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Research on Robust Generation
Scheduling with Large-Scale Wind
Power Integration
Qia Ding Lili Li
NARI ( Nanjing Automation Research Institute)
2019-05-15
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Contents
Case Study
Robust GS Method
Conclusions
Background and Motivation
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Daily Operation: Generation Scheduling(GS)
Background and Motivation
Unit Commit
Info: costs, LF Decision: which units to commit Goal: min costs. meet demand Constraints: physical, security
Economic Dispatch
Info: Unit commit, costs, LF Decision: generation level Goal: min costs meet demand Constraints: physical, security
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New Challenge: Growing Uncertainty
Background and Motivation
Forecast Error
• hard to forecast • increase the uncertainty
Wind Power Installed Capacity
• Increasing rapidly to large scale
Wind Power Daily Curve
• Variability and stochastic nature
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Original Practice: Reserve Capacity for Uncertainty
Background and Motivation
• Uncertainty not explicitly modeled • Both system and locational reserve requirement are
• preset • heuristic • static
• Deterministic Reserve adjustment approach • Incorporating extra resources reserve
Problem:
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Popular Proposal: Stochastic Optimization.
Background and Motivation
T1 T2 T3 T4
Stochastic optimization
• Uncertainty modeled by distributions • generating a lot of scenarios
• Hard to forecast the probability distribution for the wind plant
output • Restricted by sample scenarios, hard to select “right”
scenarios in large systems • Computational burden for more scenarios
Problem:
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Contents
Case Study
Robust GS Method
Conclusions
Background and Motivation
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Robust Optimization
Robust GS Method
T1 T2 T3 T4 T1 T2 T3 T4
Robust optimization
Stochastic optimization
• models wind forecast results with uncertainty sets
• protects the system against all realizations instead of typical value
• computationally tractable
Selected Scenarios
All Scenarios
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Robust Optimization:Model of Uncertainty
Robust GS Method
ˆwtp
wtp
wtp
ˆwtp
• No scenarios • No probabilities
ˆ ˆ ˆ, : ,W wt wt wt wt wt wt wtP p p p p p p p
• Uncertainty Set - Box – Expected values
– Uncertain intervals
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Robust Optimization:Model of Uncertainty
Robust GS Method
| |,
ˆ
| |ˆ, , , : ,
ˆ
ˆ ˆ,
wt wtw
t T wt
wt wtwt wt w t t
w W wt
wt wt wt wt wt
p p
p
p pPW p p
p
p p p p p
w tBudget of uncertainty
1 2 3 4 5 6 Hour
Wind power
• The level of conservatism is adjusted by uncertainty sets!
• Uncertainty Set – Box of wind power variation – Correlation between difference sources of renewable generation
– Correlation between time steps
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Two-Stage Decision-Making
Robust GS Method
Non-adjustable variables: decisions that must be made before the actual realization of the uncertain data. here-and-now Adjustable variables: decisions can be made when the uncertain data become known,. adjust correspondingly. wait-and-see
Two-stage robust optimization framework • UC decisions (non-adjustable) are made before the realization of wind power, first stage variable • Economic dispatch decisions (adjustable) are made assuming full observation of wind power, second stage variable, it is a function of the uncertain load
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Adaptive Robust UC Model
Robust GS Method
, ( , )1 1 1 1
min max minit wtwt
T I T I
i it i itu y p Q u pp PW
t i t i
S y C p
Find worst case w for dispatch
For a fixed u, w minimize dispatch cost
Second-Stage Problem
. .
, 0
s t
F u y
, 0,it wt wtF p p p PW
Unit physical constraints (e.g., start-up/shut-down, min up/down-time constraints).
Dispatch constraints and coupling constraints for commitment and dispatch decisions
startupCost + WorstcCaseDispatchCost OBJECT
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Weighted summation of total dispatch cost
Modified Robust UC Model
Robust GS Method
Dispatch cost under the nominal scenario
Dispatch cost under the worst-case scenario
ˆ, ( , ) ( , )1 1 1 1 1 1
min min (1 ) max minit wt it wtwt
T I T I T I
i it i it i itu y p Q u p p Q u pp PW
t i t i t i
S y C p C p
Consider both the nominal-case scenario and the worst case scenario, so the resultant decisions may be more balanced
0,1
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Solution Methodology
Robust GS Method
• Linear Decision Rules (LDR)
• LDR approach makes the assumption that the adjustable
decisions depend linearly on the uncertain parameters.
• Therefore, two-stage RO can be reformulated into a single
stage optimization problem.
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Solution Methodology
Robust GS Method
• The power dispatch depends on uncertain wind power ,based on LDR :
• where and are newly introduced intermediate variables
• After applying LDR, we reach the following equivalent reformulation
itp
wtp
0
, , , , ,i t i t i t w w t
w
p y y p 0
,i ty , ,i t wy
=
~
~
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Contents
Case Study
Robust GS Method
Conclusions
Background and Motivation
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Case Study
• A case of modified Reliability Test System (RTS-1996)
• 32 generators
• 24 buses
• peak load 14136 MW
• 24 hours
• 7 representative transmission constraints
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Case Study
1200
1500
1800
2100
2400
2700
3000
0 4 8 12 16 20 24
Time period
Load
(MW
)
0
100
200
300
400
500
600
Win
d po
wer
(MW
)
load wind power forecastwind upper limit wind lower limit
• Wind power integrated in node 16 and 22 - Max interval for wind power uncertainty is 20% of the expected value
• Compare Robust Optimization with Reserve Adjustment (RA)
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Robustness Analysis
Case Study
UC
result source
ED calculation
number of times
ED convergence
number of times
reserve
adjustment 10000 9645
robust
optimization 10000 10000
Convergence result of economic dispatch with 10000 scenarios
0
100
200
300
400
500
600
0 4 8 12 16 20 24
Time period
Win
d p
ow
er (
MW
)
wind upper limit
wind lower limit
wind power
Typical Infeasible scenario of reserve adjustment method
• Infeasible scenarios exist for RA, why?
Ramp down
Commitment result from RA cannot adapt the ramp down between 5th and 6th period!
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Economic Analysis
Case Study
Cost comparison under the wind power nominal scenario
Method Total cost Dispatch cost Commitment
cost Penalty cost
reserve adjustment 449420 444450 4970 0
robust optimization 452937 445624 7313 0
Average cost comparison with 10000 scenarios
Method Total cost Dispatch cost Commitment
cost Penalty cost
reserve adjustment 457641 446826 4970 5845
robust optimization 453715 446402 7313 0
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Weighted parameter Analysis
Case Study
Total cost under different weighted parameter
454000
456000
458000
460000
462000
0 0.2 0.4 0.6 0.8 1
Weighted parameter
To
tal
cost
• Weighted parameter α controls the impact of the worst-case cost on generation scheduling decisions
• As the value of α becomes bigger, the total cost reduced accordingly
• When α is 1, the model is a deterministic problem
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Contents
Case Study
Robust GS Method
Conclusions
Background and Motivation
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Conclusions
• Robust UC provides a systematic way to manage the increasing level of uncertainty in system operations, especial for large scale wind power integration.
• Compared with the deterministic reserve adjustment UC, robust UC achieves better robustness and economic efficiency
• Robust UC can offers not only the UC result, but also the worst scenario of the uncertain sets under this UC result.
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Thank you!