Contents Introduction Unit Commitment Problem Formulation Objective Function Constraints A Brief Overview of Some Optimization Techniques Cost Comparison of different Optimization Techniques applied to UCP 10 Unit Standard Test System Load profile of 24 hour (Tabular and Graphical) Tabular Summary of Results from Research Papers Graphical Summary of Results from Research Papers Binary Unit Commitment and Unit Allocation data Conclusion References
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Contents · 2019-05-23 · Solving Unit Commitment Problem Using Multi-agent Evolutionary Programming Incorporating Priority List Solution to Unit Commitment Problem using La-Grangian
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Contents Introduction
Unit Commitment Problem Formulation
Objective Function
Constraints
A Brief Overview of Some Optimization Techniques
Cost Comparison of different Optimization Techniques applied to UCP
10 Unit Standard Test System
Load profile of 24 hour (Tabular and Graphical)
Tabular Summary of Results from Research Papers
Graphical Summary of Results from Research Papers
Binary Unit Commitment and Unit Allocation data
Conclusion
References
Introduction
• Steps of Power System Operation• Load Forecasting
• Hydrothermal Coordination
• Unit Commitment
• Economic Dispatch
• Unit Commitment Overview• Determination of Generation mix to achieve estimated output
level to meet the demand of electricity for a specified time
interval while satisfying all constraints.
Objective Function
Minimization of Total Cost including:
Fuel Cost
𝐹𝐶𝑖 𝑃𝑖 𝑡 = 𝐴𝑖 + 𝐵𝑖𝑃𝑖 𝑡 + 𝐶𝑖𝑃𝑖2(𝑡)
Startup Cost
Shutdown Cost
Shutdown Cost is Constant and is zero in Typical Systems
Total Cost
Constraints
Definition:
Constraint is limitations in power system avoiding it cause serious
problem.
This limitation can be technical for unit or technical limitation for power
system or can be environmental limitations.
We can classified into
Unit constraints.
System constraints.
Environmental constraints.
Network constraints.
Cost constraints.
Unit commitment constraints
Unit constraint :
1. Maximum generating capacity.
2. Minimum stable generation.
3. Minimum up time.
4. Minimum down time.
5. Ramp rates.
1. Ramp up rate.
2. Ramp down rate.
3. Start-up ramp rate.
4. Shut down ramp rate
5. Running-up ramp rate
6. Running down ramp rate.
Unit commitment constraints
System constraints:
1- Load / generation balance / system power balance.
2- Spinning reserve constraint.
Network constraint:
Environmental constraint:
Cost constrain:
1- Start-up cost.
2- Running cost.
Unit commitment constraints
Maximum generating capacity:
That constraint state that the power generated from the unit must not exceed
specific value because of thermal stability of the unit exceeding this constraint cause damage to the unit.
Mathematical formula.
X (i,t) < P max
X (i,t) is the output power of the unit i, in the time t.
Minimum stable generation:
As the above constraint the power outage from the unit must not fall down
specific value because of technical limitation like flame stability in the gas and steam units.
Mathematical formula.
X (i,t) > P min
The maximum and minimum generated power of each scheduled unit must not be exceeded
p min < X (i, t) < p max
Unit commitment constraints
Minimum up time:
This constraint state that once the unit is running must not shunt down
immediately due technical limitation and mechanical characteristic of the unit.
Mathematical formula:
Where
u(i, t) : status of unit i at period t.
u(i, t) = 1 unit i is ON during period t.
u(i, t) = 0 unit i is Off during period t.
Unit commitment constraints
Ramp rates:
Definition:
To avoid damaging the turbine, the electrical output of a unit cannot
change by more than a certain amount over a period of time.
Minimum down time:
This constrain state that once the unit is running must not shunt
down immediately due technical limitation and mechanical characteristic of the unit.
Unit commitment constraints
Ramp-up rate:
Start-up ramp rate:
According to this constraint the unit cannot start immediately but taking
time this time called start up time.
Running-up ramp rate:
According to this constraint the unit cannot immediate changing the power
up without taking time called ramp rate running up time. The change here means
increasing outage power.
Mathematical formula:
x(i, t+1) x(i, t)
Unit commitment constraints
Ramp down rate:
Shut down ramp rate:
Look like previse constraint the unit take time to shut down.
Running down ramp rate:
According to this one in case of running condition. The unit cannot
immediate changing the power down without taking time called ramp rate running
down time. The change here means decreasing outage power.
Mathematical formula:
x (i, t) x (i, t+1)
Unit commitment constraints
System constraints:
State as the power generated from all unit must be equal the load and
the losses.
Mathematical formula:
u(i,t) * x(i,t) = l(t)
Where l(t) is the load power at time t.
Spinning reserve constraint:
Spinning reserve:
Spinning reserve is the on-line reserve capacity that is synchronized to
the grid system and ready to meet electric demand within 10 minutes of a dispatch
instruction by the ISO (International Standards Organization) . Spinning reserve is
needed to maintain system frequency stability during emergency operating conditions
and unforeseen load swings.
Unit commitment constraints Reason to keep reserve power.
1- Sudden unexpected increase in the load demand.
2- Underestimating the load due to error in load forecasting.
3- Local shortage in the generated power
4- Force outage of some generating units.
5- Force outage of supplementary equipment’s due to stability problem.
In Electrical engineering, Force outage is the shutdown condition of a power station, transmission
line or distribution line when the generating unit is unavailable to produce power due to unexpected
breakdown.
Condition of reserve.
1- Reserve must be higher than largest unit.
2- Should be spread around the network.
3- The unit must operate at 80-85% of its rated.
Unit commitment constraints
Network constraint:
Transmission network may have effect on the commitment of units because of
Some units must run to provide voltage support.
The output of some units may be limited because their output would exceed the
transmission capacity of the network.
Environmental constraint:
Unit commitment study is effected by environmental constrains because of
Constraints on pollutants such SO2, NOx various forms:
1- Limit on each plant at each hour.
2- Limit on plant over a year.
3- Limit on a group of plants over a year.
Unit commitment constraints
Constraints on hydro generation:
1- Protection of wildlife.
2- Navigation, recreation.
Cost constraints:
Cost constrain taking two type of cost in consideration.
1- Start-up cost:
Start up cost depends on varicose factor like
Warming up because the unit cannot bring on line immediately.
Start up cost depends on time unit has been off.
Unit commitment constraints
Running cost:
A balance between start-up costs and running costs is important because of
1- How long should a unit run to “ recover” its start up cost ?
Example:
Diesel generator : Low start-up cost, High running cost.
Coal plant : High start-up cost, Low running cost.
Spinning Reserve:
“Spinning” means the generator is running and may have be synchronized, so it is ready to provide the desired power in short time.
when some sudden load demand is there we increase steam input and delta increases a little bit and sudden requirement is supplied. This capacity of generators is called "Spinning Reserve".
A Brief Overview of Some
Optimization Techniques
Algorithms used in UC
Solving Unit Commitment Problem
Using Modified Sub-gradient
Method Combined with Simulated
Annealing Algorithm
A New Heuristic Algorithm for Unit
Commitment Problem (Modified
Harmonic Search)
Solving Unit Commitment Problem
Using Multi-agent Evolutionary
Programming Incorporating Priority
List
Solution to Unit Commitment
Problem using La-Grangian
Relaxation and Mendel’s GA Method
A New Priority List Unit
Commitment Method for Large-
Scale Power Systems
Three meta heuristic techniques:
Charged Search System
Particle Swarm Optimization
Ant Colony Search
Simulated Annealing
Strong technique for solving hard combinatorial optimization problems without specific structure
Inspired by Annealing in Metallurgy which involves:
Heating and Controlled cooling of a material to increase the size of its crystals and reduce their effect (Wikipedia)
Basic Working Steps:
Random Selection of a solution close to current solution
Decision on the basis of two probabilities:
Probability of finding a better solution (kept 1)
Probability of finding a worse solution (kept 0)
Main Features:
Lesser Memory Requirements (Advantage)
Ability to escape Local Minima
Large Computation Time Required (Disadvantage)
Simulated Annealing Algorithm Steps
Harmony Search (HS) Algorithm
Population based metaheuristic Algorithm
Based on natural musical performance processes that occur when a musician
searches for a better state of Harmony
Algorithm Steps
Initialization of Harmony Memory
Improvisation of new Harmony vector
Harmony Memory Updating
Multi-agent Evolutionary Programming
Incorporating Priority List
Multi-agent Evolutionary Programming incorporating Priority List optimization
technique (MAEP-PL) is proposed to solve the unit commitment problem
Combination of three techniques:
The Multi-agent system (MAS)
Multiple Interacting Intelligent Agents working together to achieve common goal
The Evolutionary Programming (EP) optimization technique
The Priority List optimization Technique (PL)
Rule 1: based on Maximum Power Generation Rate
Rule 2: based on Maximum Generation Rate and Capacity
Cost Comparison of different Optimization
Techniques applied to UCP
Standard 10 Unit Test System
Load Profile of 24 hr (Tabular)
Load Profile of 24 hr (Graphical)
0
200
400
600
800
1000
1200
1400
1600
0 5 10 15 20 25 30
LO
AD
IN
MW
HOURS
LOAD PROFILE OF 24 HR
Tabular Summary of Results from
Research Papers (1/3)
Ref. # Technique used Abbreviation Year Best Cost ($)
1 GA Genetic Algorithm 2012 565,825.00
2 EP Evolutionary Programming 2012 564,551.00
3 SA Simulated Annealing 2012 565,828.00
4 DE Differential Evolution 2012 563,977.00
5 IPSO Improved Particle Swarm Optimization 2012 563,954.00