Power statement is valid for MW Or KiloWatts? If I can talk to someone and tell him that a new power plant inaugurated by Prime Minister will produce $60$ megawatts per hour, will it be true to use $\mathrm{MW}$ unit for Power?
 A: You're right that the unit "megawatt" is abbreviated MW.
However, as Aniket comments, watt itself means "energy per unit time", so saying that the power plant produces 60 MW per hour doesn't make sense.
In your comment, you question whether MW is a "basic unit". I'm not exactly sure what you mean by this, but the SI unit of power is watt, so if you want to express your statement in SI units, you should say


*

*"The power plant produces energy at a rate of 60 millon watt",


but either of the following statements are equally true:


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*"The power plant produces energy at a rate of 60 MW".

*"The power plant produces energy at a rate of 60 megajoules per second".

*"The power plant produces energy at a rate of 80461.3 British horsepower".

*"The power plant produces energy at a rate of 44 million foot-pounds-force per second".


Being an astronomer I was brainwashed to cgs units, so I'd go for


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*"The power plant produces energy at a rate of roughly $10^{15}\,\mathrm{erg}\,\mathrm{s}^{-1}$".

A: $\mathrm{Watt}$ (or Joule per second or $\mathrm{J/s}$) is the SI unit of power. So megawatt is a valid unit of power (expressing power with order of magnitude $10^6$) and is used mainly in commercial statements.
Definition: Power means the quantity of energy consumed or produced  per unit time.
So $\mathrm{MW/hr}$ actually makes no sense since it expresses the quantity of energy consumed or produced  per unit time  per unit time i.e. the quantity of energy consumed or produced  per unit time squared. In other words it refers to the rate of change in power generation.
A: Notice, the unit of power is $~\mathrm{J/s}$ or $~\mathrm{W(Watt)}$. 
The unit $~\mathrm{MW}$ indicates the energy (in $~\mathrm{mega\ joules}$) produced by power-plant per unit time (in $~\mathrm{seconds}$) 
The unit $~\mathrm{60 \ MW\ per \ hour}$ doesn't represent a physical quantity.    
