Consider the green hydrogen $($H$2$V$)$ supply chain, aiming to produce clean energy, transform

it to hydrogen, and then back to clean energy to match the intermittent energy supply of

renewable energy sources with the energy demand of cities. In this energy supply chain, when renewable energy sources provide more energy than

needed at that time, a chemical process called electrolysis can be executed to produce and

then store green hydrogen from electricity. Afterward, when the supply from renewable electricity sources is not sufficient to match the

demand, the stored hydrogen can be used to generate clean electricity via a fuel cell. Through these process steps, a circulation of green hydrogen and decarbonization of the grid

can be achieved. Some technical specifications to help envision the problem are:

$$ Around $50$ kWh are required to produce $1$ kg of hydrogen using an electrolyzer.

$$ With $1$ kg of hydrogen, the fuel cell can produce approx. $33$ kWh of electricity.

$$ Most onshore wind turbines have a capacity of $2-3$ megawatts $($MW$),$ producing over

$6$ million kilowatt hours $($kWh$)$ of electricity annually, and costing $$2-4$ million.

$$ A $10$kW solar system is fit for a large house with numerous appliances or a small

business of any kind.

$$ The average cost of solar panel installation in Ireland is between $6,000$ and $18,000.$ For the city of Dublin, by using public funds, please consider the problem of setting up such a

green hydrogen and energy supply chain to match the supply of green energy with the energy

demand at the grid. How would you structure such a problem as a mathematical model? What would be the decisions $($decision variables$),$ evaluation criteria $($objective function$),$

limitations $($constraints$)?$ What kind of parameters would be needed to form a modelling

approach for this problem? What kinds of data would be needed to gather? In terms of using

a mathematical modelling approach, please describe as specifically as you can the decision

variables, objective function, and constraints; and then please describe how you would

provide insights from sensitivity analysis reports of such a model.

If possible, you can also provide the structure of the model generically; to give an example of

the structure, for production mix problems, some model elements could be expressed

generically as:

Objective function Value Z $=$ Total Profit $=$ Sum of $($unit profit for product i $*$ production

amount for product i$)$

Constraint $1$: Sum of $($usage of raw material per unit for product i $*$ production amount for

product i$)<=$ Available amount of raw material, etc.if we want to take objectives function only as to increase the or maximise the efficiency of hyderogen power plant whatwoulwhat would be the decision variables and constraints