psoc unit 1 notes

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SEMESTER VIIEE1401 – POWER SYSTEM OPERATION AND CONTROL

UNIT I GENERAL BACKGROUND AND SPEED GOVERNORS 9General characteristics, evolution and structure of modern power systems – Transfer of power between active sources – Concept of complex power flow – Operating problems in power systems – Fundamentals of speed governing – Modeling of Generator, turbine, governor and load – Generator response to load change – Load response to frequency deviation – Governors with speed-droop characteristics: Ideal and actual – Numerical problems – Control of generating unit power output – Composite regulating characteristics of Power systems.

1.1 GENERAL CHARACTERISTICS, EVOLUTION AND STRUCTURE OF MODERN POWER SYSTEMS

Over the past century, the electric power industry continues to shape and contribute to the welfare, progress, and technological advances of the human race. The growth of electric energy consumption in the world has been nothing but phenomenal. In the United States, for example, electric energy sales have grown to well over 400 times in the period between the turn of the century and the early 1970s. This growth rate was 50 times as much as the growth rate in all other energy forms used during the same period. It is estimated that the installed kW capacity per capita in the U.S. is close to 3 kW.

Edison Electric Illuminating Company of New York inaugurated the Pearl Street Station in 1881. The station had a capacity of four 250-hp boilers supplying steam to six engine-dynamo sets. Edison’s system used a 110-V dc underground distribution network with copper conductors insulated with jutewrapping. In 1882, the first water wheel-driven generator was installed in Appleton, Wisconsin. The low voltage of the circuits limited the service area of a central station, and consequently, central stations proliferated throughout metropolitan areas.

The invention of the transformer, then known as the “inductorium,” made ac systems possible. The first practical ac distribution system in the U.S. was installed by W. Stanley at Great Barrington, Massachusetts, in 1866 for Westinghouse, which acquired the American rights to the transformer from its British inventors Gaillard and Gibbs. Early ac distribution utilized 1000-V overhead lines. The Nikola Tesla invention of the induction motor in 1888 helped replace dc motors and hastened the advance in use of ac systems.

The first American single-phase ac system was installed in Oregon in 1889. Southern California Edison Company established the first three phase 2.3 kV systems in 1893. By 1895, Philadelphia had about twenty electric companies with distribution systems operating at 100-V and 500-V two-wire dc and 220-V three-wire dc, single-phase, two-phase, and three-phase ac, with frequencies of 60, 66, 125, and 133 cycles per second, and feeders at 1000-1200 V and 2000-2400 V.

The subsequent consolidation of electric companies enabled the realization of economies of scale in generating facilities, the introduction of equipment standardization, and the utilization of the load diversity between areas. Generating unit sizes of up to 1300 MW are in service, an era that was started by the 1973 Cumberland Station of the Tennessee Valley Authority.

Underground distribution at voltages up to 5 kV was made possible by the development of rubber-base insulated cables and paper-insulated, lead covered cables in the early 1900s. Since then, higher distribution voltages have been necessitated by load growth that would otherwise overload low-voltage circuits and by the requirement to transmit large blocks of power over great distances. Common distribution voltages presently are in 5-, 15-, 25-, 35-, and 69-kV voltage classes.

The growth in size of power plants and in the higher voltage equipment was accompanied by interconnections of the generating facilities. These interconnections decreased the probability of service interruptions, made the utilization of the most economical units possible, and decreased the total reserve capacity required to meet equipment-forced outages. This was accompanied by use of sophisticated analysis tools such as the network analyzer. Central control of the interconnected systems was introduced for reasons of economy and safety. The advent of the load dispatcher heralded the dawn of power systems engineering, an exciting area that strives to provide the best system to meet the load requirements reliably, safely, and economically, utilizing state-of-the-art computer facilities.

Extra higher voltage (EHV) has become dominant in electric power transmission over great distances. By 1896, an 11-kv three-phase line was transmitting 10 MW from Niagara Falls to Buffalo over a distance of 20 miles. Today, transmission voltages of 230 kV, 287 kV, 345 kV, 500 kV, 735 kV, and 765 kV are commonplace, with the first 1100-kV line already energized in the early 1990s. The trend is motivated by economy of scale due to the higher transmission capacities possible, more efficient use of right-of-way, lower transmission losses, and reduced environmental impact.

In 1954, the Swedish State Power Board energized the 60-mile, 100-kV dc submarine cable utilizing U. Lamm’s Mercury Arc valves at the sending and receiving ends of the world’s first high-voltage direct current (HVDC) link connecting the Baltic island of Gotland and the Swedish mainland. Currently, numerous installations with voltages up to 800-kV dc are in operation around the world.

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In North America, the majority of electricity generation is produced by investor-owned utilities with a certain portion done by federally and provincially (in Canada) owned entities. In the United States, the Federal Energy Regulatory Commission (FERC) regulates the wholesale pricing of electricity and terms and conditions of service.

Electrical Technology was founded on the remarkable discovery by Faraday that a changing magnetic flux creates an electric field. Out of that discovery, grew the largest and most complex engineering achievement of man: the electric power system. Indeed, life without electricity is now unimaginable. Electric power systems form the basic infrastructure of a country. Even as we read this, electrical energy is being produced at rates in excess of hundreds of giga-watts (1 GW = 1,000,000,000 W). Giant rotors spinning at speeds up to 3000 rotations per minute bring us the energy stored in the potential energy of water, or in fossil fuels. Yet we notice electricity only when the lights go out! While the basic features of the electrical power system have remained practically unchanged in the past century, there are some significant milestones in the evolution of electrical power systems:

First complete DC power system built by Edison (1882): Incandescent lamps supplied by steam driven DC generators (electrical cable system at 110V). 59 customers spread over an approximate area with 1.5 km radius. Development of transformers led to supersession of DC systems by AC systems.

Nikola Tesla - polyphase induction motors: led to development of AC 3 phase systems.

Interconnection of systems led to standardization of frequency, 60 Hz in North America and 50 Hz in most other countries. Use of higher and higher voltage levels (up to 1000 kV line-line rms AC). Standardization of voltage levels.

Development of Mercury Arc Valves, and subsequently thyristors led to high voltage dc transmission (HVDC): DC transmission suited for very long distance bulk transmission and underwater cable links. First commercial DC link in 1954.

Several new developments: Gas turbines, static excitation systems, fast acting circuit breakers, microprocessor based relaying, use of communication technologies etc.

Need for better utilisation and operation of AC transmission systems by use of high power electronic converters suggested. Several such converters are now in operation.

1.2 Structure of modern power systems

Electric power systems vary in size and structurel components. However, they all have the same basic characteristics: Air comprised of three-phase ac systems operating essentially at constent voltage. Generation and gtransmission facilities use three-phase residential and industrial and commercial loads are distributed equally among the phases so as to effectively from a blanced three-phase system.

Use synchronous machines for generation of electricty. Prime movers convert the primary of energy (fossil, nuclear, and hydrolic) to mechanical energy that is, in turn, converted to electrical energy by synchronous generators.

Transmit power over significant distances to consume spread over a wide area. This requires a transmission system comprising subsystems operating at different voltage levels.

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1.3 Power system control

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The Indian Power Grid is not quite as big as North American power systems, but still has a large generating capacity of about 200 GW (200,000 MW). It is actually made up of three synchronised grids:

1. NORTHERN REGIONAL GRID

2. SOUTHERN REGIONAL GRID

3. WESTERN REGIONAL GRID

4. EASTERN REGIONAL GRID 5. NORTH-EASTERN REGIONAL GRID

A synchronised grid implies that the generators in that grid are connected to one another by at least one AC transmission path. This also means that the synchronous generators in that grid are all operating at the same electrical frequency (what happens if they do not ? ).

For a well designed and operated system, inter-connected synchronous generators are seen to "stick together" in synchronism (by virtue of the physical equations which govern their motion). However they may lose synchronism if subjected to large disturbances. A generator when connected to a power system has to be connected by a special procedure known as 'synchronisation'. You will learn some of these things in forthcoming lectures.

A load can be connected in a synchronous grid by simply connecting it in shunt (after suitable voltage transformation using transformation and ensuring that the system is capable of servicing that extra load).

Did you know? In the WR-ER-NER grid, a synchronous machine in Panandhro Thermal Power Station (Kutch, Gujarat) operates "in synchronism" with Ranganadi, a hydro-generator in Arunachal Pradesh, a distance of more than 2000 km!

There may be a very small number of induction generators in a synchronous grid. Induction generators do not run at synchronous speed and are sometimes used in conjunction with wind turbines. However, since induction generators always absorb reactive power, they are limited to small applications wherein reactive power is supplied externally by capacitors and synchronous generators.

The three synchronous grids in India have the same nominal frequency (50Hz) but may not operate exactly at the same frequency. They are operated independently. However, the synchronous grids are connected by DC links which allow for a limited and controlled power exchange. It is planned to make a national grid consisting of large capacity links between all grids in the future ( why is there such a high degree of interconnection?).

1.3 TRANSFER OF POWER BETWEEN ACTIVE SOURCES

Two sources connected by an inductive reactance as shown in Figure 1.1 Such a system is representative of two sections of a power system interconnected by a transmission system, with power transfer from one section to the other.

Figure.1.1 a) Power transfer between two sources. b) Phasor diagram

Consider a purely inductive reactance interconnecting the two sources. This is because impedances representing

transmission lines, transformer, and generators are predominantly inductive. When the full network is represented by an appropriate model for each of its elements and then reduced to a two-bus system, the resulting impedance will be essentially an

=load angle=power factor

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inductive reactance. The shunt capacitances of transmission lines do not explicitly appear in the model shown in fig1.1; their effects are implicitly represented by the net reactive power transmitted. Analysis of the transmission of active and reactive power through an inductive reactance thus gives useful insight into the characteristics of ac transmission systems.

Referring to figure 1.1 the complex power at the receiving end is

Hence

(1.1) (1.2)

(1.3) (1.4)

Equation 1.1 to 1.4 describes the way in which active and reactive power is transferred between active parts of a network.

Let us examine the dependence of active and reactive power transfer on the source voltages by considering separately the effects of differences in voltage magnitudes and angles.

Case study: a) Condition with load angle =0. Equation 1.1 to 1.4 become Pr = Ps = 0,

(1.5) and (1.6)The active transfer is now zero. With Es>Er, Qs and Qr are positive, that is, reactive power is transferred from the sending end to the receiving end. The corresponding phasor diagram is shown in figure 1.2 a. with Es<Er, Qs and Qr are negative, indicating that reactive power flows from the receiving end to the sending end. The phasor diagram is shown in figure 1.2 b.Figure 1.2 Phasor diagram with load angle =0

An alternative way of interpreting the above results is as follows: Transmission of lagging current through an inductive reactance causes a drop in receiving end voltage.Transmission of leading current through an inductive reactance causes a rise in receiving end voltage . In each case

(1.7) therefore, the reactive power consumed by X is XI2 .Case study: b) Condition with Es=Er, but with load angle ≠0. From Equations 1.1 to 1.4 become

(1.8), (1.9)

Figure 1.3 Phasor diagram with Es=ErFigure 1.3.

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Figure 1.4 Phasor diagram with I In phase with Er

Case study: c) Finally Consider a general case applicable to any values of , Es, and Er. The current I is

(1.10) from equations 1.1 to 1.4 we have

Figure 1.4.

(1.11)

(1.12)

(1.13)

(1.11)

(1.12) (1.13)

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1.2 CONCEPT OF COMPLEX POWER FLOW

Here we will develop the concept of Complex Power and Power Triangle. These two are very important concepts used frequently by power engineers.

The following points are clear. The instantaneous power p is composed of real power and reactive power. The time average value of instantaneous power is the real power (true power) is |V | | I | cos φ (1.14) The instantaneous reactive power oscillates about the horizontal axis, so its average value is zero The maximum value of the reactive power is |V | | I | sin φ (1.15) It should be remembered that real power is the average value and the reactive power is maximum value.

Complex PowerIn power system analysis the concept of Complex Power is frequently used to calculate the real and reactive power. This is a very simple and important representation of real and reactive power when voltage and current phasors are known. Complex Power is defined as the product of Voltage phasor and conjugate of current phasor. See Fig-A

Let voltage across a load is represented by phasor V and current through the load is I.If S is the complex power then, S = V . I* (1.15)V is the phasor representation of voltage and I* is the conjugate of current phasor. So if V is the reference phasor then V can be written as |V| ∠0. (Usually one phasor is taken reference which makes zero degrees with real axis. It eliminates the necessity of introducing a non zero phase angle for voltage)

Let current lags voltage by an angle φ, so I = | I | ∠-φ (current phasor makes -φ degrees with real axis)

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I*= | I | ∠φ (1.16)So, S = |V| | I | ∠(0+φ) = |V| | I | ∠φ (1.17) (For multiplication of phasors we have considered polar form to facilitate calculation) Writing the above formula for S in rectangular form we get S = |V| | I | cos φ + j |V| | I | sin φ (1.18) The real part of complex power S is |V| | I | cos φ which is the real power or average power and the imaginary part |V| | I | sin φ is the reactive power. So, S = P + j Q (1.19) Where P = |V| | I | cos φ (1.20) and Q = |V| | I | sin φ (1.21)

It should be noted that S is considered here as a complex number. The real part P is average power which is the average value, where as imaginary part is reactive power which is a maximum value. So I do not want to discuss further and call S as phasor. If you like more trouble I also advise you to read my article about phasor or some other articles on phasor and complex numbers.

Returning to our main point, from the above formula it is sure that P is always more than zero. Q is positive when φ is positive or current lags voltage by φ degrees. This is the case of inductive load. We previously said that inductance and capacitance do not consume power. The power system engineers often say about reactive power consumption and generation. It is said that inductive loads consume reactive power and capacitors produce reactive power. This incorrect terminology creates confusion.

The fact is that most of the loads are inductive and they unnecessarily draw more current from source. Although in each cycle both inductance and capacitance draw power from the source and return same amount of power to the source but the behavior of inductance and capacitance are opposing to each other. When capacitors are connected in parallel to inductive load the power requirement of inductive load is supplied by capacitor in half cycle and in next half cycle the reverse happens. Depending upon the values of capacitor this power requirement of inductance in the load may be fully or partially satisfied. If partially satisfied the rest will be drawn from the distant source. By properly selecting the capacitance the maximum value of reactive power (Q) drawn from the distant source (or returned to the distant source) is reduced. This reduction in reactive power results in reduction of line current so the reduction of losses in transmission line and improvement in voltage at load end.

Power TriangleReturning to the complex power formula, P, Q and S are represented in a power triangle as shown in figure below.

S is the hypotenuse of the triangle, known as Apparent Power. The value of apparent power is |V|| I |or |S| = |V|| I | It is measured in Volt Amp or VA.P is measured in watt and Q is measured in Volt Amp-Reactive or VAR. In power systems instead of these smaller units larger units like Megawatt, MVAR and MVA is used.The ratio of real power and apparent power is the power factor of the load.Power factor = Cos φ = |P| / |S| = |P| / √(P 2+Q 2) (1.22)The reactive power Q and apparent power S are also important in power system analysis. As just shown above the control of reactive power is important to maintain the voltage within the allowed limits. Apparent power is important for rating the electrical equipment or machines.

Total Power of Parallel CircuitsIn real world the loads are usually connected in parallel. Here we will show the total power consumed by parallel branches. See Figure-C. It has two branches.

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First we have to draw the individual power triangles for each branch. Next the power triangles are arranged back to back keeping real power in positive x direction as shown. The total power consumed is obtained by connecting starting point O to the tip of last triangle. This is actually the result of addition of complex numbers.If S1 = P1 +j Q1 S2 = P2 +j Q2 Then, S = S1+ S2 or S = (P1+ P2 ) + j (Q1+ Q2 )

P = P1+ P2 Q = Q1+ Q2

In the above diagram S1, P1 , Q1 and φ 1 correspond to branch1 and S2 P2 , Q2 and φ 2 correspond to branch 2. S, P, Q and φ correspond to total power consumption as seen by the generator

1.3 OPERATING PROBLEMS IN POWER SYSTEMS

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Some of other operating problems Transmission of lagging current through an inductive reactance causes a drop in receiving end voltage. Transmission of leading current through an inductive reactance causes a rise in receiving end voltage. Active power transfer depends mainly on the angle by which the sending and voltage leads the receiving end voltage. Reactive power transfer depends mainly on voltage magnitudes. It is transmitted from the side with higher voltage

magnitude to the side with lower voltage magnitude. Reactive power cannot be transmitted over long distances science it would require a large voltage gradient to do so. An increase in reactive power transfer causes an increse in active as well as reactive power losses.

1.4 FUNDAMENTALS OF SPEED GOVERNING Power system operation considered so far was under condition of study state. However, both active and reactive power

demands are never steady and they continually change with the rising or falling trend. Steam input to turbo generators( or water input to hydro-generator ) must, therefore, be continuously regulated to match the active power demand, failing which the machine speed will vary with consequent change in frequency which may be highly undesirable*( maximum permissible change in power frequency is ± 0.5 Hz). Also the excitation of generators must be continuously regulated to match the reactive power demand with reactive generation, otherwise the voltages at various system buses may go beyond the prescribed limits. In modern large interconnected systems, manual regulation is not feasible and therefore automatic generation and voltage regulation equipment is installed on each generator. Small changes active power is dependent on internal machine angle and is independent of bus voltage: while bus voltage is dependent on machine excitation (therefore on reactive generation Q) and is independent of machine angle , Change in is caused by momentary change in generator speed. Therfore, load frequency and excitation voltage controls are non-interactive for small changes and can be modelled and analysed independently. Furthermore, excitation voltage control is fast acting in which the major time constant encountered is that of the generator field; while the power frequency control is slow acting with major time constatnt contributed by the turbine and generatr moment of inertia – this time constant is much larger than that of the generator field. Thus, the transients in excitation voltage control vanish much faster and do not affect the dynamics of power frequency control.Figure:1.9 Speed Governing System

The Speed Governing System consists of the following parts:-1. Speed Governor: This is a fly-ball type of speed governor and constitutes the heart of the system as it senses the change in speed or frequency. With the increase in speed the fly ball move outwards and the point B on linkage mechanism moves downwards and vice versa.2. Linkage Mechanism: ABC and CDE are the rigid links pivoted at B and D respectively. The mechanism provides a movement to the control valve in the proportion to change in speed. Link4 (l4) provides a feed back from the steam valve movement.3. Hydraulic Amplifier: This consists of the main piston and pilot valve. Low power level pilot valve movement is converted into high power level piston valve movement which is necessary to open or close the steam valve against high pressure steam.4. Speed Changer: The speed changer provides a steady state power output setting for the turbine. The downward movement of the speed changer opens the upper pilot valve so that more steam is admitted to the turbine under steady condition. The reverse happens when the speed changer moves upward.

A

BC D

El1 l3l2 l4

Speed changer

Lower

Raise

Speed governor

High

pressure oil

Pilot valve

XDirection of positive movement

steam

To turbine

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Consider the steady state condition by assuming that linkage mechanism is stationary, pilot valve closed, steam valve opened by definite magnitude, the turbine output balances the generator output and the turbine/generator is running at a normal speed or at a normal frequency f° ,the generator output PGO and let the steam valve setting corresponding to these conditions be XE.

Let the point A of the speed changer lower down by an amount ∆XA as a result the commanded increase in power ∆PC then ∆XA = K1∆PC. The movement of linkage point A causes small position changes ∆XC and ∆X D of the linkage points C and D. With the movement of D upwards by ∆X D high pressure oil flows into the hydraulic amplifier from the top of the main piston thereby the steam valve will move downwards a small distance ∆XE which results in increased turbine torque and hence power increase, ∆PG. This further results in increase in speed and hence the frequency of generation. This increase in frequency ∆f causes the link point B to move downward a small distance ∆XB proportional to ∆f. Assume the movements are positive if the points move downwards.

1.5 Modeling of Power System Components

Modeling of different power system components i.e. Speed governing system, Turbine, Generator-load are described and the various block diagrams representing the components are presented in this section.

1.5.1 Modeling of Speed Governing System

Consider the steady state condition by assuming that linkage mechanism is stationary, pilot valve closed, steam valve opened by definite magnitude, the turbine output balances the generator output and the turbine/generator is running at a normal speed or at a normal frequency f° ,the generator output PGO and let the steam valve setting corresponding to these conditions be XE.

Let in fig 1.09 the point A of the speed changer lower down by an amount ∆X A as a result the commanded increase in power ∆PC then ∆XA = K1∆PC. The movement of linkage point A causes small position changes ∆XC and ∆X D of the linkage points C and D. With the movement of D upwards by ∆X D high pressure oil flows into the hydraulic amplifier from the top of the main piston thereby the steam valve will move downwards a small distance ∆XE which results in increased turbine torque and hence power increase, ∆PG. This further results in increase in speed and hence the frequency of generation. This increase in frequency ∆f causes the link point B to move downward a small distance ∆XB proportional to ∆f. Assume the movements are positive if the points move downwards.

Two factors contribute to the movement of C:i) Increase in frequency causes B to move by ∆XB when the frequency changes by ∆f as then the fly-ball moves

outward and B is lowered by ∆XB . Therefore, this contribution is positive and is given by K1∆f.

ii) The lowering of the speed changer by an amount ∆XA lifts the point C upwards by an amount proportional to ∆XA, i.e. K2∆PC. ∆XC = K1∆f - K2∆PC …………………..1.23 Where K1 and K2 are the positive constants depends upon the length of the linkage arms AB and BC and upon the proportional constants of the speed changer and the speed governor.

The movement of D is contributed by the movement of C and E. Since C and E move downwards when D moves upwards, therefore, ∆X D= K3∆XC + K4∆XE ……………………1.24

Where K3 and K4 are positive constants depend upon the length of the linkage CD and DELet the oil flow into the hydraulic cylinder is proportional to position ∆X D

of the pilot valve, the value of ∆XE is given by

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∆XE=K5 -(∆X D )dt ……………………1.25

Where the constant K5 depends upon the fluid pressure and the geometries of the orifice and the cylinder.Taking Laplace transforms to equations 1.23, 1.24 & 1.25 ∆XC (s)= K1∆F(s) - K2∆PC(s)

∆X D (s)= K3∆XC (s)+ K4∆XE (s) ∆XE (s)= -K5∆X D (s) /s = -K5 (K3.( K1∆F(s) - K2∆PC (s))+ K4∆XE (s))

sEliminating the variables ∆XC and ∆X D ,

∆XE (s) = K2K3 ∆PC(s) - - K3 K1∆F(s) K4+s/K5

∆XE(s)= K G [∆PC (s) -∆F(s)/R] ……………….1.26 1+sTG

Where R = K2/K1 → speed regulation of governor. K G = K2K3/K4 → gain of speed governor. TG = 1/K4K5 → time constant of speed governor.The above equation 1.24 can be represented as a block diagram shown in Fig1.11

Fig. 1.10 Block diagram of speed governing system for steam turbine

1.5.2 Modeling of TurbineThe turbine power increment ∆P T depends entirely upon the valve power increment ∆Pv and the response

characteristics of the turbine. A non-reheat turbine with a single gain factor K T and a single time constant T T is considered and in the crudest model representation of the turbine the transfer function is given as

G T (s)= ∆P T (s) = K T ….……………..1.25 ∆XE (s) 1+sT T

The above transfer function is represented in the form of Block diagram along with the governor as shown in fig 1.12

Fig.1.11 Block diagram of power control mechanism of turbine

1.5.3 Modeling of Generator-Load The model gives relation between the change in frequency as a result of change in generation when the load changes by a small amount. Let ∆PD be the change in load demand, as a result the generation also swings by an amount ∆P G. The net power surplus at the busbar is ∆PG-∆PD and this power will be absorbed by the system in two waysa) Rate of increase of stored kinetic energy in generator rotor Let Wo be the Kinetic Energy before change in load occurs when the frequency is f o.

Let ∆f be the change in frequency.

KG

1+sTG

+-

∆PC∆XE(s)

∆F(s)

1/R

KG 1+sTG

+-

1/R

∆PC∆XE(s)

∆F(s)

KT 1+sTT

∆PT(s)

2

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Let W be the Kinetic Energy when the frequency is ∆f+ f o.

As K.E. is proportional to square of the speed of the generator W= W° f° +∆f f° → W=W° (1+2∆f/f°) (neglecting the higher terms)…………1.26

By Differentiating equation 1.26, dW = 2W° . d (∆f) ………………1.27 dt f° dt

b) The load on the motors increases with increase in speed. The load on the system being mostly motor load the rate of change of load w.r.t. frequency can be regarded as nearly constant for small changes in frequency, i.e. D=∂PD where D, Load Frequency Constant, can be obtained empirically ∂f

Therefore, the net power surplus at the busbar is given by ∆PG-∆PD = 2W° . d (∆f) +D ∆f ………………1.28 f° dt

Let H be the inertia constant of the generator in MW-sec/MVA Let P be the rating in MVA, then W° =H*P.Substituting W° in equation 1.28,

∆PG-∆PD =2HP. d (∆f) +D ∆f ……………….1.29

f° dt Dividing equation 1.29 throughout by P,

∆PG (p.u.)-∆PD (p.u.) = 2H . s∆F(s) +D(s)∆F(s) f° = ∆F(s){D(s)+2Hs/f°} i.e. ∆F(s) = ∆PG (s)-∆PD (s) D(s)+2Hs/f°

Or ∆F(s) = [∆PG (s)-∆PD (s) ] KP ……………..1.30 1+sTP

Where Tp=2H/Df° →power system time constant Kp=1/D →power system gain

The transfer function in equation 1.30 is represented in the form of a block diagram as shown in fig1.12

Fig1.12 Block diagram of Generator- Load model

+-

∆PG

∆F(s)

∆PD

KP 1+sTP

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1.5 GENERATOR RESPONSE TO LOAD CHANGE

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1.6 LOAD RESPONSE TO FREQUENCY DEVIATION

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1.7 GOVERNORS WITH SPEED-DROOP CHARACTERISTICS: IDEAL AND ACTUAL

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1.8 CONTROL OF GENERATING UNIT POWER OUTPUT

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1.9 COMPOSITE REGULATING CHARACTERISTICS OF POWER SYSTEMS

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Possible questions:

1. Derive the mathematical modeling of generator and turbine.2. Drive the mathematical modeling of Governor and generator load.3. Two synchronous generators are operating in parallel. Their capacities are 300MW and 400MW. The droop characteristics of

their governor are 4% and 5% from no load to full load. Assuming that the generators are operating at 50Hz at no load, how would be a load of 600MW shared between them. What will be system frequency at this load? Assume free governor actions.

4. Explain ideal and actual speed droop characteristics of the governor.5. Describe the Generator response to load change.6. Explain the Load response to frequency deviation7. Explain the following i) Control of generating unit power output ii) Composite regulating characteristics of Power systems.8. Explain the need for voltage and frequency regulation in power system. (16) 9. What are the components of speed governor system of an alternator? Derive a transfer function and sketch a block diagram.

(16) 10. Draw and explain the basic P-f and Q-V control loops. (16) 11. Briefly explain about the plant level and the system level controls. (16) 12. Briefly discuss the classification of loads and list out the important characteristics of various types of loads. (16) 13. i) Briefly explain the overview of system operation. (8)

ii) Explain about the Static characteristics of various loads (8)

psoc unit 1 notes

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