Reliability of a Solar Power Grid

Simulate the lifetime performance of a multi-array solar panel system with inverter dependence

Open in Cloud
Download Notebook

A solar panel system consists of five arrays of 10 photovoltaic cells each. Define lifetime distributions for 10 cells in one array and their overall reliability distribution:

In[1]:=

dists=Table[{

,WeibullDistribution[5.87,50]},{i,10}];bexpr=And@@Table[

,{i,10}];=ReliabilityDistribution[bexpr,dists];

The system requires three out of five arrays to function, and all are dependent on an inverter:

In[2]:=

ℛSolarGrid=ReliabilityDistribution[BooleanCountingFunction[{3,5},{x,y,z,v,w}]∧inverter,{{x,},{y,},{z,},{v,},{w,},{inverter,ExponentialDistribution[1/170]}}];

Find the mean time to failure in years:

In[3]:=

NExpectation[t,tℛSolarGrid]

Out[3]=

28.8064

Simulate the lifetimes of solar panels:

In[4]:=

Histogram[RandomVariate[ℛSolarGrid,1000],{2},"ProbabilityDensity",ChartStyleDirective[Opacity[0.8],ColorData[97][3]],FrameTrue,FrameLabel{"Lifetime (years)","Probability Density"},AxesFalse,ImageSize500,Epilog{{Thick,Red,Dashed,Line[{{NExpectation[t,tℛSolarGrid],0},{NExpectation[t,tℛSolarGrid],0.05}}]},Text[Style["E[t]",14,Bold,Red],{NExpectation[t,tℛSolarGrid],0.055}]}]

Out[4]=

A company that sells solar panels gives a 10-year warranty. An additional 10 years can be added. Find out how the company should price this extended warranty. The net cost to the company of selling one policy is given below and is equal to zero when the company breaks even:

In[5]:=

price-Probability[10<t≤20,tℛSolarGrid]*meanCostOfRepair

Out[5]=

-0.0546244meanCostOfRepair+price

Related Symbols

ReliabilityDistribution
WeibullDistribution
ExponentialDistribution
BooleanCountingFunction
NExpectation
RandomVariate

Publisher Information

Contributed by: Wolfram Staff