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Latest Computational and Mathematical Tools for Transmission Expansion

IEEE PES T&D Meeting, Chicago IL

Clayton Barrows, PhD

April 15, 2014

2

Grid Decision Horizons

Source: Alexandra von Meier

Planning Operations

“Dynamics”

(Automation)

3

Grid Integration Studies

Scenario Development Penetration of Renewables, Flexibility of Existing Fleet,

Additional Flexibility, Retirements, Firm Capacity

Transmission Expansion (per scenario, iterative to

based on congestion threshold)

System Operation Reserve Requirements,

Dispatch Time Step, Forecast Error Distribution, Market

Horizon

Renewable Resources: Location, Cost,

Production Profile, Capacity Factor

System Model: System, Year, Load

Growth Assumptions, Power Plant Operation

Flexibility: Storage, Demand Side

Resources, Electric Vehicles, etc.

Reliability Stability Flexibility

Production Cost Simulation AC-Optimal Power Flow

Detailed Distribution

System Modeling

Emissions Impact

Costs: Capital, Fuel,

VO&M, Cycling

Barriers Analysis: Regulatory, Economic,

Attitude/Perception

Unit commitment, dispatch, reserve provision, AGC signal, ACE, LMP

(data synthesis by scenario and across simulation horizons (planning, commitment,

dispatch, operation)

Results, Analysis, Knowledge

Planning Models

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Resource Planning Model (RPM)

• Capacity expansion model for a regional electric system over a utility planning horizon (10-20 year)

• Includes hourly chronological dispatch and detailed system operation representation

• High spatial resolution informs mid- to long-term generator (renewable and non-renewable) siting options

• Nodal (DCOPF) transmission representation with transmission expansion along existing and planned corridors

• Flexible structure to enable easy definition of focus region

Mai, T.; Drury, E.; Eurek, K.; Bodington, N.; Lopez, A.; Perry, A. (2013). Resource Planning Model: An Integrated Resource Planning and Dispatch Tool for Regional Electric Systems. 69 pp.; NREL Report No. TP-6A20-56723.

http://www.nrel.gov/docs/fy13osti/56723.pdf

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RPM: consistent high resolution data

• 10 km renewable resource grid cells

• Nodal (bus level) power system data

7

Data: Complete Western Interconnection data for all major generation units and transmission lines

1,836 Units

Coal 126

Gas-CC 219

Gas-CT 422

Other Gas 164

Nuclear 8

Hydro 763

Pumped Hydro 15

Geothermal 57

Biomass 62

238 GW

Coal 36

Gas-CC 60

Gas-CT 20

Other Gas 17

Nuclear 10

Hydro 75

Pumped Hydro 4

Geothermal 3.1

Biomass 1.6

21,939 Transmission Lines *In

clu

des

all

un

its

and

lin

es o

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e in

20

10

as

rep

rese

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d in

WEC

C T

EPP

C

dat

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WSI

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To

tals

incl

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e w

ind

an

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ola

r

8

Data: Detail maintained for Rocky Mountain Region, reduced for rest of Western Interconnection

305 Units

Coal 41

Gas-CC 26

Gas-CT 61

Other Gas 8

Nuclear 0

Hydro 164

Pumped Hydro 5

Geothermal 0

Biomass 0

21.8 GW

Coal 6.8

Gas-CC 3.8

Gas-CT 3.4

Other Gas 0.1

Nuclear 0

Hydro 7.1

Pumped Hydro 0.6

Geothermal 0

Biomass 0

1,796 Transmission Lines *In

clu

des

all

un

its

and

lin

es o

nlin

e in

20

10

in R

MP

P a

s re

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TE

PP

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lar

31 zones (pseudo-

BAs)

9

Data: Flexible structure enables shift in focus region (e.g. Southwest region for NGS phase 2 study)

187 Units

Coal 22

Gas-CC 42

Gas-CT 53

Other Gas 18

Nuclear 3

Hydro 45

Pumped Hydro 2

Geothermal 0

Biomass 2

35.5 GW

Coal 8.3

Gas-CC 15

Gas-CT 2.4

Other Gas 1.5

Nuclear 4

Hydro 4

Pumped Hydro 0.1

Geothermal 0

Biomass 0.03

1,935 Transmission Lines *In

clu

des

all

un

its

and

lin

es o

nlin

e in

20

10

in S

W r

egio

n a

s re

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ted

in

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C T

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atab

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use

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10

Data: Flexible structure enables shift in focus region (e.g. CAISO model)

445 Units

Coal 7

Gas-CC 68

Gas-CT 174

Other Gas 66

Nuclear 4

Hydro 58

Pumped Hydro 7

Geothermal 26

Biomass 31

48.6 GW

Coal 0.2

Gas-CC 16.5

Gas-CT 6.5

Other Gas 9

Nuclear 4.5

Hydro 7.4

Pumped Hydro 1.8

Geothermal 2

Biomass 0.6

5,142 Transmission Lines *In

clu

des

all

un

its

and

lin

es o

nlin

e in

20

10

in S

W r

egio

n a

s re

pre

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ted

in

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C d

atab

ase

use

d in

WW

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2 s

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Data clustering: k-means

• Reduce the number of represented data points

o Group similar data points

o Ensure that groups represent similar amounts of data

o … other user defined rules

• K-means clustering

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Clustering Methods: Solar regions identified based on 8760 profile similarity

• K-means clustering algorithm used instead of arbitrary boundaries

• Higher resolution in focus region (e.g. RMPP)

• Higher resolution in better resource areas (lower latitude)

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Clustering Methods: Wind regions identified based on annual capacity factors

• WWSIS data and sites used

• Map shows voronoi polygons, but centroid of individual WWSIS sites (within each wind region) used to estimate cost of spur lines

• Consider updating to high resolution 3Tier data and applying clustering methods if time/budget allows

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Data clustering: Demand

• K-means clustering used to select 3 representative weeks for dispatch modeling

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High resolution opens opportunities to explore land ownership/management issues

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Transmission Constraints

• Linearized-DC power flow o Constrained by Kirchhoff's

laws:

𝑓𝑖,𝑗 = 𝑃𝑇𝐷𝐹𝑘,(𝑖,𝑗)𝑠 𝑃𝑘

𝑘

• Transmission constraints: o Inside focus region are defined

by transmission line flow ratings

o Outside focus region are defined by inter-zonal constraints (WECC prescribed corridor limits)

Distribution of flow along linei,j due to a power injection at busk

Power injected at busk

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Transmission Constraints

• Transmission network reduction: o Outside focus region use

equivalent line representation

o Inside focus region represent each transmission line

o Inside-outside focus region boundary use equivalent line representation

Focus From To Impedance Constraint

Out BA BA Reduced WECC Interface

Border BA Bus Reduced Line Limit

Border Bus BA Reduced Line Limit

In Bus Bus Line Line Limit

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Transmission Expansion

• Expansion is allowed along existing and “planned” corridors only

𝑓𝑖,𝑗 ≤ 𝑓𝑖,𝑗𝑚𝑎𝑥 + 𝑓𝑖,𝑗

𝑒

o Expansion influences flow ratings (impedances remain static) o Eliminates the requirement to re-calculate power transfer

distribution matrix (just update constraints) o Requires a quantification of uncertainty introduced by these

simplifications. – Is it realistic to assume that re-conductoring/expanding transmission

corridors yields ‘similar’ branch impedances?

• Enables dynamic linear modeling of transmission expansion decisions while retaining DC model: 𝐶𝑖,𝑗

𝑒 ∙ 𝑓𝑖,𝑗𝑒

• Transmission expansion costs derived from existing literature1

1Mills, Andrew D.(2009). The Cost of Transmission for Wind Energy: A Review of Transmission Planning Studies. Lawrence Berkeley National Laboratory: Lawrence Berkeley National Laboratory. Retrieved from: http://escholarship.org/uc/item/2z12z7wm

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Location Dependent Results

• Operational value

o Energy markets

• Capacity value

o Reliability standards

o Renewable portfolios

Operations Simulations

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Unit commitment and economic dispatch

optimization horizon: 48 hours

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Unit commitment and economic dispatch

rolling forward in 24 hour increments

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Unit commitment and economic dispatch

The state of the system at time t=0 is dependent on:

1. Generator commitment status: on/off 2. If “on”: hours of continuous operation;

current ramp rate 3. If “off”: hours since last operation

(minimum shut down duration)

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Unit commitment and economic dispatch

Each optimization problem takes between 2 minutes and 7 hours to solve. Annual solutions can range from hours to weeks.

PLEXOS

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Changes to generator configuration…

• Annual solutions are important because load and renewable generation have seasonal variations.

• Increasing renewable penetration increases the number and magnitude of short duration ramps. • Investment decisions are based on both investment costs and long–term operational costs &

savings. Production cost models are the choice tool for evaluating the majority of operational costs & savings, however they do not estimate make investment decisions.

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Eastern Renewable Generation Integration Study (ERGIS)

• 6,500 Generators o ~850 GW Capacity

o 3,300 TWh

• 62,000 Busses

• 57,000 Transmission Lines

• 23,000 Transformers

• ~850GW Capacity

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Inter-Area Transmission

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UC on NREL’s HPC

Peregrine Characteristics: • 11520 Intel Xeon E5-2670 "SandyBridge" cores • 14400 next-generation Intel Xeon "Ivy Bridge"

core • 576 Intel Phi Intel Many Integrated Core (MIC)

core co-processors with 60+ cores each • 32 GB DDR3 1600Mhz memory per node • Peregrine will deliver a peak performance of 1

petaFLOPS

NR

EL P

IX 2

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80

Domain

Decomposition

PCM

Solution

Analysis

Partitioning

PCM PCM PCM

Solution Solution

Reassembly

PLEXOS PLEXOS PLEXOS

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Change in UC/ED with no overlap

Started UC/ED on January 31 at 12:00 am

Started UC/ED on January 1 at 12:00 am

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Idea: Parallelize in the time domain

Hypothesis: a decision at time t is not dependent on the state of the system at previous time intervals, given a delay of n time periods.

Plotted here: Autocorrelation of the generator unit commitment decision variable for a group of generators.

The duration of the lag necessary for the autocorrelation of the Unit Commitment to reach a local minimum is called the Unit Commitment Decision Persistence, or just Persistence

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Effect of Overlap on Dispatch

Normalized root mean square difference (NRMSD) in generation dispatch, by type of generator, relative to the annual solution. This calculation is made each day and plotted relative to the number of overlap days (number of days since the start of the optimization).

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ST Solution Time

9-day simulations: weekly with 2-days of overlap.

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Speedup in hourly UC simulation (RMPP) Annual solution takes 131.7 minutes. With 52 partitions (with increasing overlap days):

52

par

alle

l 7-d

ay s

imu

lati

on

s

52

par

alle

l 8-d

ay s

imu

lati

on

s

52

par

alle

l 9-d

ay s

imu

lati

on

s

(4.3 minutes)

(4.4 minutes)

(5.1 minutes)

(5.3 minutes)

(6.0 minutes)

(6.6 minutes)

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ERGIS Simulation Time Comparison

Windows 12 Partitions: 155 hr (6.4 days)

HPC 52 Partitions: 64 hr (2.7 days)

Windows 1 Partition: 1,610 hr (67 days)

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Conclusions

• Many operations and planning problems remain computationally intractable

• Simplifications can be made through constraint relaxation or transmission network equivalencing o Current methods may not be robust to network

augmentation

• Ongoing work: o Heuristic techniques to identify relevant constraints

o Further parallelism through spatial domain decomposition

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Contact:

Clayton Barrows

National Renewable Energy Laboratory

Energy Forecasting and Modeling Group

Strategic Energy Analysis Center

clayton.barrows@nrel.gov

303-275-3921

Questions?