Max Power Output

Current out of source $V_S$ :

$I_S = \frac{V_S - V_R}{1 + j X}$

Active power out of source $V_S$ :

$P_S = Re(V_S I_S^*)$

Sweep $X$ over a range and find the maximum value of $P_S$ . This occurs when $X \approx 0.7673$ .

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import math

VSmag = 10.0
VRmag = 10.0

VSang = math.pi/6.0
VRang = 0.0

VS = complex(VSmag*math.cos(VSang),VSmag*math.sin(VSang))
VR = complex(VRmag*math.cos(VRang),VRmag*math.sin(VRang))

R = 1.0

##################################################################

dX = 10.0**(-2.0)

PSmax = 0.0
X_store = 0.0

X = 0.0

while X <= 20.0:

    Z = complex(R,X)

    IS = (VS - VR)/Z

    ISconj = complex(IS.real,-IS.imag)

    SS = VS*ISconj

    PS = SS.real

    if PS > PSmax:
        PSmax = PS
        X_store = X

    #print X,PS

    X = X + dX

print ""
print ""
print dX
print X_store

##################################################################

#>>> 
#0.0001
#0.7673
#>>> ================================ RESTART ================================
#>>> 
#1e-05
#0.767329999999
#>>> ================================ RESTART ================================
#>>> 
#1e-06
#0.767327000001
#>>>