How to predict timing and quantity of pre-emptive safe discharge – a dam simulation model
How to predict timing and quantity of pre-emptive safe discharge – a dam simulation model
THIS IS IT! As the saying goes, a dam simulation model that could be easily implemented and calibrated with actual rainfall and river gauging data and compared with actual power generation and spillway discharge to predict dam height and dam water volume is now available to government agencies, dam operators, dam designers and ordinary laymen. Please write the author for arrangements on how to secure this state-of-the-art dam simulation model.
As a sequel to my original blog on “How to predict early dam water release – the key to minimizing flooding during typhoons” found in the link below:
your energy technology expert now ventures into the realm of dam simulation.
The author has been invited to provide technical expertise as a result of the above blog to Technical Working Group (TWG) of the Congressional Ad Hoc Committee on Dams Management & Safety of the current Philippine Congress chaired by the Honorable Congressman Mark Cojuangco.
This committee has been tasked to determine the sequence of events that lead to the catastrophic release of dam waters at the height of Typhoon “Pepeng” and its return for a second land fall, after an earlier Typhoon “Ondoy”. It also aims to revisit and revise as soon as possible the DAM WATER RELEASE PROTOCOL currently being followed by dam operators with the aim of ensuring that dam safety and prevention of flood damage and lose of lives shall be the paramount consideration over and above all contractual obligations of dam operators and managers.
This existing protocol may have inadvertently caused the delayed safe release of excess water so that an incoming storm or prolonged heavy rainfall could not be stored inside the dam without overflowing the dam’s spillway leading to massive releases of over 5,000 cubic meters per second (cms) of excess water that overwhelmed the carrying capacity of downstream structures of the Agno River Flood Control and Dike System in the province of Pangasinan.
The proposed new DAM PROTOCOL will provide trigger mechanisms for the shifting from regular dry season rule curve to typhoon or rainy season mode of operation. Among the proposals includes the authorized maximized generation of power to the rated and overload capacity of the dam turbines and generators and if need be, to allow release of pre-determined safe discharge of excess water so that the dam could maximize its flood control potential to capture the expected rainfall from the approaching storm.
And after the storm event has ebbed and rainfall has stopped, the dam operator is likewise mandated and authorized to continue releasing safe volumes of water in order to reach a target level that will restore its flood control capability again as a precautionary move in the event a new storm is approaching.
In the event that the rainy season is about to end, and as a result of undertaking pre-emptive discharges as required by the new DAM PROTOCOL, the dam operator is authorized to maximize water storage and refrain from power generation in order to go back as quickly as possible into the rule curve for the current month in order to ensure adequate water supply for the entire year specially during the dry season.
It is further proposed that any action of the dam owners and operators arising from following the revised DAM PROTOCOL will not result in economic or financial penalties due to contractual issues. Likewise during the period where the typhoon season mode is in effect, the trading of hydro capacity in the WESM is suspended.
However, the timing and quantity of pre-emptive discharge has to be quantified and the use of a dam simulation model is the logical choice.
The fundamental basis for dam simulation is shown below. It simulates a cup with water that is being fed by rainfall from above but is leaking at the bottom due to power generation and if it is over-filled, will spill over the brim.
The differential equation is given by:
dQ/dt = d(AH)dt = (catchment area, km2) x (rainfall, mm/hr) x 1000 + (Upstream River Flow, m3/hr) = C x R x k + URF
where Q = volume of water in dam, m3 (cubic meters)
dQ/dt = volumetric flow rate, m3/hr
A = cross sectional area of dam at given elevation H, m2 (square meters)
C = catchment area = rainfall catchment area of the given river system bounded by the high ridges of the mountains until it exits to the sea, km2
R = rainfall on catchment area, could be measured by the “Doppler radar”, mm of rainfall per hour
k = constant to convert (km2 x mm/hr) to (m3/hr) = 1000
URF = upstream river flow (Binga dam release), m3/hr
= (URF, m3/sec) x (3600 sec/hr)
The next step is to integrate the equation over time to come up with the height of the water elevation (H):
integral (dQ) = integral d(AH) = integral (C x R x k + URF) dt
The above equation could then be integrated either numerically in a digital computer or spreadsheet or analytically into formulas.
If we assume that near the crest (highest point the dam) the cross sectional area is approximately constant as Am, then integrating between the limits (t = to to t; H = Ho to H) we get:
Am x (H – Ho) = (C x R x k + URF) x (t – to)
And the height of the dam water at time t is:
H = Ho + (C x R x k + URF) / Am) x (t – to)
The volume of water dumped by the typhoon is also given by:
V = (C x R x k + URF) x (t – to) = Am x (H – Ho)
The time needed for the dam to overtop itself or reach the critical spillway height is calculated as follows:
(t – to) = Am x (H – Ho) / (C x R x k + URF)
Once the computer model or the analytical model has been derived, the next step is to do simulation on its behavior over time using the above equation for height H and volume V.
The dam simulation model starts with the following initial values:
Vo = starting dam volume at time 0, in m3
Ho = starting dam height at time 0, in m
Then the beginning dam volume and height at time 0100 hour are:
V1 = Vo, in m3
H1 = Ho, in m
The ending dam height and volume at time 0200 hour are:
V2 = V1 + Inflow – Outflow
Where Inflow = Rainfall in dam watershed + upstream river flow, in m3/hr
= C x R x k + URF
Since the plant data log also provided inflow measurements in cms, the author decided to use the average of the calculated inflow (from rainfall and Binga outflow) and the reported inflow:
Inflow(ave) = (calculated inflow + reported inflow) / 2
where calculated inflow = C x R x k + URF
Outflow = Power generation and spillway discharge, m3/hr
= (Power Water + Spillway) x 3600
Power Water = (Power, MW) x 1000 / (9.81 x H x E), in m3/sec
H = dam water head = water elevation – tailrace elevation
= H1 – 100 (example for a dam)
E = energy efficiency for water turbine/generator = 86.75%
Spillway = spillway discharge = function of opening height and width
= this value is based on actual release, in m3/sec
= or assumed release during the simulation to see its effect
However, the ending volume V2 must be checked if it exceeds the maximum volume of the dam at its highest elevation (top of spillway) or if it is lower than the lowest point of the spillway (“Ogee” elevation).
If V2 is greater than Vmax, then the amount of surplus water over and above water used for power generation is:
If V2 > Vmax, then Surplus = (V2 – Vmax) / 3600, in m3/sec
And the rate of surplus water is added to the other volumes to arrive at the revised outflow from the dam:
Outflow(rev) = (Power water + Spillway + Surplus) x 3600, in m3/hr
The ending volume is then recalculated to take into account the surplus water:
V2 = V1 + Inflow(ave) – Outflow(rev)
The ending height is then calculated from the dam height vs dam volume calibration table. My model assumes a linear relationship every 10 meters of elevation change from 200 to 300 meters. The linear interpolators for both dam height and dam volume are given below:
Dam height = x = x1 + (x2 – x1) / (v2 – v1) * (v – v1)
Dam volume = v = v1 + (v2 – v1) / (x2 – x1) * (x – v1)
Hence, the ending dam height is:
H2 = function of V2 = interpolate using Dam height formula, in m
= x1 + (x2 – x1) / (v2 – v1) x (V2 – v1)
where the small letters x1, v1 and x2, v2 are the data points along the dam height vs dam volume calibration curve.
If your country or your dam operator needs assistance in developing and customizing your own dam simulation model, kindly email the author and visit his website for a snippet of the dam simulation model and its resulting graph.
Marcial T. Ocampo
Energy & Pricing Expert
Dam Simulation Modeler
Project Finance & Financial Modeling
Energy & Business Development Consultant
Email: mars_ocampo@yahoo.com
Website: http://www.energytechnologyexpert.com
(Friendly note: All content written by Engr. Marcial T. Ocampo are copyrighted and may not be redistributed in any way or form.)
Leave a Reply
