sum of three currents at any instant is zero , this does not mean that the current in each phase is zero. Similarly, even though the sum of reactive power instantaneously 3 -phase system is zero but in each phase it does exist and is equal to VI sin Φ and therefore, for 3 -Φ the reactive power is equal to where Q is the reactive power in each phase, it is to be noted here that the term , makes as little physical sense as would the concept of three phase currents nevertheless the reactive power in a 3 -phase system is expressed as
Continue complex power Consider a single phase network and let Where are the angles that v and I subtend with respect to some reference axis. We calculate the real and reactive power by finding the product of V with the conjugate of I i. e.
Continue Here the angle is the phase difference between the phasor V and I and is normally denoted by Φ
Continue The quantity S is called the complex power. The magnitude of is termed As the apparent power and its units are volt-amperes and the larger units are KVA or MVA. The practical significance of apparent power is as a rating unit of generators and transformers, as the apparent power rating is a direct indication of heating of machine which determines the rating of the machines. It is to be noted that Q is positive when is positive i. e. when V leads /
Continue i. e. the load is inductive and Q is -ve when V lags / i. e. the load is capacitive. This agrees with the normal convention adopted in power system i. e. taking Q due to an capacitive load as +ve and Q due to an inductive load as negative. Therefore, to obtain proper sign for reactive power it is necessary to find out V I* rather than V*I which would reverse the sign for Q as
Inductance of stranded conductors
Load characteristics In an electric power system it is difficult to predict the load variation accurately, the load devices may vary from a few watt night lamps to multi-megawatt induction motors, the following category of loads are present in a system: (i) motor devices 70 % (ii) heating and lighting equipment 25% (iii) electronic devices 5%
Continue The heating load maintains constant resistance with voltage change and hence the power varies with (voltage)2 whereas lighting load is independent of frequency and power consumed varies as rather than V 2 For an impedance load i. e. lumped load
Continue From this it is clear that both P and Q increase as the square of voltage magnitude. Also with increasing frequency the active power p decreases whereas Q increases. The above equations are of the form
Continue Composite loads which form a major part of the system load arc also function of voltage and frequency and can in general be written as in equation (1. 21). For this type of load, however, no direct relationship is available as for impedance loads. For a particular composite load an empirical relation between the load, and voltage and frequency can be obtained. Normally we are concerned with incremental changes in P and Q as a function of
Continue incremental changes in |V| and f from equation 1. 21 The four partial derivatives can be obtained empirically, however, it is to be remembered
Continue that where an impedance load P decreases with increasing frequency, a composite load will increase, this is because a composite load mostly consists of induction motors which always will experience increased load, as frequency or speed increases. The need for ensuring a high degree of service reliability in the operation of modem electric systems can hardly be over-emphasized.
Continue The supply should not only be reliable but should be of good quality i. e. The voltage and frequency should vary within certain limits, otherwise operation of the system at subnormal frequency and lower voltage will result in serious problems especially in case of fractional horse-power motors. Incase of refrigerators reduced frequency results into reduced efficiency and high consumption as the motor draws larger current at reduced power factor.
Continue The system operation at subnormal frequency and voltage leads to the loss of revenue to the suppliers due to accompanying reduction in load demand. The most serious effect of subnormal frequency and voltage is on the operation of thermal power station auxiliaries. The output of the auxiliaries goes down as a result of which the generation is also decreased.
Continue This may result in complete shut-down of the plant if corrective measures like load shedding is not resorted to Load shedding is done with the help of under frequency relays. Which automatically disconnect blocks of loads or section the transmission system depending upon the system.
With Our Best Wishes
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