unit commitment

Unit commitment

Ahmed Mohamed abdel-hakeem Elkholy

Economic operation of power system

March 19, 2016

1. Introduction

1.1 Definition

determining the mix of generators and their estimated output

level to meet the expected demand of electricity over a given

time horizon (a day or a week), while satisfying constraints such

as ramp rate limits, up-time and down-time constraints, reserve

and energy requirements. While the load profile is given and also

the unit available to work is given.

Example 1.1

To fully illustrate the uc study the following sample example is

shown. There are three unit with following data.

Unit 1:

PMin = 250 MW, PMax = 600 MW

C1 = 510.0 + 7.9 P1 + 0.00172 P12 $/h

Unit 2:


C2 = 310.0 + 7.85 P2 + 0.00194 P22 $/h

Unit commitment | Ahmed Mohamed abdel-hakeem Elkholy Page 1 of 14

Unit 3:


C3 = 78.0 + 9.56 P3 + 0.00694 P32 $/h

What combination of units 1, 2 and 3 will produce 550 MW at minimum cost?

How much should each unit in that combination generate?

Solution:

Taking consideration of above given using excel sheet to solve all possible scenarios of operations for illustration we will solve one case manual

Case 6

Scenario is

Unit 1 is off

Unit 1 is on

Unit 1 is on

λ=pd+∑

i=1

n β i2∗γi

∑i=1

n 12∗γi

=550+ 7.85

2∗.00194+ 9.562∗.00694

12∗.00194

+ 12∗.00694

=9.891369369

And the power will be

p= λ−β2∗γ

Power generated from unit 2 =


¿ 9.891369369−7.852∗.00194

=526.1261261MW

To meet constrains the power of unit 2 will be 400 mw

P2=400 mw

The power generated from unit3

¿ 9.891369369−9.562∗.00694=23.87387387MW

Also to meet constrains of unit 3 will be 150 mw

P2=150 mw

Also we also cheek constrain of power demand that’s

Pload =p1+p2=400+150=550 mw

The total cost by substituted in cost equation (given)

Total cost will be = 5428.55

This is for one case.

All case in table below


in above example for one loading case imagine that we can

consider above example for one hour in a day so we have to

calculate for 24 hour imagine for a week or month

so we find it possible to solve uc problem in that way not just for

long calculation but also considering constrains above example

not taking all constrain as we will illustrate in this report .

But we can learn from example 1.1 that


pmin pmax

U1 U2 U2 250 600 U1 U2 U2α for units 510 310 78 200 400 510 310 78β for units 7.9 7.85 9.56 150 500 7.9 7.85 9.56γ for units 0.0017 0.0019 0.0069 0.002 0.002 0.007case 1 0 0 0 #DIV/0! 0 0 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

case 2 0 0 1 17.194 150 500 0 0 0 0 0 0 0 0

case 3 0 1 0 9.984 200 400 0 0 0 0 0 0 0 0

case 4 1 0 0 9.792 250 600 1 550 0 0 5375.3 0 0 5375.3

case 5 0 1 1 9.89136937 350 900 1 0 400 150 0 3760.4 1668.15 5428.55

case 6 1 1 0 8.87936612 450 1000 1 284.7 265.3 0 2898.538 2529.155 0 5427.693

case 7 1 0 1 9.74592148 400 1100 1 400 0 150 3945.2 0 1668.15 5613.35

case 8 1 1 1 8.95839745600 1500

0 0 0 00 0 0 0

cost

cost

Units data

λ opration p1 p2 p3

1. When the few units committed then the units can’t meet the demand.

2. When the units is not enough to be committed then some units operate above optimum.

3. When the units is many to be committed then some units below optimum.

4. When the units is too many to be committed then minimum generation exceeds demand.

5. No-load cost affects choice of optimal combination.

1.2 Type of units or stations.

If we take considerable load profile like


100

50

210 6 1Tim

Loa

And solve for every hour then

LOAD UNIT 1 UNIT 2 UNIT 3

1100 On On On

1000 On On Off

900 On On Off

800 On On Off

700 On On Off

600 On Off Off

500 On Off Off

From solution we find that

1. There is unit will operate all time so we called it base unit.2. There is unit will operate part time so we called it

intermediate unit3. There is unit will operate few time so we called it peak unit

As coming figure describe


2. Constrains

2.1Definition

Constrain 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 constrains System constrains Environmental constraints Network Constraints


Unit 3 or peak unit

Unit 2 or intermediate unit

Unit 1 or base unit

24180 6 12Time

Load

2.2Unit constrains

2.2.1 Maximum generating capacityThat constrain stat that the power generated from the unit mustn’t exceed specific value because of thermal stability of the unit exceeding this constrain cause damage to the unit. Represented in mathematical formula as below.

x (i , t )< pmax

Wherex (i , t ) is output power oftheunit i∈thetime t

2.2.2 Minimum stable generationAs above constrain the power outage from the unit mustn’t fall down specific value because of technical limitation like flam stability in the gas and steam units. Represented in mathematical formula as below.

x (i , t )> pmin

2.2.3 Minimum up timeThis constrain stat that once the unit is running mustn’t shut down immediately due technical limitation and mechanical characteristic of the unit. This constrain represented mathematically as:


Where

2.2.4 Minimum down timeThis constrain stat that once the unit is running mustn’t shut down immediately due technical limitation and mechanical characteristic of the unit. This constrain represented mathematically as:

2.2.5 Ramp rates 2.2.5.1 Definition

To avoid damaging the turbine, the electrical output of a unit cannot change by


Status of unit i at period t

Unit i is on during period t

Unit i is off during period t

more than a certain amount over a period of time.

2.2.5.2 Ramp Up rate2.2.5.2.1 Start-up ramp rate

According to this constrain the unit can’t start immediately but taking time this time called start up time.

2.2.5.2.2 Running up ramp rateAccording to this one in case of running condition. the unit can’t immediate changing the power up without taking time called ramp rate running up time. The change here means increasing outage power.

2.2.5.3 Ramp down rate2.2.5.3.1 Shut down ramp rate

Look like previse constrain the unit take time to shut down.

2.2.5.3.2 Running down ramp rateAccording to this one in case of running condition. the unit can’t immediate changing the power down without taking time called ramp rate running down time. The change here means decreasing outage power.

2.2.5.4 Mathematical representationramp up rate

ramp down rate

2.3 System constrainsThis constrain that effect more than one unit divide into:

2.3.1 Load / generation balanceStat as the power generated from all unit must be equal the load and the losses. Mathematically represented as


∑i=1

n

u (i , t )∗x ( i ,t )=l (t )

where l (t ) isthe load power at time t2.3.2 Reserve constrain2.3.2.1 Reason to keep reserve power

Sudden unexpected increase in the load demand Force outage of some generating units Force outage of supplementary equipment’s due to stability

problem Underestimating the load due to error in load for casting Local shortage in the generated power

2.3.2.2 Type of reserve2.3.2.2.1 Cold reserve

Cold reserve is unit kept reserved for service but they are not available in the immediate loading.

2.3.2.2.2 Hot (spinning) reserveHot reserve refers to the extra amount of capacity that unit can provide immediately when require.

2.3.2.2.3 Operating reserve Operating reserve is referring to the capacity that already in service in excess of peak demand.

2.3.2.3 Other source of reserveThere is other source of reserve like

Pumped hydro plants Demand reduction (e.g. voluntary load shedding)

2.3.2.4 Condition of reserve Reserve must be higher than largest unit Should be spread around the network Must be able to deploy reserve even if the network

is congested The unit must operate at 80-85% of its rated

2.4 Network constrainTransmission network may have an 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

2.5Environmental constrainuc study is effected by environmental constrains because of

constraints on pollutants such SO2, NOx various forms:o Limit on each plant at each houro Limit on plant over a yearo Limit on a group of plants over a year

Constraints on hydro generationo Protection of wildlifeo Navigation, recreation

2.6Cost constrains Cost constrain taking two type of cost in consideration

2.6.1 Start-up costStart-up cost depends on varicose factor like

warming up because the unit can’t bring on line immediately Start-up cost depends on time unit has been off


2.6.2 Running cost

A balance between start-up costs and running costs is important because of

How long should a unit run to “recover” its start-up cost?

Start-up one more large unit or a diesel generator to cover the peak?

Shutdown one more unit at night or run several units’ part-loaded?

Example: Diesel generator: low start-up cost, high running

cost Coal plant: high start-up cost, low running cost

3 SummaryThe summary of all above that• Some constraints link periods together• Minimizing the total cost (start-up + running) must be done over the whole

period of study• Generation scheduling or unit commitment is a more general problem than

economic dispatch• Economic dispatch is a sub-problem of generation scheduling

4 Type of units according flexibility4.1Flexible unit

Power output can be adjusting within limitsExample of this unit

– Coal-fired– Oil-fired


– Open cycle gas turbines– Combined cycle gas turbines– Hydro plants with storage

4.2Inflexible unit Power output cannot be adjusted for technical or commercial reasonsExample of this unit

– Nuclear– Run-of-the-river hydro– Renewables (wind, solar,…….)– Combined heat and power (CHP, cogeneration)

4.2.1.14.2.1.24.2.2

4.34.4

4.4.1.14.4.1.2

4.4.1.2.1 4.4.1.2.2

4.4.1.3


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