Residential electricity: poss. cost to go solar

The tutor offers an estimate about the price of going solar.

In an earlier post , I reported my research findings of possibly 22W per $100 for a residential solar application.

Here in BC, according to BC Hydro, the typical household use is 11000kWh per year, or about 917kWh per month. Use fluctuates from minute to minute; taking the average power, we get

    \[\frac{917kWh}{month}\times \frac{month}{(30*24h)}=1.274kW=1274W\]

So, typical household average power usage is 1274W.

At 22W per $100, we can estimate what solar power might cost, installed, to replace the Hydro bill:

    \[1274W\times \frac{\$100}{22W} = \$5790.91\]

So, maybe around $6 grand to replace Hydro with solar in your house?

There are several key variables to be considered surrounding this very rough estimate. The first is hours of sun: in Osyoos, which is desert, you can probably expect much more output from solar panels than on the rainy coast. Installation costs no doubt vary widely as well. Next, there’s usage: this example is for a typical house; it likely doesn’t fit many cases.

That being said, the $6 grand estimate is a great starting point – and quite a value, from a certain point of view.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Solar energy: price per Watt

The tutor continues from his last post about the value of solar energy dollars.

In my last post I discussed the Wattage one might expect from solar energy for $100. Based on a graph from Scientific American, the equation for Watts per $100, W, at time t (with 1980 as year 0 and 2008 as year 28) turns out to be

    \[W=4.2e^{0.0787t}\]

Extrapolating, one can plug in 35 for t to get the predicted Watts per $100 today:

    \[W=4.2e^{0.0787(35)}=66Watts for \  \$100\]

In fact, just talking about the hardware itself, one can get more than 100W for $100 in 2015 (see sunelec.com, for example.) However, for a typical residential application the price per Watt might be more like $4.50, installed. Thus, the Watts available for use might be more like 22 per $100.

Interestingly, taking the average of the “theoretical” 100W for $100, along with the “practical” 22W per $100, one arrives at 61W per $100, which is fairly close to the 66W predicted by the graph.

I’ll be talking more about solar energy for households in coming posts:)

Source not already mentioned:

pv-magazine.com

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Solar energy: yield trend

The tutor begins an exploration of the changing feasibility of solar energy.

There is a graph provided by Scientific American that shows the Watts one might get for $100 from solar cells by year. As they point out, it’s a logarithmic graph; here I’ll show some analysis.

The two points I’ve fetched from the graph, in the format (year, watts) are (1980, 4.2) and (2008,38). The linear shape is accomplished by the relationship

    \[lnw=mt+b\]

where t=time, while w=Watts.

I’m imagining 1980 as year 0; the two points mentioned earlier become (0,4.2) and (28,38). Then b, the lnw intercept, is given by

    \[ln4.2=m(0) +b\]

giving

    \[ln4.2=1.4351=b\]

m is solved by the slope formula:

    \[m=\frac{ln38-ln4.2}{28-0}=0.0787\]

We arrive at

    \[lnw=0.0787t + 1.4351\]

Taking the exponential of both sides, we get

    \[w=e^{0.0787t + 1.4351}\]

This can be rewritten, by an exponent law, as

    \[w=e^{1.4351}e^{0.0787t}\]

which becomes

    \[Watts=4.2e^{0.0787t}\]

The exponential argument 0.0787t suggests growth of 7.9%. Rounding it to 8%, and applying the rule of 72, the Wattage per $100 should double every 9 years.

I’ll follow up some implications of this analysis in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.