# Projecting Future Load – Compound Growth

**Q:**

Thanks for your insightful answer in your previous post, “Why does the load matter?” How important is the future load growth? Our planning team gives me a range instead of a single value; they suggest 2-3%. I have sent you some real data for several of our circuits. Can you teach me?

**A:**

Albert Einstein is said to have once quipped, “The most powerful force in the universe is compound interest.” He was talking about money, but the same principle applies to compound growth of any kind as you shall see if you read on.

Your planners undoubtedly consider whether the geography served by the circuit is mature or whether there is still new development likely. On top of the growth rate from new services, how are existing customer electrical demands changing? In general, more and more electrical applications are being deployed, but greener, more energy efficient appliances may mitigate or even reverse that load growth. Also demand management may reduce peak loads. I picture the planners pulling out their crystal balls to determine how fast plug-in hybrid cars will be deployed. These are just a few of the considerations in estimating future load growth. The impact is huge, so the exercise is well worth considering.

To test that impact, let’s do a sensitivity analysis on a single 3-phase feeder circuit, your Carrollton AM-1215. Nearby, I have plotted estimated temperature data for the circuit for most of 2010 in 30 minute increments. The lowest curve on this graph is the ambient soil temperature at cable depth. The temperature of the individual cables for phases A, B, and C, are displayed as fine red, grey and blue lines respectively. The flux weighted temperature, that is the equivalent constant temperature that provides the same permeation of fluid through a cable, are the three heavy horizontal lines using the same red, grey, and blue color scheme. I described this process generally in my previous post and I have promised a future post to examine in more detail what flux weighting means.

The next illustration of three graphs stacked on top of each other shows the extrapolation of the Carrollton AM-1215 data with 1%, 2% and 3% annual load growth. First allow me to explain the common elements of each graph. The x-axis is the year. The red, grey, and blue dashed lines are projections of flux weighted amperage for phases A, B, and C respectively. All dashed lines are plotted against the left-y-axis. The corresponding flux weighted annual temperatures are like-colored solid lines and are plotted against the right-y-axis. The top-most horizontal dashed line (purple) at 603 amperes is the rated ampacity of each cable. The lower horizontal dashed line (violet) at 469 amperes is the maximum flux weighted load. Based upon the historical difference between the peak and flux weighted temperatures for all three phases, when the flux weighted current grows to be greater than or equal to the flux-weighted maximum load, the circuit will experience significant thermal excursions above the maximum operating temperature during periods of peak load.

In the top graph of 1% annual growth, the cable is approaching its ampacity limit in the year 2050—40 years from now. All is well. In the middle graph of 2% annual ampacity growth, constraints are experienced in about 2031 or 20 years from now. The doubling of the growth rate halved the ampacity-life of the circuit. In the bottom graph of 3% annual ampacity growth, constraints are experienced in about 2025 or 14 years from now.

Einstein was right—the compounded growth rate is the most powerful force in the universe! The difference between 1%, 2%, and 3% is bigger than my belly. For the Carrollton AM-1215 circuit, 40 years of life is simply not possible in the 2% and 3% load growth scenarios unless a portion of its load is transferred to another circuit.

If you don’t expect to keep a circuit in service for 40 years, don’t ask Steve to warrant it for that long. Ask him for a shorter life and a discount. The cost of the technology to obtain 40 years of life is more than the cost to reach 20 years.