View
3
Download
0
Category
Preview:
Citation preview
By
Turaj Amraee
Fall 2012
K.N.Toosi University of Technology
Planning Criteria
Chapter 2
Outline
1- Introduction
2- System Adequacy and Security
3- Planning Purposes
4- Planning Standards
5- Reliability Assessment
Introduction
Planning could be interpreted as an optimization task
The planning decision are made as the result of a
reasonable tradeoff between Technical and Economical
constraints.
How to quantify the reliability
Reliability and Planning
Reliability begins with Planning
System Adequacy and Security
Adequacy - The ability of the electric systems to supply the aggregate electrical demand and energy requirements of
their customers at all times, taking into account scheduled and
reasonably expected unscheduled outages of system elements.
Security - The ability of the electric systems to withstand sudden disturbances such as electric short circuits or
unanticipated loss of system elements.
Reliability of the interconnected bulk electric systems is defined using
the following two terms:
Planning Purposes
Power systems must be planned, designed, and constructed to operate reliably within thermal, voltage, and stability limits while achieving their major purposes. These purposes are to:
Deliver Electric Power to Areas of Customer Demand
Provide Flexibility for Changing System Conditions
Reduce Installed Generating Capacity
Allow Economic Exchange of Electric Power Among Systems
Planning Standards
Standards
NERC WECC IEC
System Modeling Data Requirements
System Protection and Control
System Restoration
Facility Connection Requirements
Voltage Support and Reactive Power
Transfer Capability
WESTERN ELECTRICITY COORDINATING COUNCIL
North American Electric Reliability Corporation International Electrotechnical Commission
Planning Standards
S1. The interconnected transmission systems shall be planned, designed, and
constructed such that with all transmission facilities in service and with normal (pre-
contingency) operating procedures in effect, the network can deliver generator unit
output to meet projected customer demands and projected firm (non-recallable
reserved) transmission services, at all demand levels over the range of forecast
system demands, under the conditions defined in Category A of Table I (attached).
Cat. A
• Normal
Cat. B
• N-1
Cat. C
• N-2 and higher
Cat. D
• Cascading
NERC Example
NERC Planning Criteria
NERC Planning Criteria
Reliability – An introduction
Running
Fault
Repair
Planned maintenance
Temporary maintenance
Power equipment such as generator, transformers, Trans. Lines, etc., are
generally considered to be system components. In their service life time,
they can be in many states:
Reliability – failure characteristics
Characteristics of component failure
Continuous working time T of a component is a random variable.
F(t) : failure function of a component,
R(t) : the probability that a component still operates after a designated time t, and
is called the reliability function of a component or Reliability
f ( t ) is the failure probability density function
0)()( ttTPtF
0)()( ttTPtR
)()()(
1)()(
tfdt
tdF
dt
tdR
tRtF
Reliability – failure characteristics
The conditional probability that a component is
working before the time instant t and develops a
fault in the unit time Del(t) after the time instant t,
Failure rate function
)(1
lim)( 0 tTttTtPt
t t
dt
tdR
tRtR
tft
)(
)(
1
)(
)()(
Reliability – failure characteristics
The mean of the random variable T is called a
component's mean time between failures (MTBF), which is
another index to evaluate a component's reliability.
Mean time between failures (MTBF)
1MTBF
Reliability – repair characteristics
The repair rate can be defined in a form similar to that for the failure rate:
Mean time to repair (MTTR)
The mean of a component's repair time TD or the mean time to repair can be written as
Characteristics of component repair
)(1
lim)( 0 tTttTtPt
t DDt
1MTTR
Reliability – Availability
The probability PA(t) that a component is in service state is called the availability
Availability
)(UPPA
)(1: DnPAUFOR
MTTRMTBF
MTBFA
MTTRMTBF
MTTRU
Reliability – Evaluation Process
Define the boundary of the system and list all the components included
Provide reliability data such as failure rate, repair rate, repair time,
scheduled maintenance time, etc., for every component.
Establish reliability models for every component.
Define the mode of system failure, or define the criterion for normal and faulty systems.
5. Establish a mathematical model for the system reliability
assumptions.
6. Select an algorithm to calculate the system reliability
Reliability Calculation
Reliability – Evaluation Process
Generation: Transmission is ignored Composite: Generation+Transmission Distribution: Gen+Trans. Are ignored
•Generation: Two or three states model •Transmission Line, Transformer: Two or three states model •Load: Load Duration Curve
Here HLI is considered
Gen Load
Reliability – Generation Model
1- State Probability Model: The system loses capacity c with a certain probability when the
generating unit to stop due to random failures. Therefore, the capacity or the X is considered to be a random variable in power system. The unit model is the probability table of a generator unit's capacity state.
Probability model The dual-state model assumes that a unit only has two states:
operation and failure (repair).
Example- Dual State Generation Model
0
1)(
i
i
ixFOR
cxFORxXP
cx
cxFOR
x
xXP
i
i
i
i
1
0
00
)(
Individual state probability cumulative state probability
Reliability – Generation Model
2- State Frequency Model:
Suppose p(i) = P(X = xi) is the individual probability of ith state
(capacity), fi is the ith state frequency and fij is the transition
frequency from state i to state j.
Example- Dual State Generation Model
)1( FORppf ijiji
ijii
)(FORppf jijji
jiij
ki
ixfxXFxF )()()(
Individual state frequency cumulative state frequency
Reliability – Example
Example- Dual State Generation Model
Capacity Outage Probability Table
Reliability – Example
Example- Dual State 2-Units Generation Model
For multi-generator unit model COPT is constructed using
recursive algorithm
the table is revised as units are added one after another until the last one and the capacity
model for the whole generating system is formed.
Reliability – Load Model
From 1 and 2
Primary load data Normally primary load data include:
1. The maximum monthly load or weekly load in a year.
As a percentage of the maximum load in a year(52 weeks)
2. The maximum load in each day in a week.
As a percentage of the maximum load in a week(7 days)
It is assumed that it is valid for all the seasons
3. The load in 24 hours in a typical day in each season.
As a percentage of the maximum load in every hour(24 hours)
For each season a typical different load curve is assumed
Maximum load for the 365 days
in a year
From 1,2 and 3 Maximum load for the 8760 hrs
in a year
Reliability – Load Model
Load outage capacity table
Tha aim is to replace the load curve with a load outage capacity
j
ij
iT
tLP )(
ijt
T
The pause time of Li inside T
The examination period: 365 days or 8760 hrs
The load level Li is the negative of operation capacity
Reliability – Load Model
Generating System Reliability Evaluation
The system margin state probability and frequency table is formed by
convolution of the parallel calculation formula applied to the generator
outage table and the load capacity table
Generating unit's cumulative P and F: aiaia NiXFXP ,...,1,0)(),(
bibib NiXFXP ,...,1,0)(),( Load cumulative P and F:
Margin state cumulative probability
)]()([)()( 10
jbjbikN
j
akc XPXPXXPXPb
)]}()([)(
)]()([)({)(
1
1
0
jbjbika
jbjbik
N
j
akc
XFXFXXP
XPXPXXFXFb
Margin state cumulative frequency
Reliability Indices
The power generation system reliability indices are usually a measure of power
supply reduction to customers (load point) as a result of faults developed in the
power generating unit
1. Loss of load probability (LOLP),
LOLP is defined as the probability of the effective system capacity not meeting
the load demand, which can be written as
)( RXPLOLP
X: system outage capacity
R=C-L: system reserve capacity
C: system effective capacity
L: Maximum load
Reliability Indices
The expected number of days or number of hours in the
period investigated when the maximum load exceeds
the system effective capacity:
2. Loss of Load Expectation (LOLE)
Based on load model:
T is 8760 hours or 365 days
TLOLPLOLE * hrs/year or day/year
Reliability Indices
EENS is the expectation of the energy loss caused to
customers by insufficient power supply:
3.Expected energy not served (EENS)
yearMWhpMEENS kM
k
k
/8760*0
Mk=Cj-Li: system margin capacity
Reliability Indices
If the cost to customers is affected by the frequency of power interruption over a certain period instance to customers e.g. chemical industry or metallurgical then the indices of power interruption duration is needed.
4. Frequency and duration (F& D)
The cumulative system interruption frequency and duration
yeartimesRXFF /)( hoursRXF
RXPD
)(
)(
Reliability Indices
The SM index is the ratio of energy loss due to power
interruption as a result of insufficient system
generation over the annual maximum load
5. System-minutes (SM)
utesL
EENSSM
p
min
Lp the annual maximum load
Exercise 1.
Write a computer program to obtain the results of
Examples 2.2 and 2.3 of the reference # 1.
End
؟
Recommended