In an unbalanced, three-phase, star-delta system has a frequency of 50 Hz, and CBA phase rotation.The phase impedances
of the load are as follows:
Zab =29.41∠ 54.69°Ω ; Zbc=25.61∠-38.66° Ω ; Zca =17.8 ∠ 51.84° Ω
The emf of the source is represented by:ec(t)=221.831 𝐬𝐢𝐧 (𝛚𝐭 +(𝟓𝝅/𝟏𝟖) ) V
Calculate the phase current,( Iab, Ibc & Ica) of the load in polar form.
Calculate the active power( Pab, Pbc , Pca) in phase AB of the load in phasor form.
Determine the line current,( Ia, Ib & Ic) in polar form.
If two wattmeters are connected in lines a and b respectively of the above circuit to
measure the active power,
Determine the reading of the wattmeter,(Wa) connected in line a.
Determine the reading of the wattmeter,(Wb) connected in line b.
"e_C(t) =221.831 sin (wt+ \\frac{5 \\pi}{18})V\\\\\ne_B(t)=e_C(t) \\angle-240^0\\\\\ne_B(t)=221.831 sin (wt+ \\frac{5 \\pi}{18}-\\frac{2 \\pi}{3})\\\\\ne_B(t)=221.831 sin (wt- \\frac{7 \\pi}{18})\\\\\ne_A(t)=e_C(t) \\angle-240^0\\\\\ne_A(t)=221.831 sin (wt+ \\frac{5 \\pi}{18}+\\frac{2 \\pi}{3})\\\\\ne_A(t)=221.831 sin (wt+\\frac{7 \\pi}{18})\\\\\nI_{ab}=\\frac{E_A-E_B}{Z_{AB}}\\\\\nE_A=\\frac{221.831}{\\sqrt{2}}\\angle(\\frac{17}{18}\\pi)= 156.86 \\angle 170^0\\\\\n E_B=\\frac{221.831}{\\sqrt{2}}\\angle(-\\frac{7}{18}\\pi)= 156.86 \\angle -70^0\\\\\nZ_{ab}=29.41\\angle54.69^0 \\Omega\\\\\nI_{ab}=\\frac{156.86 \\angle 170^0-156.86 \\angle -70^0}{29.41\\angle54.69^0}\\\\\nI_{ab}=9.238\\angle85.31^0"
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