In[]:=
$Assumptions=VL>0&&0.5≤ksag≤0.9&&Vs>0&&Pi/18≤fai≤Pi/3&&ZL>0​​Reduce[0≤VL*Ishp+(1-ksag)*Vs*Sqrt[4*VL^2-3*VL^2*Cos[fai]^2+Ishp^2*ZL^2+2*Ishp*VL*ZL*Cos[fai]]/ZL,VL*Ishp+(1-ksag)*Vs*Sqrt[4*VL^2-3*VL^2*Cos[fai]^2+Ishp^2*ZL^2+2*Ishp*VL*ZL*Cos[fai]]/ZL≤VL^2/ZL*Cos[fai],Ishp]//FullSimplify​​
Out[]=
VL>0&&0.5≤ksag≤0.9&&Vs>0&&
π
18
≤fai≤
π
3
&&ZL>0
Reduce
:Warning: Ishp is not a valid domain specification. Assuming it is a variable to eliminate.
Reduce
:IshpVL+
(1-ksag)Vs
4
2
VL
+
2
Ishp
2
ZL
+2IshpVLZLCos[fai]-3
2
VL
2
Cos[1]
ZL
≤
2
VL
Cos[fai]
ZL
is not a valid variable.
Out[]=
Reduce(-1+ksag)Vs
4
2
VL
+
2
Ishp
2
ZL
+VLCos[fai](2IshpZL-3VLCos[fai])
≤IshpVLZL,IshpVLZL≤
2
VL
Cos[fai]+(-1+ksag)Vs
4
2
VL
+
2
Ishp
2
ZL
+VLCos[fai](2IshpZL-3VLCos[fai])
,Ishp