Question $3$

a$)$ Explain how pumped storage plants can reduce the operating cost of power systems. $(5$ marks$)$

b$)$ A power system has a maximum demand of $2000$ MW and a load factor of $0\mathrm{.}3.$ It is to be supplied by either one of the following two schemes:

Scheme $1$: A single coal fired power station of $2000$ MW$,$ OR

Scheme $2$: A small coal fired power station $(1200$ MW$)$ in conjunction with a pumped storage plant of $800$ MW and able to supply $\backslash (10^\{6\}\backslash$mathrm$\{$MW$\}\backslash )$ per year at an overall efficiency of $\backslash (75\backslash \%\backslash ).$

The relevant data of the stations are:

Calculate the average generation cost per MWh for both schemes and explain the difference. $(12$ marks$)$

c$)$ In addition to the capital and operational costs, what other constraints have to be considered when building pumped storage plant?

$(3$ marks$)($Total: $20$ marks$)$