Introduction to Electrical Systems Course Code: EE 111 Course Code: - PowerPoint PPT Presentation

Introduction to Electrical Systems Course Code: EE 111 Course Code: EE 111 Department: Electrical Engineering Department: Electrical Engineering Instructor’s Name: B G Fernandes Instructor s Name: B.G. Fernandes E ‐ mail id: bgf @ee iitb ac in E ‐ mail id: bgf @ee.iitb.ac.in EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 1/12 31, 2009

Sub ‐ Topic: • Measurement of Power EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 2/12 31, 2009

REVIEW • Balanced system: 3 Voltage sources have same magnitude & ‘f’, but phase displaced by 120 o • Balanced load: |Z| & θ are same in all 3 phases 3 • In Y connected system, |V L | = |V ph | & V by 30 o leads V y Ph L L 3 • In Δ connected system, |V L | = |V ph | & |I L | = |I ph | & p p by 30 o lags I I L Ph EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 3/12 31, 2009

• Phase sequence & reference vector should be known to write ‘V’ equations for all 3 phases it ‘V’ ti f ll 3 h 3 Ø, 440V, 50Hz ⇒ 440 V is L ‐ L Voltage (R.M.S value) g ( ) • In 3 phase 4 wire system • In 3 ‐ phase 4 ‐ wire system, ( ) = + + I I I I N A B C EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 4/12 31, 2009

Power in 3 ‐Ф circuits: ⇒ Recall ‘p’ in 1 Ф circuits pulsates at 2f ⇒ Recall p in 1 Ф circuits pulsates at 2f ∴ 1 ‐Ф motors require special resilient mountings π π π π ⎛ ⎛ ⎞ ⎞ ⎛ ⎛ ⎞ ⎞ 2 2 4 4 = ω = ω − = ω − 2 sin 2 sin 2 sin Let , ⎜ ⎟ & ⎜ ⎟ v V t v V t v V t a b ⎝ 3 ⎠ c ⎝ 3 ⎠ π π ⎛ ⎛ ⎞ ⎞ ⎛ ⎛ ⎞ ⎞ 2 4 ( ( ) ) = ω θ − θ = ω − − θ θ = ω − − θ θ 2 sin 2 i , 2 sin 2 i , 2 sin 2 i and and ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ i i I I t t i i I I t t i i I I t t a b c ⎝ 3 ⎠ ⎝ 3 ⎠ ∴ Instantaneous power ( ) = = ⎡ θ − ω − θ ⎤ cos cos 2 p v i VI t ⎣ ⎦ a a a ( ( ) ) ⎡ ⎡ ⎤ ⎤ = = θ θ − ω − θ θ − 0 0 cos cos 2 2 240 240 p v i i VI VI t t ⎣ ⎦ b b b ( ( ) ) ⎡ ⎤ = = θ − ω − θ − 0 cos cos 2 480 p v i VI t ⎣ ⎣ ⎦ ⎦ c c c EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 5/12 31, 2009

∴ Total instantaneous 3 ‐Ф power = 3VI cos θ = 3V ph I ph cos θ 3V ph I ph cos θ θ = ∠ I = Average power ph V ph = Constant If system is ‘Y’ connected v = = ∴ ∴ = θ θ , , 3 3 cos cos L v I I P P V I V I ph ph ph ph L L 3 L L L L = = 3 If Load is delta connected V V I I , L L Ph Ph L L Ph Ph ∴ P = 3 cos θ W V I L L Independent of type of connection ∴ * Q = 3 Q sin θ VAr S = 3 VA V I V I L L L L L L L L EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 6/12 31, 2009

Measurement of Power: I I cos ∠ = I V ‘W’ ‘W’ reading di Flowing Flowing Applied V Applied How many wattmeters to use? How many wattmeters to use? Incase of 3 ‐ phase 4 wire system, if the load is balanced ⇒ One meter is sufficient Total power = W * 3 Total power W 3 If the load is unbalanced, ⇒ use 3 meters 3 Total power = W 1 +W 2 +W 3 EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 7/12 31, 2009

In case of 3 ‐ phase 3 wire load: Two wattmeter method: T tt t th d = = ∠ ∠ A I cos cos W W V V I I A 1 V AB A AB = + I I I A AB Ac ∠ ∠ = = α α I Let Let A A V AB α α θ θ + + θ θ cos cos I = I cos cos cos cos I I I I AB 1 A AC EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 8/12 31, 2009

∴ = α cos W V I 1 AB A = ∠ + θ V cos cos(60+ ) V I AB V I I AB AB AB AC AB + + θ θ cos(60+ ) cos(60 ) V I V I = Power in phase AB Power in phase AB L L AC AC = = ∠ ∠ I cos cos Similarly Similarly W W V I V I C C 2 V CB C CB = + I I I C CB CA = ∠ cos I W V I CB 2 CB CB V CB + ∠ cos I I V I CA CB CA V CB ∠ ∠ = − θ θ (60 (60 ) ) I CA V V CB EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes 9/12 31, 2009

( ) ( ) + θ + − θ cos 60 cos 60 V I V I L AC L AC = cos θ ⇒ Power in 3 rd phase V I L AC Observations: If load is balanced θ = ∠ I I ph h ⇒ cos θ = + 3 V I W W 2 1 V L L ph If load is unbalanced + = + + ≠ cos θ θ 3 3 W W W W P P P P P P V I V I 1 2 A B C L L Power in phase A EE 111: Introduction to Electrical Systems EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes B.G.Fernandes 10/12 31, 2009

= ∠ A cos I W V I 1 AB A V AB = + + θ θ V I cos(30 cos(30 ) ) V I L L = ∠ C cos I W V I 2 CB C V CB = − θ cos(30 ) V I L L If θ = 0 ⇒ Load is ‘R’, W 1 = W 2 If θ = π /3, one of the Wattmeter would read zero ⇒ If θ > π /3, read ‐ ve ( (interchange M & L) h & ) ⎛ ⎞ − W W θ = − 1 2 1 tan 3 ⎜ ⎜ ⎟ ⎟ + ⎝ ⎝ ⎠ ⎠ W W W W 1 2 EE 111: Introduction to Electrical Systems EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes B.G.Fernandes 11/12 31, 2009

Note: Phase sequence & lines in which they are connected should be known to determine whether connected should be known to determine whether θ is +ve or ‐ ve EE 111: Introduction to Electrical Systems EE 111: Introduction to Electrical Systems Mon, Aug Lecture 14 B.G.Fernandes B.G.Fernandes 12/12 31, 2009