Challenges in Modelling Challenges in Modelling Active Electric Power Active Electric Power NetworksNetworks

Dr. S. K. ChakravarthyDr. S. K. Chakravarthy

Department of Elect. Engg., Department of Elect. Engg., KFUPMKFUPM

Aspects to be addressedAspects to be addressed

The conventional electric power transmission network.

Analytical methods used. What is an active electric power

transmission network? Use of numerical simulations. Why is a new analytical method

required? Some advantages of the new

approach.

Aspect OneAspect One

The conventional electric power transmission network.

R L

C1 C1

Modelling a Conventional Power Transmission Network

Purpose of conventional Purpose of conventional transmission networkstransmission networks

An electric power transmission network is designed to transfer bulk power between two points.

Performance of an electric power transmission network is obtained from the nominal Pi-equivalent circuit.

Aspect TwoAspect Two

Analytical methods used.Analytical methods used.

Analytical Methods UsedAnalytical Methods Used

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,,

puxg

puxfx

Analytical Methods UsedAnalytical Methods Used

For initial values of control vector u and load vector p one can find the state variable x.

State variable x represents the bus voltages in the network.

),,0 puxg

Analytical Methods UsedAnalytical Methods Used

Knowing the initial values of ( x, u,p) one obtains the solution at a future instant t.

This solution represents the slowly evolving dynamics of the system (due to the moment of inertia of rotating machines.

puxfx ,,

Aspect ThreeAspect Three

What is an active electric power What is an active electric power transmission network?transmission network?

R L

C1 C2

L-TCR

Two anti-parallel thyristor-pair for each phase.

Bus-1V1

Bus-2V2

An Active Power Transmission NetworkAn Active Power Transmission Network

An active electric power An active electric power network?network?

The extent of power that can be transferred between two points can be controlled by FACTS or Static VAR Systems.

By the use of these local controllers, the surge impedance and propagation constant change rapidly.

An active electric power An active electric power network?network?

The changes in these parameters can be enforced at least once every cycle.

Consequently, the network parameters become time dependent (that is, they need to be represented by differential equations).

The ProblemThe Problem

In modeling:•The resonant frequencies of the

network will (dynamically) change. •The switching operation of the

controllers makes the transmission network nonlinear.

•There is a distinct possibility of the occurrence of switching bifurcations.

Aspect FourAspect Four

Use of numerical simulations.

Analytical Solution (system Analytical Solution (system involving fast and slow involving fast and slow dynamics)dynamics)

yxy

yxx

xx 22

Analytical Solution (system Analytical Solution (system involving fast and slow involving fast and slow dynamics)dynamics)

210

00

x

xy

y

x

y

x

Aspect 5Aspect 5

Why is a new analytical method Why is a new analytical method required?required?

Why a new method?Why a new method?

The odes along with the nonlinear transformation can solved by packages such as EMTP or EMTDC.

However, one cannot rule out the possibility of numerical instability providing erroneous results.

Numerical instability arises from the existence of zero eigenvalues in a nonlinear system.

Why a new method?Why a new method?

The system of ode’s have zero eigenvalues.

The inclusion of nonlinear transformations and the presence of zero eigenvalues will give rise to bifurcation leading to several periodic and aperiodic (numerical) oscillations.

Why a new method?Why a new method?

Problem: The numerical solution of a stable (physical) system may be unstable. The conditions that may initiate any of these numerical instability depend on the initial conditions, which are never completely known.

Aspect SixAspect Six

Some advantages of the new Some advantages of the new approach.approach.

Advantages of the new Advantages of the new approachapproach..

Provide tractability to a nonlinear system with large dimension such as a power system.

The large dimensional nonlinear system can be modeled as an equivalent reduced order system.

ConclusionsConclusions

In summary, the challenges involved in In summary, the challenges involved in modelling active EPTN’s involve:modelling active EPTN’s involve:• Determining the number of eigenvalues with Determining the number of eigenvalues with

zero real parts for a large scale system;zero real parts for a large scale system; Eliminating the fast transient by determining Eliminating the fast transient by determining

the invariant manifold while still retaining the invariant manifold while still retaining their influence on the nonlinear behaviour of their influence on the nonlinear behaviour of the system;the system;

Eliminating time dependence by the method Eliminating time dependence by the method of averaging.of averaging.

ConclusionsConclusions

• Since the solutions are dependent on Since the solutions are dependent on the choice of initial conditions, the choice of initial conditions, numerical methods must be numerical methods must be integrated with symbolic processing integrated with symbolic processing software;software;

• Methods are required for Methods are required for dimensionally reducing the problem. dimensionally reducing the problem.

ConclusionsConclusions

THANK YOU FOR THANK YOU FOR YOUR ATTENTIONYOUR ATTENTION