Example of Use: Operating Plan Implementation

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This page is a translated version of the page Anwendungsbeispiel: Umsetzung eines Betriebsplans and the translation is 100% complete.
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Taking the Wehebach-Dam as an example of use, the implementation of an operating plan in accordance with applying laws is illustrated.

The Wehebach-Dam is a multi-purpose reservoir used for water supply and flood protection. In addition, a standard discharge of 100 l/s to the downstream watercourse is to be maintained. The operator of the dam is the Water association Eifel-Rur. The operation responsibilities include the drinking water supply of the greater Aachen area, the northern Eifel region and the supply of service water for several industrial companies. The catchment area of the dam is 43.61 km², the average annual inflow is 21 million m³, and the storage capacity is 119.3%. Built as a rockfill dam, the construction of the reservoir was completed in 1983.

The following operating plan was drawn up for the Wehebach-Dam:

  • Characteristics of the dam:
Max. content at crest level: 27.1M m³
Capacity to the spillway: 25.06M m³
Capacity level (normal water level): see flood control areas
  • Release volume for water supply:

The reservoir provides two water supply companies with drinking water. The companies request water via daily demand values. Concerning the water supply, it is set that up to 11 million m³ must be provided annually as drinking water, of which no more than 2.5 million m³ may be discharged each month.

  • Standard discharge:

The standard discharge is intended to provide a minimum flow downstream of the dam and is set depending on the inflow, as follows:

  Inflow ≥ 200 l/s Standard discharge = 200 l/s
100 l/s ≤ Inflow < 200 l/s Standard discharge = Inflow
  Inflow < 100 l/s Standard discharge = 100 l/s

Every water resources management year, not later than the end of March, 4 m³/s must be discharged to the downstream watercourse as a flushing wave over a period of 6 hours.

  • Flood control areas:

To ensure sufficing flood protection, a time-variable pool-based flood level is defined. The lower limit of the flood control areas is defined as the capacity level.

1.10. - 31.10. Flood control area = 1.00M m³ Capacity level = 24.06M m³
1.11. - 30.11. Flood control area = 2.75M m³ Capacity level = 22.31M m³
1.12. - 15.1. Flood control area = 4.50M m³ Capacity level = 20.56M m³
16.1. - 31.3. Flood control area = 2.50M m³ Capacity level = 22.56M m³
1.4. - 30.4. Flood control area = 1.75M m³ Capacity level = 23.31M m³
1.5. - 30.9. Flood control area = 1.00M m³ Capacity level = 24.06M m³

Clearance of flood control areas is done at the maximal permitted discharge.

  • Maximal permitted discharge:

As long as the normal water level has not yet been reached, no more than 5 m³/s may be discharged to the downstream watercourse.

If the normal water level of the dam is exceeded and the inflow exceeds the maximum discharge of 5 m³/s, no more than 5 m³/s may be discharged from the bottom outlet. Additional inflow is to be discharged via the spillway.

  • Capacity curve of the spillway:

The characteristic curve is given as a X-Y curve with interpolation points.

The realization of the operating plan considering the terminology described above, first requires the identification of all expectations and uses for the dam and a definition of the discharge functions. The following information is provided only to illustrate the operating plan concept and does not claim to be complete or an accurate representation of actual conditions.

  • Use: Water supply
Temporal dependency: Constant annualized discharge function, variable demand
External dependencies: Yes
  1. Current water demand [m³/s]: Factor1 (calculation rule: multiplication)
  2. Monthly balance of withdrawals: Factor2 (calculation rule: multiplication)
  3. Annual balance of withdrawals: Factor3 (calculation rule: multiplication)
Discharge per time step: Calculation of the use 'water supply' with:

Discharge = Factor1 × Factor2 × Factor3 × f(Storage volume)

Conditions Discharge functions
Fulfillment of demand [%]:

Period of validity: Jan. 1 - Dec. 31.

Explanation: Starting from a storage capacity of < 10 million m³, the fulfillment of demand is reduced to 80%. If the storage volume falls below 2 million m³, no more water is withdrawn.

Theorie Bsp01.png
Conditions System State Functions
Actual water demand [m³/s]:

(Factor 1)

Time reference: current value

Calculation rule: multiplication

No function necessary
Monthly balance of discharge [-]:

(Factor 2)

Time reference: monthly balance

Period of validity: Jan. 1 - Dec. 31.

Limit value: 2.5M m³

Calculation rule: multiplication

Theorie Bsp02.png
Annual balance of discharge [-]:

(Factor 3)

Time reference: annual balance

Period of validity: Jan. 1 - Dec. 31.

Limit value: 11.0M m³

Calculation rule: multiplication

Theorie Bsp03.png


  • Use: Flood Protection
Time dependency: Yes
External dependencies: No
Discharge per time step: The use 'flood protection' is given directly as a function of the date.

Discharge = f(storage volume)

Conditions Discharge Functions
Period of validity: Dec. 1 - Jan. 15.

Maximal permitted discharge: 5 m³/s

Capacity level: 20.56M m³

Theorie Bsp04.png
Period of validity: 16 Jan - 31 March

Maximal permitted discharge: 5 m³/s

Capacity level: 22.56M m³

Theorie Bsp05.png
Period of validity: April 1 - April 30

Maximal permitted discharge: 5 m³/s

Capacity level: 23.31M m³/s

Theorie Bsp06.png
For the remaining periods, the discharge functions are analogous.


  • Use: Standard discharge
Time dependency: Yes
External dependencies: Yes
  1. Current inflow {m³/s]: Factor 1 (calculation rule: multiplication)
Discharge per time step: Calculation of the use 'standard discharge' with:

Discharge = Factor × f(storage volume)

Conditions Discharge Functions
Factor standard discharge [-]:

Period of validity: Jan. 1 - Dec. 31.

Explanation: If the storage volume declines below 2 million m³, a standard discharge is no longer maintained.

Theorie Bsp07.png
Conditions System State Functions
Current inflow [m³/s]:

(Factor 1)

Period of validity: Jan. 1 - Dec. 31.

Maximal permitted discharge: 5 m³/s

Explanation: If the inflow exceeds 0.2 m³/s, a discharge of 0.2 m³/s continues.

Theorie Bsp08.png


Abbildung 26: Skalierte Abgabenfunktionen

For a selected time and an assumed initial storage volume of S0 = 23K m³, all relations are plotted in Abbildung 26. For illustration purposes, a different y-axis scale is chosen for the flood control function.

Parameters Defaults Affected Parameters:
Time January 30 flood protection, water supply. (Factor1, Factor2)
Initial storage volume 23M m³ all discharge functions
Average daily inflow 0.180 m³/s standard discharge
Average water demand 0.300 m³/s discharge for water supply
Discharge for water supply since 1.Jan. 0.750M m³ discharge for water supply