What is a power double? Nominally, PDs show 15+ HCP and tend to be balanced. Since NTOs are not 100% forcing, a PD can also be made on very strong takeout doubles (15-16+ with a doubleton in their suit, 18+ with shortness), on strong jump overcalls, or extremely strong two-suiters inappropriate for Michaels. A PD neither confirms nor denies a stopper in their suit. We'll have plenty of time to find one below 3NT.
We can make a PD on hands that would not overcall 1NT, either because they are a little bit too weak, or because they don't have a stopper.
Minimum power doubles do not have singletons. Very strong hands can be most any shape, unless this is played in conjunction with Overcall Structure, in which case, they tend not to be one-suited or two-suited. If the hand has a little extra, a stiff honor on the side is OK. If the hand has a lot extra, a small singleton is OK. I've never seen a PD with a void.
Power doubles apply even if the 1 or 1 opening is semi-artificial, as in a Precision 1 or a 1 = natural or 15-17 or a Polish club (usually 11-13 balanced). They do not apply to big clubs. They do not apply above the one-level. They do not apply by passed hands, although partner can have passed. They are very effective against light third-seat openings.
Simple suit responses: show about 0-7 points, four-
card suits at the one-level, usually 5-card
suits at the 2-level. Not forcing. Balanced
hands will have a choice between a suit and 1NT.
Use judgment: with
1NT: doesn't show anything, not even a stop in
their suit. Denies as much as a decent 7-count.
One may often have a choice between one of a suit
and 1NT. Location of high cards and length in
their suit should influence that choice. With
truly atrocious hands, try to bid the cheapest
suit. With stuff and/or length in their suit,
tend to bid 1NT. (Remember, partner tends to
have length there, so adverse ruffs are threatened
in a suit contract.) I once held
2NT: 7+-9- HCP, balanced. Usually at least half a stop in their suit.
2X: (Cue) game forcing, about a good 7-count and up. This can be done agressively, since the cards rate to be well-placed. We can get out in four of a minor.
Jump suit responses: invitational, 7-9ish, five-card suits.
4-level responses are natural, except that a 4-level double-jump cue is namyats-like, in either major. Responses to that are: 4 = interest in slam, 4 = P/C, 4 = huge hand for hearts, not so huge for spades. In mid-chart events, all 4-bids are namyats.
3-level triple jumps are preemptive.
Others: same. I've seen a few psyched redoubles here.
After (1X)-X-(1Y or 2X)-?
Dbl: takeout. Can be done on shortness in the bid suit. If they have bid only one major, the double shows exactly four cards in the other major and shows nothing more than tolerance for the unbid suits. Double does not promise much in the way of values. At the 3-level, it promises values. At the 2-level, forcing partner to bid vulnerable at the 3-level requires something, but less than you think---partner has a good hand, and a weak advancer has to help out. When advancer passes, minimum PDers usually pass, too, so most of the responsibility to compete is upon advancer. Repeat, at the one-level, this does not promise any values, just the unbid major.
New suits: natural, some values, competitive, not forcing, not invitational
Cue of X: game forcing
Cue of Y: natural, forcing one round. They can psych here, and it's effective without this treatment. Later "cues" of responder's "suit" are natural, also.
Jump cue of X: natural, forcing, good six-card suit.
Jumps in new suits: invitational
1NT: some values, some stoppers. Usually about 4-7- HCP (Rule: Free bid of 1NT shows values. Free bid of suit or shows shape.)
2NT: Natural, invitational
Rebids by the PDer:
2 after a new suit is artificial and shows 19-21 or so. (Good 18s shade up sometimes.) Responses to 2 are natural and non-forcing if not a jump or cue. 2 is not forcing.
2 after a NT response is Stayman.
Response to a cue-bid: New suits by doubler tend to be five-card suits except for the cheapest suit. NT promises a stopper; return cues tend to deny one.
Jumps in new suits show good strong jump overcalls. (In OS, this only happens in /, / or /.)
Jump cue shows a mammoth takeout double with a void.
Jump to 2NT is a huge hand, 22-23 or so.
Raises show extra values, either by way of fit, shape, or high card. They promise at least 3-card support, usually four.
New suits after a simple suit response are five-card suits and don't promise any extra values. They are not forcing. (Yes, sometimes you'll be stuck. Thus, the cheapest new suit can (rarely) be a four-bagger.)
Cues after simple suit or 1NT responses are very strong. Herbert Negatives apply.
If the opponents open one of a minor, we are now using a jump cue to show very big hands with shortness in their suit, so power doubles pretty much guarantee two or more trumps.