research on robust generation scheduling with large-scale ... · popular proposal: stochastic...

5/21/2019 1 http://www.narigroup.com © 2019 NARI Group Corporation 15th EPCC, May 12 – 15, 2019 // Reykjavik, Iceland

Research on Robust Generation

Scheduling with Large-Scale Wind

Power Integration

Qia Ding Lili Li

NARI ( Nanjing Automation Research Institute)

2019-05-15


Contents

Case Study

Robust GS Method

Conclusions

Background and Motivation


Daily Operation： Generation Scheduling（GS）


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


New Challenge: Growing Uncertainty


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


Original Practice: Reserve Capacity for Uncertainty


• Uncertainty not explicitly modeled • Both system and locational reserve requirement are

• preset • heuristic • static

• Deterministic Reserve adjustment approach • Incorporating extra resources reserve

Problem:


Popular Proposal: Stochastic Optimization.


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:


Contents

Case Study

Robust GS Method

Conclusions



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


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


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


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


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


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


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.


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

=

~

~


Contents

Case Study

Robust GS Method

Conclusions



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


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)


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!


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


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


Contents

Case Study

Robust GS Method

Conclusions



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.


Thank you！

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