How to calaulate the output power of the hydropower project?
How a hydro turbine works?
The reservoir stores the water. As the intakes opened, the water is flowing through the penstock. When the water flows(Qm3/s) through the penstock, it builds up a pressure (water head H (m)) that strikes the turbine and its kinetic energy turns the blades of the turbine. This process is causing the generator to turns as well, so it can produce the electricity(output power KW). The amount of generated electricity depends on the volume of the water flow and the height difference between the reservoir surface and the turbines.
The basic formula for calculate the output of hydro turbine
Nt=9.81*Hn*Qr*η1, Ng=Nt*η2
- Nt (rated output power of turbine, KW)
- Ng (output power of generator,KW)
- Hn (net water head of project ,m)
- Qr (rated water flow of project, m3/s)
- η1,η2 (efficiency of turbine, generator)
How to calculate the net water head?
Hn=Hg-Hl
- Hg (gross head) = Upstream water level – Downstream water level
- Hl(loss head) =Head loss of the forbay, trash rack, penstock pips, etc
Water Head of turbine
Gross Head (max.water head of plant)
- Water level elevation difference between the normal water storage level upstream of the hydropower station and the lowest tailrace water level downstream
Minimum gross head of plant
- The minimum water level elevation difference between the upstream and downstream water levels of the power station under various combinations
Net head
- Effective head for water turbine working,it’s total water level difference at the inlet and outlet sections of the turbine
Maximum Net head
- Maximum head of the power station （gross head) minus all head loss of the water diversion system during one unit no-load operation
Minimum Net head
- Minimum gross head of plant minus all head loss of the water diversion system during the units load operation.
Weighted average head
- Under the specified operating conditions, considering the power and working duration，the weighted average of the water head of the turbine
Design water head
- Net Water head at maximum turbine efficiency
Rated water head
- Minimum work head required by the turbine when the generator is rated output
Water flow of turbine
Unit discharge Q11
The rated flow of a turbine with 1m nominal diameter under 1m water head .
Turbine Discharge Q(m3/s)
Volume of water flowing through the turbine per unit time
Rated discharge Qr(m3/s)
Flow required by water turbine for output rated power at rated head and speed.
No load discharge Qo(m3/s)
Flow of the turbine during no-load operation at rated head
Speed of Water turbine
Unit speed n11
A speed of water turbine with 1m nominal diameter runner, at 1m water head.
rated speed nr(r/min)
water turbine steady-state synchronous speed according to the design of the power station
Specific speed ns
Speed of water turbine at 1m water head and 1KW output power.
- ns-specific speed
- n-water turbine speed (r/min)
- P-output power of turbine (KW)
- H-water head of turbine (m)
Runaway speed(r/min)
The highest steady-state speed that the water turbine can reach when the shaft end load torque is zero
Power of water turbine
Unit power P11
the output power of water turbine with 1m nominal diameter, at 1m water head.
Input power of water turbine Ph(KW)
Hydraulic power of water flowing through the water turbine
Output power of the turbine runner Pm(KW)
Mechanical power transmitted between the runner and shaft
Mechanical power loss of water turbine Plm(kW)
Loss of mechanical power in guide bearings, thrust bearings and main shaft seals of hydro turbines
Hydro turbine power P(KW)
Output Power of runner minus mechanical power loss of hydro turbine (P=Pm-Plm)
Rated power of hydro turbine Pr(KW)
hydro turbine nameplate power specified by design or contract at rated head and speed
Optimum operation condition power Popt(kw)
Hydro Turbine power when operating under optimal conditions
Maximum turbie power Pmax(KW)
Designed or contracted maximum hydro turbine power within specified working water head range
Efficiency of the Hydro turbine
Hydraulic Efficiency ηh
Ratio of runner output power to hydro turbine input power ηh=Pm/Ph
Mechanical Efficiency ηm
Ratio of hydro turbine power to runner output power ηm=P/Pm
Hydro turbine efficiency η
Ratio of hydro turbine power to hydro turbine input power η=(P/Pm)x(Pm/Ph)=ηm*ηh
Optimum Efficiency ηopt
Maximum efficiency in various operating conditions of the hydro turbine
Water level of hydropower plant
Maximum flood level Zfl max (m)
The highest water level reached in front of the dam when the reservoir encounters the check flood of the dam, which is the highest flood level allowed by the reservoir under unconventional operating conditions
Design flood level Zfl.d(m)
The highest water level reached in front of the dam when the reservoir encounters the check flood of the dam, which is the highest flood level allowed by the reservoir under normal operating conditions
Normal pool water level Zpl.n (m)
Reservoir meets water resources requirements and maintains high water levels under normal operating conditions(normal high water level or Designed reservoir level)
Minimum pool water level Zpl.min(m)
Reservoir meets water resources requirements and hydro turbine under normal operating, allowed the reservoir to fall to the lowest level （dead level)
Maximum tail water level Ztl.max (m)
The highest water level at the section of the draft tube outlet when checking the flood flow of a hydropower station
Design tail water level Ztl.d (m)
water level at the section of the draft tube outlet used for determining turbine installation elevation.
Minimum tail water level Zfl.mim(m)
The water level at the section of the draft tube outlet when minimum water flowing given by hydropower station.
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