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So Cal Edison bill was $344.35

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I checked my banking statement and So Cal Edison is on autopay. And this time I checked it was $344.35 on November 20, 2023. Should autopay be paying off 1 months statement each time?

Would my Tesla most likely be the most expensive electronic consuming most of the energy contributing to the electric bill? I thought of a possible cheap skate way to get free charging for life.

If you are lucky enough to live near a shopping center that has free EV charging, maybe less than a mile, or 1-2 miles max, you could charge it there overnight all the time. And use an E-scooter to transport yourself to the car each day and put the E-scooter in your trunk. How much money could that save if I always used the free charging at a shopping center overnight and no one stopped me? I did this in Arizona when I visited my friend's apartment, he lived near a shopping center with free EV charging and I used my scooter to access them because it was 1-2 miles away. Like far to walk, but not too far for an E-scooter. Being free was nice, but the most important thing was that it saved time on the commute not having to charge. So I had free charging for 3 days during that trip.
 
You need to separate the concepts of kwh used from the charges for those kwh. You clearly care about both.

1) Autopay for a utility bill would most likely be paid monthly.

2) Your Tesla may or may not be the most power hungry thing, it depends on how much you drive and what other big loads you might have. Note that the amount of power something uses and the amount of cost can be very different(in some locales) depending on what time of day the power is consumed.

3) Your Tesla takes something like 75kwh for a full tank(assuming its a long range variety). You need to figure out what your real utility bill is (in KWH, not dollars) to see what portion of your bill is likely due to your Tesla. Lets suppose you drive the typical 12000 miles a year at 350wh/mile(including vampire/idle losses). That's 4,200,000 wh per year, or 4200 kwh/year, or 350kwh/month. At the average Orange County rate ot 0.33/kwh, that's $115.50 a month. But I understand California has very variant rates based both on location and time of day and what 'plan' you are on. Maybe you decided on a very expensive renewables-only electric plan that has cheap power from noon to 3pm when the sun is out, then you get an extremely high rate during your actual time of charging.
 
You need to delve in a little bit deeper than just looking at the dollar amount of your bill if you want to effectively manage your costs.

@Sophias_dad already raised out some good points, but one thing that was not mentioned is that if you are on a time-of-use rate, you probably also pay a monthly demand charge. This is a charge for the largest instantaneous power draw you incur during peak periods over the given month. It is billed by the kW, not the kWh, and if you are not careful it can be the most expensive part of your bill (and a component that is most likely not captured by the charging costs summary you see in the app, even if you carefully put in your provider/electricity costs). (although I just went to look at the SCE tariff sheets, and I can't really find the demand charge spelled out, so I'll have to make up an example).

Let's say that the demand charge is $10 per kW. During a quiet time, your house might be drawing 0.5-0.75 kW, but then your AC kicks on and pulls 5kW during a peak period. That's $50 bucks added to your bill for the month. And then you throw a load of clothes in the dryer which pulls another 3kW (total of 8kW). Now you're up to $80. Fortunately the AC turns off and you're back down to 3kW, but then you turn on the oven (4kW) and you're back up to 7kW...not over your peak, but getting up there. But then the AC kicks back on and you're pulling a total of 5+3+4 = 12kW. Now you're up to $120 on your bill. But wait: you plug in your Tesla and it starts drawing 7kW, and bam, now you're up to 19kW, adding $190 to your bill. And this is before you even start adding up the kWh that all those things are pulling.

Now that you know this, you decide to be a little smarter about how you use electricity. You shift using the drier to off peak times, or at least avoid drying clothes while the oven is on. You turn off the AC while cooking to avoid those being on simultaneously. And you shift your car charging to off peak times as well, or if you do need to charge during on-peak, you turn down the charge power. By being smart about it, you can reduce your demand charges down to 6kW or $60, saving a whopping $130 on your bill the next month.

And maybe you even look at the different rate options available to you and choose one that gives you special EV rates.

As for your plan to get free charging, well, there is nothing stopping you from this, but if it's free, you typically get what you pay for. If everyone did this, the charging may not be available when you need it (plus, you'd be tying up a valuable resource after your car is done charging). It also may break and the host would not have much incentive to fix it. Plus there is the loss of convenience, not to mention lack of security where your car is parked all night.
 
Far too many variables in people's driving amounts and houses and lifestyles for us to just take a blind guess if your car is the biggest consumer of your electricity. I remember the person here on the forum who was shocked (shocked, I say!!) to see his electric bill that he had never paid attention to before and blamed it on the car. The electricity amounts made no sense for just car usage, so after some questions from the forum, it was revealed that the person kept his vintage guitar collection in his garage and ran a space heater in there all the time to keep the guitars from getting too cold and damaged, but he thought that would be an insignificant amount of usage.