If you're interested in the direct answer and not in the reasoning behind it, scroll to the bottom of the post!
A simple option is to just only use the new plants. Their internal balance is somewhat improved. That being said, it does change the game dynamic from the regular game. Early plants are more effective, so a game can be shorter. That can actually be detrimental; it's easier to exploit an early lead.
A second option is to play more of a 'teacher' role: just explain why you're interested in a plant openly and fairly, or answer a question like "Why do you think I should bid on plant X?". The problem is that it can take away agency and that you're not really playing to win. It's hard to do this well.
Rather, I would suggest this preferred (if somewhat complicated) solution instead. Take the old deck, and remove all the plants that are bought almost 100% of the time they are in the game, as well as the plants that are bought almost 0% of the time. Replace these with the new plants, shuffling a few plants around so we have as few double numbers as possible.
These things are 'harsh' about the game's regular plant deck:
1> Bad early plants. These "traps" are just something you learn to avoid. They're bad enough that they'll cripple you in 99% of games, only serving to 'block' the market. Instead, it would be better if the worst plants are at worst mediocre, allowing you to at least make a bit of money, instead of just costing you.
2> Really good plants new players won't immediately realize the value of. The experienced player can oftentimes get a steal for an amazing power plant like the 21, 25, 26, or 30. This problem is somewhat less of a concern if you take the time to explain that 5 or bigger plants are really good, because you don't have to replace them later on, even if they use up a lot of resources, i.e. go through a few example evaluations of the plant market.
3> Low capacity late-game plants. Again there's another trap here. If these are bought at the start of phase 3, you could simply get into a situation where you don't power enough stuff.
4> The '3' and '4' capacity plant trap: new players will often buy too many of these, leaving them strapped for cash in phase 3. Adding a few 7 and 8 capacity plants allow players to keep one 3- or 4-capacity plant and still get 17 total capacity (3-6-8 or 3-7-7 or 4-5-8 or 4-6-7).
What we do NOT want to do is alter the game's resource balance. The default deck is well tuned with respect to the resources available, so we want our new deck to have roughly the same number of 'resource symbols' total on the cards, as well as keep the amount of symbols in each phase of the game similar.
In order to make the deck somewhat more forgiving, I suggest the following:
Start out with the regular Power Grid deck.
1) Replace the  plant with the new [2*] plant. In our new configuration the old  would not be good enough. Here having it be 1 cheaper means it is comparable to the  in value.
2) Add the new [5*] plant, leaving the old  in as well. (The new  counts as higher). The new [5*] offers an interesting capacity option, much like the .
3) Replace the  plant. The new [6*] is a great efficiency plant, though it suffers in turn order. The old  is essentially bought only on non-standard maps with cheap starting trash, or to break a stall.
4) Replace the  plant. The new [7*] has good efficiency. The old  is a mediocre plant bought only very rarely, it tends to not make enough money.
The starting market ends up as 2* 4 5 5*, 6* 7* 8 9, 13.
Phase 1 and 2 plants:
5) Replace the  plant. The old  is quite literally a garbage plant, and is basically never bought.
6) Replace the  plant. This adds an extra windmill early on. The  is usually a mistake when bought, but is quite insidious: it seems good at first glance but turns out not to be great.
7) Remove the  plant. The worst plant in the game.
8) Replace the  plant. The  is mediocre at best at this point in the game.
9) Replace the  plant. This gives back another Trash option, and the default  is arguably a bit strong. The new [21*] is also a 3-resource plant, keeping the resource use the same for Trash.
10) Replace the  plant. The default  is the second-best plant in the game. The new [25*] is a worse version of the old , the best plant. Removing the  also removes a bit of mid-game coal, allowing plants like the  and the new  to be less risky.
11) Replace the  plant. This gives us a 3-power wind plant.
12) Replace the  plant. Trading the wind plant for another decent Trash plant.
The midgame deck is thus 10 11 12 14* 15* 16 18 19* 20 21* 22 23 24 25* 26* 27* 28 29 30 31 32 33
13) Remove the  plant. A wind plant with only 4 cities and this high of a number is a trap.
14) Replace the  plant. Again, only 5 cities is not really good enough. With 6 cities the new plant is generally a great pickup.
15) Add the new  plant. (It ranks above the old ). This adds a good high-capacity hybrid plant.
16) Replace the  plant. This 8-capacity plant makes 3- and 4-capacity plants less bad. We already replaced the  so the equivalent of the old  is still in the game.
The endgame deck becomes 34 35 36 38 39 40 42 44* 46 46* 50*
Then follow the standard game rules with this new deck.