Challenges%20in%20Modelling%20Active%20Electric%20Power%20Networks

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Challenges in Modelling Active Electric Power
Networks

• Dr. S. K. Chakravarthy
• Department of Elect. Engg., KFUPM

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Aspects 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.

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Aspect One

• The conventional electric power transmission
  network.

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Modelling a Conventional Power Transmission
Network
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Purpose of conventional transmission 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.

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Aspect Two

• Analytical methods used.

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Analytical Methods Used
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Analytical 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.

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Analytical 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.

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Aspect Three

• What is an active electric power transmission
  network?

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An Active Power Transmission Network
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An active electric power 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.

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An active electric power 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).

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The 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.

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Aspect Four

• Use of numerical simulations.

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Analytical Solution (system involving fast and
slow dynamics)
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Analytical Solution (system involving fast and
slow dynamics)
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Aspect 5

• Why is a new analytical method required?

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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.

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Why a new method?

• The system of odes 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.

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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.

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Aspect Six

• Some advantages of the new approach.

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Advantages of the new approach.

• 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.

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Conclusions

• In summary, the challenges involved in modelling
  active EPTNs involve
• Determining the number of eigenvalues with zero
  real parts for a large scale system
• Eliminating the fast transient by determining the
  invariant manifold while still retaining their
  influence on the nonlinear behaviour of the
  system
• Eliminating time dependence by the method of
  averaging.

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Conclusions

• Since the solutions are dependent on the choice
  of initial conditions, numerical methods must be
  integrated with symbolic processing software
• Methods are required for dimensionally reducing
  the problem.

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Conclusions

• THANK YOU FOR YOUR ATTENTION