Transcript Slide 1
Electric Power Industry Overview
WESEP REU
June 3, 2013
Iowa State University
James D. McCalley
Harpole Professor of
Electrical &
Computer Engineering
Outline
1. The electric power industry
2. Control centers
3. Electricity markets
2
Organizations comprising the Electric Power Industry
•
Investor-owned utilities: 239 (MEC, Alliant, Xcel, Exelon, …)
•
Federally-owned: 10 (TVA, BPA, WAPA, SEPA, APA, SWPA…)
•
Public-owned: 2009 (Ames, Cedar Falls, Muscatine, …)
•
Consumer-owned: 912 (Dairyland, CIPCO, Corn Belt, …)
•
Non-utility power producers: 1934 (Alcoa, DuPont,…)
•
Power marketers: 400 (e.g., Cinergy, Mirant, Illinova, Shell Energy, PECO-
•
•
•
•
•
•
•
•
•
•
Power Team, Williams Energy,…)
Coordination organizations: 9
(ISO-NE, NYISO, PJM, MISO, SPP, ERCOT,
CAISO, AESO, NBSO), 7 are in the US.
Oversight organizations:
•
•
•
Regulatory: 52 state, 1 Fed (FERC)
Reliability: 1 National (NERC), 8 regional entities
Environment: 52 state (DNR), 1 Fed (EPA)
Manufacturers: GE, ABB, Toshiba, Schweitzer, Westinghouse,…
Consultants: Black&Veatch, Burns&McDonnell, HD Electric,…
Vendors: Siemens, Areva, OSI,…
Govt agencies: DOE, National Labs,…
Professional organizations: IEEE PES …
Advocacy organizations: AEWA, IWEA, Wind on Wires…
Trade Associations: EEI, EPSA, NAESCO, NRECA, APPA, PMA,…
Law-making bodies: 52 state legislatures, US Congress
3
Big changes between 1992 and about 2002….
Apr 1990:
UK Pool
opens
Overseas
Jan. 1991:
Norway
launches
Nordpool
1990
1992
North
America
1994
Oct 1996:
New
Zealand
NZEM
Dec 1998:
Australia
NEM opens
Jan. 1996:
Sweden in
Nordpool
Jan. 1998:
Finland in
Nordpool
1996
1998
Feb 1996
MISO
formed.
1996:
ERCOT
becomes
ISO.
Mar 2001:
NETA
replaces UK
Pool
Jan. 2000:
Denmark in
Nordpool
Jan 1998:
PJM ISO
created
May 1999:
ISO-NE
opens
Mar 1998:
Cal ISO
opens
Nov 1999:
NY ISO
launches
2000
July 2001:
ERCOT
becomes
one
control
area
Jan. 2001:
Alberta
Pool opens
2002
Jan 2002
ERCOT
opens retail
zonal mrket
May
2002:
Ontario
IMO
launches
2004
2006
April 2005
MISO
Markets
Launch
2008
Feb 2007
SPP
Markets
Launch
Dec 2008
ERCOT
Nodal
Market
Launched
Dec 2001
MISO
becomes
first RTO
4
Transmission and
System Operator
G
G
G
G
G
G
G
G
Transmission
Operator
G
G
G
Transmission
Operator
G
Independent
System
Operator
G
G
Transmission
Operator
Vertically Integrated Utility
1900-1996/2000
G
G
Today
5
What are the North American Interconnections?
“Synchronized”
6
What is NERC?
• NERC: The North American Reliability Corporation, certified by federal government
(FERC) as the “electric reliability organization” for the United States.
• Overriding responsibility is to maintain North American bulk transmission/generation
reliability. Specific functions include maintaining standards, monitoring compliance
and enforcing penalties, performing reliability assessments, performing event
analysis, facilitating real-time situational awareness, ensuring infrastructure security,
trains/certifies system operators.
• There are eight NERC regional councils (see below map) who share NERC’s mission
for their respective geographies within North America through formally delegated
enforcement authority
• Western Electricity Coordinating
Council (WECC)
• Midwest Reliability Organization (MRO)
• Southwest Power Pool (SPP)
• Texas Reliability Entity (TRE)
• Reliability First Corporation (RFC)
• Southeast Electric Reliability Council
(SERC)
• Florida Reliability Coordinating Council
(FRCC)
• Northeast Power Coordinating Council
(NPCC)
7
What is FERC?
• An independent agency that regulates the interstate transmission of electricity,
natural gas, and oil. It does the following:
• Regulates transmission & wholesale sales of electricity in interstate commerce;
• Regulates all wholesale natural gas transmission;
• Reviews mergers/acquisitions /corporate transactions by electricity companies;
• Can review some siting applications for electric transmission projects;
• Licenses and inspects private, municipal, and state hydroelectric projects;
• Protects the reliability of the high voltage interstate transmission system through
mandatory reliability standards;
• Monitors and investigates energy markets;
• Enforces FERC regulatory requirements via civil penalties/other means;
• Oversees environmental matters related to natural gas/hydroelectric projects;
• Administers accounting/financial reporting regs+conduct of regulated companies
• FERC does not:
• Regulate retail electricity and natural gas sales to consumers;
• Regulate activities of municipals or federal power marketing agencies;
• Regulate nuclear power plants (NRC does this);
• Address reliability problems related to failures of local distribution facilities;
• Consider tree trimmings near local distribution power lines in residential
neighborhoods
8
Regional Transmission Organizations/Independent System Operators
•
•
•
•
•
•
The regional system operator: monitors and controls grid in real-time
The regional market operator: monitors and controls the electricity markets
The regional planner: coordinates 5 and 10 year planning efforts
They own no electric power equipment.
None of them existed before 1996.
They are central to electricity production and transmission today.
9
Energy Control Centers
Energy Control Center (ECC):
• SCADA, EMS, operational personnel
• “Heart” (eyes & hands, brains) of the power system
Supervisory control & data acquisition (SCADA):
• Supervisory control: remote control of field devices, including gen
• Data acquisition: monitoring of field conditions
• SCADA components:
» Master Station: System “Nerve Center” located in ECC
» Remote terminal units: Gathers data at substations; sends to Master
Station
» Communications: Links Master Station with Field Devices, telemetry is
done by either leased wire, PLC, microwave, or fiber optics.
Energy management system (EMS)
•
•
•
•
Topology processor & network configurator
State estimator and power flow model development
Automatic generation control (AGC), Optimal power flow (OPF)
Security assessment and alarm processing
10
Energy control
centers
11
ECCs: EMS & SCADA
Communication link
Remote
terminal
unit
SCADA Master Station
EMS 1-line diagram
Substation
Energy control center with EMS
EMS alarm display
12
ECCs: SCADA, Telemetry, EMS, RT, DA Markets
Breaker/Switch Status
Indications
SCADA
System Model Description
Network
Topology
program
Telemetry &
Communicatio
ns equipment
Updated System
Electrical Model
Power flows,
Voltages etc.,
State
Estimator
Display to Operator
Analog Measurements
State Estimator
Output
(AC power flow)
AGC
Gen base
points
Real-time
market
Automatic Generation
Control (AGC) is a feedback
control system that regulates
the power output of electric
generators to maintain a
specified system frequency
and/or scheduled interchange.
Intra-day & dayahead reliability unit
commitment (RAC)
EMS
Bad Measurement
Alarms
Generator Outputs,
Frequency, Tie-line flows
Generation
Raise/Lower Signals
Substation
and power
plant RTUs
Display to Operator
Locational
marginal
prices
SCED1
Contingency
Analysis &
Loss Analysis
Display to Operator
ContingencyAlarms
Dayahead
market
SCED2
Real-time operating
plan
Day-ahead
market
solution
SCUC
Nodal
injections
SCED3
SFT
Intra-day reliability unit commitment (RAC)
Day-ahead operating
plan
SCUC
Day-ahead reliability unit commitment (RAC)
Predefined
constraint
list
SCUC
Contingency
constraints &
loss sensitivities
Day-ahead market
13
Balancing authorities
Performs AGC within designated area.
105 BAs in N. Am.: 67 in EI, 38 in WI, 1 in Texas.
Every ISO is a BA. Not every BA is an ISO.
14
Basic market design used by all ISOs today.
Schedules entire “nextday” 24hr period.
Schedules interchange
for entire “next-day” 24hr
period, starting at current
hour, optimizing one hour
at a time (1 value per hr)
Computes dispatch
every 5 minutes.
15
Balancing Systems
min
ENERGY &
ΣΣ zit{Cost(GENit)+Cost(RSRVit)} RESERVE
sbjct to ntwrk+status cnstraints SELL OFFERS
LARGE MIXED INTEGER PROGRAM
BOTH CO-OPTIMIZE: energy & reserves
min
ΣΣ {Cost(GENit)+Cost(RSRVit)}
sbjct to ntwrk cnstraints
LARGE LINEAR PROGRAM
NETWORK
ENERGY &
RESERVE
SELL OFFERS
DAY-AHEAD ENERGY
BUY BIDS
MARKET
1 sol/day gives
24 oprting cdtns
REQUIRED
RESERVES
REAL-TIME
MARKET
ENERGY
BUY BIDS
1 sol/5min gives
1 oprtng cdtn
REQUIRED
RESERVES
AUTOMATIC
GENERATION
CONTROL SYSTEM
FREQUENCY DEVIATION FROM 60 HZ
16
Basics of electricity markets
1. Locational marginal prices (LMPs), $/MWhr,
indicate the energy price at each bus.
2. Markets compute LMPs via an internetbased double auction that maximizes
participant benefits. The LMPs are
computed from SCED every hour in the
DAM and every 5 minutes in the RTM.
3. The DAM and the RTM are 2 separate
settlement processes.
17
Internet-based two-sided auction markets
Sellers submit offers
to sell in terms of
• Price ($/MWhr)
• Quantity (MWhr)
B1
S1
Internet System
S2
Price at which seller is willing to sell
increases with amount (cost of
producing 1 more energy unit
increases as a gen is loaded higher)
This table
orders offers
and bids for
each agent.
18
B2
Offers to sell 1 MWhr
S1
S2
$10.00
$10.00
$50.00
$50.00
$65.00
$70.00
$70.00
$70.00
∞
∞
∞
∞
∞
∞
B3
Buyers submit bids
to buy in terms of
• Price ($/MWhr)
• Quantity (MWhr)
Price at which buyer is willing to buy
decreases with amount (first unit is used to
supply most critical needs and after those
needs are satisfied, next units of energy
are used to satisfy less critical needs)
Bids to buy 1 MWhr
B1
B2
B3
$70.00 $70.00 $25.00
$70.00 $50.00
0
$65.00 $25.00
0
$65.00
0
0
0
0
0
0
0
0
0
0
0
Internet-based two-sided auction markets
This table
orders offers
and bids for
each agent
(same as
previous slide)
Offers to sell 1 MWhr
S1
S2
$10.00
$10.00
$50.00
$50.00
$65.00
$70.00
$70.00
$70.00
∞
∞
∞
∞
∞
∞
Offer/bid
order
This table
orders offers
and bids
across all
selling and
buying agents,
respectively.
19
1
2
3
4
5
6
7
8
Bids to buy 1 MWhr
B1
B2
B3
$70.00 $70.00 $25.00
$70.00 $50.00
0
$65.00 $25.00
0
$65.00
0
0
0
0
0
0
0
0
0
0
0
Offers to sell 1 MWhr
Seller
S1
S2
S1
S2
S1
S2
S1
S2
Price
$10.00
$10.00
$50.00
$50.00
$65.00
$70.00
$70.00
$70.00
Bids to buy 1 MWhr
Buyer
B1
B1
B2
B1
B1
B2
B2
B3
Price
$70.00
$70.00
$70.00
$65.00
$65.00
$50.00
$25.00
$25.00
Market clearing price
L. Tesfatsion, “Auction Basics for Wholesale Power Markets:
Objectives and Pricing Rules,” Proceedings of the 2009 IEEE
Power and Energy Society General Meeting, July, 2009.
Computed as the price where the supply
schedule intersects the demand schedule.
SUPPLY
Price
($/MWhr)
DEMAND
20
Quantity (MWhr)
Market clearing price
L. Tesfatsion, “Auction Basics for Wholesale Power Markets:
Objectives and Pricing Rules,” Proceedings of the 2009 IEEE
Power and Energy Society General Meeting, July, 2009.
Computed as the price where the supply
schedule intersects the demand schedule.
SUPPLY
Price
($/MWhr)
DEMAND
21
Quantity (MWhr)
Security-constrained economic dispatch (SCED)
min g C d U r R w W
i
Subject to
i
i
i
i
i
i
i
i
i
i
i
Production Costs
DemandValu e
Reserve Costs
Reserve Value
1. SCED obj
fnct also
includes
regulation
term,
separating
reg-up from
reg-down.
Max demand
Σ di+wi<DMAXi
for all i
(9)
2. “Value”
terms in obj
fnct can be
set by
stepped
curves
established
by ISO.
We allow offers and bids to be made on energy and reserves.
This problem is solved for a single operating condition.
The operating condition is representative for
a certain time period (either 1 hour or 5 minutes).
The above is a simplified version. The MISO Business Practice Manual BPM-002-r11, Chapter 6, provides a detailed
description of the SCED. See
https://www.midwestiso.org/Library/BusinessPracticesManuals/Pages/BusinessPracticesManuals.aspx.
22
Security-constrained unit commitment (SCUC)
z F
gitCit d itU it yit Sit xit H it rit Rit witWit
t
i
t
t
t
t
t
i
t
i
i
i
i
i
min
it it
Fixed (no -load) Costs
Production Costs
Subject to
power balance
DemandValu e
git Dt dit
i
reserve
rit SDt
Startup Costs
Shutdown Costs
t,
(2)
t,
(3)
Reserve Costs
Reserve Value
i
i
min generation
max generation
max spinning reserve
ramp rate pos limit
ramp rate neg limit
start if off-then-on
shut if on-then-off
normal line flow limit
git zit MINi
i, t ,
git rit zit MAX i
i, t ,
rit zit MAXSPi
i, t ,
git git 1 MxInci
i, t ,
git git 1 MxDeci
i, t ,
zit zit 1 yit
i, t ,
zit zit 1 xit
i, t ,
aki ( git dit ) MxFlowk
k , t,
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
i
security line flow limits
Max demand
(12)
aki( j ) ( git dit ) MxFlowk( j ) k , j, t ,
i
Σ di+wi<DMAXi
for all I,t
(13)
1. SCUC obj
fnct also
includes
regulation
term,
separating
reg-up from
reg-down.
2. “Value”
terms in obj
fnct can be
set by
stepped
curves
established
by ISO.
We allow offers and bids to be made on energy & reserves. This
problem is solved across multiple time periods, usually 24 hrs (1 hr
at a time) but sometimes fewer (e.g, 4 or 6) and sometimes more.
The above is a simplified version. The MISO Business Practice Manual BPM-002-r11, Chapter 4, provides a detailed
description of the SCUC. See
https://www.midwestiso.org/Library/BusinessPracticesManuals/Pages/BusinessPracticesManuals.aspx.
23
1.
2.
3.
4.
5.
6.
Two markets - comments
Two markets: “Energy & operating reserve” are 2 different markets, 1 for
buying/selling energy, 1 for buying/selling operating reserve.
Co-optimization: The first “SC” in SC-SCED/SC-SCUC stands for
“simultaneous co-optimized” referring to the fact that both energy &
operating reserve markets are cleared within 1 optimization formulation.
Reserves: Regulation reserve supplies minute-by-minute variation in netdemand via AGC. Spinning/supplemental reserve provide backup for
contingencies (gen loss). Spinning is inter-connected, supplemental need not
be; both must be available within 10 mins of a request.
Use of SC-SCED: In DAM, SC-SCUC solves once per hour and then for that
hour, SC-SCED is also solved. RTM uses the RT commitment as input to SCSCED in computing RT dispatch every 5 minutes.
LMPs: SC-SCUC gives hourly commitment & dispatch, but no nodal prices
(LMPs). SC-SCED (given a commitment) gives dispatch & nodal prices.
Contingencies: Transmission security constraints for SC-SCUC are enforced
via a predefined constraint list for the SCUC and a simultaneous feasibility
testing (SFT) function iterating with SCED.
24
Electricity “two settlement” markets
Energy &
reserve
offers from
gens
Internet
system
Energy
bids from
loads
Day-Ahead Market
(every day)
Generates 100 mw;
paid $100.
Energy
offers from
gens
Energy
bids from
loads
Which gens get
committed, at roughly
what levels for next 24
hours, and settlement
Internet
system
Real-Time Market
(every 5 minutes)
Generation levels for
next 5 minutes and
settlement for deviations
from day-ahead market
Generates 99 mw;
pays $1.
25
Locational marginal prices
LMPk
M
t
j 1
j jk
Ploss
Pdk
1. Units are $/MWhr
2. One for each bus in the network.
3. If the network is lossless, transmission capacity is infinite,
then all buses have the same LMP, λ. In this case, λ is
the increase in system cost if total load increases by 1
unit (corresponds to simple market we will see).
4. With a lossy and congested network, LMPk is the
increase in cost of bus k MW load increases by 1 unit.
26
MISO and PJM balancing areas
27
RT LMPs in the MISO and PJM balancing areas
7:20 am (CST) 9/8/2011
Source: MISO - PJM Interconnection Joint and Common Market Web site, previously at www.miso-pjm.com/ but not maintained.
28
RT LMPs in the MISO and PJM balancing areas
7:40 am (CST) 9/8/2011
Source: MISO - PJM Interconnection Joint and Common Market Web site, previously at www.miso-pjm.com/ but not maintained.
29
Average annual locational marginal prices
30
Locational marginal prices – effect of
transmission.
31
RT LMPs in the MISO and PJM balancing areas
- temporal variation for four different nodes
6:00 am-noon (CST) 8/28/2012
32
RT LMPs in the MISO balancing area
March 4, 2013, 10:20 CST
https://www.midwestiso.org/MarketsOperations/RealTimeMar
ketData/Pages/RealTimeMarketData.aspx
33
Ancillary services in the MISO balancing area
March 4, 2013, 10:20 CST
https://www.midwestiso.org/MarketsOperations/RealTimeMar
ketData/Pages/RealTimeMarketData.aspx
34
Market prices - Energy
Real-Time 8:25 am (CST) 6/4/2013
35
Market prices – Ancillary Services
Day-ahead: hour ending 9 am (CST) 6/4/2013
Real-Time: 8:25 am (CST) 6/4/2013
36
Day-ahead LMPs in ISO-NE balancing areas
For hour ending 11:00 am (EST) 9/8/2011
New England ISO website, at http://www.iso-ne.com/portal/jsp/lmpmap/Index.jsp but no longer available.
37
RT LMPs in the ISO-NE balancing areas
10:25 am (EST) 9/8/2011
New England ISO website, at http://www.iso-ne.com/portal/jsp/lmpmap/Index.jsp but no longer available.
38
RTAncillary service prices in ISO-NE bal areas
TMSR=10min spinning rsrv
TMNSR=10min non-spinning rsrv
TMOR=30min operating rsrv
Regulation clearing
price is $5.11/MW.
Load Zones: Connecticut (CT),
Southwest CT (SWCT), Northeast
Massachusetts/Boston (NEMABSTN)
10:25 am (EST) 9/8/2011
New England ISO website, at http://www.iso-ne.com/portal/jsp/lmpmap/Index.jsp but no longer available.
39
Market time line
Ref: A. Botterud, J. Wang, C. Monteiro, and V. Miranda “Wind Power Forecasting and Electricity Market Operations,” available at
www.usaee.org/usaee2009/submissions/OnlineProceedings/Botterud_etal_paper.pdf
40
Base point calculation via real-time market
Focus on interval 2, { t+5, t+10}.
ADS: automatic dispatch system
DOT: dispatch operating target
For interval 2, a short-term net
load forecast is made 7.5 min
before interval 2 begins, at t-2.5,
and generation set points are
computed accordingly via SCED.
At t+2.5, which is 2.5 minutes
before interval 2 begins, the units
start to move.
The units are ramped at a rate
which provides that they reach the
desired base point at t+7.5 min,
which is 2.5 min after the interval
begins.
Source: Y. Makarov, C. Loutan, J. Ma, and P. de Mello, “Operational
impacts of wind generation on California power systems,” IEEE Trans
on Power Systems, Vol. 24, No. 2, May 2009.
Key point: The base point is computed
from a net load forecast. There is error in
this forecast, which typically increases as
wind penetration increases. This error
contributes to power imbalance and
therefore frequency deviation.
41
How did wind participate in markets?
“Old” approach
Price
($/MWhr)
•
•
•
•
•
•
•
Participates in day-ahead energy market
Does not participate in day-ahead AS market
Does not participate in RTM
Wind generates what it can (self-scheduled/price-taker)
No deviation penalties
Paid based on computed LMP without wind, Point X below
Marginal unit backed off
Demand schedule
without wind
Point X
Does not affect
supply curve!
Supply schedule
without wind
Quantity (MWhr)
An excellent summary of wind and markets for all North American ISOs (as of Oct.
2011) can be found at http://www.uwig.org/windinmarketstableOct2011.pdf.
42
How does wind participate in markets?
“New” Midwest ISO approach:
Dispatchable intermittent resource (DIR)
• Participates in day-ahead energy
• Makes offer into RT market like any other
generator. But one unique DIR feature:
•
•
•
Instead of capacity max offered in by other generation
resources, the forecasted wind MW is used as the
operation capacity maximum;
Units are expected to follow the dispatch signal;
Units missing “schedule band” of 8% on either side of
dispatch instruction for four consecutive 5-min periods
are penalized.
• What are implications?
43
How does wind participate in markets?
What are implications?
Wind is dispatchable! Forecasting is key!
•
•
•
DIRs are expected to provide rolling forecast of 12 fiveminute periods for the Forecast Maximum Limit.
If forecast not submitted in time, MISO forecast is used.
Each 5 minute dispatch optimization uses Forecast
Maximum Limit based on the following order
1. Participant submitted Forecast for the interval
• Must be less than or equal to the Feasibility Limit
• Must have been submitted less than 30 minutes ago
2.MISO Forecast
• Must be less than or equal to the Feasibility Limit
• Must have been created less than 30 minutes ago
3.State Estimator
44
How does wind participate in markets?
45
Midwest ISO’s wind forecasting accuracy?
46
Why is DIR beneficial? (from MISO document)
1. The entire market benefits when more resources are fully integrated into the Energy
Market. Specifically, operational efficiency and market transparency will be
improved, since fewer manual wind curtailments will be necessary, and LMPs will
reflect each resource that impacts a constraint(s). For these reasons, registration as
DIR is consistent with Good Utility Practice.
2. The automated dispatch for DIRs will be more efficient than the manual
curtailment process currently in place for Intermittent Resources. This will lead to
more optimal economic solutions that utilize wind more completely than a manual
process.
3. The make -whole provisions of the tariff apply to DIRs, whereas they do not
apply to Intermittent Resources. If a DIR is unprofitably dispatched above its DayAhead position, it is eligible for the RT Offer Revenue Sufficiency Guarantee (RSG)
Payment provisions of the tariff. If a DIR is dispatched below its Day-Ahead position, and
does not maintain its Day-Ahead margin, it is eligible for the Day Ahead Margin
Assurance Payment provisions of the Tariff. This provides DIRs with assurance that
dispatches, both upward and downward, will be economical.
See https://www.midwestiso.org/Library/Repository/Communication%20Material/Strategic%20Initiatives/DIR%20FAQ.pdf.
47
Why is DIR beneficial?
Inclusion of the DIRs in the RT dispatch provides that
DIR offers are optimized by SCED.
•
•
This provides more flexibility to manage constraints. Therefore,
there will be fewer manual curtailments, which benefits wind for
increased MWhrs produced, and benefits others because it can
be predicted (improves transparency).
Benefits to system because wind offers low and therefore affects
all time periods some (has very large effect during peak periods)
– see next slide.
Why does wind offer low when its LCOE is high?
Because markets incentivize agents to offer their marginal cost (cost of producing
the next MW) to be dispatched. This is the value for which they break-even in the
short-term. Since wind requires no fuel, its marginal costs are mainly maintenancerelated and subsequently low compared to marginal cost of fuel-based units.
How then, can wind energy be profitable in the long-term, if it is offering prices that are
lower than its LCOE?.
It is because markets settle at the clearing price, i.e., (assuming infinite transmission
& no losses), everyone gets paid the clearing price, not their offer price
48
Why is DIR beneficial?
Difference in prices with (solid) and without (dashed) wind.
Slanted lines are demand curves for night, day, and peak.
Without wind, prices are slightly higher at night, significantly
higher during the day, and much higher during the peak.
“Wind energy and Electricity Prices: Exploring the “merit order effect”,” a literature review by Poyry for the European Wind Energy
Association, April , 2010., available at www.ewea.org/fileadmin/ewea_documents/documents/publications/reports/MeritOrder.pdf. 49