There are many potential problems- it is not possible to specify which from the following (non exhoustive) list may apply to your situation without more information. I have listed them more or less in order of probability.

(1)Inept/unqualified "electrician"

(2)new circuit breaker(s) too small or the wrong type for application/devices

(3)more than one circuit fed from a single breaker in new panel.

(4)some combination of 1, 2 and 3.

(5)defective appliance(s)

In addition to what Wayne brought up:

It is possible to have a bad breaker, new, right out of the box. It is rare so having two or three of them all in the same new panel would be exceptionally rare. It might explain one of them, or maybe the electrician discovered a new source of junk electrical equipment.

It is possible that someone dangerously/illegally substituted the wrong, larger breaker in your old panel. Your electrician might have gone by the conductor size when installing the panel rather than looking at the old breakers. It will be hard to tell without having the old equipment.

Who installed the new panel, the solar installer, their subcontractor or your electrical contractor? I don't see why your old panel would not have the capacity to handle the solar. That could only occur if you are making a lot more power than you use which would be very unusual for a residential situation. OTOH, maybe you were out of spaces for breaker and the panel old and decayed (outdoor location). If it was in good shape, you could have just installed a sub panel to add circuits.

Are these small appliance circuits that are tripping 20 or 15 amp? Are the appliances tripping the breakers when they are the only device drawing power? What are the requirements for the range vs. its circuit breaker?

The suggestion that you need a new range smells bad. When employing more burners, do you always select them in the same order (1,2,3,4) or do you mix it up (3,4,2,1). If not, give another combination a try. Do you see why I ask? If that third burner is always the same one, it might be an internal problem with the range. Usually when an electric range stops working in some way, it stops heating, or it makes a sound sort of like popcorn accompanied by a burning smell that is not like popcorn at all. The second case is a short circuit. The first is an open circuit.

great ideas, here.

As it turns out, the appliances (coffee maker and toaster) add up to more then 20 amps when both used on the same circuit, explaining why the breaker was tripped. However, did it all the time with old service entry and never had a problem. Perhaps it used to be a 30 amps circuit, i.e., connected to a 30 amp breaker in the service entry?

As far is the stove goes, my handyman friend took a look at the service entry. It seems clear that the breaker for the stove IS USED! unbelievable. (I have an office job, took the handiman to notice such things). about a quarter of the breakers are used....I am lucky the oven is the only problem (as stated, I think the appliances combined were greater then the breaker load used, so I don't think this is a problem.)

I am therefore hoping it is the breaker, which would be the best case scenario. I'll check for pattern in the oven combination of burners. Really think the oven/stove is fine though.

The reason I upgraded the service panel (could have gotten a subpanel) was some mumbo jumbo about it not handling enough electricity for what was being produced, but OTOH it was old and decaying, and I got a rebate for 1/3 of the price of the new one.

I got the electrician for the service panel completely independent of the solar company.

The specs on my oven
100 kw at 120/240 volts
7.5 kw at 120/208 volts

Not sure what this means, exactly.

On my service entry, it is hooked up to a 50 amp breaker, which I understand should handle the oven with every burner on.

I meant
10.0 kw at 120/240 volts.

If I understand you correctly, the electrician installed used breakers. What is the brand of the breaker box? If it is something like Federal Pacific, only used breakers are available. Or, was the entire service updated including the breaker box? A used breaker is not always a bad thing. Do You have GFCIs in your kitchen to handle counter top recepticles? These protect you from defective small appliances.

"On my service entry, it is hooked up to a 50 amp breaker, which I understand should handle the oven with every burner on."

Yes, it should. The observations are that the range circuit/range were working fine with your previous 50 amp circuit breaker. Electrician installed a used 50 amp circuit breaker. Newly-installed, used circuit breaker trips when you are using half or less than the capacity of the range.

That is excellent evidence that the contemporary circuit breaker is at fault. The electrician should replace it. At the very least, he should measure the current that the range is drawing with a clamp-on ammeter.

It is a little concern that the circuit breaker on the "overloaded" circuit was not tripping before. You might have had a faulty, dangerous circuit breaker there. I suppose that is possible with the range circuit as well, but the fact is, you should not be able to overload it with your normally-operating range.

Give the guy a chance to make it right and while you are on the phone, give him a chance to alleviate the overloading situation with the appliance circuit by installing another circuit. I hope that he will give you a reasonable price and not punish you for asking him to fix a problem he probably responsible for.

Just spoke to him. He states that the circuit breaker was new, not used. Maybe got some dings at home depot prior to sale? nevertheless, he will come over to replace, though I'm not confident that it will solve the problem.

He's now saying the most likely scenario, as we moved the stove around, it got bumped and damaged electrically speaking. This does not at all sound likely to me: we move it out once to inspect the circuitry AFTER the breaker was tripping.

He mentioned (though he later tried to obscure this) that breakers will trip if the electrical system is not grounded properly. When he put in the service entry/breaker box, he did put in grounding, but I am now wondering if it was done properly. While he is willing to put in new breaker, not willing to consider problem with grounding. I am thinking I have to hire a second person to look at the entry, the grounding etc.

He kept repeating that the city inspector said the grounding was fine.

My main concern, especially if the system is not grounded properly, is I will come home and find my home a pile of smoking cinders. After that, would like to cook a meal.

My (uneducated) hunch is that it is the grounding.

Based on the post above, particularly
"breakers will trip if the electrical system is not grounded properly..."

I believe that my list item, (1)Inept/unqualified "electrician"
is the root of your problems.

"breakers will trip if the electrical system is not grounded properly..."

The only thing the earth ground is for is lightning and pole transformer leakage.
It is NOT a normal part of the operation of the circuit feeding your house.

The current is supplied on the two hots (120 V each to the neutral and 240 V each between them) and any imbalance in the 120 V current used on each leg returns on the neutral to the pole transformer.

While a poor earth ground can cause all sorts of voltage buildup, it is not going to be tripping larger breakers.
The leakage currents are high voltage, but NOT high amperage.

The type of inept sparky victimizing the OP is often known in So-Fla as a "licensed electrician"... and actually has a license... I kid you not.

Personally, I just *HAVE* to know the BRAND of panel and breakers (and whether they MATCH, lol), installed by this charlatan. Sorry if I missed that nugget, but I don't think I did.

Needless to say, a fire at the OP's house would NOT help the cause of residential solar power. ;')

It an Eaton Panel with Cutler Hammer Breakers, which do in fact match.

An update: he finally showed up after one more call (before giving up). He put in another circuit breaker. He said that the old breaker was fine, and it was likely a partial short in the system because of old wiring. I told him that my main concern was safety. He said the house is safe, but the short is probably tripping the breaker. Then he said the oven was probably malfunctioning and tripping the breaker. On his way out, he said"o by the way, I put in a 40A breaker instead of a 50A breaker, to keep me safe".

Not sure what he meant by that. Confused about why he would downsize the breaker. Isn't the breaker size related to the size of the wire? If so, perhaps he put in too large a breaker for the wire in the beginning, or perhaps he is now putting in too large a breaker for the wire.

LIkely I'll be getting a new electrician to look over my system, at this point.

Thanks guys for all your thoughts!

You can always use a smaller breaker than the wire size might allow, but not a larger.

If the equipment specifies a breaker size you must follow that.