Control Theories for Load 1

8/12/2019 Control Theories for Load 1

1/63

Harsha Anantwar

DSCE,Bangalore


2/63


3/63

Power quality


4/63


5/63


6/63

The loads which cause fluctuations in the supply voltageunbalanced and harmonics, d.c components require

compensation. Typical loads requiring compensation

Arc furnaces,Induction furnaces,

Arc welders,Steel rolling mills,

Winders,Very large motors, which start and stop frequently

Other serious loads which degrade power quality Adjustable speed drives which include power electronic circuitry,All power electronics based convertersRectifiers

Cyclo converters


7/63

Important aspects to be consider to provide the loadcompensation for power quality improvement.

1. Type of Load (unbalance , harmonics and dccomponent)

2. Real and Reactive power requirements (maximum,minimum and concurrence of maximum real and reactivepower requirements in multiple loads)

3. Rate of change of real and reactive power etc.

To correct load with unbalance and harmonics,instantaneous load compensation methods are used.

Theory of Load Compensation-

fundamental relation ship between supply system ,the loadand the compensator


8/63

Fundamental Theory of Load Compensation

The supply system can be modeled as a Theveninsequivalent circuitwith an open circuit voltage and a seriesimpedance,

The compensator can be modeled asvariable impedanceor as avariable source (or sink) of reactive current.

This modeling and analysis done is on the basisof steady state and phasor quantities are used to note the

various parameters in system.


9/63

Conventional methods of load compensation can

eliminate only the fundamental reactive power andunbalance in the steady state.

These kinds of compensators can be realized using

passive LC filters.

However, when harmonics are present in the system,

these methods fails to provide correct compensation

To correct load with unbalance and harmonics,instantaneous load compensation methods are used.


10/63

The active and reactive power with sinusoidal source and

linear loads are well established,With the non linear load, understanding the reactive and

harmonic power is an actual necessity for understandingreactive compensation or harmonic filtering.

A new and concise theory to deal with this problem wellknown in Japan as "instantaneous power theory or pqtheory

conventional active and reactive power theory, is valid for

steady-state analysis

New concepts of instantaneous real and imaginarypower, as introduced by Akagi, valid for steady-and-transient states


11/63

Conventional Theory of active and reactive power

Part "1" has an average value equal to VI cosand has an alternatingcomponent 011 it, oscillating at twice the line frequency.

This part "1" never becomes negative and therefore, is an unidirectional (dc)power. The average (active) power=VI cos

Part "2" is also an alternating component, oscillating at twice the linefrequency, has peak value equal to VI sinand zero average value. conventional

reactive power is just defined as the peakvalue of part "2"


12/63

Case2 -Three-phase

- Consider a balanced, three-phase system with phasesa, b and c and linear loads,

The instantaneous three phase active power is given by

However in the conventional concepts, Q3=3*Q

Because this type of power exists in each phase independently.Its instantaneous sum in the three-phases is equal to zero.


13/63

Sinusoidal Voltage Source and Non-linear Loads

(current contains harmonics at frequencies multiples of )

S2= P2+ Q2+ H2


14/63

P and Q are, dependent only on the current component

(frequency

) ; H is dependent on the current components with

frequencies different from (harmonics);

The connection of an L or C component in parallel with

the load allows the generation of a current atfrequency that absorbs or generates the reactivepower Q required by the load.

The H depends on frequencies different from can

not be eliminated by a single capacitor or inductor. The elimination of H depends on filtersthat work as a

Short circuit for the harmonic current generated by theload.


15/63

As the load may change continuously and the harmoniccontents. too, a theory for transient conditions is

necessary.

Akagi et al. have proposed new concepts of instantaneousactive and reactive power, that can be used in transientstates


16/63

The two important theories for load compensation are

Instantaneous Theory of load compensation known aspq theory

( The instantaneous reactive power is defined as aunique value for arbitrary three-phase voltage andcurrent waveforms including all distorted waveforms)

Instantaneous Symmetrical Component Theory

h


17/63

A new instantaneous reactive powercompensator can eliminate not only thefundamental reactive power in transient statesbut also some harmonic currents.

pq theory,

we shall first recall the --0 transformation


18/63

The instantaneous space vectors, eaand iaare set on the a -axis, and their amplitude and (,-) direction vary with thepassage of time.

In the same way, eband ibare on the b axis, ecand icare onthe c axis.

These space vectors are easily transformed into a

--0 coordinates

e, and iare on the axis, and eand iare on the,axis.

Their amplitude and (,-) direction vary with the passage oftime

pq theory

.


19/63

Instantaneous Imaginary Power

To deal with instantaneous voltages and currents in three-

phase circuits mathematically, it is adequate to expresstheir quantities as the instantaneous space vectors.

In order to define the instantaneous reactive power,instantaneous imaginary power space vector defined by

q space vector is the imaginary axis vector and isperpendicular to the real plane on the - -coordinates, Taking into consideration that eis

parallel to i,, and eto i,and that eis perpendicularto i and eto i. the conventional instantaneous power,p and the instantaneous imaginary power q,


20/63

p = e* i+e* iit is defined by the product of the instantaneous voltagein one axis and the instantaneous current in the sameaxis.

p is the real power in the three-phase circuit.

Conversely, q= e* i and e* i are defined by the

product of the instantaneous voltage in one axis and theinstantaneous current in the perpendicular axis.

q is the instantaneous imaginary power .


21/63

pq theory,

For three-phase system shown in Fig. 1,.

Three-phase balanced system is expressed using following voltages andcurrents.

Va Vb, Vc are phase voltages.


22/63

In a-b-c coordinates, the a, b, and c axes are fixed on the sameplane, apart from each other by 2/3,

, and , axes are the orthogonal coordinates.


23/63

The --0 transformation for voltages and currents are given below


24/63

The instantaneous active, p(t)


25/63

The instantaneous active, p(t)

advantage of using the--0 transformation is to separatethe zero-sequence component of the system.


26/63

The instantaneous reactive power, q(t)


27/63


28/63


29/63


30/63


31/63


32/63


33/63

The sum of the instantaneous powers, ppand ppcoincides with the instantaneous real power in thethree-phase circuit.

Therefore, ppand pp are named instantaneous activepower.

The instantaneous powers, Pq and pq cancel eachother and make no contribution to the instantaneous

power flow from the source to the load. Therefore, Pq and pq are named instantaneous

reactive power.


34/63

Quantities in equation are all instantaneous and valid for

transient or steady state, and harmonics may be present involtage and/or current.

In the conventional concepts the reactive powercorresponds to the peak value of the of the instantaneouspower whose mean-value is zero

Now, in the new concepts the reactive power corresponds tothe parts of the instantaneous power, that is dependent on

the instantaneous imaginary power q, exists in eachphase independently, butvanishes when added


35/63

Three-phase Sinusoidal Voltage Supplying

a Non-linear Load Suppose an electrical system with the voltages sources

as


36/63


37/63


38/63

Unbalanced Three-phase 4-Wire System


39/63


40/63

The zero-sequence power po is exactly equal to the

power in a single-phase circuit, having an average partand an alternating component.

Its characteristics is similar to the real power p(gives theamount of energy being transported per second from

source to load There is no reactive power in Po.

Both positive and negative sequence produces, and

Only positive and negative sequences can producereactive power,


41/63


42/63


43/63


44/63

Instantaneously, the reactive power required by one

phase can be supplied by the other one. Therefore, noenergy storage element is necessary to compensate forthese power terms.

compensation of q, means compensation of the

conventional reactive power q and q~( the harmonicimaginary power)

Since p, represents the power that is

effectively converted into work and therefore has to besupplied by the source, only

may be compensated.


45/63

COMPENSATION OF


46/63


47/63


48/63


49/63


50/63


51/63


52/63


53/63


54/63

A new instantaneous reactive power compensator can eliminate notonly the fundamental reactive power in transient states but also someharmonic currents.


55/63


56/63

Supply

Voltage

Linear

Load

Supply

Impedance

Normal Operating Conditions

Supply

Current

PCC

VPCC

+

-


57/63

Supply

Voltage

Nonlinear

Load

Supply

Impedance

Nonlinear Operating Conditions

PCC

Supply

Current

VPCC

+

-


58/63

Harmonics from Arc Furnaces


59/63

Passive Filters

Use L - C tuned components Filter banks tuned for the undesired harmonics

CL

L

C


60/63

Active Filters

Use active switching components

Only one filter needed to eliminate all

the unwanted harmonics

Used for power factor correction


61/63

Typical Active Filter Circuit

~ Non-linearLoad

Actual Signal

Feedback

Reference CurrentGenerator

Power Circuit

Overall SystemController

PWM

Switching Strategy


62/63

Actual Current

Feedback

Non-linear

Load~

Reference CurrentGenerator

Power Circuit

PWM

Switching Strategy Overall SystemController

Typical Active Filter Circuit


63/63

Thank You

Documents

Control Theories for Load 1