contents · 2019-05-23 · solving unit commitment problem using multi-agent evolutionary...

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.


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.


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


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.


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.


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.


x(i, t+1) x(i, t)


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.


x (i, t) x (i, t+1)


System constraints:

State as the power generated from all unit must be equal the load and

the losses.


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.


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.


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.


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

6 IQEA Improved Quantum Evolutionary Algorithm 2012 563,977.00

7 QBPSO Quantum-Inspired binary PSO 2012 563,977.00

8 BNFO Binary Neighbourhood field Optimization 2012 563,938.00

9 SPL Stochastic Priority list 2013 564,950.00


11 PSO Particle Swarm Optimization 2013 574,153.00

12 BPSO Binary Neighbourhood field Optimization 2013 565,804.00

13 PSO-LR PSO Combined with Lagrangian relaxation 2013 565,869.00

14 LR Lagrangian relaxation 2013 566,107.00

15 LRGA Lagrangian relaxation combined with Genetic Algorithm 2013 564,800.00

16 ALR Augmented Lagrangian relaxation 2013 565,508.00


18 BCGA Binary Coded Genetic Algorithm 2013 567,367.00

19 ICGA Integer Coded Genetic Algorithm 2013 566,404.00

20 DP Dynamic Programming 2013 565,825.00

21 MA Memetic Algorithm 2013 565,827.00

22 PM Prposed method 2013 564,703.00


Research Papers (2/3)23 MIP Mexed Integer Programming 2014 564,647.00

24 QEA Quantum-Inspired Evolutionary Algorithm 2014 563,938.00

25 IBPSO Improved Binary Particle Swarm Optimization 2014 563,977.00

26 BGSO Binary Glowwarm Swarm Optimization 2014 563,938.00

27 SDPSP Semi Definite Programming combined with selective Pruning 2016 563,977.00



30 ICA Imperialist Competitive Algorithm 2016 563,938.00

31 BRABC Binary Real Coded Artificial Bee Colony 2016 563,937.72

32 QIEA Quantum-Inspired Evolutionary Algorithm 2016 563,938.00

33 GHS-JGT Guassian Harmony Search and Jumping Gene Transposition Algorithm 2016 563,937.68

34 QOTLOB Quasi-oppositional Teaching Learning Based Optimization 2016 563,937.69

35 ELRPSO Langrangian Relaxation and Particle Swarm Optimization 2016 563,938.00

36 LR Lagragian Relaxation 2016 565,673.13


38 LRGA Lagrangian Relaxation & Genetic Algorithm 2016 564,800.00

39 BFA Bacteria Foraging Algorithm 2016 564,842.00

40 IBPSO Improved Binary PSO 2016 563,977.00

41 Mendel's GA Mendel's Genetic Algorithm 2016 563,937.00

42 LRMGA Lagrangian Relaxation & Mendel's Genetic Algorithm 2016 562,587.00

43 SPL Stochastic Priority list 2017 564,950.00



Research Papers (3/3)45 EPL Extended Priority List 2017 563,977.00

46 PLEA Priority List Based Evolutionary Algorithm 2017 563,977.00


48 BPSO Binary Neighbourhood field Optimization 2017 565,804.00

49 PSO-LR Particle Swarm Optimization- Langrangian Relaxation 2017 565,869.00

50 LR Langrangian Relaxation 2017 566,107.00

51 LRGA Lagrangian Relaxation & Genetic Algorithm 2017 564,800.00

52 ALR Augmented Lagrangian relaxation 2017 565,508.00


54 FPGA Floating Point Genetic Algorithm 2017 564,094.00

55 BCGA Binary Coded Genetic Algorithm 2017 567,367.00

56 ICGA Integer Coded Genetic Algorithm 2017 566,404.00

57 UCC-GA Unit Characteristic Classification-Genetic Algorithm 2017 563,977.00

58 ACSA Ant Colony search Algorithm 2017 564,049.00

59 DP Dynamic Programming 2017 565,825.00

60 DPLR Dynamic Programming and Langrangian Relaxation 2017 564,049.00

61 TS-RP Tabu Search based Hybrid Algorithm 2017 564,551.00

62 MA Memetic Algorithm 2017 565,827.00

63 MRCGA Modified Real Coded Genetic Algorithm 2017 564,244.00

64 CSS Charge Search Algorithm 2017 563,938.00


66 ACS Ant Colony search 2017 563,938.00

Graphical Summary of Results from

Research Papers

574,153.00

562,587.00

574,153.00

562,000.00

564,000.00

566,000.00

568,000.00

570,000.00

572,000.00

574,000.00

576,000.00

0 10 20 30 40 50 60 70

BEST C

OST A

CH

EIV

ED

REFERENCE NUMBER OF TECHNIQUE USED TO SOLVE UC PROBLEM

COST COMPARISON W.R.T DIFFERENT TECHNIQUES

Some Binaries extracted from

Research Papers

contents · 2019-05-23 · solving unit commitment problem using multi-agent evolutionary...

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