2011 IEEE PES Power Systems Conference & Exhibition (PSCE), Phoenix, AZ
Marginal Unit Generation Sensitivity and its Applications in Transmission Congestion Prediction and LMP Calculation
Fangxing Lia, Rui Bob aUniversity of Tennessee, Knoxville bMidwest ISO Mar 21, 2011 1
Outline
Background Motivation Problem Statement MUGS Formulation Applications Conclusions
2
Background
LMP step change phenomenon in LMP versus Load curve
Shift of marginal units Congestions Price spikes
3
Example 1: LMP step changes
PJM 5 bus system
4
Example 1: LMP step changes (Cont’d)
LMP
5
Example 1: LMP step changes (Cont’d)
Marginal Units and Congestions versus Load
6
Example 2: NYISO
NYISO “CAPITAL” Zone LMP w.r.t. load based on real-time market data for 10-11AM on July 24, 2009.
7
Motivation
Locate the step changes Critical Load Level (CLL)
8
Approach 1: Brute-force simulation
Brute-force simulation
Narrow segment: may be missed Broad segment: waste of computation Hard to pinpoint CLLs
9
Approach 2: MUGS
What happens at CLLs?
Change in marginal unit set
How to detect change in marginal unit set?
Marginal Unit Generation Sensitivity (MUGS) Local vs Global
10
Problem Statement (1) To analyze the “global” pattern of marginal unit generation dispatch w.r.t. system load variation. (2) Apply marginal unit generation sensitivity to estimate CLLs 11
With-loss DCOPF Model
12
MUGS Formulation Equalities of binding constraints at optimal solutions
Introducing load variation participation factor fi Applying derivative to above equations w.r.t. DΣ
a is function of MG b is a constant vector
13
MUGS Formulation (Cont’d)
Marginal Unit Generation Dispatch
Can be numerically approximated by quadratic function of DΣ Variable Substitution Method (paper in submission)
MUGS
Numerically a linear function of DΣ Can be proved for some special cases
14
MUGS Formulation: Special Cases
Special Case I: One marginal unit at the reference bus
Marginal unit generation at the reference bus is a quadratic function of DΣ
All other marginal unit generations are linear function of DΣ
Special Case II: Lossless network
MUGS is constant 15
Application 1: Congestion Prediction
Marginal unit generation: quadratic function of DΣ Line flow: linear function of MG (i.e., quadratic function of DΣ)
16
Application 1: Congestion Prediction (Cont’d)
Change of marginal unit
17
Application 2: LMP Calculation
18
Conclusions
Marginal Unit Generation Sensitivity (MUGS)
Numerically: quadratic function of DΣ Proved for a special case
when there is a marginal unit at the reference bus
Mar 21, 2011 - Example 1: LMP step changes. (Cont'd). â Marginal Units and Congestions versus Load. Page 7. 7. Example 2: NYISO. â NYISO âCAPITALâ Zone LMP w.r.t. load based on real-time market data for 10-11AM on July 24, 2009. Page 8. 8. Motivation. â Locate the step changes. â Critical Load Level (CLL) ...
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