No. In theory, that new gas plant is "planned" and replacing aging capacity, while meeting expected demand.

Rates are separate.

Many power utilities are granted a monopoly, especially the transmission (high voltage, long distance) and distribution ("last mile" / neighborhood wires) horizontals as they're true natural monopolies.

In exchange for that concession, their profits are capped. The cap is a function of their "rate base" -- i.e. qualifying capex -- and an approved rate. These rates are adjusted periodically, requiring public utility commission (State) or FERC (federal) rate setting sessions.

For example, "Total Revenue Requirement = Rate Base [assets] × Allowed Rate of Return + Expenses" [0]

Without having looked into this, it's easy to over-estimate how easy (hard) life as a public utility is.

[0] http://blog.aee.net/how-do-electric-utilities-make-money

There is very little competition in electrical utilities. The theory is that in order to prevent competing electric lines from being built, government must control prices. However, many utilities still have private investors, who want prices to go up. Since existing prices already pay these investors a fair return, they have to find a more objective reason than "we want more money". Often this takes the form of unnecessary capital spending, the costs of which can be inflated and passed on to captive customers. After all, if the capital spending (e.g. on a power plant) were necessary, it would itself generate a return (e.g. by selling power) that would attract investors. The public is victim of the principal-agent problem when public utilities commissions approve such arrangements. This has led to a situation in which California and other states have more generation capacity than they need.

Yes, but, this is not an open market, this is the CPUC and they have a captive audience they can force to pay whatever they want to force them to pay.