Planning of Cascade Hydropower Stations with the Consideration of Long-Term Operations under Uncertainties

Table 1

Model variables.

Types of variables	Symbol	Description
Sets	R	Set of hydropower station candidates
	S	Set of scenarios of the operational stages
Deterministic variables	T	The planning horizon is composed of T operational stages
	Rmin	The minimum required number of hydropower stations in the plan
	e	Unit construction fee (RMB/m^3)
	f	Unit profit of power generation (RMB/KWh)
	Δt	Time interval of each operational stage (h, which is the abbreviation of hour)
	ci	Penalty coefficient per unit in hydropower station candidate i (RMB/m^3)
	Ki	Coefficient of output of candidate i (kg/(m^2·s^2))
	Nimin	The minimum output of candidate i (kW)
	Nimax	The maximum output of candidate i (kW)
	Hi	Water head of candidate i (m)
	Vimin	The minimum required water storage of candidate i when it is selected (m^3)
	Qimax	The maximum discharge limit of local area around candidate i (m^3/h)
	QFimax	The upper limit water discharge of candidate i (m^3/h)
	QFimin	The lower limit water discharge of candidate i (m^3/h)
	ri(t)	Unit operational cost of candidate i at stage t (RMB/(m^3·h))
Stochastic variables	p^s	The probability of stagewise scenario s
		Outside water inflows in candidate i at stage t under scenario s (m^3/h)
		Water demands in candidate i at stage t under scenario s (m^3/h)
		Acceptance level of water discharge in local area surrounding candidate i at stage t under scenario s (m^3/h)