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MODULE IV
ECONOMIC OPERATION OF POWER SYSTEM
INTRODUCTION
One of the earliest applications of on-line centralized control was to provide a central facility, to
operate economically, several generating plants supplying the loads of the system
...
The capital investment, operation and
maintenance costs are different for different types of plants
...

i) Problem of economic dispatch, which deals with determining the power output of each plant to
meet the specified load, such that the overall fuel cost is minimized
...
In this chapter we consider the
problem of economic dispatch
...

ii) Base supply with regulation: output power is regulated based on system load
...

iv) Automatic economic regulation: output level is adjusted, with the area load and area control
error, while tracking an economic setting
...
The factors influencing the cost of generation
are the generator efficiency, fuel cost and transmission losses
...
Further, if the
plant is located far from the load centers, transmission losses may be high and running the plant
may become uneconomical
...
Modern generating plants like nuclear plants,
geo-thermal plants etc, may require capital investment of millions of rupees
...


PERFORMANCE CURVES
INPUT-OUTPUT CURVE
This is the fundamental curve for a thermal plant and is a plot of the input in British thermal
units (Btu) per hour versus the power output of the plant in MW as shown in Fig
...
1

Fig
...
1: Input output curve
HEAT RATE CURVE
The heat rate is the ratio of fuel input in Btu to energy output in KWh
...
The reciprocal of heat – rate is called fuel – efficiency
...
A typical plot is shown in Fig
...
4
...

Incremental fuel rate =∆Input/∆Output
The unit is again Btu / KWh
...
4
...
3: Incremental Fuel Rate Curve

Incremental cost curve
The incremental cost is the product of incremental fuel rate and fuel cost (Rs / Btu or $/Btu)
...
4
...
The unit of the incremental fuel cost is Rs / MWh or $ /MWh
...
4
...

2

Fi  a i  b i PGi  c i PGi Rs/h
The incremental fuel cost is given by

dFi
 bi  2ci PGi Rs/MWh
dPGi
The incremental fuel cost is a measure of how costly it will be produce an increment of power
...
which can be taken to be some percentage of the incremental fuel
cost, instead of resorting to a rigorous mathematical model
...
While there is negligible operating cost for a hydel plant, there is a limitation
on the power output possible
...

ECONOMIC

GENERATION

SCHEDULING

NEGLECTING

LOSSES

AND

GENERATOR LIMITS
In an early attempt at economic operation it was decided to supply power from the most efficient
plant at light load conditions
...
With further
increase in load, the next most efficient plant would supply power till its maximum efficiency is
reached
...
Unfortunately however, this method failed to minimize the total cost
of electricity generation
...

The simplest case of economic dispatch is the case when transmission losses are neglected
...
Since losses are neglected,
the total generation is equal to the total demand PD
...
If Fi is the
cost of plant i in Rs/h, the mathematical formulation of the problem of economic scheduling can
be stated as follows:
ng

Minimize

FT   Fi
i 1

ng

Such that

P

Gi

 PD

i 1

Where

FT= total cost
PGi= generation of plant i
PD= total demand

This is a constrained optimization problem, which can be solved by Lagrange’s Method
...
The cost of a plant Fi
depends only on its own output PGi, hence

Fi
dFi
FT


PGi PGi dPGi
Using the above,

dFi
L

  0
dPGi dPGi

We can write

bi  2ci PGi  

i = 1, 2, -----------, n g

i = 1, 2, -----------, n g

The above equation is called the co-ordination equation
...

ECONOMIC SCHEDULE INCLUDING LIMITS ON GENERATOR (NEGLECTING LOSSES)

The power output of any generator has a maximum value dependent on the rating of the
generator
...
The economic dispatch
problem now is to schedule generation to minimize cost, subject to the equality constraint
...
e
...
As soon as a plant reaches the limit (maximum or
minimum) its output is fixed at that point and is maintained a constant
...

ECONOMIC DISPATCH INCLUDING TRANSMISSION LOSSES

When transmission distances are large, the transmission losses are a significant part of the
generation and have to be considered in the generation schedule for economic operation
...
ng

n

g
L
 PD   PGi  PL  0

i 1

(same as the constraint)

dFi
FT

PGi dPGi

Since

dFi
dP
 L 
dPGi
dPGi


dFi 
1


dPL
dPGi
1
dPGi


The term








1
is called the penalty factor of plant i, Li
...
,n g

The minimum operation cost is obtained when the product of the incremental fuel cost and the
penalty factor of all units is the same, when losses are considered
...

For a two plant system
PL  B11 PG1  2 PG1 B12 PG 2  B22 PG 2

as B12=B21

AUTOMATIC LOAD DISPATCH
Economic load dispatching is that aspect of power system operation wherein it is required to
distribute the load among the generating units actually paralleled with the system in such a
manner as to minimize the cost of supplying the minute to minute requirements of the system
...
The objective
of automatic load dispatch is to minimise the cost of supplying electricity to the load points while
ensuring security of supply against loss of generation and transmission capacity and also
maintaining the voltage and frequency of the system within specified limits
...
Hence automatic control of load dispatch
problem is required
...

The components for automatic load dispatching are
Computer-The computer predicts the load and suggests economic loading
...


Fig
...
5: Schematic diagram of automatic load dispatching components

Data Input: The computer receives a lot of data from the telemetering system and from the paper
tape
...
Paper tape stores all
the basic data required e
...
the system parameters, load predictions, security constraints, etc
...
He can
obtain certain information required for some action to be taken under emergency condition or he
can put data into it if needed
...

Machine Controller: The computer sends information regarding the optimal generation to the
machine controller at regular intervals which in turn implements them
...
These are referred to as controller power loops
...
A summed error signal is formed from these two
components and is converted in the motor controller to a train of pulses that are applied to a
speed governor reference setting motor called the speeder motor
...
The
pulses are applied as raise or lower command to the speeder motor in accordance with the error
signal and thus the output of the generator is increased or decreased accordingly
...
e
...
Typical long-range scheduling goes anywhere
from 1 week to 1 yr or several years
...

Short-Range Hydro-Scheduling
Short-range hydro-scheduling (1 day to 1 wk) involves the hour-by-hour scheduling of all
generation on a system to achieve minimum production cost for the given time period
...
A set
of starting conditions (e
...
, reservoir levels) is given, and the optimal hourly schedule
that minimizes a desired objective, while meeting hydraulic steam, and electric system
constraints, is sought
...
The schedules are usually developed to minimize
thermal generation production costs, recognizing all the diverse hydraulic constraints that may
exist
...
4
...
That is, for any time period j,

PHjmax  Ploadj

j=1,2,
...

j max

j max

 PHj n j   Ploadj n j
j 1

n j is the no of hours in period j

j 1

j max

n

j

 Tmax = Total Interval

j 1

Steam plant energy required is
j max

j max

 Ploadj n j   PHj n j  E
j 1

j 1

Ns

Where E 

P n
sj

Ns is the no of periods the steam plant is on

j

j 1

Ns

n

j

 Tmax

j 1

So the scheduling problem and the constraint are
Ns

Min FT 

 F (P

sj

)n j

j 1

Ns

Subject to

P n
sj

j

E 0

j 1

Lagrange function is

Ns
Ns


L   F ( Psj ) n j    E   Psj n j 
j 1
j 1



dF ( Psj )
L

  0
Psj
dPsj

dF ( Psj )
dPsj



for j=1,2,
...
Let this
optimum value of steam-generated power be Ps*, which is the same for all time intervals
the steam unit is on
...
Optimal hydrothermal schedule is as shown below:

Fig
...
7: Optimal Hydrothermal Scheduling

FACTS
The large interconnected transmission networks are susceptible to faults caused by
lightning discharges and decrease in insulation clearances
...
While the loads in a power system vary by the time of the
day in general, they are also subject to variations caused by the weather (ambient temperature)
and other unpredictable factors
...

The factors mentioned in the above paragraph point to the problems faced in maintaining
economic and secure operation of large interconnected systems
...
The required safe operating margin
can be substantially reduced by the introduction of fast dynamic control over reactive and active
power by high power electronic controllers
...

Flexible AC Transmission System (FACTS) is used as Alternating current transmission systems
incorporating power electronic-based and other static controllers to enhance controllability and
increase power transfer capability
...

Benefits of utilizing FACTS devices: The benefits of utilizing FACTS devices in
electrical transmission systems can be summarized as follows:
1
...

2
...

3
...

4
...

FACTs controllers: Structures & Characteristics of following FACTs Controllers
The FACTS controllers can be classified as—
1
...


Series connected controllers

3
...


Combined shunt-series controller

Static Var Compensator (SVC)
Static Var compensator is a static Var generator whose output is varied so as to maintain or
control specific parameters (e
...
voltage or reactive power of bus) of the electric power
system
...
A pair of anti parallel
thyristors is connected in series with a fixed inductor to form a TCR module while the
thyristors are connected in series with a capacitor to form a TSC module
...
The primary task of an SVC is to maintain the voltage of a particular bus by
means of reactive power compensation (obtained by varying the

firing angle of the

thyristors)
...
Static VAR Compensator (SVC) is a
shunt connected FACTS controller whose main functionality is to regulate the voltage at a
given bus by controlling its equivalent reactance
...


Fig
...
8: Static Var Compensator
Thyristor Controlled Series Capacitor (TCSC)
A TCSC is a capacitive reactance compensator, which consists of a series capacitor bank
shunted by a thyristor controlled reactor in order to provide a smoothly variable series

capacitive reactance
...
The power flow over a transmission line can
be increased by controlled series compensation with minimum risk of sub-synchronous
resonance

(SSR)
...
A
TCSC module comprises a series fixed capacitor that is connected in parallel to a thyristor
controlled reactor (TCR)
...
In a TCSC, a Metal Oxide Varistor (MOV)
breaker

is

connected in parallel to

along with

a bypass

the fixed capacitor for overvoltage protection
...
TCSC controllers
use thyristor-controlled reactor (TCR) in parallel with capacitor segments of series capacitor
bank
...

TCSC is an effective and economical means of solving problems of transient stability,
dynamic stability, steady state stability and voltage stability in long transmission lines
...


Fig
...
9: Thyristor Controlled Series Capacitor
Static Synchronous Series Compensator (SSSC)
A SSSC is a static synchronous generator operated without an external electric energy source as
a series compensator whose output voltage is in quadrature with, and controllable

independently of the line current for the purpose of increasing or decreasing the overall
reactive voltage drop across the line and thereby controlling the transmitted electric power
...

A SSSC incorporates a solid state voltage source inverter that injects an almost sinusoidal
voltage of variable magnitude in series with a transmission line
...
The injected voltage is mainly in quadrature with the line
current
...
Most of injected voltage, which is in quadrature with the line
current, emulates a series inductance or a series capacitance thereby altering the transmission line
series reactance
...


Fig
...
10: Static Synchronous Series Compensator
SSSC is a solid-state synchronous voltage source employing an appropriate DC to AC
inverter with gate turn- off thyristor
...
In SSSC, the
resonance phenomenon has been removed
...
The main control objective of the SSSC is to directly control the
current, and indirectly the power, flowing through the line by controlling the reactive
power exchange between the SSSC and the AC system
...

Static Synchronous Compensator (STATCOM)
A STATCOM is a static synchronous generator operated as a shunt connected static var
compensator whose capacitive or inductive output current can be controlled independent of the
ac system voltage
...
A STATCOM
incorporate a voltage source inverter (VSI) that produces a set of three phase ac output
voltages, each of which is in phase with, and coupled to the corresponding ac system
voltage via a relatively small reactance
...
The VSI is driven by a dc storage
capacitor
...
The Static Synchronous
Compensator (STATCOM) is a power electronic-based Synchronous Voltage Generator (SVG)
that generates a three-phase voltage from a dc capacitor in synchronism with the
transmission line voltage and is connected to it by a coupling transformer
...
4
...
In STATCOM, the resonance phenomenon has been

removed
...


Unified Power Flow Controller (UPFC)
The UPFC, by means of angularly unconstrained series voltage injection, is able to control,
concurrently or selectively, the transmission line voltage, impedance, and angle or,
alternatively, the real and reactive power flow in the line
...

The UPFC is the most versatile and powerful FACTS device
...

Simultaneous control of multiple power system variables with UPFC poses enormous
difficulties
...
The Unified Power Flow Controller
(UPFC) is used to control the power flow in the transmission systems by controlling the
impedance, voltage magnitude and phase angle
...
The basic structure of the UPFC consists of
two voltage source inverter (VSI); where one converter is connected in parallel to the
transmission line while the other is in series with the transmission line
...
Series converter or Static Synchronous Series Compensator (SSSC) is
used to add controlled voltage magnitude and phase angle in series with the line, while shunt
converter or Static Synchronous Compensator (STATCOM) is used to provide reactive power to
the ac system, beside that, it will provide the dc power required for both inverter
...
These two voltage source
converters share a common dc capacitor
...
Therefore, active power drawn by the shunt converter should be equal to the
active power generated by the series converter
...
The coupling transformer is used to connect the device to the system
...
4

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