[PPT] - Stochastic Economic Dispatch for Power Stochastic Economic Dispatch PowerPoint Presentation

SLIDE 1

Stochastic Economic Dispatch for Power Stochastic Economic Dispatch for Power Grids with High Penetration of Wind Power Grids with High Penetration of Wind Power

Ali Al Ali Al Awami Awami

PhD Student PhD Student Department of Electrical Engineering Department of Electrical Engineering

1 1

SLIDE 2

Outline Outline

Overview

Overview

Why Is This Research Important?

Why Is This Research Important?

Different Economic Dispatch Algorithms

Different Economic Dispatch Algorithms

Statistical Characterization of Wind Power Output

Statistical Characterization of Wind Power Output

Simulation Results

Simulation Results

– – Single Objective Single Objective – – Multiple Objectives Multiple Objectives

Conclusions

Conclusions

2 2

SLIDE 3

Overview Overview

What Is Economic Dispatch (ED)?

What Is Economic Dispatch (ED)?

– – Generation Generation-

load balance, A MUST at all times

load balance, A MUST at all times

– – ED is the process of allocating generation levels among ED is the process of allocating generation levels among generating units in order to meet the load in the most generating units in order to meet the load in the most economical way economical way

ED is a lot easier with traditional generating units

ED is a lot easier with traditional generating units

How do you run ED for a power system with high penetration

How do you run ED for a power system with high penetration

f wind power?
f wind power?
Remember:

Remember: – – Traditional generating units are very controllable. Wind Traditional generating units are very controllable. Wind units are not. units are not. – – Wind power is great, except for most Power System Wind power is great, except for most Power System Engineers! Engineers! – – Reason: it is highly unpredictable and uncontrollable Reason: it is highly unpredictable and uncontrollable – – Limited bulk storage capabilities Limited bulk storage capabilities

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SLIDE 4

Overview Overview

Stochastic dispatch for a power grid with wind and thermal

Stochastic dispatch for a power grid with wind and thermal units is presented. units is presented.

The formulation takes into account:

The formulation takes into account:

– – Wind power uncertainty Wind power uncertainty – – Imbalance charges Imbalance charges

Simultaneous optimization of:

Simultaneous optimization of:

– – Operating cost Operating cost – – Emissions Emissions

Multi

Multi-

objective particle swarm optimization (MO
bjective particle swarm optimization (MO-
PSO) is

PSO) is employed. employed.

4 4

SLIDE 5

Why is this important? Why is this important?

Power system operations:

Traditionally deterministic
Now/Future stochastic

Stochastic dispatch – An enabling tool for RES integration The new cap-and-trade policies necessitates the inclusion

f environmental objectives

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SLIDE 6

Deterministic Dispatch Deterministic Dispatch – – Single Objective Single Objective

This is the conventional way to do ED
Objective: Minimize the operating cost of the power system

subject to the generation-load balance constraint.

For wind, schedule whatever you forecast.

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SLIDE 7

* TP: Thermal Plant * TP: Thermal Plant * WP: Wind Plant * WP: Wind Plant

7 7

Deterministic combined

perating cost of TPs and WPs

OCd Output of ith TP Pgi Scheduled output of ith WP wi Forecast output of ith WP wfci System load including losses L

Minimize

OCd(Pgi,wi )

Subject to

min max gi gi gi

P P P ≤ ≤

1 1 m n gi fci i i

P L w

= =

= −

∑ ∑

wi = wfci

Deterministic Dispatch Deterministic Dispatch – – Single Objective Single Objective

SLIDE 8

Stochastic Dispatch Stochastic Dispatch – – Single Objective Single Objective

Objective: Minimize the expected value of the operating cost of

the power system subject to the generation-load balance constraint.

Takes into account the uncertainty associated with wind

power output.

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SLIDE 9

9 9

Minimize

E[OCs(Pgi,wi )]

Subject to

min max gi gi gi

P P P ≤ ≤

Stochastic Dispatch Stochastic Dispatch – – Single Objective Single Objective

i ri

w w ≤ ≤

1 1

m n

gi i i i

P w

L

= =

+

=

∑ ∑

SLIDE 10

The stochastic combined operating cost (

The stochastic combined operating cost (OC OCs

s) can be formulated

) can be formulated as as

, , 1 1 1 1

[ ] ( ) ( ) [ ( )] [ ( )]

M N N N s i gi wi i pi i ac i ri i i ac i i i i

E OC C P C w E C W w E C w W

= = = =

= + + − + −

∑ ∑ ∑ ∑

Operating cost

f TPs

Operating cost

f WPs

Imbalance cost due to over-generation Imbalance cost due to under-generation Scheduled wind power

where where

2

=

+ +

i i gi i gi i

a C P b P c

=

wi i i

C d w

,

[

[ ] ( )] ( ) ) ( |

ri i

w pi pi i ac i p W fci i i w

E k

f w w E C W w k w w dw

=

− = −

∫

,

[

( | [ ] ( )] ( ) )

i

w ri ri i i ac ri i W fci

E k

E C w W k w w dw f w w

=

− = −

∫

Penalty cost coeff. for over-generation Reserve cost coeff. for under-generation cpdf of wind power output given the forecast level 10 10

Stochastic Dispatch Stochastic Dispatch – – Single Objective Single Objective

Actual wind power

SLIDE 11

Perfect Scheduling Perfect Scheduling – – Single Objective Single Objective

Objective: Minimize the operating cost of the power system

subject to the generation-load balance constraint.

Scheduled and actual wind power output ate identical It is the theoretical lower bound

11 11

wi = Wi,ac

SLIDE 12

12 12

Minimize

OCp(Pgi,wi )

Subject to

min max gi gi gi

P P P ≤ ≤

1 1 M N gi i i i

P L w

= =

= −

∑ ∑

wi = Wi,ac

Perfect Scheduling Perfect Scheduling – – Single Objective Single Objective

SLIDE 13

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast -
Find

Find

13 13

1. Normalize 10 minute WP output, wi, for a year
2. Generate hour-ahead persistence forecast, wfci
3. Re-arrange data based on forecast in an ascending
rder
4. Divide data according to forecast level into 25 bins
5. For each bin, find the pdf fits of the WP output, wi.

Consider Weibull, Extreme Value, and Beta

6. Among the three pdf functions, pick the one that

best fits the bin data

( | )

W fci

f w w

SLIDE 14

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

14 14

1. Normalize 10 minute WP
utput, wi, for a year
2. Generate hour-ahead

persistence forecast, wfci

3. Re-arrange data based on

forecast in an ascending

rder
4. Divide data according to

forecast level into 25 bins

5. For each bin, find the pdf

fits of the WP output, wi. Consider Weibull, Extreme Value, and Beta

6. Among the three pdf

functions, pick the one that best fits the bin data

50 100 150 200 250 300 350 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (Days) Wind power output and forecast (pu)

Actual wind power output Wind power forecast 1 2 3 4 5 6 7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (Days) Wind power output and forecast (pu)

Actual wind power output Wind power forecast

0.5 1 1.5 2 2.5 3 3.5 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (hours) W in d p o w er o u tp u t an d fo recast (p u )

Wi,ac wfc

T k T t t-T t+k t+k+T

SLIDE 15

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

15 15

1. Normalize 10 minute WP
utput, wi, for a year
2. Generate hour-ahead

persistence forecast, wfci

3. Re-arrange data based on

forecast in an ascending

rder
4. Divide data according to

forecast level into 25 bins

5. For each bin, find the pdf

fits of the WP output, wi. Consider Weibull, Extreme Value, and Beta

6. Among the three pdf

functions, pick the one that best fits the bin data Actual FC

0.34

0.52

0.44

0.30

0.44

0.27

0.44

0.56

0.61

0.66

0.61

0.73

0.61

. . . . . . . . . .

Actual FC

0.41

0.00

.

0.52

0.44

.

0.34

0.52

.

0.66

0.61

.

0.59

1.00

SLIDE 16

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

16 16

1. Normalize 10 minute WP
utput, wi, for a year
2. Generate hour-ahead

persistence forecast, wfci

3. Re-arrange data based on

forecast in an ascending

rder
4. Divide data according to

forecast level into 25 bins

5. For each bin, find the pdf

fits of the WP output, wi. Consider Weibull, Extreme Value, and Beta

6. Among the three pdf

functions, pick the one that best fits the bin data

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 104 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points W in d p

w

er o u tp u t an d fo re ca st (p u )

Actual wind power output Wind power forecast

SLIDE 17

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

17 17

1. Normalize 10 minute WP
utput, wi, for a year
2. Generate hour-ahead

persistence forecast, wfci

3. Re-arrange data based on

forecast in an ascending

rder
4. Divide data according to

forecast level into 25 bins

5. For each bin, find the pdf

fits of the WP output, wi. Consider Weibull, Extreme Value, and Beta

6. Among the three pdf

functions, pick the one that best fits the bin data

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 104 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points W in d p

w

er o u tp u t an d fo re ca st (p u )

Actual wind power output Wind power forecast

3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.1 3.11 3.12 3.13 x 10

4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points Wind power: output and forecast (pu)

Actual wind power output Wind power forecast 4.14 4.15 4.16 4.17 4.18 4.19 4.2 4.21 4.22 4.23 4.24 4.25 x 10

4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points Wind power: output and forecast (pu)

Actual wind power output Wind power forecast

Bin # 1 7 19 25 2

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Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

18 18

1. Normalize 10 minute WP
utput, wi, for a year
2. Generate hour-ahead

persistence forecast, wfci

3. Re-arrange data based on

forecast in an ascending

rder
4. Divide data according to

forecast level into 25 bins

5. For each bin, find the pdf

fits of the WP output, wi. Consider Weibull, Extreme Value, and Beta

6. Among the three pdf

functions, pick the one that best fits the bin data

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 104 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points W in d p

w

er o u tp u t an d fo re ca st (p u )

Actual wind power output Wind power forecast

Bin # 1 7 19 25 2

3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.1 3.11 3.12 3.13 x 10

4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points Wind power: output and forecast (pu)

Actual wind power output Wind power forecast 4.14 4.15 4.16 4.17 4.18 4.19 4.2 4.21 4.22 4.23 4.24 4.25 x 10

4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points Wind power: output and forecast (pu)

Actual wind power output Wind power forecast 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30

Histogram of actual data and pdf fits: wfc = 0.24 - 0.28 pu Frequency (%)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30

Actual data and simulated data using best pdf fit parameters Frequency (%) Wind power output (pu)

Actual data Weibull Extreme value Beta Actual data Weibull Extreme value Beta 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40

Histogram of actual data and pdf fits: wfc = 0.72 - 0.76 pu Frequency (%)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40

Actual data and simulated data using best pdf fit parameters Frequency (%) Wind power output (pu)

Actual data Weibull Extreme value Beta Actual data Weibull Extreme value Beta

SLIDE 19

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

19 19

1. Normalize 10 minute WP
utput, wi, for a year
2. Generate hour-ahead

persistence forecast, wfci

3. Re-arrange data based on

forecast in an ascending

rder
4. Divide data according to

forecast level into 25 bins

5. For each bin, find the pdf

fits of the WP output, wi. Consider Weibull, Extreme Value, and Beta

6. Among the three pdf

functions, pick the one that best fits the bin data

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 104 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of data points W in d p

w

er o u tp u t an d fo re ca st (p u )

Actual wind power output Wind power forecast

Bin # 1 7 19 25 2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30

Histogram of actual data and pdf fits: wfc = 0.24 - 0.28 pu Frequency (%)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30

Actual data and simulated data using best pdf fit parameters Frequency (%) Wind power output (pu)

Actual data Weibull Extreme value Beta Actual data Weibull Extreme value Beta 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40

Histogram of actual data and pdf fits: wfc = 0.72 - 0.76 pu Frequency (%)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40

Actual data and simulated data using best pdf fit parameters Frequency (%) Wind power output (pu)

Actual data Weibull Extreme value Beta Actual data Weibull Extreme value Beta

Weibull Extreme Value

SLIDE 20

The absolute error (AE) between the actual data and the data

The absolute error (AE) between the actual data and the data generated by the generated by the pdf pdf fit parameters is used fit parameters is used

Statistical characterization of WP Statistical characterization of WP

utput given the forecast
utput given the forecast

20 20

Absolute Error (AE) Bin # WBL EV Beta 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 4.74 46.82 2.48 8.28 45.26 11.20 23.31 40.54 19.21 21.25 42.94 21.63 31.48 33.57 32.58 16.28 50.41 28.63 11.43 48.82 19.00 20.85 43.41 25.34 17.18 51.15 30.46 17.68 40.00 19.38 20.34 36.73 23.42 12.57 41.11 17.30 26.82 27.77 31.71 11.79 22.51 13.50 17.10 11.75 19.87 19.68 12.44 15.40 16.51 12.33 15.11 28.34 12.38 38.07 23.64 15.37 30.32 20.81 9.52 24.62 30.58 20.58 30.48 27.48 19.51 38.80 8.04 13.18 10.49 34.61 30.93 36.53

SLIDE 21

Test System Test System

For the base case,

10-minute, 11-month-worth of wind data for
Condon (50 MW), and
Stateline (90 MW)
The actual BPA’s load profile of 2007 is scaled down so

that it ranges from 50 MW to 380 MW.

21 21

Pg1 Pg2 w1 w2

SLIDE 22

22 22

Simulation Results Simulation Results

Single Objective Single Objective

TABLE I I I The Actual Operating Costs and Savings of SD and PS as Compared to DD

DD SD SD Savings PS PS Savings Month ($/MW) ($/MW) (%) ($/MW) (%) Jan 594.2 591.54 0.45 558.15 6.07 Feb 543.86 534.7 1.68 501.83 7.73 Mar 485.16 472.89 2.53 423.35 12.74 Apr 502.57 489.68 2.56 451.45 10.17 May 488.59 477.41 2.29 436.43 10.68 Jun 497.76 484.95 2.57 445.58 10.48 Jul 536.14 524.38 2.19 485.76 9.40 Aug 503.61 489.55 2.79 444.22 11.79 Sep N/A N/A N/A N/A N/A Oct 464.09 451.62 2.69 410.17 11.62 Nov 456.29 449.33 1.53 420.43 7.86 Dec 520.59 510.91 1.86 471.85 9.36 Average 506.55 496.4 2.13 457.54 9.85

SLIDE 23

23 23

Simulation Results Simulation Results

Single Objective Single Objective

5 10 15 20 25 30 200 400

System load (MW)

5 10 15 20 25 30 50

Condon schedules (MW)

5 10 15 20 25 30 50 100

Stateline schedules (MW)

5 10 15 20 25 30 500 1000

Time(Days) AOC ($/MW)

SD DD SD DD SD DD

SLIDE 24

24 24

Simulation Results Simulation Results

Single Objective Single Objective

1 2 3 200 400 System Load (MW) 1 2 3 20 40 Condon schedule using DD and SD (MW) 1 2 3 50 100 Stateline schedule using DD and SD (MW) 1 2 3 400 600 800 1000 Time (Days) AOC using DD and SD ($/MW) DD SD

SLIDE 25

25 25

Simulation Results Simulation Results

Single Objective Single Objective

TABLE I V Mean Absolute Error between Scheduled and Actual Wind power Outputs

Mean Absolute Error (%) Wind Plant DD SD Condon 10.49 13.68 Stateline 7.99 11.06

SLIDE 26

Stochastic Dispatch Stochastic Dispatch – – Multiple Objectives Multiple Objectives

Objective: Minimize two conflicting objectives simultaneously:

The expected value of the system operating cost Emissions of thermal units.

No single optimal solution! Rather, there is a group of Pareto-
ptimal solutions.

26 26

SLIDE 27

27 27

Minimize Subject to

Stochastic Dispatch Stochastic Dispatch – – Multiple Objectives Multiple Objectives

[E[OCs(Pgi,wi )] , S(Pgi)]

min max gi gi gi

P P P ≤ ≤

1 1 M N gi i i i

P w

L

= =

+

i ri

w w ≤ ≤

=

∑ ∑

1

2

exp( )

M i

i i gi i gi i i gi

S

P P P α β γ ζ λ

=

+ + +

⎡ ⎤ ⎣ ⎦

∑

, , 1 1 1 1

[ ] ( ) ( ) [ ( )] [ ( )]

M N N N s i gi wi i pi i ac i ri i i ac i i i i

E OC C P C w E C W w E C w W

= = = =

= + + − + −

∑ ∑ ∑ ∑

SLIDE 28

Pareto Multi Pareto Multi-

objective
bjective

Optimization Optimization

E OC E OC E OC Pareto Optimal NOT Pareto Optimal E OC 28 28

SLIDE 29

Multi Multi-

objective Particle Swarm
bjective Particle Swarm

Optimization (MO Optimization (MO-

PSO)

PSO)

Particle swarm optimization is: Particle swarm optimization is:

Fast

Fast

Easy to code

Easy to code

Has memory

Has memory

– – Every particle remembers its local best position ( Every particle remembers its local best position (lbest lbest) & the ) & the group group’ ’s global best position ( s global best position (gbest gbest) )

Maintains the initial population

Maintains the initial population

– – No need for applying operators No need for applying operators

29 29

SLIDE 30

Multi Multi-

objective Particle Swarm
bjective Particle Swarm

Optimization (MO Optimization (MO-

PSO)

PSO)

x xid

id =

= x xid

id +

+ v vid

id

v vid

id = w*

= w*v vid

id + c

+ c1

1*rand( )*(

rand( )(p pid

id-

x

xid

id) + c

) + c2

2*Rand( )*(

Rand( )(p pgd

gd-

x

xid

id)

)

I nertial component Personal best component Global best component

30 30

SLIDE 31

Multi Multi-

objective Particle Swarm
bjective Particle Swarm

Optimization (MO Optimization (MO-

PSO)

PSO)

E OC E OC E OC E OC

31 31

SLIDE 32

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives Emission curves Emission curves

Emissions are at minimum at a

certain power output, Pgi,opt.

Emissions are higher at any
utput below or above Pgi,opt.
In this case,
Pg1,opt = 43.0 MW
Pg2,opt = 53.5 MW

Fig 2. Emissions vs. power output for thermal plants

32 32

50 100 150 200 250 300 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Power output (MW) Emissions (tons/MW)

Thermal unit 1 Thermal unit 2

SLIDE 33

Condon’s forecast = 36.3 MW
Stateline’s forecast = 39.2 MW
Total load + losses = 215.3 MW
Comparison between SD and DD
Effect of load level
Effect of reserve cost
Effect of penalty cost

33 33

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives

SLIDE 34

Pareto Front Plants’ Outputs

34 34

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives Base case Base case

613.72 613.74 613.76 613.78 613.8 613.82 613.84 613.86 613.88 0.044 0.044 0.044 0.0441 0.0441 0.0441 0.0441 0.0441 0.0442 0.0442

Average operating cost ($) Emissions (tons)

613.72 613.74 613.76 613.78 613.8 613.82 613.84 613.86 613.88 35 40 45 50 55 60 65 70 75 80

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2 600 620 640 660 680 700 720 740 760 0.039 0.04 0.041 0.042 0.043 0.044 0.045 0.046 0.047 0.048

Average operating cost ($) Emissions (tons)

600 620 640 660 680 700 720 740 760 30 40 50 60 70 80 90

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2

D D S D

SLIDE 35

Wind inc Operating cost inc
Wind inc Emissions dec
Why?
Increasing scheduled wind

power causes imbalance charges to increase at a higher rate than the decreasing rate of the fuel cost of thermal plants.

Thermal plants’ outputs slide

between Pgi,opt and Pgi,max. So, emissions are directly proportional to thermal power

utputs.

35 35

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives Base case Base case

600 620 640 660 680 700 720 740 760 0.039 0.04 0.041 0.042 0.043 0.044 0.045 0.046 0.047 0.048

Average operating cost ($) Emissions (tons)

600 620 640 660 680 700 720 740 760 30 40 50 60 70 80 90

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2

SLIDE 36

Load is reduced by half
Load dec Operating cost dec
Now, TPs’ outputs slide between

Pgi,min and Pgi,opt. Hence,

Thermal inc emissions dec
Thermal inc Operating cost

inc

This is the exact opposite trend

to that of the base case

36 36

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives Effect of load level Effect of load level

430 435 440 445 450 455 460 465 470 0.039 0.04 0.041 0.042 0.043 0.044 0.045

Average operating cost ($) Emissions (tons)

430 435 440 445 450 455 460 465 470 5 10 15 20 25 30 35 40 45 50 55

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2

50 100 150 200 250 300 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Power output (MW) Emissions (tons/MW)

Thermal unit 1 Thermal unit 2

SLIDE 37

kri is cost due to under-

generation

kri is decreased from 8 to 4
kri dec

Wind inc (motivated by lower

under-generation cost)

Thermal dec

37 37

580 600 620 640 660 680 700 720 740 760 0.038 0.04 0.042 0.044 0.046 0.048 0.05

Average operating cost ($) Emissions (tons)

kri = 4.0 kri = 8.0 580 590 600 610 620 630 640 35 40 45 50 55 60 65 70 75 80

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives Effect of reserve cost coefficient Effect of reserve cost coefficient

600 620 640 660 680 700 720 740 760 30 40 50 60 70 80 90

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2

SLIDE 38

kpi is cost due to over-

generation

kpi is decreased from 2 to 1
kpi dec

Wind dec (motivated by

lower over-generation cost)

Thermal inc

This is opposite to decreasing kri

38 38

Simulation Results Simulation Results

Multiple Objectives Multiple Objectives Effect of penalty cost coefficient Effect of penalty cost coefficient

560 580 600 620 640 660 680 700 720 740 760 0.038 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056

Average operating cost ($) Emissions (tons)

kpi = 2.0 kpi = 1.0 570 580 590 600 610 620 630 640 650 20 30 40 50 60 70 80 90

Average operating cost ($) Emissions (tons)

Pg1 Pg2 w1 w2 600 620 640 660 680 700 720 740 760 30 40 50 60 70 80 90

Average operating cost ($) Power schedules (MW)

Pg1 Pg2 w1 w2

SLIDE 39

Conclusion Conclusion

A new stochastic dispatch algorithm for a system that

incorporates thermal and wind plants is presented

The stochastic nature of wind power output is taken into account. SD can result in savings of up to 2% over conventional DD. SD is extended for multiple objectives MO-PSO is used to identify the Pareto-optimal solutions. Several simulation runs are conducted to study the effect of

different system conditions on the Pareto-optimal solutions.

The proposed technique can help integrate wind power into the

grid more efficiently.

39 39