1. EXTENSIONS TO THE INHERENT STRUCTURAL THEORY OF POWER NETWORKS, AND APPLICATIONS
Prof. John T. Agee
Head of the Control and Process Control Cluster
Department of Electrical Engineering
Tshwane University of Technology. Pretoria. South Africa

2. Others Mr. Humble Tajudeen Sikiru Prof. A. A. Jimoh Prof. Alex Haman
Prof. Roger Ceschi

3. Well Known
Generally, generator would be located near sources of primary energy
There are main electricity consumption points or load centres supports industrial and commercial activities as manufacturing, mining, etc
In a simplistic manner, a power system network consists of the network of transmission lines, the generators and load centres.

4. A Re-statement of the Nature of Power Systems
Can we view power system networks as interconnections of sources, sinks and circuit elements?

5. Alternatively
Instead of the traditional, computationally intensive power system analysis techniques based on non-linear load flow equations,
Can power systems be analysed using simple circuit analysis laws?

6. Summary of Presentation
Thought-provoking comments on the classical load flow approach
The inherent structural theory of power systems networks(ISTN): in history
Our recent extension of the ISTN with the introduction of new indices
Illustrate the use of some of our ISTN indices in power system analysis.

7. A Q-V Sensitivity Presentation
Consider
Where I: injected currents, Ybus : bus admittance matrix and, V:nodal voltages

8. ...Q-V

9. The Lesson from the Q-V Methods
The load flow methods introduce nonlinearities that are not inherent in the original problem
May thus add several orders of complexity in arriving at a solution of the problem
The sub-optimality of solutions of some power flow problems, arise from the method of solution: and may not be inherent in the problem itself

10. ......
If the complexity of a power system network is increased by the volatility of microgrids/ distributed generation/intermittent renewable sources, shall classical load flow methods improve or complicate the ease of solution of network problems?

11. The Theory of the Inherent Structural Characteristics of Transmission Networks (ISTN)
The earliest thoughts in this regard, were formulated by Laughton (1964)
This approach argues that, the interactions of voltages V, and currents I (and hence power flows)in a power system networks are governed by ohms law of the form V=ZI or I=YZ

12. Classical ISTN
That variations of V or I creates variations of the other.
That Z (Y) remains constant in a given network
That the behaviour of the network is preserved in the structure of its Y matrix: the Y matrix thus contains all the information on the inherent (electrical) structure or behaviour of the network.

13. Success of the Classical ISTN
Several successful applications of classical ISTN have been reported:
location of capacitors & harmonic filters
Power quality studies
Generator allocation
Identification of weak nodes in power systems

14. Challenges of Classical ISTN
Was not very successful in the analysis of highly interconnected networks
Extensions of this theory, providing the so-called T-index is also found to be highly complex in practical applications

15. Recent Extensions to the ISTN Theory
Realised that buses in a power system do not have the same play: generator impedances YG, load impedances YL and transmission line or generator-load impedances YGL had different contributions to the I-V behaviour of the network.

16. New ISTN Terminology
Parallels were drawn with nuclear forces: proto-proton attraction (affinity), electron-electron attractions, and proton-electron attractions
A related partitioning of the Y matrix of the network:

17. Hence

18. INSTN Indices
Re-write

19. 1. The Ideal Generator Contribution
absolute values give the ideal
generator contribution, of each generator, at load buses
The summation of each row is approximately equal to unity (Thukaram & Vyjayanthi, 2009)

20. 2. Generator-Generator Attraction Region
The eigenvalues of AGG define the ‘structural impact of the generator-electrical attraction region’
The generator associated with the least eigenvalue has the highest impact on generator voltages

21. .... Impact of Generator-Generator Attraction Region
Now,
Decompose
with as appropriate eigenvalues
Yielding

22. 3. Generator Affinity
Re-write

23. ... Generator Affinity
represents the influence of generators over load buses and is termed the “generator affinity”
The absolute value of the summation of each row of this matrix is approximately equal to unity

24. 4. Load-load Electrical Attraction
represents the equivalent load buses admittance or load-load attraction
The eigenvalues of CLL determine the “structural impact of the electrical load attraction region” or how load buses affect load voltage
The load bus with the lowest eigenvalue participation in CLL affects load voltages most.

25. .... Structural Impact of Load Electrical Attraction Region
Now,
Decompose
with as appropriate eigenvalues
Yielding

26. Summary of ISTN Indices
Ideal generator contribution, derived from FLG, gives how a generator contributes to load voltage at a given load bus
Structural impact of the load electrical attraction region: captures the critical behaviour of load-load buses to power system networks & and can be used to counter the limitation of the ideal generator contribution
Structural impact of generator electrical attraction: valuable in identifying generators that are located at structurally weal nodes
Generator affinity: clarifies which load buses will be supplied with larger power levels, based on their low impedance links

27. APPLICATIONS

28. Southwest England 40 bus network

29. Device Location Number of Compensators Proposed method
bus number bus number
Classical Q-V sensitivity 1 33 29 2
33, 36
29, 37 3
33, 36, 38
29, 37, 33 4
33, 36, 38, 25
29, 37, 33, 35

30. Standard Deviation of Voltages
Number of SVCs
Proposed method Classical
Q-V sensitivity 1
0.0193
0.0235 2
0.0122
0.0198 3
0.0123
0.0121 4
0.0120
0.0118

33. Example
Topologically strong versus topologically weak networks

34. IEEE 30 bus network

35. Eigenvalue
The Y matrix has a zero eigenvalue ( actually, less than a given precision value)
Eigen vectors
S?N
Bus Number
Ranking 1
1st 2
0.7370
2nd 3
1.5385
3rd 4
2.3619
4th 5
3.1080
5th

36. Not Easily Improved

37. Southwest England 40 bus network

38. ....
The smallest eigenvalue (in absolute value) is greater that the precision defined for this test network and it is Eigen vector