Chapter 3 hydro thermal scheduling
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Transcript of Chapter 3 hydro thermal scheduling
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Contents
Problems definition
Mathematical model of long and short termproblems
Dynamic and incremental dynamic programming Methods of local variation
Hydro thermal system with pumped hydro units
Solution by local variation
Treating Pumped Hydro unit for loadmanagement and spinning reserve
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Ethiopian power system
Generation potential
Supply system
ICS supplied from hydro power plants
SCS mini hydro plants and diesel generators
Type of energy source Potential
Hydropower Above 4,000MW
Wind Above 1,350,000MW
Geothermal Above 5000MW
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Generation trend
Generation trend is increasing
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Electrification status
According to EEPCO report 48.3%
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Installed capacity
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Installed capacity
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Percentage contributions
Largest portion is supplied from hydro 89.8%
hydro
diesel
geothermal
wind
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Transmission system
Total length 11,796.32Km with 5 voltage levels
There are 143 substations with 127 supplying
distribution systems
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Distribution system
Distribution system consists of 148745.5km
and 18,888 transformers
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Customers
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Energy sales
Total number of customers by tariff group is as
shown below
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Historic energy sales
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Total energy soled
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Problem definition
Generation scheduling
Determining optimal operation strategy for the next
scheduling period
subject to a variety of constraints
Limited energy storage capability of water reservoirs
Stochastic nature of availability of water
Can be broken down into sub problems Hydrothermal coordination (yearly, monthly and weekly )
Unit commitment (weekly or daily)
Economic dispatch (hourly)
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Problem definition
Generation planning problem is
Nonlinear optimization problem
With continuous and discrete variable s
Non explicit objective function
With equality and inequality constraints
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Problem formulation
Hydro thermal coordination (HCP)
Determining optimal amount of hydro andthermal generation to be used in a scheduling
period Can be classified into short, mid and long term
scheduling
Constraints
Irrigation Recreation
Effect on downstream users
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Problem formulation
Hydrothermal scheduling problem
Long range
This involves
Long range forecasting of water availability Scheduling of water releases
Affected by
assumption used to calculate water replacement (Usestatistical mean or Worst case )
Load, hydraulic inflows, unit availabilities
Medium range
Short range
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Mathematical model of long and short
term problems
Mid term hydro scheduling (1week to 1 day)
This involves
Long range forecasting of water availability
Scheduling of water releases
Affected by
assumption used to calculate water replacement
Use statistical mean
Worst case
Load, hydraulic inflows, unit availabilities
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Problem formulation
Short range ( 1 day to 1 week)
Hour by hour scheduling of all generators to
achieve minimum production cost
Load, hydraulic inflow and unit availability is
known
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Operational factors affecting
hydrothermal scheduling
Type of turbine used
Francis turbine may operate at 65 to 125% of ratednet head
Loading At light unit loading, efficiency may drop to 70% and
at full load may rise to 87%
Hence
unit loading must be at best efficiency gate position Water releases schedule must coordinate with inflow
Note: better one full than two halves
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Types of hydrothermal scheduling
All hydro Difficult to meet the demands and operate
economically
Simulate the water system
Find a schedule which leaves maximum stored
energy in reservoir
Hydro dominated
Schedule the system for minimum cost of thermal
Balanced or with most thermal
Minimize thermal production costs
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Scheduling of mostly hydro case
Problem formulation
One hydro and one thermal
Rated hydro power is enough to cover load but
available hydro energy is not enough
Use thermal energy to fill the gap
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Problem formulation
Symbols used
EH- total available hydro energy
Time period to use all energy is TMAX
Hence
Where PHj is hydro generation limit at time j
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Problem formulation
ES=total thermal energy used
PSj- thermal generation level at time j
TS- total thermal run time
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Problem formulation
Total energy used by the load
Where PLj is load at time j
The thermal energy used is then
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Problem formulation
Then the problem statement is to minimize
the cost of generation of Es
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Solution using Lagrangian method
Form the Lagrangian
Apply necessary condition
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Solution using Lagrangian Method
Solving the two equations, from the first one
Which means the thermal must run at
constant generation level for all time
If the generation level is assumed to be PS*
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Solution by Lagangian Method
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Solution by Lagrangian Method
Substituting into the second equation
If the cost function of the thermal unit is givenbye
(*)
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Solution by Lagrangian Method
The total cost of running the thermal unit is
then
Substituting from equation (*) above
Now we have nonlinear unconstrained
optimization with single variable
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Solution by Lagrangian Method
Solving for Ps
This means the thermal unit must be operated
at the maximum efficiency point for as long as
it produced the demanded energy Es
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Example 7A page 217
Given the following characteristics for the
hydro and thermal plants, they have to supply
a load of 90MW for a week (15120MWhr)
Case I- if the hydro is limited to 10, 000MWh
energy, solve the run time of the thermal
Required energy from thermal is 5120MWhr
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Example 7A
The steam plants maximum efficiency point is
at 50MW, hence it has to run for 102.4hr
Hence
Steam run at 50MW for the first 102.4 hr of the
week
Hydro runs at 40MW for the first 102.4hr and then
for the rest 65.6hr, it runs at 90MW
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Example 7A
Case II- if the limit is on the amount of water
drawn from the reservoir 250,000 acre-fit
The water drawn from the reservoir is
determined by the amount of power
generated
Giving Ts=36.27h
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Short term hydrothermal scheduling
Problem definition
Given a hydro and thermal unit supplying a load
and constraints of total water discharge, starting
volume, ending volume etc, find a schedule whichminimizes the total cost
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Short term hydrothermal scheduling
Problem formulation
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Short term hydrothermal scheduling
Forming the Lagangian
Applying the necessary conditions
Sh t t h d th l h d li
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Short term hydrothermal scheduling
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Example 7B
Solve example 7B
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Assignment
Explain the idea of pumped hydro systems
List some of world famous pumped hydro
systems and explain how they are used, i.e
Load management
Spinning reserve
Discuss the hydrothermal scheduling of
generation units which are in series cascad like
that of Gibe dam units
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Dynamic programming
Is a systematic way of determining optimal
solution in a problem having multiple stages
and with many possible decisions at each
stage
Is developed by Bellman in 1957
Has nothing to do with computer
programming
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Dynamic programming
Consider the following graph, numbers
correspond to time to travel between nodes
Find a path from A toB, travelling on to the
right, such that the
total sum of numbers
is minimum
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DP algorithm
Forward DP- start with A and find the cost of
moving forward until B
Backward DP start with B and find backward
the optimal path
In both cases, we have to decisions at each
stages
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DP algorithm
There are 20 possible routes
The optimal path can be computed using DP
as follows
Start at B and move one step back
Find the minimum path to arrive at B from one
step back
Repeat this for each stage
Stop when arriving at A
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DP algorithm
Solution
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DP used for hydrothermal scheduling
Consider the following situation where a
single hydro and single thermal units supply
power to a load
Total scheduling time
Tmax is divided into
time periods j
Given: loads at time
periods, starting andending volume Vo
and Vmax
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DP for hydrothermal scheduling Assumptions
The thermal unit is on for the whole time period
Water use rate of hydro is given by
Maximum flow rate qmax is limitedcorresponding to the maximum power output ofthe hydro
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DP for hydrothermal scheduling
The volume in storage changes as
For two consecutive intervals Vj and Vj-1
Problem is
find the volume at each stage sothat the total cost is minimum
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DP for hydrothermal scheduling
DP algorithm
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DP hydrothermal scheduling Example
A thermal unit and hydro unit have the
following characteristics curves
1200P200and
2000
PP8.4700F
s
2
s
s
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DP hydrothermal scheduling Example
Initial and final volumes are 10,000m3 and
storage volume limits are 6000 and 18000m3
The scheduling period is 24h divided by 4h
intervals
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DP for hydrothermal scheduling Example
If the storage volume steps are 2000m3Discharge at any
time interval j is
given by
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DP for hydrothermal scheduling Example
The first and second stage computations
becomes
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DP example
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Linear programming
Is a mathematical method used to allocate
scarce resources to competing alternatives in
an optimal manner
Linear objective function and
Constraints are linear inequality
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Example Linear programming
Consider the following profit function
Subject to the constraints
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Example LP
Solution methods
Graphical method for two dimensional case
Draw the graph of constraints
The closed boundary formed from constraints is thefeasible solution region
Corner points of the boundary are max/min points
Check for these points
Simplex method
for multi variable case
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Hydrothermal scheduling with LP
To apply LP
Objective function has to be linear
Divide the cost function of the steam turbine into
sections and approximate it by linear function withknown slope
Hydro turbine output versus the discharge has to be
approximated by linear
Constraints have to be linear Approximate water
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Hydrothermal scheduling using LP
For thermal characteristics, if 3 steps are used
For the hydro
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Hydrothermal scheduling using LP
Thermal and hydro linear approximation
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Hydrothermal scheduling using LP
Spill characteristics approximated by linear
Water spills out if volume is above a limit
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Hydrothermal scheduling using LP
Problem formulation
Minimize the linear cost function
Subject to