ࡱ>  Gy bjbj /{{Ji]`) j) z*z*z****8*d*,*e, 9"99:O6TOhO $ z*AKN"AA v)v)9:A v)9z*:Af0*J:P+W(д50epAAPAz*DtOehntT € tOtOtO tOtOtOeAAAAAtOtOtOtOtOtOtOtOtO &(: Module G1 Electric Power Generation and Machine Controls Primary Author: James D. McCalley, Iowa State University Email Address:  HYPERLINK mailto:Vittal@vulcan.ee.iastate.edu jdm@iastate.edu Co-author: None Last Update: 7/30/99 Prerequisite Competencies: 1. Steady-state analysis of circuits using phasors, typically covered in an introductory circuit course 2. Three-phase circuit analysis and three-phase power relationships, found in module B3 3. Conversion between three-phase analysis and per-unit analysis, found in module B2 Module Objectives: 1. Identify the physical structure and essential components of a synchronous generator. 2. Perform analysis of a three-phase synchronous generator using the Equivalent Circuit Model. 3. Describe reactive operation of a synchronous generator in terms of reactive power generation, excitation voltage magnitude, power angle, leading generator operation versus lagging generator operation, capacitive load versus inductive lad, and current angle. 4. Express terminal voltage, excitation voltage, real and reactive power, and armature current using phasor diagrams. G1.0 Introduction Generation of electrical power is a process whereby energy is transformed into an electrical form. There are several different transformation processes, among which are chemical, photo-voltaic, and electromechanical. Electromechanical energy conversion is used in converting energy from coal, petroleum, natural gas, uranium, water flow, and wind into electrical energy. Of these, all except the wind energy conversion process take advantage of the synchronous AC generator coupled to a steam, gas, or hydro turbine such that the turbine converts steam, gas, or water flow into rotational energy, and the synchronous generator then converts the rotational energy of the turbine into electrical energy. It is the turbine-generator conversion process that is by far most economical and consequently most common in the industry today. In this chapter, we will study this conversion process with particular emphasis on the synchronous machine and the controls that are used to govern its behavior.  G1.1 Generator Operation A turbine-generator is illustrated in its basic form in Figure G1.1.  Figure G1.1 Block Diagram for Turbine-Generator System The governor and excitation systems are known as feedback control systems because it is the feedback loops which provide for good control of certain parameters. The governor and excitation systems are typical feedback controllers in that the quantities to be controlled (speed and voltage, respectively) are also providing the feedback signal. We will study these controllers more closely. However, we must first take a closer look at the operation of the generator itself. The generator is classified as a synchronous machine because it is only at synchronous speed that it can develop electromagnetic torque. If the nominal system frequency is  EMBED Equation.2 (60 Hz in North America), synchronous speed is computed as  EMBED Equation.2  (G1.1) where  EMBED Equation.2 is the frequency in rad/sec and  EMBED Equation.2 is the number of poles on the rotor of the machine. The machine speed in RPM can be computed as  EMBED Equation.2 . The synchronous generator has two iron structures. The rotor is the revolving part of the machine, and is located inside the stator, which is the stationary part of the machine. Hydroelectric generators have their rotors built with saliency; the rotor poles protrude from the central axis. Because hydro-turbines are relatively slow (600 to 1800 RPM hydro-turbine generators are typical ), the number of poles must be high in order to produce 60 Hz voltages (see eqn. G1.1). Salient pole construction is simpler and more economical when a large number of poles are required. Steam plants, on the other hand, have very high speeds (1800 and 3600 RPM steam-turbine-generators are typical), and saliency would create significant mechanical stress at these speeds. Therefore, smooth or round rotor construction is employed for these generators. The two types of rotor construction are illustrated in Figure G1.2.  Figure G1.2 Salient Pole (left) and Smooth (right) Rotor Construction A magnetic field is provided by the DC-current carrying field winding, which induces the desired AC voltage in the armature winding. For synchronous generators, field winding voltages are typically much lower in magnitude than armature winding voltages; in addition, armature voltages must be available external to the machine. It is therefore simpler to locate the armature winding on the stator where there is no rotation. The field winding is always located on the rotor where it is connected to an external DC source via slip rings and brushes or to a revolving DC source via a special brushless configuration. The armature consists of three windings, all of which are wound on the stator, physically displaced from each other by 120 degrees. It is through these windings that the electrical energy is produced and distributed. A typical layout for a 2 pole, smooth rotor machine would appear as in Figure G1.3.  EMBED Word.Picture.8  Figure G1.3 Winding Layout for Two-Pole Smooth Rotor Synchronous Machine A complete theoretical analysis of synchronous machine operation is beyond the scope of this course, but there are many good texts on the subject; a representative sample of these is [2,3,4]. It will suffice here to discuss the basics of steady-state, balanced operation only. G1.2.1 The Revolving Magnetic Field The DC current in the revolving field windings on the rotor produces a revolving magnetic field. We denote the flux associated with this field that links the armature windings as  EMBED Equation.2  (the subscript f indicates field windings). By Faradays Law of Induction, this rotating magnetic field will induce voltages in the three armature windings. Because these three windings are physically displaced by 120 degrees (for a two-pole machine), the induced voltages will be phase displaced in time by 120 degrees. If each of the three armature windings is connected across equal impedances, balanced three phase currents will flow in them. These currents will in turn produce their own magnetic fields. We denote the flux associated with each field as  EMBED Equation.2 ,  EMBED Equation.2 , and  EMBED Equation.2 . The resultant field with associated flux obtained as the sum of the three component fluxes EMBED Equation.2 ,  EMBED Equation.2 , and  EMBED Equation.2  is the field of armature reaction. We designate the associated flux as  EMBED Equation.2 . Using electromagnetic field theory and a trigonometric identity, one can show that  EMBED Equation.2  revolves at the same velocity as the rotor. Therefore the two fields represented by  EMBED Equation.2  and  EMBED Equation.2  are stationary with respect to each other. The armature field is effectively locked in with the rotor field and the two fields are said to be rotating in synchronism. The total resultant field is the sum of the field from the rotor windings and that associated with armature reaction:  EMBED Equation.2 . G1.2.2 The Phasor Diagram From Faradays Law of Induction, a voltage is induced in each of the three armature windings according to  EMBED Equation.2  where ( is the number of winding turns. Because  EMBED Equation.2  is a sinusoidal function of time, the negative sign captures the fact that the induced voltage will lag the flux by 90 degrees. Letting  EMBED Equation.2 ,  EMBED Equation.2 , and  EMBED Equation.2  be the voltages induced in winding a by the fluxes  EMBED Equation.2 ,  EMBED Equation.2 , and  EMBED Equation.2 , respectively, we can represent the relationships in time between the various quantities using the phasor diagram, illustrated in Figure G1.4.  EMBED Word.Picture.8  Figure G1.4 Phasor Diagram for Synchronous Machine Regarding Figure G1.4, take note that All voltages lag their corresponding fluxes by 90 degrees. The current in winding a, denoted by  EMBED Equation.2 , is in phase with the flux it produces  EMBED Equation.2  If  EMBED Equation.2  (no load conditions), then  EMBED Equation.2 , and in this case,  EMBED Equation.2 , and  EMBED Equation.2  All resistances have been neglected. G1.2.3 The Equivalent Circuit Model We develop the equivalent circuit model for winding a only; the same model applies to windings b and c with appropriate 120 degree phase shifts in all currents and voltages, assuming balanced operation such that the loading on each winding is the same. From Figure G1.4, the component voltages are related via  EMBED Equation.2  (G1.2) However, because  EMBED Equation.2  and  EMBED Equation.2  is directly proportional to  EMBED Equation.2  (assuming constant permeability), we can write that  EMBED Equation.2 . Assuming  EMBED Equation.2  is sinusoidal, the angle EMBED Equation.2  must be -90 degrees; therefore the constant of proportionality  EMBED Equation.2  must be a reactance, which we will denote as  EMBED Equation.2 . These changes result in  EMBED Equation.2  or  EMBED Equation.2  Substitution into eqs.(G1.2) yields  EMBED Equation.2  We obtain the terminal voltage by subtracting from  EMBED Equation.2 , a voltage drop caused by  EMBED Equation.2  to account for the leakage flux. This refinement results in  EMBED Equation.2  Defining  EMBED Equation.2  as the synchronous reactance, we have that  EMBED Equation.2  The circuit model corresponding to this equation is illustrated in Figure G1.5.  Figure G1.5 Equivalent Circuit Model of Synchronous Machine The phasor diagram corresponding to the equivalent circuit, when the load is inductive, is shown in Figure G1.6.  Figure G1.6 Phasor Diagram for Equivalent Circuit Inductive Load The phasor diagram corresponding to the equivalent circuit, when the load is capacitive, is shown in Figure G1.7.  Figure G1.7 Phasor Diagram for Equivalent Circuit Capacitive Load When the load is inductive, the current  EMBED Equation.2  lags the voltage  EMBED Equation.2 ; the generator is said to be operating lagging. When the load is capacitive, the current  EMBED Equation.2  leads the voltage  EMBED Equation.2 ; the generator is said to be operating leading. The angle between  EMBED Equation.2  and  EMBED Equation.2  is  EMBED Equation.2 i, i.e.,  EMBED Equation.2 i if EMBED Equation.2 . This implies that  EMBED Equation.2 lagging,  EMBED Equation.2 leading  Example G 1.1 A 10 MVA, 3 phase, Y-connected, two pole, 60 Hz, 13.8 kV (line to line) generator has a synchronous reactance of 20 ohms per phase. Find the excitation voltage EMBED Equation.3 if the generator is operating at rated terminal voltage and supplying (a) 300 Amperes at 30 degrees lagging, (b) 300 Amperes at 30 degrees leading. Solution EMBED Equation.3 EMBED Equation.3 (a) EMBED Equation.3 (b) EMBED Equation.3 Note that the excitation voltage magnitude EMBED Equation.3 is much higher in the lagging case. We sometimes refer to the lagging case as overexcited operation; here we have that EMBED Equation.3, where ( is the angle between EMBED Equation.3 and EMBED Equation.3. The leading case results in under-excited operation; in this case we have EMBED Equation.3. G1.2.4 Power Relationships From our equivalent circuit in Figure G1.5, we write that  EMBED Equation.2 . Solving for  EMBED Equation.2  yields  EMBED Equation.2  Define the power angle,  EMBED Equation.2 , where  EMBED Equation.2 ,  EMBED Equation.2 so that  EMBED Equation.2  is the angle at which the excitation voltage leads the terminal voltage. Therefore,  EMBED Equation.2   EMBED Equation.2  (G1. 3) But  EMBED Equation.2 . (G1.4) since  EMBED Equation.2  and  EMBED Equation.2  because  EMBED Equation.2  is the reference phasor. Equating real and imaginary parts of eqns. G1.3 and G1.4, we have  EMBED Equation.2  and  EMBED Equation.2 . Multiplying both sides of the previous equations by  EMBED Equation.2  yields  EMBED Equation.2  (G1.5)  EMBED Equation.2  (G1.6) In eqn. G1. 6, reactive power out of the machine is positive when the machine is operated overexcited, i.e., when it is lagging implying  EMBED Equation.2 .It is important to realize that eqns. G1.5 and G1.6 are based on the assumption that stator winding resistance is zero.  Example G 1.2 Find  EMBED Equation.2  and  EMBED Equation.2  for the conditions (a) and (b) described in the previous example. Solution (a)  EMBED Equation.2   EMBED Equation.2   EMBED Equation.2  (b)  EMBED Equation.2   EMBED Equation.2   EMBED Equation.2  The student should consider the following questions regarding this example: Why is real power the same under the two conditions? When the generator is operating lagging, is it absorbing VAR from or supplying VAR to the network? What about when the generator is operating leading? For a particular angle  EMBED Equation.2 , are the terms lagging and leading meaningful with respect to real power? With respect to reactive power? G1.2.5 Generator Pull-Out Power From eqs.(G1.5), the electrical power output  EMBED Equation.2  can be plotted against the power angle  EMBED Equation.2 , resulting in sinusoidal variation as shown in Figure G1.8.  Figure G1.8 Power Angle Curve For simplicity, and without loss of generality, we neglect all real power losses associated with windage and heat loss in the turbine and friction in turbine and generator bearings. Continuing with the assumption that stator winding resistances are zero, in steady-state operation, the mechanical power input to the machine is equal to the electrical power:  EMBED Equation.2 . (In reality,  EMBED Equation.2  in steady-state operation so that  EMBED Equation.2 .) Consider what happens to this lossless machine operating at EMBED Equation.2  ( EMBED Equation.2 ) when the steam valve opening is increased so that  EMBED Equation.2  becomes slightly larger. In this case, the power angle  EMBED Equation.2  increases beyond  EMBED Equation.2 , and the electrical power begins to decrease. However, the mechanical power is only dependent on the steam valve opening, i.e., it is unaffected by the decrease in  EMBED Equation.2 . This can only mean that  EMBED Equation.2 . The difference  EMBED Equation.2  causes the machine to accelerate beyond its synchronous speed. When this happens, we say that the machine has pulled out, gone out of step, or lost synchronism. The generation level at which this happens is called the pull out power. It is given by  EMBED Equation.2  This limit is lower when the generator is under-excited (leading current) because  EMBED Equation.2  is lower.  Example G 1.3 Compute the pull-out power for the two conditions described in Example G1.1. Solution (a) Overexcited case (lagging):  EMBED Equation.2  (b) Under-excited case (leading):  EMBED Equation.2  G1.3 Excitation Control In examples G1.1 and G1.2, we saw two different conditions, summarized as follows: a.  EMBED Equation.2  (lagging),  EMBED Equation.2  (supplying) b.  EMBED Equation.2  (leading),  EMBED Equation.2  (absorbing) We recall that in both conditions, the terminal voltage was constant at  EMBED Equation.2 . One observes that although terminal voltage is constant,  EMBED Equation.2  and  EMBED Equation.2  are not. These effects are achieved via control of the generator field current, which produces the field flux  EMBED Equation.2 . Field current control can be done manually, but it is also done automatically via the excitation control system. The excitation control system is an automatic feedback control having the primary function of maintaining a predetermined terminal voltage by modifying the field current of the synchronous generator based on changes in the terminal voltage. Without excitation control, terminal voltage would fluctuate as a result of changes in  EMBED Equation.2  or external network conditions. The control is referred to as negative feedback because when terminal voltage increases, field current is decreased, and when terminal voltage decreases, field current is increased. A simplified block diagram of an excitation control system is shown in Figure G1.9.  Figure G1.9 Block Diagram of Excitation Control System There are three fundamental components to any excitation system. The main exciter, or more simply, the exciter, is the device that provides the field current for the synchronous generator. The automatic voltage regulator (AVR) couples the terminal voltage to the input of the main exciter. The amplifier increases the power of the regulating signal to that required by the exciter. If the amplifier is electromechanical, it is called the pilot exciter or the rotating amplifier. If the amplifier is solid state, it is usually considered as part of the AVR. There are three basic types of excitation systems. These are: rotating DC commutator rotating AC alternator static These are illustrated in Figures G1.10, G1.11, and G1.12.  Figure G1.10 Rotating DC Commutator Type Excitation System  Figure G1.11 Rotating AC Alternator Type Excitation System  Figure G1.12 Static Type Excitation System The DC commutator excitation system utilizes a DC generator mounted on the shaft of the synchronous generator to supply the field current. This type of system is no longer used in new facilities because it is slow in response, and because it requires high maintenance slip rings and brushes to couple the exciter output to the field windings. The AC alternator excitation system uses an AC alternator with AC to DC rectification to supply the field winding of the synchronous generator. An important advantage over DC commutator systems is that AC alternator systems may be brushless, i.e., they do not use slip rings to couple the exciter to the rotor-mounted field winding. For example, the General Electric Althyrex( uses an inverted alternator to supply the field voltage through a rectifier. The alternator is inverted in that, unlike the power generator, the field winding is on the stator and the armature windings are on the rotor. Therefore the alternator field can be fed directly without the need for slip rings and brushes. Rectification to DC, required by the synchronous generator field, takes place by feeding the alternator three-phase output to a thyristor controlled bridge. The thyristor or silicon controlled rectifier (SCR) is similar to a diode, except that it remains off until a control signal is applied to the gate. The device will then conduct until current drops below a certain value or until the voltage across it reverses. This device will be further discussed in Chapter 7. The third type of excitation system is called a static system because it is composed entirely of solid state circuitry, i.e., it contains no rotating device. The power source for this type of system is a potential and/or a current transformer supplied by the synchronous generator terminals. Three-phase power is fed to a rectifier, and the rectified DC output is applied to the synchronous generator field via slip rings and brushes. Static excitation systems are usually less expensive than AC alternator types, and the additional maintenance required by the slip rings and brushes is outweighed by the fact that static excitation systems have no rotating device. G1.4 Turbine Speed Control We have already seen that the mechanical speed of a synchronous generator  EMBED Equation.2  (rad/sec) is related to the electrical frequency  EMBED Equation.2 through  EMBED Equation.2  where  EMBED Equation.2  is the number of poles. This implies that control of speed also means control of frequency. But what causes frequency to deviate from its nominal value of 60 Hz? If you consider your own daily use of electricity, you will realize that the load level seen by supplying generators is constantly changing, and at least one generator must compensate for these changes. In discussion of pullout power, we saw that when  EMBED Equation.2 , the generator accelerated. In the same way, if  EMBED Equation.2  is greater than the load,  EMBED Equation.2 , the generator will also accelerate, resulting in a frequency increase; if  EMBED Equation.2  is less than  EMBED Equation.2 , the generator will decelerate, resulting in a frequency decrease. The effect of a generation-load imbalance on frequency, and the relation between generator speed and frequency, offers an elegant way to maintain a generation-load balance: use deviation from rated turbine speed ( EMBED Equation.2 ) as a control signal to cause appropriate action regarding adjustment of the energy supply valve. If  EMBED Equation.2 , causing  EMBED Equation.2 , the difference signal  EMBED Equation.2  is fed back to an actuator, which adjusts the energy supply valve so as to reduce the energy supply and thus reduce  EMBED Equation.2 . Likewise, if  EMBED Equation.2 , causing  EMBED Equation.2 , the difference signal  EMBED Equation.2  is fed back to an actuator, which adjusts the energy supply valve so as to increase the fuel intake and thus increase  EMBED Equation.2 . The actuator, which accomplishes these actions, is called the speed governor. A simplified block diagram of the complete speed governing control system is shown in Figure G1.13.  Figure G1.13 Block Diagram of Speed Governing Control System The purpose of frequency control is not only to maintain power balance, but also to protect frequency-sensitive loads from experiencing large frequency excursions. Some types of loads are designed to operate best at nominal frequency, and the performance of these loads may degrade substantially when frequency deviates from its nominal value. Frequency sensitive loads include some types of motor drives, electronic loads (including computers), and clocks. In North America, frequency is normally regulated to remain within  EMBED Equation.2  ( EMBED Equation.2  Hz), but this is considered tight; many power systems in other regions of the world are operated under looser regulation. Indeed, there is ongoing debate in the U.S. today regarding loosening the frequency control criterion. Because speed-governors act to maintain load balance and frequency constancy, the overall control system of which they are a part is often referred to as load-frequency control. The speed-governor constitutes what is known as the primary control; the higher level aspects of load frequency control are known as secondary control and constitute automatic generation control (AGC). We will not discuss AGC here. Speed governing equipment for steam and hydro turbines are conceptually similar. Most speed governing systems are one of two types; mechanical-hydraulic or Electro-hydraulic. Electro-hydraulic governing equipment use electrical sensing instead of mechanical, and various other functions are implemented using electronic circuitry. Some Electro-hydraulic governing systems also incorporate digital (computer software) control to achieve necessary transient and steady state control requirements. The mechanical-hydraulic design, illustrated in Figure G1.14, is used with older generator units.  Figure G1.14 Mechanical-Hydraulic Governor Design Basic operation of this feedback control system for turbine under-speed is indicted by movement of each component as indicated by the arrows. As  EMBED Equation.2  decreases, the bevel gears decrease their rotational speed, and the rotating flyweights pull together due to decreased centrifugal force. This causes point B and therefore point C to raise. Assuming, initially, that point E is fixed, point D also raises causing high pressure oil to flow into the cylinder through the upper port. The oil causes the main piston to lower, which opens the steam valve (or water gate in the case of a hydro machine), increasing the energy supply to the machine in order to increase the speed. If rod CDE was not connected at point E, the previous actions would provide constant frequency, as long as no more than one machine in the system was regulating. However, if two or more machines were regulating, each machine would continuously correct frequency changes made by the others, i.e. they would fight each other. The connection at point E solves this problem. This connection forces point D to move down slightly as point E moves down. This action provides for a nonzero steady state frequency deviation according to  EMBED Equation.2  where  EMBED Equation.2  is called the steady state droop or regulation constant, and  EMBED Equation.2  and  EMBED Equation.2  are the per unit steady state deviations in frequency and power, respectively. The so-called steady state droop characteristic is illustrated in Figure G1.15.  Figure G1.15 Steady-State Droop Characteristic  Example G 1.4 Two machines on speed-governor control are interconnected and supplying the same load when the load suddenly increases such that the steady state frequency deviation is 0.01 Hz. If both machines have a droop of 5% ( EMBED Equation.2 ), machine A is rated at 100 MW and machine B is rated at 200 MW, compute the steady state deviation in power for each machine. Solution A sudden increase in load will decelerate the machine and therefore frequency must decrease.  EMBED Equation.2   EMBED Equation.2   EMBED Equation.2   EMBED Equation.2   EMBED Equation.2  The student should answer the following questions: Why is steady state frequency deviation the same for both machines? Why is the steady state change in per unit power the same for both machines? Basic intuition might suggest that, for a given load change, we would like all machines to respond, but bigger machines should respond more than smaller machines. By studying the above example, you should be able to state a simple requirement regarding coordination of governing systems that would provide for this. A key point is that the droop characteristic does result in nonzero steady state frequency deviation. This frequency deviation must be corrected so that the system frequency returns to 60 Hz. This is the function of the secondary load-frequency control loop, to be discussed in Chapter 5. G1.5 Summary The operating costs of generating electrical energy is determined by the fuel cost and the efficiency of the power plant. The efficiency depends on generation level and can be obtained from the heat rate curve. We may also obtain the incremental cost curve from the heat rate curve. In Module E3 it is illustrated how this very important generator characteristic is used to find optimal (least cost) allocation of demand among all of the interconnected generators. The AC synchronous machine is the most common technology for generating electrical energy. It is called synchronous because the composite magnetic field produced by the three stator windings rotate at the same speed as the magnetic field produced by the field winding on the rotor. We use a simplified circuit model to analyze steady-state operating conditions for a synchronous machine. The phasor diagram is an effective tool for visualizing the relationships between internal voltage, armature current, and terminal voltage. The excitation control system is used on synchronous machines to regulate terminal voltage, and the turbine-governor system is used to regulate the speed of the machine. References A. Bergen, Power Systems Analysis, Prentice-Hall, New Jersey, 1986. V. Del Toro, Electric Power Systems, Prentice-Hall New Jersey, 1992. P. Kundur, Power System Stability and Control, McGraw-Hill, New York, 1994. W. Stevenson, Elements of Power System Analysis, 4th edition, McGraw-Hill, New York, 1982. D. Fink and H. Beaty, editors, Standard Handbook for Electrical Engineers, 13th edition, 1993, Graw-Hill, Inc., New York. L. Matsch, Electromagnetic and Electromechanical Machines, 2nd edition, Ahrper and Row, new York, 1977. A. Fitzgerald, C. Kingsley, and A. Kusko, Electric Machinery, 3rd edition, McGraw-Hill, New York, 1971. V. Mablekos, Electric Machine Theory for Power Engineers, Harper and Row, Cambridge, 1980. S. Dewan and A. Straughen, Power Semiconductor Circuits, John Wiley and Sons, New York, 1975. P. Anderson and A. Fouad, Power System Control and Stability, The Iowa State University Press, 1977. E. Kimbark, Power System Stability, Synchronous Machines, Dover Publications, 1956.  P R O B L E M S  Problem 1 A three-phase, 60 Hz generator has a synchronous reactance of  EMBED Equation.3  and negligible resistance. The generator is delivering 50MW at 0.8 power factor lagging. The terminal voltage remains constant at 30kV line to line throughout this problem. Determine the excitation voltage per phase (angle and magnitude ) and the reactive power out of the machine. With the field current held constant at the level of part (a), the mechanical power into the machine is reduced to 25MW. Determine the reactive power out of the machine. With the machine initially generating 50MW at 0.8 power factor lagging, as in part (a), a change is made so that the excitation voltage is reduced to 79.2% of its value. Determine the reactive power out of the machine.  Problem 2 A three-phase, 6-pole, 60 Hz, Y-connected synchronous generator has a synchronous reactance of  EMBED Equation.3 . It is operating so that the terminal voltage is constant at 13.8kV line-to-line. The three-phase real power output of the machine is 6MW. Assume the line-to-neutral terminal voltage is the reference (angle = 0 degree) for all calculation below. What is the synchronous speed of this generator in RPM? The excitation voltage magnitude is 19kV line-to-line. What is the power angle delta (the angle between the excitation voltage and the terminal voltage) ? Based on this answer, indicate whether the generator is operating leading or lagging and how you can tell. What is the magnitude and angle of the current  EMBED Equation.3 ? Based on this answer, indicate whether the generator is operating leading or lagging and how you can tell. Compute the three phase reactive power out of the machine. Based on this answer, indicate whether the generator is operating leading or lagging and how you can tell.  Problem 3 In each of the following questions circle the answer that is most likely to be correct based only on the information for that question and the following two sentences. In all cases a single generator is directly connected to a single load. All voltages are line to neutral. i) A generator is supplying 20 MVAR to a load. The angle 'theta' of the load impedance is ____. a) negative b) zero c) positive d) not enough information ii) The terminal voltage of a generator is  EMBED Equation.2 kV. The excitation voltage is  EMBED Equation.2  kV. This generator is operating with a power factor that is ______. a) leading b) unity c) lagging d) not enough information iii) A generator has an armature current of  EMBED Equation.2 A when the terminal voltage is  EMBED Equation.2 kV. The generator is _______. a) overexcited b) under-excited c) neither d)not enough information iv) The excitation voltage of a generator is very large in magnitude. The load is _______. a) resistive b) inductive c) capacitive d) not enough information v) The real power output of a generator is positive. The current is ________ the terminal voltage. a) leading b) in phase with c) lagging d) not enough information vi) The load is inductive. The angle of the terminal voltage is 0 degrees. The angle of the current is _______. a) positive b) negative c) zero d) not enough information vii) The DC current to the field winding is very small. The generator is ________ reactive power. a) supplying b) absorbing c) neither d) not enough information viii) The angles of the excitation voltage and the terminal voltage are both 0 degrees. The real power of the machine is ________. a) positive b) negative c) zero d) not enough information ix) The real power consumed by the load suddenly increases. The system frequency will ___. a) increase b) decrease c) stay the same d) not enough information x) The system frequency increases. The speed of the machine must have ________. a) increased b) decreased c) stayed the same d) not enough information  Problem 4 Draw a rough sketch of a three-phase two-pole smooth-rotor synchronous generator. Label the stator, rotor, field winding, and armature winding.  Problem 5 Why are the armature windings in a three-phase two-pole synchronous generator spaced 120 degrees apart?  Problem 6 In Germany normal appliances use 50 Hz AC power. What is the ideal speed (in RPM) of the rotor in a three-phase four-pole synchronous generator supplying this power?  Problem 7 Why is it necessary to control the speed of the turbine? What would the problem be (for power consumers) if the turbine speed were not controlled? In a broad sense, how is control of turbine speed accomplished?  Problem 8 A three-phase synchronous generator is operating with terminal voltage (line-to-neutral) of  EMBED Equation.2 V. Its per-phase internal excitation voltage is  EMBED Equation.2 V. The synchronous reactance is  EMBED Equation.2 . a) Compute the three phase real power out of the generator. b) Compute the three phase reactive power out of the generator. c) Compute the total current supplied by the generator. d) Draw the phasor diagram for this operating situation. Show terminal voltage, internal voltage, and current. e) Indicate whether this operating condition is leading or lagging. f) Compute the angle of  EMBED Equation.2 (denoted as delta) required if the operating condition were changed so that the magnitude of  EMBED Equation.2  remains unchanged, but the reactive power being produced by the generator is zero (i.e. unity power factor).  Problem 9 A three-phase synchronous generator, having rated terminal voltage (line-to-line) of 220 volts, is operating so that its per-phase internal (excitation) voltage is  EMBED Equation.2 V. Assume constant terminal voltage at rated voltage. The synchronous reactance is  EMBED Equation.2 . Compute the reactive power out of the generator. The field current is now changed so that the reactive power supplied by the machine is 600 VAR. The real power out of the machine is 3kW. Find the excitation voltage  EMBED Equation.2 (magnitude and angle).  Problem 10 A three-phase synchronous generator is supplying a load over a transformer connected to a transmission line. The circuit is illustrated below. Impedance data (in per-unit) are:  EMBED Equation.2    Operating information:  EMBED Equation.2   EMBED Equation.2  Base Voltages: 13.8kV, 230kV Base Power: 100MVA a) Draw the vector diagram, showing  EMBED Equation.2 and  EMBED Equation.2  for this operating condition. Also, redraw the phasor diagram for the case when  EMBED Equation.2 per-unit. It is unnecessary to do calculations, but the length and angles of the three vectors relative to each other should be approximately correct. Identify each phasor diagram as either leading, lagging, or neither. b) Compute the real and reactive power supplied at the generator terminals (at bus 1), in MW and MVAR. c) Compute the real and reactive power flowing into the transmission line from bus 3, in MW and MVAR. d) Are the answers to (b) and (c) different? Why or why not?  Problem 11 A Y-connected three-phase synchronous generator has a synchronous reactance of  EMBED Equation.3 . The terminal voltage of the generator is  EMBED Equation.3  (line-to-line) and the armature current is  EMBED Equation.3  (referenced to line-to-neutral terminal voltage). (a) Compute the internal voltage phasor of the machine, Ef (line-to-neutral). (b) Determine the magnitude of this phasor, |Ef | necessary to provide 0 vars reactive power out of the machine terminals, assuming that the angle of this phasor, (Ef , is held constant at the value obtained in your calculation of part (a).  Problem 12 A synchronous generator having synchronous reactance of XS=2 ohms is operating with an 18.0 line-to-line terminal voltage. The power out of the machine terminals is Pout=140 MW, Qout=0. Compute the magnitude |Ef| and angle (( of the internal (excitation) voltage. A large reactor (e.g., inductive element) is suddenly connected in parallel with the load RL, and the field current is adjusted. Indicate what would happen to each of the below by checking the appropriate space: Field current increase______ decrease_____ Reactive power out of the generator increase______ decrease_____ no change_____ Current lead_________ lag_________ neither________  Per unit frequency deviation is given by  EMBED Equation.2  when 60 Hz is the nominal frequency.     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P3i'oӗ,nCZ-H%ERiq5B> 9)@͆CyߑEg#Ύ=J{6Ot#|Z;>煞h\z@JF?0=g@\R^mi<tEh~eӆL)86X%-H4I قhV&<(َH9;o i[^ۂ+ g;h&DjSdxU]%~6-[~$(p8 q'!cNv%: 21lζO]e"92E~ZuɅ,b*2碭F%Wv?~d%7-Ml&d}\^W6p Ydv/6 ɺD /mBN<T(Yc?blė+0,'@XɕԚ^`JaS "e`a:g-s{'z][S:JT V3_$2ORr@.>I~R#,:Zp(y3<6Kˇ2ϯ;Gs?"s8 (TjIfeo̲eM)ɛ$Jb N[4*h\;p(RmY#*`C*@bۚQF†KtO`ֻ=@\ص3L:l|3Ҡlۖ {Q#`3DLj 7h0(FTn*2уHa ؃k\rڽ_nWKfFEp!P#|SI)"]Y%V>5\3h'<~mjЉ%Z}kd=x I`,G&2 ^Na&Z3Xv9vjc'[ fiՐL9`T/@ [p)gN5;tG,+o$H5(F8i* & "System-V؋vvV6_ tFFP dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman + fdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F&WA*WA f fL4,@Equation Native l<_989715130;FOle mPIC :=nLMETA pCompObj<>wfObjInfo?yEquation Native z64N  .1  & & MathTypePSymbolv- 2 `%f Times New Roman- 2  ap & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q5  aL4,@4N  .1  & &_9897151359GBF)Ole {PIC AD|LMETA ~ MathTypePSymbolv- 2 `%f Times New Roman- 2 bp & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjCEfObjInfoFEquation Native 6_989715139IF))\  bL4@4N  .1  & & MathTypePSymbolv- 2 `%f Times New Roman-Ole PIC HKLMETA CompObjJLf 2  cb & "System-Ez FE F*F FMicrosoft Equation 3.0 DS Equation Equation.39q\  cObjInfoMEquation Native 6_989715145mPF))Ole PIC ORLMETA CompObjQSfObjInfoTL4,@4N  .1  & & MathTypePSymbolv- 2 `%f Times New Roman- 2  ap & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qWtZ  aL4,@Equation Native 6_989715149WF)POle PIC VYLMETA PICT X[CompObjfObjInfoZ\4N  .1  & & MathTypePSymbolv- 2 `%f Times New Roman- 2 bp & "System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +bdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qn,q  bEquation Native 6_989715153Ue_FPPOle PIC ^aLL4@4N  .1  & & MathTypePSymbolv- 2 `%f Times New Roman- 2  cb & "System-Ez FE META PICT `cCompObjfObjInfobd F*F  dPPNTSymbol  , Symbol .+ fdPPNTTimes New Roman,Times New Roman +cdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native 6_989715157gFPPOle PIC fiLhT  cL{4h@{4~N  .1  @& & MathTypePSymbolv- 2 `%f Times New Roman-META PICT hkCompObjfObjInfojl 2  arpW & "System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qn]  arL{4h@{4~N  .1  @& &   )  "!$#&%'(*+u,-.0/2143cH6789:;<>?@ABCDEFGZJKLMNOPQSTUVWXYd\]^_`abefghikjmlonpqrtsvwxyz|{~}Equation Native :_989715163]}oFPwOle PIC nqLMETA PICT psCompObjfObjInfort MathTypePSymbolv- 2 `%f Times New Roman- 2  arpW & "System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qh,  arL4{@hEquation Native :_989715169wFwwOle PIC vyLMETA PICT x{CompObjfObjInfoz|4{N  .1  @& & MathTypepSymbolv- 2 `%f Times New Roman- 2 Jf> & "System-V؋vvV6_ tFFP dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman + fdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qh   fEquation Native 6_989715174uFwOle PIC ~L    !#&)+,-./0123469<>?@ABCEJLMNOPQSXZ[\]^_afhijklmopqsxz{|}~L{4h@{4~N  .1  @& & MathTypePSymbolv- 2 `%f Times New Roman- 2  arpW & "System-META PICT  CompObj fObjInfo dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native :_989715177FOle PIC LhԬ  arL {dh {M  .1  @&` & MathTypepSymbolv- 2 `%f 2 `Jf 2 `f META (PICT CompObj"fObjInfo$Times New Roman- 2  rW 2 EarpW 2 f>Symbol- 2 `= 2 `+ & "System-E EdPPNTSymbol E, Symbol .+ f)f)fdPPNTTimes New Roman,Times New Roman ( r)ar)fdPPNTSymbol ( =)+dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qJhL  r = ar + fEquation Native %f_989715208FOle 'PIC (LLElE~N - .1  & & MathType-wTimes New Roman- 2 `4v 2 `N 2 ad 2 dtk Times New Roman- 2 rMETA *CompObj5fObjInfo7Equation Native 8\WSymbol- 2 `P= 2 `-Symbol- 2 af & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q@h v="Nd r dtL4@4M  .1  & & MathTypePSymbolv- 2 `%_989715212FOle :PIC ;LMETA =f Times New Roman- 2  rW & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q\  rCompObjDfObjInfoFEquation Native G6_989715218FOle HPIC ILMETA KCompObjRfL44@@44M  .1  & & MathTypePTimes New Roman1- 2 `LE Times New Roman- 2 MrW & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qmtZ E rL4|@ObjInfoTEquation Native U6_989715222FOle VPIC WLMETA YCompObj`fObjInfob4M  .1  `&  & MathTypePTimes New RomanV- 2 `LE Times New Romanp- 2 MarpW & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q E arL{{hh{{M  .Equation Native c:_989715226FOle dPIC eLMETA gPICT nCompObjrfObjInfot1  @@& & MathTypepTimes New RomanV- 2 `LE Times New Roman- 2 wf> & "System- dPPNTTimes New Roman ,Times New Roman .+ EdPPNTTimes New Roman + fdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q8 E fL4@Equation Native u6_989715231FOle vPIC wL4M  .1  & & MathTypePSymbolv- 2 `%f Times New Roman- 2  rW & "System-META yPICT CompObjfObjInfo  dPPNTSymbol  , Symbol .+ fdPPNTTimes New Roman,Times New Roman +rdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q(  rEquation Native 6_989715235FOle PIC LL{4h@{4M  .1  @& & MathTypePSymbolv- 2 `%f Times New Roman- 2  arpW & META PICT CompObjfObjInfo"System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q8  arL4{@h4{M  .1  @& & MathTypepSymbolv- 2 `%Equation Native :_989715239FOle PIC LMETA PICT CompObjfObjInfof Times New Roman- 2 Jf> & "System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman + fdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q(  f  FMicrosoft Office Word Picture MSWordDocWord.Picture.89q Equation Native 6_1153814814 FData 51Table=Dd AD  3 @@"?@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No List = != @V=!%*.27>H" !$%)*-.1267:>0000y00y00y0 0y0  |0y0  |0y0zzx=_8@@(   -- #  s"*?`  c $X99?--t  # C"?X $t"& t  # C"? !!(# t  # C"?l!<# t  # C"?`'D%0*`' t  # C"?((+0* t  # C"?t"*$- ZB  S DX |)(|)ZB  S DX #X |)ZB   S DX |)$+ZB   S D(&*|)ZB   S DX &*|)ZB   S DX X #ZB   S DX X |)t  # C"?&0*(L, B S  ?=Ht!#*,.02579>.02579>:::!#%(*,.02579>79>]:9&cm '@ =pUnknownG: Times New Roman5Symbol3& : Arial"qhbc+!<>43QHX)?cm2James D. McCalleyJames D. McCalleyCompObjoObjInfoWordDocumentI4SummaryInformation(R{` zbjbjFF 4,,nnnn z h$hn " "RxT _n:80hA^,  hnn  SHAPE \* MERGEFORMAT  Ia Er Ear Ef f ar r 0248:<>@DFHLPRVXZ^`bfjlprtxzhcmhcmH* hcmH*h]:jhcmUmHnHuhcmjhcmU:@BHJRTZ\bdlntvxz:x21h:pcmN N!"##<$!% Oh+'0  < H T`hpxJames D. McCalleyNormalJames D. McCalley2Microsoft Office Word@@V鈀@ZoDocumentSummaryInformation8[_989715247F ; ;Ole PIC L՜.+,0 hp  Iowa State UniversityG  TitleL4@4NM  .1  &` & MathTypePTimes New Roman6- 2 `LI~ Times New Roman<- 2 ap & "System-META PICT CompObjfObjInfo  dPPNTTimes New Roman  ,Times New Roman .+ IdPPNTTimes New Roman +adPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native 6_989715252F ; ;Ole PIC L8 I aL{4h@{4~N  .1  @& & MathTypePSymbolv- 2 `%f Times New Roman-META PICT CompObjfObjInfo 2  arpW & "System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q(   arL4@46M  .1  @& &Equation Native :_865487806F ;0bOle PIC LMETA PICT *CompObjZObjInfo MathTypePTimes New Roman- 2 `LI~ Times New Roman- 2 apSymbol- 2 `=Times New Roman- 2 `;0 & "System-*" "dPPNTTimes New Roman ",Times New Roman .+ IdPPNTTimes New Roman +adPPNTSymbol, Symbol ( =dPPNTTimes New Roman) 0dPPNT"System FMicrosoft Equation 2.0 DS Equation 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MathTypepTimes New Roman- 2 `LE 2 `E 2 `E Times New RomanR- 2 MrW 2 f> 2 arpWSymbol- 2 `L= 2 `+ & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qJh E r =E   ObjInfo.Equation Native /f_989715292F@POle 1 f +E arL El EL 8 .1   &`  & MathType-iS Times New Roman- 2 `LE PIC  2LMETA 4CompObj  ?fObjInfo A2 `N 2 a}d 2 <dtk Times New Roman- 2 MarpW 2 8arpWSymbol- 2 `= 2 `-Symbol- 2 a=f & "System-Symbo= 2 ` FMicrosoft Equation 3.0 DS Equation Equation.39qV8 E ar ="Nd ar dtL{4h@{4~N  .Equation Native Br_989715315FPPOle DPIC ELMETA GPICT NCompObjRfObjInfoT1  @& & MathTypePSymbolv- 2 `%f Times New Roman- 2  arpW & "System- dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q5  arL4@Equation Native U:_989715301FPPOle VPIC WL4NM  .1  &` & MathTypePTimes New Roman6- 2 `LI~ Times New Roman<- 2 ap & "System-META YCompObj`fObjInfobEquation Native c6 FMicrosoft Equation 3.0 DS Equation Equation.39q I aL 4@@ 4 J ._989715305+FP`Ole dPIC  eLMETA g1   &  & MathTypePTimes New Roman4- 2 `LE 2 `K 2 `I Times New Roman- 2 MarpT 2 2 apSymbol- 2 `= 2 ` Times New Roman4- 2 `( 2 `)Symbol- 2 `y & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qHWZ E ar =(K ")I aCompObj!rfObjInfo"tEquation Native ud_989715319%F``Ole wPIC $'xLMETA zPICT &)L{4h@{4N  .1  @& & MathTypePSymbol- 2 `%f Times New Roman- 2  arpW & "System-A  dPPNTSymbol , Symbol .+ fdPPNTTimes New Roman,Times New Roman +ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfo(*Equation Native :_989715310-F``  arL 4@@ 4 J .1   &  & MathTypePTimes New Roman4- 2 `LE 2 `K 2 `IOle PIC ,/LMETA CompObj.0f Times New Roman- 2 MarpT 2 2 apSymbol- 2 `= 2 ` Times New Roman4- 2 `( 2 `)Symbol- 2 `y & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q  LL  .1  &`` &ObjInfo1Equation Native )_9897153274FppOle PIC 36LMETA HPICT 58CompObjf MathType Times New Roman- 2 @LK & "System-@ WM  dPPNTTimes New Roman ,Times New Roman .+ KdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q \ KL4@4~L  .1  &` &ObjInfo79Equation Native )_989715323#2<Fp% Ole PIC ;>LMETA PICT =@CompObjf MathTypePTimes New Roman- 2 `dX Times New Roman,- 2 }arpW & "System- cartindex1 cartindex2 dPPNTTimes New Roman ,Times New Roman .+ XdPPNTTimes New Roman + ardPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q5 X arL4@ObjInfo?AEquation Native :_989715334DF% % Ole PIC CFLMETA CompObjEGfObjInfoH4nL B .1   &  & MathTypePTimes New Roman- 2 `LE 2 `X 2 `o I~ Times New Roman+- 2 MarpW 2 arpW 2  apSymbol- 2 `= 2 `# 2 `2-Times New Roman+- 2 `(~ 2 ` )~ 2 `S 90 & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qpm E ar =(X ar  ""90 o )IEquation Native _989715332:QKF% % Ole PIC JML aL 4@ 4.N  .1   & & MathTypePTimes New Roman- 2 `LE 2 `%jXk 2 `I~ META (PICT LO$CompObjfObjInfoNPTimes New Roman- 2 MarpW 2 arpW 2 QapSymbol- 2 `= 2 `- & "System-$I IdPPNTTimes New Roman I,Times New Roman .+ E)'jX)IdPPNTTimes New Roman ( 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U^>jEd XJxO Q1~f(RRjxŎb1%;<u1:s}g"IJl;ǢDciPI&SWTʣ cEeJw:&99&x &xr`4dpxn"Q$uyV*vؿu ?=ua5xqBO GZMn #̿>ޑn6Dd ,B 1 S A1? 02[5D' ;|7ɇ`!/5D' ;|Rxcdd``> @c112BYL%bL0Yn B@?6 17T obIFHeA*C0l? @Hfnj_jBP~nbCp ˛8620p1si# W@:+!Gy91ps]zVrA]!#t] `p021)W2_Hagban FDd l @B 2 S A2? 12439&Ve}bVJ Q`!439&Ve}bVJ Q x=KAg.Ds&B((iR3ARzBb 1@Fl 6H*kX+๳[sAԃ湙ٙwv  O-z%ĵu[3d6K=oHd)XYi`00U CnLVF1ky4f^%_j܇Kak:,n=H2qz[4-_|#($dK 7nw߄$˖rNpkϗas 9%8p.g`aB -L9 \^Y`?!E~V&4ݱ% vI+@]|Ff0d: G^]y=D 8(P\8POle mPIC x{nLMETA pPICT z}|c3 4 {  J .  & Times-!V Times-!t PSymbol-!= Times-!E Times-!f !PSymbol-!- (Times-!jX 2Times-!s =Times-!I ATimes-!a E & '-)cJdxpr  J"J currentpoint ",Times .+ V +t, Symbol ( =) E +f ( (-) jX + s ( AI +a/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2368 div 512 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (V) -16 261 sh (E) 740 261 sh (jX) 1563 261 sh (I) 2031 261 sh 224 ns (t) 180 357 sh (f) 1005 358 sh (s) 1908 357 sh (a) 2164 357 sh 384 /Symbol f1 (=) 400 261 sh (-) 1221 261 sh end MTsave restore d]MATHQ  V t =E f -jX s I a1  FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfo|~Equation Native x_865650165F  \5m V t =E f "jX s I aL4@4L  .1  &` &Ole PIC LMETA PICT  MathTypePTimes New Roman- 2 `LI~ Times New Roman0- 2 ap & "System-"Syst  dPPNTTimes New Roman  ,Times New Roman .+ IdPPNTTimes New Roman +adPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F+WA2WA I aET#,CompObjZObjInfoEquation Native <_865650218F  Ole PIC TMETA PICT <#     .  & TimesNe-!V TimesNe-!t  & 'an< dxpr   " currentpoint ",Times .+ V +t/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 352 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (V) -16 261 sh 224 ns (t) 180 357 sh end MTsave restore d$MATH5 V treFMicrosoft Equation Editor 2.0DNQE Equation.2 V tL4@CompObjZObjInfoEquation Native 4_865650326F  Ole PIC LMETA PICT 4L  .1  &` & MathTypePTimes New Roman- 2 `LI~ Times New Roman0- 2 ap & "System-"Syst  dPPNTTimes New Roman  ,Times New Roman .+ IdPPNTTimes New Roman +adPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F+WA2WA I aECompObjZObjInfoEquation Native <_945477825FF  Ole PIC LMETA CompObjfL,4K  .1  & & MathTypePTimes New Roman- 2 `LE Times New RomanJ- 2 Mt> & "System-@@@@@@ FMicrosoft Equation 3.0 DS Equation Equation.39q cI0gI V tL4@ObjInfoEquation Native 8_865650394F  Ole PIC LMETA PICT CompObjZ4L  .1  &` & MathTypePTimes New Roman- 2 `LI~ Times New Roman0- 2 ap & "System-"Syst  dPPNTTimes New Roman  ,Times New Roman .+ IdPPNTTimes New Roman +adPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F+WA2WA I aEObjInfoEquation Native <_945477857F !Ole L,4K  .1  & & MathTypePTimes New Roman- 2 `LE Times New RomanJ- 2 Mt> & PIC LMETA CompObjfObjInfo"System-@@@@@@ FMicrosoft Equation 3.0 DS Equation Equation.39qxI8yI V tL`Equation Native 8_865650423F!!Ole PIC L  "%(*+,-./012356789:;<=>?@ABCDEGJMOPQRSTUVX[^`abcdefgiloqrstuvxyz|`K  .1  @& & MathType0Symbol- 2 `q & "System-  dPPNTSymbol , Symbol .+ qdMETA (PICT CompObj ZObjInfo PPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F+WA2WA q L4@Equation Native  <_865650475F!!Ole  PIC LMETA PICT jCompObj!ZObjInfo#4vK < .1  @& & MathTypePTimes New Roman- 2 `LI~ 2 `LI~ Times New Romant- 2 ap 2 apSymbol- 2 `= 2 `#Times New Roman- 2 `|E 2 `|ESymbol- 2 `q & "System- n   j: :dPPNTTimes New Roman :,Times New Roman .+ I)IdPPNTTimes New Roman (a)adPPNTSymbol, Symbol ( =)dPPNTTimes New Roman( |)|dPPNTSymbol) qdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2@Fp,WA0WA I a =|I a |qT4,Equation Native $\_865650594fF!6!Ole &PIC 'T4 \  < .  & TimesNe-!V Times-!t PSymbol-!= Times-!| Times-!V TimeMETA )PICT 4MCompObjFZObjInfoHs-!t Times-!| &PSymbol-! +Times-!0 5 & 'M<dxpr  <"< currentpoint ",Times .+ V +t, Symbol ( =)|)V +t ( &|)) 0,/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1920 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (V) -16 261 sh (V) 772 261 sh 224 ns (t) 180 357 sh (t) 968 357 sh 384 /Symbol f1 (=) 400 261 sh (\320) 1335 261 sh 384 /Times-Roman f1 (|) 610 261 sh (|) 1166 261 sh 384 /Times-Roman f1 (0) 1639 261 sh end MTsave restore dDMATH8 D V t =|V t |0roFMicrosoft Equation Editor 2.0DNQE Equation.28 V t =|V t |0L33  .1  &`Equation Native IT_945477891NF6!6!Ole KPIC LLMETA NCompObjWfObjInfoYEquation Native ZD & MathType0Symbol- 2 `qTimes New Roman-- 2 `ilSymbol- 2 `< 2 `Times New Roman,- 2 `0 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q(`II  i <0!L33  ._945481323F6!6!Ole \PIC ]LMETA _1  &` & MathType0Symbol- 2 `qTimes New Roman8- 2 `ilSymbol- 2 `> 2 `Times New Roman8- 2 `0 & "Systemn-ICompObjhfObjInfojEquation Native kD_958299175F^!^! FMicrosoft Equation 3.0 DS Equation Equation.39q(LIaI  i >0!L{{hhOle mPIC nLMETA pPICT w{{.W  .1  @@& & MathTypepTimes New Roman- 2 `LE Times New Roman r- 2 wf> & "System-"System- dPPNTTimes New Roman ,Times New Roman .+ EdPPNTTimes New Roman + fdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q F/WA3WA E f~CompObj{fObjInfo}Equation Native ~<_989715614wF^!^!Ole PIC LMETA CompObjfL D  u   .  & Times-!VTimes-!tPSymbol-!=Times-!13 !. $!8 'Times-!kV -Times-!3* "-$#"%' "-($#)'-*'%$-'0*$6':   \'PSymbol-!=?Times-!7I!.O!97RTimes-!kV^PSymbol-!oTimes-!V}Times-!tPSymbol-!=Times-!7!.!97PSymbol-!Times-!10Times-!3 PSymbol-!Times-!0PSymbol-! & ' FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native _989715569F^!!Ole 5 V t =13.8kV 3  =7.97kV!V t =7.9710 3  "0VT@PIC TMETA CompObjfObjInfo {  J .  & Times-!E Times-!f PSymbol-!= Times-!V Times-!t "PSymbol-!+ (Times-!jX 2Times-!s =Times-!I ATimes-!a E & ' 1 FMicrosoft Equation 3.0 DS Equation Equation.39q\ E f =VEquation Native x_989715682F!!Ole PIC L t +jX s I aL77I  .1  2&`24 & MathTypepTimes New Roman- 2 LI~ 2 2 E 2 +kV META hCompObjfObjInfoEquation Native 7Times New Roman=- 2 ap 2 ] f>Symbol- 2 = 2 x# 2 - 2   2 @ x 2 q= 2  2 # 2 + 2 # 2  2 !# 2 8#- 2 % 2 z'= 2 p-# 2 1Times New Roman=- 2 ;300 2 30 2 7 2 97 2 10 2 0 2 20 2 G90 2 300 2 Y$30 2 (12 2 L*14 2 .25 2 M034 Times New Roman- 2 3pTimes New Roman=- 2 e.` 2 (~ 2 |)(~~ 2 &)~ 2 *.` 2 /.` & "System-  FMicrosoft Equation 3.0 DS Equation Equation.39qL I a =300 ""30A!E f =7.9710 3  "0+(20 "90)(300 ""30)=12.14 "25.34kVL3t3>X  .1   /&.4 & MathTypepTimes New Roman-_989715695F!!Ole PIC LMETA H 2 LI~ 2  E 2 `(kV Times New Roman- 2 ap 2  f>Symbol- 2 = 2 x# 2  2 x 2  = 2  2 O# 2 /+ 2 # 2 O 2 V # 2 " 2 $= 2 )# 2 W.Times New Roman- 2 ;300 2 30 2 @7 2 H97 2 10 2 |0 2 220 2 90 2 300 2 !30 2 %7 2 &19 2 +46 2 ,27 Times New RomanSy- 2 3pTimes New Roman- 2 .` 2 (~ 2 )(~~ 2 #)~ 2 &.` 2 ,.` & "System- ,,%20  FMicrosoft Equation 3.0 DS Equation Equation.39q I a =300 "30A!E f =7.9CompObjfObjInfoEquation Native +_989715713F ! !710 3  "0+(20 "90)(300 "30)=7.19 "46.27kVL{{hh{{nJ  .1  @@& &Ole PIC LMETA CompObjf   !"#$&+-./01249;<=>?@ABCEHKMNOPQRSTUVWXY[^acdefghjoqrstuvwxyz{|}~ MathTypepTimes New Roman- 2 `LE Times New Roman- 2 wf> & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native ?_989715717_6F ! !Ole  #p- |E f |L4@4   @ .  & Times-!E Times-!f PIC  LMETA  HCompObjfObjInfoTimes-!cos PSymbol-!d PSymbol-!> +Times-!E 5Times-!t < & ' FMicrosoft Equation 3.0 DS Equation Equation.39qQ( |E f |cos>|V t |L{{hh{{nJ  .1  @@& &Equation Native m_989715722F !0!Ole PIC  LMETA CompObj %fObjInfo 'Equation Native (6 MathTypepTimes New Roman- 2 `LE Times New Roman- 2 wf> & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q E fL{{hh{{.W  .1  @@& & MathTypepTimes New Roman- 2 `LE Times New Roman r_989715726F0!0!Ole )PIC  *LMETA ,- 2 wf> & "System-"System- FMicrosoft Equation 3.0 DS Equation Equation.39qH$ V tCompObj3fObjInfo5Equation Native 66_989715730F0!@!Ole 7PIC 8LMETA :HCompObjDfL4@4   @ .  & Times-!E Times-!f Times-!cos PSymbol-!d PSymbol-!< +Times-!E 5Times-!t < & ' FMicrosoft Equation 3.0 DS Equation Equation.39q@H E f cosObjInfoFEquation Native G\_989715797 (F@!@!Ole I<V tL3 4@3 4V;   J .  & Times New Roman0-!V Times New RomanA-!t PIC JLMETA LhCompObjZfObjInfo \Symbole-!= Times New RomanA-!E Times New Roman0-!f !Symbole-!- (Times New Roman0-!jX 2Times New Roman P-!s =Times New Roman0-!I ATimes New Roman P-!a E & 'J FMicrosoft Equation 3.0 DS Equation Equation.39q\5 V t =E f "jX s I aEquation Native ]x_989715801#F@!@!Ole _PIC "%`LL4@4I  .1  &` & MathTypePTimes New Roman2- 2 `LI~ Times New Roman- 2 ap & "System-META bCompObj$&ifObjInfo'kEquation Native l6 FMicrosoft Equation 3.0 DS Equation Equation.39q I aL_989715805!/*F@!P!"Ole mPIC ),nLMETA pH   !> .  & Times New Roman0-!ITimes New Roman P-!aSymbole-!=Times New Roman P-!E Times New Roman0-!f "Symbole-!- )Times New Roman0-!V 2Times New Roman P-!t 8Times New Roman0-!jX$Times New Roman P-!s. "-;]' & 't 3 -1 roll sub neg  FMicrosoft Equation 3.0 DS EqCompObj+-fObjInfo.Equation Native _9897158101FP!"P!"uation Equation.39qe I a =E f "V t jX sL`Ole PIC 03LMETA (CompObj24f[`K  .1  @& & MathType0Symbol- 2 `#d & "System-F FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo5Equation Native )_989715813]8FP!"`H"Ole  &D' L; {<h; {J < .1  @`&  & MathTypepTimes New RomanSy- 2 `LE 2 `E TimePIC 7:LMETA PICT 9<jCompObjfs New Roman- 2 wf> 2 f>Symbol- 2 `= 2 ` #Times New Roman- 2 `_|E 2 `|ESymbol- 2 `,d & "System-jC CdPPNTTimes New Roman C,Times New Roman .+ E)EdPPNTTimes New Roman ( f)fdPPNTSymbol, Symbol ( =)dPPNTTimes New Roman( |)|dPPNTSymbol) ddPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo;=Equation Native ]_989715817@F`H"`H"Ole Afg E f =|E f | "L,;   A .  & Times New Roman P-!V PIC ?BLMETA hPICT ADjCompObjfTimes New Romanu-!t Symbole-!= Times New Romanu-!| Times New Roman P-!V Times New Romanu-!t Times New Roman P-!| &Symbole-! +Times New Roman P-!0 5Symbole-! ; & ' AjAdxpr  A"A currentpoint ",Times .+ V +t, Symbol ( =)|)V +t ( &|)) 0)?/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2080 div 480 3 -1 roll exch div scale currentpoint translate 64 58 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (V) -16 262 sh (V) 772 262 sh 224 ns (t) 180 358 sh (t) 968 358 sh 384 /Symbol f1 (=) 400 262 sh (\320) 1335 262 sh (\260) 1831 262 sh 384 /Times-Roman f1 (|) 610 262 sh (|) 1166 262 sh 384 /Times-Roman f1 (0) 1639 262 sh end MTsave restore dGMATH; | V t =|V t |0mt FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoCEEquation Native a_913508043HF`H"po"Ole E}T V t =|V t | "0L``K  .1  @& & MathType0Symbol- 2 `#PIC GJLMETA (PICT ILCompObjZd & "System-F  dPPNTSymbol , Symbol .+ ddPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2ObjInfoKMEquation Native <_989715825>UPFpo"po"Ole  F1WAP5WA d= 2 pL(6(6 d .1   1&01 & MathType "-<G<- <<< < )<*<0PIC ORLMETA CompObjQSfObjInfoTTimes New Roman- 2 LI 2 oE 2 oQ V 2 ZjX` 2 ogE 2 oGj` 2 o1E 2 onsinl 2 o`V 2 jX` 2 o!E 2 o'V 2 #jX` 2 o*j` 2 o+E 2 o.sinl 2 ,jX` Times New RomanU- 2 ap 2 f? 2 : t? 2 (sT 2 f? 2 \f? 2 It? 2 (sT 2 D"f? 2 t(t? 2 (q%sT 2 -f? 2 (S.sTSymbol- 2 = 2 o  2 oT- 2 o   2 o  2  = 2 o+ 2 oc- 2 S= 2 o&- 2 g)+Times New RomanU- 2 oO|< 2 o|< 2 o|< 2 o8|< 2 ocos 2 o|< 2 o|< 2 o |< 2 o"|< 2 oJ#cos 2 oc+|< 2 o-|<Symbol- 2 od 2 od 2 o*d 2 oU%d 2 o/dTimes New RomanU- 2 o 0 & "Systemn-    !"#$%&'()*+,-/0123456789:;<=>?@ABCDEFGHIJKLMORSTWYZ[\]^_`abcdegjklmprstuvwxyz{|}~ FMicrosoft Equation 3.0 DS Equation Equation.39qfh I a =|E f | ""V t  "0jX s =|E f |cos+j|E f |sin"V t jX s =|Equation Native _989715831WFpo""Ole  PIC VY LE f |cos"V t jX s +j|E f |sinjX sLA A?   $ .  & META PICT X[.CompObjNfObjInfoZ\PTimes New Roman P-!ITimes New Roman P-!aSymbole-!=Times New Roman P-!| Times New Roman P-!E Times New Roman P-!f'Times New Roman P-!| .!sin 3Symbole-!d BTimes New Roman P-!X,Times New Roman P-!s!3 "-Iy'Symbole-!-MTimes New Roman P-!jWTimes New Roman P-!| aTimes New Roman P-!E gTimes New Roman P-!foTimes New Roman P-!| v!cos {Symbole-!d Symbole-!- Times New Romanu-!V Times New Roman P-!tTimes New Romanu-!XTimes New Roman P-!s!a'Symbole-! \! \! \! ! !  & 'Monotype Corsiva$dxpr  $"$ currentpoint ",Times .+I +a, Symbol (=( |)E +f ( .|)sin)d(,X +s"0 (M-) j( a|)E +f ( v|)cos)d) -)V +t (X +s"aG ( \ * (\ (  * ( X/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5632 div 1152 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 738 531 moveto 1571 0 rlineto stroke 3043 531 moveto 2302 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (I) 9 630 sh (E) 928 340 sh (X) 1355 931 sh (j) 2743 630 sh (E) 3233 340 sh (V) 5021 340 sh (X) 4026 931 sh 224 ns (a) 142 726 sh (f) 1193 437 sh (s) 1594 1027 sh (f) 3498 437 sh (t) 5217 436 sh (s) 4265 1027 sh 384 /Symbol f1 (=) 404 630 sh (-) 2401 630 sh (-) 4736 340 sh (\351) 2883 355 sh (\353) 2883 1032 sh (\352) 2883 724 sh (\371) 5368 355 sh (\373) 5368 1032 sh (\372) 5368 724 sh 384 /Times-Roman f1 (|) 744 340 sh (|) 1419 340 sh (sin) 1578 340 sh (|) 3049 340 sh (|) 3724 340 sh (cos) 3893 340 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (d) 2056 340 sh (d) 4423 340 sh end MTsave restore dMATH I a =|E f |sindX s -j|E f |cosd-V t X s []if FMicrosoft Equation 3.0 DS Equation Equation.39q}} I a =|E f |sinX s "j|E f |cos"V t X s []L4t @Equation Native Q_989715852Nk_F""Ole UPIC ^aVLMETA XHCompObj`bffObjInfochEquation Native i4nW  .1   & & MathTypePTimes New RomanSy- 2 `LI~ 2 `LI~ 2 ` jk 2 ` I~ Times New Roman- 2 ap 2 ap 2 ! apSymbol- 2 `= 2 `-+Times New Roman- 2 `|E 2 `|E 2 `cos 2 ` |E 2 ` |E 2 `& sinkSymbol- 2 `q 2 ` q & "System- .J` FMicrosoft Equation 3.0 DS Equation Equation.39q}* I a =|I a |cos i +j|I a |sin i =|I a |cos"j|I a sin|L4t @_989715903fF""Ole nPIC ehoLMETA qH4nW  .1   & & MathTypePTimes New RomanSy- 2 `LI~ 2 `LI~ 2 ` jk 2 ` I~ Times New Roman- 2 ap 2 ap 2 ! apSymbol- 2 `= 2 `-+Times New Roman- 2 `|E 2 `|E 2 `cos 2 ` |E 2 ` |E 2 `& sinkSymbol- 2 `q 2 ` q & "System- .J` FMicrosoft Equation 3.0 DS EqCompObjgifObjInfojEquation Native T_989715907drmF""uation Equation.39q85 = v " iL4t @4nW  .Ole PIC loLMETA HCompObjnpf1   & & MathTypePTimes New RomanSy- 2 `LI~ 2 `LI~ 2 ` jk 2 ` I~ Times New Roman- 2 ap 2 ap 2 ! apSymbol- 2 `= 2 `-+Times New Roman- 2 `|E 2 `|E 2 `cos 2 ` |E 2 ` |E 2 `& sinkSymbol- 2 `q 2 ` q & "System- .J` FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoqEquation Native ?_989715910tF""Ole #  v =0L,;   A .  & Times New Roman P-!V Times New Romanu-!t PIC svLMETA hCompObjuwfObjInfoxSymbole-!= Times New Romanu-!| Times New Roman P-!V Times New Romanu-!t Times New Roman P-!| &Symbole-! +Times New Roman P-!0 5Symbole-! ; & ' A FMicrosoft Equation 3.0 DS Equation Equation.39qEKtM V t =|V t | "0Equation Native a_989715914 {F""Ole PIC z}LL X >  j .1   & 0 & MathType-=a=p Times New RomanSy- 2 LI~ 2 pE 2 ,X Times New Roman- 2 ap 2 f>META CompObj|~fObjInfoEquation Native  2 )L sWTimes New RomanSy- 2 cos 2 psinkSymbol- 2 q 2 ps dSymbol- 2 = & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qkb I a cos=E f sinX sL_989715922F""Ole PIC LMETA   .1  @&3 & MathType "-<< Times New Roman 0- 2 LI 2 sinl 2 mE 2 ms V 2 3 X Times New Roman- 2 ap 2 Ff? 2 ^ t? 2 )U sTSymbol- 2 Mq 2 m5 dSymbol- 2 = 2 mr -Times New Roman 0- 2 m'cos & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfoEquation Native _989715928F" #@zL{ I a sin=E f cos"V t X sLXT,X    .  & Ole PIC LMETA LPICT fTimes-!3 TimesNe-!V Times-!t & 'fdxpr  " currentpoint ",Times .+ 3)V +t/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 544 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (3) -16 261 sh 384 /Times-Italic f1 (V) 163 261 sh 224 ns (t) 359 357 sh end MTsave restore d'MATH 3V tt  FMicrosoft Equation 3.0 DS Equation Equation.39q 3V tL CompObjfObjInfoEquation Native :_989715932F # #Ole PIC LMETA CompObjf  .1  &1 & MathType "-< <Times New Roman8- 2 XP 2 V 2  I 2 o V 2 o(E 2 osinl 2 X Times New Roman 0- 2     !"#$&)*+,/12345679>@ABCDEGHIKPRSTUVWYZ[]bdefghijklmnopqrstuvwy|}outpp? 2 t? 2 ap 2  t? 2 Sf? 2 (sTSymbol- 2 = 2  =Times New Roman8- 2 3 2 o3 3 2 cosSymbol- 2  q 2 od & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q@z P out =3V t I a cos=3V t E f sinX sObjInfo Equation Native  _989715935F #2#Ole PIC LMETA CompObj%fObjInfo'L F .1  `& 5 & MathType "-< <<n<Times New Roman- 2 4Q 2 V 2 :I 2 {sinl 2 ok V 2 o E 2 X 2  V 2  X Times New Roman- 2 Aoutpp? 2 t? 2 ap 2 T t? 2 f? 2 (sT 2 t? 2 ()sTSymbol- 2  = 2  = 2 A-Times New Roman- 2 E3 2 o 3 2 3 Times New Roman- 2 d2pSymbol- 2 7 q 2 odTimes New Roman- 2 ocos & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native (_989715940F2#2#Ole -PIC .L(| Q out =3V t I a sin=3V t E f cosX s "3V t  2 X sL"XMETA 0CompObj8fObjInfo:Equation Native ;5"  .1  & & MathType0Symbol- 2 `qTimes New Romanc- 2 `ilSymbol- 2 `<Times New Romanc- 2 `0 & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q( i<0L4@4n   ._913508032F2#2#Ole <PIC =LMETA ?1  &@ & MathTypePTimes New RomanO- 2 `XP Times New Roman - 2 outpp> & "System-  dPPNTTimes New Roman ,Times New Roman .PICT FCompObjJZObjInfoLEquation Native M<+ PdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F2WA7WA P outL4@_913508031F2#Y#Ole NPIC OLMETA Q4VJ  .1  & & MathTypePTimes New Roman- 2 `4Q Times New Roman- 2 Aoutpp> & "System-v jg5F tF~PICT XCompObj\ZObjInfo^Equation Native _< dPPNTTimes New Roman ,Times New Roman .+ QdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2 F3WA@7WA Q outF_989716285FY#Y#Ole `PIC aLMETA cL4@4    .  & PSymbol-!d PSymbol-!= Times-!25 !. !!34 $PSymbol-! 0Times-!, 5Times-!V 9Times-!t ?PSymbol-!= FTimes-!7 P!. V!97 YTimes-!kV eTimes-!, s!| vTimes-!E |Times-!f Times-!| PSymbol-!= Times-!12 !. !14 Times-!kV & '38CompObjxfObjInfozEquation Native {_989716271FY## FMicrosoft Equation 3.0 DS Equation Equation.39q5 =25.34,V t =7.97kV,|E f |=12.14kVL#Ole ~PIC LMETA CompObjf#H A .1   & & MathType-==kSymbolh- 2 /x 2 = 2   2  2  2 =Times New Romans- 2 -P Times New Roman- 2 outpp>Times New Romans- 2  3 2 B7 2 J97 2  10 2 >12 2 14 2 10 2 25 2 F34 2 20 2 6 2 21 Times New Roman- 2 3p 2 U3pTimes New Romans- 2 (~ 2 .` 2 N )(~~ 2 .` 2 )~ 2 sink 2 .` 2 .` & "System- Style: Math Size: Full Zoom: FMicrosoft Equation 3.0 DS Equation Equation.39q !P outObjInfoEquation Native _989716274F##Ole  =3(7.9710 3 )(12.1410 3 )sin25.3420=6.21MWL.|.FX  .PIC LMETA CompObjfObjInfo1   `*& * & MathType-=&==P=&Symboli- 2 /x 2 = 2 H  2  2 ! 2 #- 2 r! 2 v&=Times New Roman- 2  Q Times New Roman- 2 outpp>Times New Roman- 2 :3 2 r7 2 z97 2 P 10 2 n12 2 14 2 10 2 25 2 34 2 <20 2 d3 2 7 2 97 2 z"10 2  20 2 '3 2 (59 Times New Roman- 2 3p 2 3p 2 $3p 2 I%2pTimes New Roman- 2 (~ 2 ,.` 2 ~ )(~~ 2 .` 2 ")~ 2 cos 2 T.` 2 (~ 2 V.` 2 $)~ 2 R(.` & "System- 2 :3 2 r7 2  FMicrosoft Equation 3.0 DS Equation Equation.39qII  !Q out =3(7.9710 3 )(12.1410 3 )cos25.3420"3(7.9710 3 ) 2 20=3.59MVAREquation Native e_989716303F##Ole PIC LL4@4    .  & PSymbol-!d PSymbol-!= Times-!46 !. "!27 %PSymbol-! META CompObjfObjInfoEquation Native 1Times-!, 5Times-!V 9Times-!t ?PSymbol-!= FTimes-!7 P!. 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@ A B C D E F G H I J L O P S U V W X Y Z \ ] ^ ` e g h i j k l m n o p q r s t u v w x y { ~  s New Roman- 2 mechbbp 2 outpp>Symbol- 2 `~> & "System-\,C,C(3C(3C8 8dPPNTTimes New Roman 8,Times New Roman .+ P)$PdPPNTTimes New Roman ( mech)#outdPPNTSymbol, Symbol ( >dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qD| P mech >P outObjInfo?A Equation Native  `_989716537DFp$%Ole  PIC CF LMETA  PICT EH CompObj fL4L@4.P  .1  & & MathTypePTimes New Roman- 2 `XP 2 `P Times New Roman- 2 mechbbp 2 ioutpp>Symbol-  2 `k- & "System-\,C,C(3C(3C7 7dPPNTTimes New Roman 7,Times New Roman .+ P)#PdPPNTTimes New Roman ( mech)"outdPPNTSymbol, Symbol ( -dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qD|l P mech "P outLObjInfoGI" Equation Native # `_989716542BRLF%%Ole % PIC KN& LMETA ( LPICT MP6 CompObjK f   !A .  & Times-!PTimes-!maxPSymbol-!=Times-!3 #Times-!V (Times-!t .Times-!E 2Times-!f :Times-!X+Times-!s3 "->"Z' & 'f !Adxpr  !A"!A currentpoint ",Times .+P +max, Symbol (=( #3)V +t ( 2E +f (+X +s""/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2080 div 1056 3 -1 roll exch div scale currentpoint translate 64 57 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1048 452 moveto 914 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 6 551 sh (V) 1243 261 sh (E) 1541 261 sh (X) 1337 852 sh 224 ns (t) 1439 357 sh (f) 1806 358 sh (s) 1576 948 sh 224 /Times-Roman f1 (max) 178 647 sh 384 /Symbol f1 (=) 714 551 sh 384 /Times-Roman f1 (3) 1064 261 sh end MTsave restore diMATH] ) P max =3V t E f X s23 FMicrosoft Equation 3.0 DS Equation Equation.39qi P max =3V t E f X sObjInfoOQM Equation Native N _989716546TF%.%Ole Q L{{hh{{61  .1  @@& & MathTypepTimes New Roman- 2 `LE Times New RomanPIC SVR LMETA T PICT UX[ CompObj_ f- 2 wf> & "System-KERNELSYSTEMO dPPNTTimes New Roman ,Times New Roman .+ EdPPNTTimes New Roman + fdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q| E fL"X" c   .  & ObjInfoWYa Equation Native b 6_989716618*o\F.%.%Ole c PIC [^d LMETA f CompObj]_z fObjInfo`| Timesst-!PTimes-!maxPSymbol-!=Times-!3 #!( (!7 -!. 3!97 6PSymbol-! DTimes-!10 LTimes-!3XTimes-!)( ]!12 d!. p!14 sPSymbol-! Times-!10 Times-!3Times-!) !20[ "-"'PSymbol-!=Times-!14!.!51 & '4) FMicrosoft Equation 3.0 DS Equation Equation.39q5 P max =3(7.9710 3 )(12.1410 3 )20Equation Native } _989716625cF.%U%Ole  PIC be L =14.51MWL["`X[" c   .  & Times-!PTimes-!maxMETA  CompObjdf fObjInfog Equation Native  PSymbol-!=Times-!3 #!( (!7 -!. 3!97 6PSymbol-! DTimes-!10 LTimes-!3XTimes-!)( ]!7 e!. k!19 nPSymbol-! }Times-!10 Times-!3Times-!) !20X "-"'PSymbol-!=Times-!8!.!6 & '39 FMicrosoft Equation 3.0 DS Equation Equation.39q$- P max =3(7.9710 3 )(7.1910 3 )20=8.6MW_989716681avjFU%U%Ole  PIC il LMETA  hLp 4|@p 4=  .1  ` &  & MathTypePTimes New RomanSy- 2 `LI~ Times New Roman- 2 apSymbol- 2 `= 2 `x# 2 `- 2 ` Times New Roman- 2 `;300 2 `30 & "System-   FMicrosoft Equation 3.0 DS Equation Equation.39q?S I a =30CompObjkm fObjInfon Equation Native  [_989716691hqF|%|%0 ""30L{ h{<  .1  @& & MathTypepTimes New Roman- 2 `LE 2 `kV 2 `#Q Ole  PIC ps LMETA  (CompObjrt fTimes New Roman~- 2 wf> 2 0outpp>Symbol- 2 `= 2 `# 2 `  2 `=Times New Roman- 2 `12 2 `]14 2 ` 25 2 `^ 34 2 `43 2 `59 2 `'.` 2 ` .` 2 ` ,` 2 `.` & "System-s~ FMicrosoft Equation 3.0 DS Equation Equation.39qR3 E f =12.14 "25.34kV,Q out =3.59MVARObjInfou Equation Native  _989716688xF|%%Ole  PIC wz LMETA  HCompObjy{ fObjInfo| L 4@ 4<  .1  & & MathTypePTimes New Roman- 2 `LI~ Times New Roman- 2 apSymbol- 2 `= 2 `x# 2 `Times New Roman- 2 `;300 2 `30 & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q;k I a =30Equation Native  W_989716723F%%Ole  PIC ~ L0 "30L&{ h&{n<  .1  @& & MathTypepTimes New Roman- 2 `LE 2 `CkV 2 `| Q META  HCompObj fObjInfo Equation Native  Times New Roman- 2 wf> 2 outpp>Symbol- 2 `= 2 `# 2 `6  2 `S= 2 `-Times New Romant- 2 `7 2 `19 2 ` 46 2 ` 27 2 `h3 2 `L59 2 `{.` 2 `m .` 2 ` ,` 2 ` .` & "System- & MathTy FMicrosoft Equation 3.0 DS Equation Equation.39q E f =7.19 "46.27kV,Q out ="3.59MVAR_989716742}F%%Ole  PIC  LMETA  L @,  K  P .  & Times-!V TimesNe-!t PSymbol-!= Times-!7 !. !97 !Times-!kV -PSymbol-! :Times-!0 CPSymbol-! I & ' (aPdxpr  P"P currentpoint ",Times .+ V +PICT  aCompObj fObjInfo Equation Native  _                   ! " $ ) + , - . / 0 2 3 4 6 ; = > ? @ B G I J K L M N P Q R T Y [ \ ] ^ _ ` b g i j k l m o t v w x y z { | } ~  t, Symbol ( =) 7).)97) kV) ) 0)B/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2560 div 480 3 -1 roll exch div scale currentpoint translate 64 57 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (V) -16 263 sh (kV) 1403 263 sh 224 ns (t) 180 359 sh 384 /Symbol f1 (=) 400 263 sh (\320) 1807 263 sh (\260) 2303 263 sh 384 /Times-Roman f1 (7) 727 263 sh (97) 1015 263 sh (0) 2111 263 sh 384 /Times-Roman f1 (.) 919 263 sh end MTsave restore dCMATH7 0 V t =7.97kV0in FMicrosoft Equation 3.0 DS Equation Equation.39qC V t =7.97 "0kVL{{hh_989716752F%%Ole  PIC  LMETA  {{N<  .1  @@& & MathTypepTimes New Roman- 2 `LE Times New Roman- 2 wf> & "System- dPPNTTimesPICT  CompObj# fObjInfo% Equation Native & 6 New Roman ,Times New Roman .+ EdPPNTTimes New Roman + fdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q E f_989716756,F%%Ole ' PIC ( LMETA * L4@4&<  .1  & & MathTypePTimes New Roman- 2 `4Q Times New Roman- 2 Aoutpp> & "System-  dPPNTTimes New Roman ,Times New Roman .+ QdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qPICT 1 CompObj5 fObjInfo7 Equation Native 8 >" Q outL4@4     .  & PSymbol-!f TimesV-!f  & _989716760F%%Ole 9 PIC : LMETA < ' FMicrosoft Equation 3.0 DS Equation Equation.39q  fL4@CompObjA fObjInfoC Equation Native D 6_913507989F&&Ole E PIC F LMETA H PICT O 4<  .1  &@ & MathTypePTimes New Roman- 2 `XP Times New Roman0- 2 outpp> & "System-P  dPPNTTimes New Roman ,Times New Roman .+ PdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2e * '7L+7 P outCompObjS ZObjInfoU Equation Native V <_989717012F&@&Ole W PIC X LMETA Z CompObja fL{4h@{4D  .1  @& & MathTypePSymbol5- 2 `!w Times New Romany- 2 fm & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q  mL4@ObjInfoc Equation Native d 6_989717016F@&@&Ole e PIC f LMETA h HCompObjn fObjInfop 4^  .1  &@ & MathTypePTimes New RomanD- 2 `|fk & "System-ph_5_5 FMicrosoft Equation 3.0 DS Equation Equation.39q p fL ,  j  M .  & PSymbol-!w Equation Native q )_989717007F@&g&Ole r PIC s LMETA u CompObj fObjInfo Equation Native  [ Times-!m PSymbol-!= Times-!2 PSymbol-!p $Times-!f *Times-!( /!2 4!/ ;Times-!p BTimes-!) H & ' FMicrosoft Equation 3.0 DS Equation Equation.39q?5  m =2f(2/p)L_913507985Fg&g&Ole  PIC  LMETA  HF  .1  `&  & MathTypePTimes New RomanD- 2 dp & "System-  dPPNTTimesPICT  CompObj ZObjInfo Equation Native  < New Roman ,Times New Roman .+pdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2e *+727 p#7/7L4`@_989717022Fg& &Ole  PIC  LMETA  4^  .1  & & MathTypePTimes New Roman- 2 `XP 2 `P Times New Roman- 2 mechbbp 2 outpp>Symbol- 2 `~> & "System- .1 FMicrosoft Equation 3.0 DS Equation Equation.39qDh\T] P mech >P outCompObj fObjInfo Equation Native  `_989717027F & &Ole  PIC  LMETA  PICT  L4@4D  .1  &@ & MathTypePTimes New Roman- 2 `XP Times New Roman- 2 outpp> & "System-wwwwwwwwww dPPNTTimes New Roman ,Times New Roman .+ PdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj fObjInfo Equation Native  >_989717032F &0&"tw P outL4,@4vD  .1  & & MathTypePTimes New Roman- 2 `XP Times New RomanOle  PIC  LMETA  PICT  - 2 &L} & "System- dPPNTTimes New Roman ,Times New Roman .+ PdPPNTTimes New Roman +LdPPNT"System FMicrosoft Equation 3.0 DS EqCompObj fObjInfo Equation Native  6_989717036F0&@&uation Equation.39q P LL4@4D  .1  &@ &Ole  PIC  LMETA  PICT  MathTypePTimes New Roman- 2 `XP Times New Roman- 2 outpp> & "System-wwwwwwwwww dPPNTTimes New Roman ,Times New Roman .+ PdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q"t\a P outL4,@CompObj fObjInfo Equation Native  >_989717041F@&@&Ole  PIC  LMETA  PICT  4vD  .1  & & MathTypePTimes New Roman- 2 `XP Times New Roman- 2 &L} & "System- dPPNTTimes New Roman ,Times New Roman .+ PdPPNTTimes New Roman +LdPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39q4 P LCompObj fObjInfo Equation Native  6_989717045F@&P'Ole  PIC  LMETA  PICT  L0{P h0{D  .1  @&@ & MathTypepSymbol5- 2 `!w 2 ` p Times New RomanD- 2 fm 2 KrefWb>Times New Roman- 2 `                    " % ' ( ) * + , - . / 1 2 3 4 6 9 < > ? @ A B C D E F G H J K L M N P S V X Y Z [ \ ] _ ` a c h j k l m n o p r u x z { | } ~  fk 2 `< p 2 `L fk Times New RomanD- 2 ,8Times New Roman- 2 `(~ 2 `O /k 2 ` ),~`Symbol- 2 `= 2 ` =Times New Roman- 2 `R2 2 `;2 2 `60 & "System-u`u`u` dPPNTSymbol , Symbol .+ w)/pdPPNTTimes New Roman,Times New Roman ( m)refdPPNTTimes New Roman ( 7f)p)fdPPNTTimes New Roman (,dPPNTTimes New Roman ( >() /)),dPPNTSymbol( !=)K=dPPNTTimes New Roman( +2)2)460dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qctܶ  m,ref =2f(2/p),f=60LV4@CompObj fObjInfo Equation Native  _989717071FP'P'Ole  PIC  LMETA  PICT  V4D  .1  & & MathTypePTimes New Roman- 2 `XP 2 `.P Times New Roman+- 2 outpp> 2 L}Symbol- 2 `> & "System- 2 `>. .dPPNTTimes New Roman .,Times New Roman .+ P)PdPPNTTimes New Roman ( out)LdPPNTSymbol, Symbol ( >dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj fObjInfo Equation Native ! T_989717079FP'`*'8P LL!{h!{ND  .1  @`&  &Ole # PIC $ LMETA & HPICT 0 @ MathTypepSymbol5- 2 `!w 2 `w Times New RomanD- 2 fm 2 m 2 refWb>Symbol- 2 `> Times New RomanD- 2 ,8 & "System-@; ;dPPNTSymbol ;, Symbol .+ w)wdPPNTTimes New Roman,Times New Roman ( m)m)refdPPNTSymbol ( >dPPNTTimes New Roman +,dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj5 fObjInfo7 Equation Native 8 \_989717083 F`*'pQ'@   m > m,refL {lh {D L .1  @ &  & MathTypepSymbol5- 2 `>Ole : PIC  ; LMETA = PICT   I pDSymbol- 2 `(w 2 `w 2 ` w Times New Roman- 2 mm 2 m 2 refWb> 2  mSymbol- 2 `= 2 `- Times New Roman- 2 ,8 & "System-p_ _dPPNTSymbol _, Symbol .+ DdPPNTSymbol)w)w)(wdPPNTTimes New Roman,Times New Roman (m)m)ref) mdPPNTSymbol ( =)(-dPPNTTimes New Roman (6,dPPNT"System FMicrosoft Equation 3.0 DS EqCompObjO fObjInfo Q Equation Native R v_913507974FpQ'pQ'uation Equation.39qZ   m = m,ref " mL4@4D  .Ole T PIC U LMETA W PICT ^    i UV !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTWXYZ\[^]`_badcefghjklmnopqrtsvuywxz{|}~1  &@ & MathTypePTimes New Roman- 2 `XP Times New Roman- 2 outpp> & "System-wwwwwwwwww dPPNTTimes New Roman ,Times New Roman .+ PdPPNTTimes New Roman +outdPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2e *.727 P outLV4@CompObjb ZObjInfod Equation Native e <_989717095FpQ'x'Ole f PIC g LMETA i CompObjq fV4D  .1  & & MathTypePTimes New Roman- 2 `XP 2 `.P Times New Roman- 2 outpp> 2 L}Symbol- 2 `< & "System-F  FMicrosoft Equation 3.0 DS Equation Equation.39q8 P out <P LL!{hObjInfos Equation Native t T_989717097% Fx'x'Ole v PIC "w LMETA y HCompObj!# fObjInfo$ !{C  .1  @`&  & MathTypepSymbol5- 2 `!w 2 `w Times New Roman- 2 fm 2 m 2 refWb>Symbol- 2 `< Times New Roman - 2 ,8 & "System-"System- FMicrosoft Equation 3.0 DS Equation Equation.39q@sT]  m < m,refEquation Native  \_989717104'Fx''Ole  PIC &) LL {lh {D L .1  @ &  & MathTypepSymbol5- 2 `>DSymbol- 2 `(w 2 `w 2 ` w META  CompObj(* fObjInfo+ Equation Native  vTimes New Roman- 2 mm 2 m 2 refWb> 2  mSymbol- 2 `= 2 `- Times New Roman- 2 ,8 & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qZ  m = m,ref " mL4@4D  ._989717109n.F''Ole  PIC -0 LMETA  1  &@ & MathTypePTimes New Roman- 2 `XP Times New Roman- 2 outpp> & "System-wwwwwwwwww FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj/1 fObjInfo2 Equation Native  >_989717147;C5F''"5  P outL4vC  .1   &` & MathType Symbol4- 2 @=eKF&&\i A`lt?1q\'Dd ,B m S Ak? l2<343QbaH.my`!e<343QbaH.N`P3xcdd``Vgd``baV d,FYzP1C&,7\! 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LMETA  PICT >A 1  &` & MathType Symbol4- 2 @=Times New Romanm- 2 @0 2 @ 02 2 @.` & "System-'@+@@3!@+@]@]=]   dPPNTSymbol , Symbol .+ dPPNTTimes New Roman,Times New Roman)0)02( .dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qxw 0.02L{4h@CompObj fObjInfo@B Equation Native  9_989717196EF'(Ole  PIC DG LMETA  CompObjFH f{4NC  .1  @& & MathTypePSymbol4- 2 `!w Times New Roman- 2 fm & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q5  mL) {Th) {6C 9 .ObjInfoI Equation Native  6_9897172033XLF((Ole  PIC KN LMETA  CompObjMO fObjInfoP 1  @ &  & MathTypepSymbol4- 2 `>D 2 `)DSymbol- 2 `(w Times New Roman+- 2 pupp 2 puppTimes New Roman - 2 `?R 2 `PSymbol- 2 `= 2 `H- & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qH\  pu ="RP puEquation Native  d_989717208SF(;(Ole  PIC RU LL&C  .1  &@` & MathType Times New Roman- 2 @LR & "System-$''$  & &META  HCompObjTV fObjInfoW Equation Native  ) FMicrosoft Equation 3.0 DS Equation Equation.39q  RL"{Xh"{  ._989717212QvZF;(;(Ole  PIC Y\ LMETA                    ! " # $ & ' ( ) + 0 2 3 4 5 6 7 8 9 : ; < = ? @ A B C D F I J M O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b d g h i l n o p q r s t u v w x y z { | } ~ 1  @& & MathTypepSymbol4- 2 `>DSymbol- 2 `(w Times New Roman- 2 pupp & "System- FMicrosoft Equation 3.0 DS EqCompObj[] fObjInfo^ Equation Native  >_989717217.aF;(b(uation Equation.39q"UtV  puLq{hq{C  .1  @ & &Ole  PIC `c LMETA  CompObjbd f MathTypepSymbol4- 2 `>DTimes New Roman- 2 `(P Times New Roman"- 2 pupp & "System-X/T FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoe Equation Native  >_913507962hFb(b(Ole  "n o P puLpB  .1  &@` & MathType Times New Roman-PIC gj LMETA  PICT il% CompObj* Z 2 @LRSymbol- 2 @=Times New Roman- 2 @0 2 @05 2 @.` & "System-E F*F , , dPPNTTimes New Roman ,,Times New Roman .+ RdPPNTSymbol, Symbol) =dPPNTTimes New Roman) 0)05( .dPPNT"System FMicrosoft Equation 2.0 DS Equation Equation.2e *1757 R=0.05LE lObjInfokm, Equation Native - <_989718581JpFb((Ole . PIC or/ LMETA 1 (PICT qt> CompObjE fEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU  "*dPPNTSymbol, Symbol .+DdPPNTSymbol)wdPPNTTimes New Roman,Times New Roman + pudPPNTSymbol ( =( +-+=) -dPPNTTimes New Roman( 20)01(260(Z0)000167( 7.+(.dPPNT"System FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfosuG Equation Native H _989718546_xF((Ole K tzt}  pu ="0.0160="0.000167LRR@ |[ .1  @&t( &PIC wzL LMETA N (CompObjy{c fObjInfo|e  MathType- f Symbol\- 2 `/x 2 `;= 2 k- 2 ` = 2 `z= 2 `D 2 kDTimes New Roman- 2 `P 2 CR Times New Roman- 2 pupp 2 A 2 H A Times New Roman- 2 ,8Times New Roman- 2 k( .` 2 .` 2 `b.`Symbol- 2 kp wTimes New Roman- 2 kz 02 kv 000167 2 0 2 05 2 `0 2 `0033[&MathTypeUU DP pu,A =-DwR A =0.0001670.05=0.0033 & "System-kg F FMicrosoft Equation 3.0 DS Equation Equation.39q8df !P pu,A ="R A =0Equation Native f _989718549F((Ole j PIC ~k LE.0001670.05=0.0033LRRfB ! .1  @& & MathType-w META m hCompObj fObjInfo Equation Native  \ Symbola- 2 `/x 2 `1= 2 k- 2 ` = 2 `p= 2 `D 2 k|DTimes New Roman- 2 `P 2 >R Times New Roman- 2 pupp 2  B 2 5 B Times New Roman- 2 ,8Times New Roman- 2 k .` 2 .` 2 `X.`Symbol- 2 kf wTimes New Roman- 2 kp 02 kl 000167 2  0 2 05 2 `0 2 `0033 & "System-F FMicrosoft Equation 3.0 DS Eq uation Equation.39q8 !P pu,B ="R B =0.0001670.05=0.0033Lw4x @_989718551}F((Ole  PIC  LMETA  (w4O { .1  & & MathTypePSymbol4- 2 `>DTimes New Roman - 2 `(P Times New Roman- 2 ASymbol- 2 `= 2 ` =Times New Roman- 2 `Y(~ 2 `.` 2 `)(~~ 2 ` )~ 2 `.` 2 `0 2 `0033 2 ` 100 2 `0 2 `33 & "System-System- FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj fObjInfo Equation Native  _989718554F( (s5 P A =(0.0033)(100)=0.33MWL4 @4FP { .Ole  PIC  LMETA  (CompObj f1  & & MathTypePSymbol4- 2 `>DTimes New Roman- 2 `(P Times New Roman- 2 BSymbol- 2 `= 2 ` =Times New Roman- 2 `O(~ 2 `.` 2 `)(~~ 2 ` )~ 2 `.` 2 `0 2 `0033 2 ` 200 2 `+0 2 `'66 & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qs- P B =(ObjInfo Equation Native  _994916908)F ( (Ole  0.0033)(200)=0.66MW FMicrosoft Equation 3.0 DS Equation Equation.39q$x~IvI 0.9/CompObj fObjInfo Equation Native  @_989615047F (0&)Ole  CompObj fObjInfo Equation Native  K FMicrosoft Equation 3.0 DS Equation Equation.39q/5l X S =2/ FMicrosoft Equation 3.0 DS Equation Equation.39q_989448201F0&)0&)Ole  CompObj fObjInfo H5 I aLE lEO  .1  & & MathType-LEquation Native  6_994913485XF0&)@M)Ole  PIC  LMETA  (CompObj fObjInfo Equation Native  @Symbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39q$p~II 4.5 "0LE l_994913507F@M)@M)Ole  PIC  LMETA  (EO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj fObjInfo Equation Native  <_994913577F@M)Pt) oII 5 "30LE lEO  .1  & & MathType-LOle  PIC  LMETA  (CompObj fSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39q8p~II I a =50 "20ObjInfo Equation Native  T_994913668FPt)`)Ole  PIC  LMETA  (CompObj fObjInfo                    ! 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Equation.39qTPIoI E f =132.98 "10.23LE lOle = PIC > LMETA @ (CompObjM fEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoO Equation Native P D_994913866F))Ole R (IoI X s =2LE lEO  .1  & & MathType-LPIC S LMETA U (CompObjb fObjInfod Symbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qIPzI E fLE lEquation Native e 8_994913879F)*Ole f PIC g LEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `META i (CompObjv fObjInfox Equation Native y 8= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qIPzI E fLE lEO  .1  & & MathType-L_994915116F*7*Ole z PIC { LMETA } ( Symbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qT,vII E f =132.98 "10.23CompObj fObjInfo Equation Native  p_994917186)F7*7*Ole  PIC  LMETA  (CompObj fLE lEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39q(IoI X s =2LE lEO  .ObjInfo Equation Native  D_994915239F7*^*Ole  PIC  LMETA  (CompObj fObjInfo 1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qtII E fEquation Native  8_994915352 F^**Ole  PIC  LLE lEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w META  (CompObj fObjInfo Equation Native  Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39q\IlI X t =0.06,R t =0.01,X x =0.10,X g =0.95_1054983007F**Ole  PIC  LMETA  (LE lEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUUCompObj fObjInfo Equation Native  (_994915586F*Ь* FMicrosoft Equation 3.0 DS Equation Equation.39q| yIDI V 1 =1.00,P L =0.80,Q L =0.20,E g =1.514 "30.45Ole  PIC  LMETA  (CompObj fLE lEO  .1  & & MathType-LSymbola- 2 `>DSymbol- 2 `(w Times New Roman- 2 puppSymbol- 2 `= 2 kh- 2 ` = 2 `] -Times New Roman- 2 k;0 2 k701 2 ?60 2 `0 02 `, 000167 2 k.` 2 ` .` & "System-UUUU FMicrosoft Equation 3.0 DS Equation Equation.39qϨLrIDmI V 3 =0.97 ""4.77,I a =0.87 ""21.7ObjInfo  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