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Help understanding my meter

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We just bought a new property and I've been attempting to gauge the electric usage in preparation for sizing a solar setup. Comparing the kWh readouts for a given time interval is straightforward for my determining day usage versus night usage, etc.

What's puzzling me is the instantaneous draw. It seems to be extremely high even when nothing significant is running (no AC, no car charging, virtually every light off, etc.). The meter was showing a 5.800 kW draw this morning when the house was still cool from the AC running overnight, the AC had shut off, and nothing else of any significance was running (just refrigerator and a couple of ceiling fans). I even threw a bunch of breakers to be sure and the display never changed from 5.800 kW.

I'm wondering if this particular meter is showing the average draw for some preset interval versus showing the instantaneous draw?

I attached a picture.
 
Contact your utility about how to read your meter. I'll bet it has a cycling set of figures that show use for various periods (now, last 24 hrs, lifetime, etc). You need to let it cycle to the "in use now" display.
I guess I'll give them a call. Right now it's cycling between only two numbers: the 5.800 kW value and the kWh consumed value. The latter is behaving as I would expect. The former is definitely not instantaneous. Maybe they can push a change to the meter to give me an instantaneous display. Or a max draw over a given interval.

Time passes...

Ok. I called the electric company. The meter is set to display the peak draw during the previous 24 hour period, resetting a midnight. My other house displays an instantaneous draw, hence my confusion. Maybe after I install solar and they replace my meter with a bidirectional meter it will show instantaneous draw.
 
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The 5.8 kW is going to be your demand for the month. This is only relevant if your bill actually has you paying a demand charge. My electric meter and my electric bill displays my demand, but I don’t actually pay for it. This lets them use a single meter if you pay that or even if you don’t.

Your demand is your PEAK 15-minute average kW draw over the course of the month. It will stay there (possibly increasing if your demand goes up) until they read your meter at the end of the current billing cycle. Big draw items in the house include EV charger, A/C units, electric furnace, stove, clothes dryer and to a much lesser extent, dishwasher. Other less common items include a swimming pool and a hot tub (time machine).

If your bill has a demand charge, you want to limit the simultaneous use of those large power draws, at least during the time that they measure your demand. For example, with Evergy (local electric utility), for the residential accounts that do have a demand charge, only the afternoon non-holiday weekdays counts.

Look at the dollar values on one of your bills to see if the demand matters. Most of the time, residential bills don’t have this. One of my friends that lives a half-mile away is on a rural electric provider and has a demand charge, so he hasn’t installed 240V EV charging in an attempt to keep his demand and bill low.

Edit: just read through the thread again and saw that you said it’s for a 24 hour window. The rest still stands though. When I had solar installed, my old mechanical meter was replaced with something like what you have that tracks bi-directionally. There’s a chance that they just flip a switch inside your current meter to make it read and display both directions.
 
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Fortunately, there's no demand charge. It's an electrical co-op, so everyone pays exactly the same rate, 24/7/365. No demand charge. No on/off peak. No free night's/weekends. Nothing. Just the same flat rate for everyone (about $0.10/kWh). It's kinda nice that way.