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System Planning & Operations Spring 2010

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Presentation on theme: "System Planning & Operations Spring 2010"— Presentation transcript:

1 System Planning & Operations Spring 2010
Economic Dispatch 101a System Planning & Operations Spring 2010

2 SPO Processes and Economic Dispatch
Gas & Oil Supply Coal Supply Load Forecast Purchase Power Opportunities Maintenance Schedule Fuel Price & Availability Transmission Constraints Wholesale Transactions Unit Commitment Annual Capacity Plan Generation Resource Planning Monthly Energy Plan & Activities Next-day Activities Hourly Activities EMS Computer Real-time Dispatch Activities Annual Fuel Plan Dispatch Units Regulatory Review Accounting / Billing Pay Bills Send Invoices Prepare Intra-system Bill Rate Case Filings 2

3 Problem Statement Given Find a set of generators with
Upper and lower limits of operation Heat rate functions Fuel cost Incremental transmission losses the total generation requirement to meet Find the set of generator outputs which minimizes the total cost of meeting the total generation requirement while honoring the upper and lower limits of operation of each unit 3

4 Unit Input/Output Modeling
Thermodynamic Energy Conversion Processes FUEL ELECTRIC POWER 4

5 Four Terms Need to be Understood
Input / Output Curve – I/O Curve Average Heat Rate - AHR Incremental Heat Rate - IHR Dispatch Cost Curve - DCC 5

6 Input / Output Curve Unit I/O Curve - The rate at which input heat energy is required to produce a given MW output is measured at several output levels Result is the unit’s Input/Output curve A function of the form A + BX + CX2 is fitted to the resulting data to obtain the unit input/output coefficients A, B, C 6

7 Average Heat Rate At any given power level AHR is a measure of the rate at which heat input is needed in order to produce each MW in the output. In other words we take the total MW produced (X) and the total input required (Energy Rate In) and form the average or per MW rate AverageHeatRate = (Energy Rate In)/X ( A + B*X + C*X*X ) X AHR is the average of the I/O curve 7

8 Incremental Heat Rate Incremental Heat Rate (IHR) is a measure of the change in heat input needed to change the output by 1 MW at any given power level. The first derivative of the AHR curve taking the form of B + 2CX. IHR a straight line 8

9 Dispatch Cost Curve Converts the Incremental MMBTU rate of energy input, into a cost of fuel input, so that the cost of producing x MW’s of electrical output is: Cost = F*IHR 9

10 A Practical Example Working the numbers from I/O to SIC. 10

11 Still to Come To do this we need to convert the Incremental Heat
We will address the problem of Economic Dispatch with a practical example. To do this we need to convert the Incremental Heat Rate Curve to an Incremental Dispatch Curve But first we should review I/O and Heat Rate Curves 11

12 Average and Incremental Heat Rate Curves
15,000 10,000 8,000 1,000 100 200 300 400 500 Btu/kWh MW 12

13 But this is where it starts
15,000 10,000 8,000 1,000 100 200 300 400 500 mmBtu MW Btu/kWh 12

14 Input Output Curve mmBtu MWH 13

15 Input Output Curve Y=678 + 7.705x + 0.0015x2 mmBtu MWH
2nd Order Equation Y= x x2 mmBtu MWH 13

16 Find the AHR and IHR from the I/O Curve
Y= x x2 mmBtu MWH 14

17 Find the Average Rate from the Input Output Curve
mmBtu MWH 15

18 Divide Input by the Output
1,500 mmBtu 100 MWH mmBtu MWH 15

19 First Point of Average Heat Rate Curve
15.000mmBtu MWH mmBtu MWH 16

20 Convert to Btu/kWH 15,000Btu kWH mmBtu MWH 17

21 Continue for Each Point
2,300 mmBtu 200 MWH mmBtu MWH 17

22 Average Heat Rate Curve
I/O= x x2 AHR = x x2 x Take the Average of the I/O Curve Btu/kWH MWH 19

23 Find the Incremental Rate from the Input Output Curve
I/O= x x2 mmBtu MWH 20

24 Find the Incremental Rate from the Input Output Curve
mmBtu MWH 21

25 Find the Average at the First Point
1,500 mmBtu 100 MWH mmBtu MWH 22

26 Find the Average of the Next MWH
1, mmBtu 101 MWH mmBtu MWH 23

27 Find the Change in the I/O
Increased by mmBtu for adding 1 MWH mmBtu MWH 24

28 First Point of Incremental Heat Rate Curve
8,002 Btu 1 KWH mmBtu MWH 25

29 Continue for Each Point
8,302Btu kWH mmBtu MWH 25

30 Incremental HR Curve Take the First Derivative of the I/O Curve
I/O= x x2 IHR= *0.0015x Btu/kWH Take the First Derivative of the I/O Curve MWH 27

31 Relationship between AHR and IHR
15,000 * 100 = 1,500mmBtu 8,002 * 1 = 8.0mmBtu Btu/kWH MWH 28

32 Resulting Average HR Curve is now Lower
1,508.0 mmBtu/ 101MWH = 14,931Btu/kWH Btu/kWH MWH 29

33 Almost No Effect At Max AHR ~ 9,850 …. IHR~9,850 Btu/kWH MWH 30

34 Incremental HR Curve Btu/kWH MWH 31

35 Dispatch Cost Curve Product of Fuel Price and IHR at the next increment of production Expressed in $/MWH Example: Let’s say Unit 1 operating at 400MW has an incremental heat rate of 9,000 Btu/kWH And Gas Costs $7.00/mmBtu 32

36 Dispatch Cost Curve $7.00 mmBtu x 9,000Btu kWH 1,000 kWH MWH x 33

37 Dispatch Cost Curve $7.00 mmBtu x 9,000Btu kWH 1,000 kWH MWH x 33

38 Dispatch Cost Curve $63.00 MWH @ 400MW 34

39 Dispatch Cost Curve Gas cost $7.00/mmBtu $/MWH MWH 35

40 Let’s Talk Incremental Costs
36

41 Let’s Talk Incremental Costs
So at 25mph Average Cost was 20 Cents/Mile And the next 10mph would only add a cost of 2.5 Cents/Mile 37

42 Economic Dispatch The Problem to be Solved 38

43 Both Units at Minimum Unit 2 Unit 1
$/MWH Total output from Both Units= 200MW MWH 39

44 Load Increases by 100 MW Unit 2 Unit 1 $/MWH MWH 40

45 What if System Lambda is $60
Unit 2 Unit 1 $/MWH MWH 41

46 But This is Our System We Need a Single SIC Curve
42

47 System Incremental Dispatch Curves
Unit 2 Unit 1 $/MWH MWH 43

48 System Incremental Cost Curve In Cost Order
Unit 2 $/MWH Unit 1 MWH 44

49 System Incremental Dispatch Curves
Unit 2 Unit 1 $/MWH MWH 45

50 System Incremental Cost Curve In Cost Order
Unit 2 $/MWH Unit 1 MWH 46

51 System Incremental Cost Curve
47


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