bReeze (version 0.3-2)

aep: Calculation of annual energy production

Description

Calculates annual energy production (AEP) from a site's wind profile and wind turbine characteristics.

Usage

aep(profile, pc, hub.h, rho=1.225, avail=1, 
  bins=c(5, 10, 15, 20), sectoral=FALSE, 
  digits=c(3,0,0,3), print=TRUE)

Arguments

profile

Wind profile object created by profile.

pc

Power curve object created by createPC or read from file by readPC.

hub.h

Hub heigth of wind turbine as numeric value.

rho

Air density as numeric value. Default is 1.225 kg/m3 according to the International Standard Atmosphere (ISA) at sea level and 15°C.

avail

Availability of turbine as numeric value between 0 (not available at all) and 1 (100% available).

bins

Edges of wind speed bins as numeric vector or NULL if only total AEP is desired.

sectoral

If TRUE, wind speeds are extrapolated to hub height using the wind profiles of each direction sector. Otherwise the general profile ("all") is used for extrapolation (default).

digits

Number of decimal places to be used for results as numeric vector. The first value is used for wind.speed, the second for operation, the third for aep and the fourth for capacity results. Default is

print

If TRUE, results are printed directly.

Value

• Returns a list containing:
• wind.speed
  Mean wind speed for each direction sector.
• operation
  Operational hours per year for each direction sector.
• total
  Total annual energy production for each direction sector.
• ...
  Annual energy production per wind speed bin for each direction sector.
• capacity
  Capacity factor of the wind turbine.

encoding

UTF-8

Details

For a wind turbine the mean energy production can be expressed by $$E = T \, \int_{v_{in}}^{v_{out}} \! f(v) \, p(v)$$ where $f(v)$ is the probability density function of the wind speed $v$, $p(v)$ is the power curve of the turbine and $T$ is the production time period. Energy production starts at the turbine's cut-in wind speed $v_{in}$ and stops at cut-out wind speed $v_{out}$.

Based on this fundamental expression, aep calculates the annual energy production as follows: $$AEP = A_{turb} \, \frac{\rho}{\rho_{pc}} \, H \, \sum_{b=1}^{n} \! W(v_b) \, P(v_b)$$ where $A_{turb}$ is the average availability of the turbine, $\rho$ is the air density of the site and $\rho_{pc}$ is the air density, the power curve is defined for. $W(v_b)$ is the probability of the wind speed bin $v_b$, estimated by the Weibull distribution and $P(v_b)$ is the power output for that wind speed bin. $H$ is the number of operational hours -- the production time period of the AEP is per definition 8760 hours.

The wind speed $v_h$ at hub height $h$ of the turbine is extrapolated from the measured wind speed $v_{ref}$ at reference height $h_{ref}$ using the Hellman exponential law (see profile): $$v_h = v_{ref} \, \left(\frac{h}{h_{ref}} \right)^\alpha$$

The productive suitability of a wind turbine for a site can be evaluated by the capacity factor $CF$. This factor is defined as the ratio of average power output of a turbine to the theoretical maximum power output. Using the AEP as the average power output, the rated power $P_{rated}$ of a turbine and the maximum operational hours of a year we get: $$CF = \frac{AEP}{P_{rated} \, 8760}$$

References

Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E. (2001) Wind Energy Handbook. New York: Wiley

Fördergesellschaft Windenergie e.V. (2007) Technical Guidelines for Wind Turbines, Part 6: Determination of Wind Potential and Energy Yields, Revision 7

International Organisation for Standardization (1975) ISO 2533:1975 Standard Atmosphere. ISO Standard

Jangamshetti, S.H., Rau, V.G. (1999) Site Matching of Wind Turbine Generators: A Case Study. IEEE Transaction on Energy Conversion 14(4), 1537--1543

See Also

profile, createPC, readPC, plotAep, printObject

Examples

# load and prepare data
data(winddata)
set1 <- createSet(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set2 <- createSet(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])
ts <- formatTS(time.stamp=winddata[,1])
neubuerg <- createMast(time.stamp=ts, set1, set2)
neubuerg <- clean(mast=neubuerg)

# calculate wind profile
neubuerg.wp <- profile(mast=neubuerg, v.set=c(1,2), dir.set=1, 
  print=FALSE)

# load power curve
pw.56 <- readPC(file="PowerWind_56_900kW.wtg")

# calculate AEP
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71)

# calculate AEP with site specific air density and availability of 97aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, rho=1.195, avail=0.97)

# calculate total AEP using sectoral profiles
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, sectoral=TRUE)

# calculate AEP for 1 m/s speed bins and without binning
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, bins=seq(0,25))
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, bins=NULL)

# change number of digits and hide results
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, digits=c(1,1,1,1))
neubuerg.aep <- aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, print=FALSE)