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

؟