Presentation on theme: "5. PERFORMANCE CHARATERISTICS OF IM"— Presentation transcript:
15. PERFORMANCE CHARATERISTICS OF IM The equivalent circuits derived in the preceding section can be used to predict the performance characteristics of the induction machine.The out put parameters of IM are speed and torque and their inter relation during starting ,steady state and braking are going to be seen.The important performance characteristics in the steady state are:- the efficiency- power factor- current- starting torque- maximum (or pull-out) torque and- so forth.
2Steady state operating characteristics of an IM can be shown graphically as the shaft load increases from zero to full load.These operating characteristics during starting, steady state, and braking are governed mainly by:-- rotor resistance,- air gap length, and- shape of stator and rotor slots
34.1. Determination of induced TORQUE-SPEED characteristics of IM. When TORQUE-SPEED or POWER-SLIP characteristics arerequired, applying Thevenin's theorem is convenient.Thevenin's theorem states that, “any linear circuit that can beseparated by two terminals from the rest of the system can bereplaced by a single voltage source in series with an equivalentimpedance”. i.e.ZfabFig EQUIVALENT CIRCUIT OF IM WITHOUT CORE LOSS.
4Fig.5.2. Thevenin`s equivalent circuit Applying Thevenin's theorem for equivalent circuit of IM shown in fig. 5.1, the circuit consisting of r1, x1, xm, and source voltage can be replaced by an equivalent voltage source Ve and equivalent impedance Ze = Re + jxe.ReXeVeFig Thevenin`s equivalent circuit
5Where,Ve – Voltage appearing across terminals a,b with rotor circuitdisconnected from points a & b.Ze – Impedance viewed from terminals a,b towards the voltagesource with the source voltage short circuited.For most IMs , under normal operating conditions, (X1+Xm) >> R1,and therefore R1 can be neglected.Thus,
6From the fig. 5.2, rotor current is:- We know that, per phase induced torque is:-Where, m – is the no. stator phases.
8Fig .5.3 Torque-speed characteristics NSNS1At low value of slips( TS)At large value of slip( T1/S)TmaxFig Torque-speed characteristicsTorqueTST
9. Fig. 5.4 Torque-slip curve of IM in different mode of operation. BrakingregiontorqueMot. regionGen. regionSmTFull load oper. point.TmaxFig Torque-slip curve of IM in different mode of operation.Tstar2NsNs- Ns- Tmaxspeed-100-50501001502002.01.51.00.5-0.5-1.0slip
10Depending on the value of slip, an IM can have the following operating regions. a) Motoring mode , 1 > S > the corresponding speed values are ZERO (s = 1.0) and synchronous speed (S = 0).b) Generating mode , S < 0 - the rotor speed is above synchronous speed.c) Breaking mode , S > 1 – This condition can be achieved by driving the rotor with a prime mover opposite to the direction of rotating magnetic field.( eg. plugging action)
114.2. Determining maximum internal torque of IM Maximum torque is referred as Stalling torque; Pull out torque or Break down torque.Maximum internal torque can be obtained by using the maximum power transfer theorem of a circuit theory.i.e. power transfer becomes max. when the load impedance is equal to the source impedance. and Torque in IM is max. when power delivered to load r2/s is max.Fig. 5.5.(fig.3.5b) Exact equivalent circuit diagram of IM.
12Thus, Max. slip at which maximum torque occurs is As per the exact equivalent circuit diagram of IM, max. power delivered to r2/s is attained when load resistance r2/s(referred rotor variable resistance) becomes equal to the impedance of the voltage source. i.e. from fig. 5.2 it can be seen that,Thus, Max. slip at which maximum torque occurs isWe know that,
14directly proportional to rotor Resistance r2. These equations show that,a) Slip at which maximum torque occurs isdirectly proportional to rotor Resistance r2.b) Maximum torque is independent of r2.This means that, if rotor resistance r2 is increased by inserting external resistance in the rotor circuit (in case of WRIM), the max. internal torque is Unaffected; but slip at which it occurs is affected proportionally.
15From the equation of Tem, it can be seen that, a) Tem is directly proportional to the square of applied stator voltage.( Kt ∞ V1)b) Tem is reduced by increasing stator resistance r1 (i.e.Re)c) Tem is reduced by an increase in stator and rotor leakage reactance (x1 of stator and x2 of) rotorThus, to obtain higher maximum torque, the air –gap between rotor and stator must be kept as small as possible in which mutual flux will be maximum and leakage reactance could be minimum.
16Typical TORQUE-SPEED curves for an IM with variable rotor circuit resistance and the effect of rotor resistance on the stator current are shown belowr23r22r21TmaxFig.5.6. IM Torque-speed curve with different values of r2r24>r23>r22>r21r24Slipsm3sm2sm1
17Fig.5.7 Effect of rotor resistance r2 on stator S1Fig.5.7 Effect of rotor resistance r2 on statorcurrent-slip charact.Torquer22r24 > r23 > r22 > r21r23r24Stator current , p.u.Stator curr.Tstar
184.3. Starting torque of IM - Tst, We know that, the Induced motor torque is:AT starting, slip S = 1.00, thus torque at starting is:-
19Induced motor torque Te in terms of max. torque Tem.
22Summary of performance characteristics. SpeedTorqueStator currentPfEfficiencySpeed, Torque,Stator current, Pf,Efficiency1.0KEYSpeedTorqueStator currentPf0.2EfficiencyPout1.0Fig Operating characteristics of IM.
23stator slots Shape effect on operating charac. For a given slot area, slot shape can be:-- More deep, less width- Less depth, more widthSlot leakage flux is directly proportional to slot depth.IMs with deeper slots have more leakage reactance, and more leakage reactance results in less Tstar, less Tem and less SmT (look corresponding formula)Slots can also be- open- Semi closed- closed.Open slots have less leakage reactance than semi-closed slots and semi-closed slots have less leakage reactance than closed slots.
24Air-gap Effect on operating charac. If the air-gap length is increased, air gap flux which must be constant requires more magnetisation current.This reduces cosθ0,and cosθrat . In order an IM to have better power factor, the air-gap length must be as small as is mechanically possible.- For open type slots, the air-gap is larger, so that more Im isrequired which results poor operating power factor. However,they have less leakage reactance, therefore better Test and Tem.- For semi closed slots, the air-gap length is smaller, thus smallIm is required and cosθrat is better. But they have moreleakage reactance ,therefore reduced Test and Tem.Thus, during designing an IM, a compromise is made between the operating power factor and Test,Tem to obtain optimum operating characteristics for a given working condition..