Report

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 Others • Mr. Humble Tajudeen Sikiru • Prof. A. A. Jimoh • Prof. Alex Haman • Prof. Roger Ceschi 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. A Re-statement of the Nature of Power Systems • Can we view power system networks as interconnections of sources, sinks and circuit elements? 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? 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. A Q-V Sensitivity Presentation • Consider I YbusV • Where I: injected currents, Ybus : bus admittance matrix and, V:nodal voltages ...Q-V N I i YikVk j 1 Si Pi jQi Vi I i* N Pi Vi YikVk cos( i k ik ), k 1,2, N k 1 N Qi Vi YikVk sin( i k ik ), k 1,2, N k 1 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 ...... • 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? 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 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. 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 Challenges of Classical ISTN • Was not very successful in the analysis of highly interconnected networks • Extensions of this theory, providing the socalled T-index is also found to be highly complex in practical applications 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. New ISTN Terminology • Parallels were drawn with nuclear forces: proto-proton attraction (affinity), electronelectron attractions, and proton-electron attractions • A related partitioning of the Y matrix of the network: YGG Y YLG YGL YLL Hence I G YGG I Y L LG YGL VG YLL VL INSTN Indices • Re-write VL Z LL FLG I L I K A V G GL GG G Z LL YLL1 , FLG YLL1YLG K GL YGL YLL1 AGG YGG YGL YLL1YLG 1. The Ideal Generator Contribution • KGL YGLYLL1 absolute values give the ideal generator contribution, of each generator, at load buses V Z I F V L LL L LG G • The summation of each row is approximately equal to unity (Thukaram & Vyjayanthi, 2009) 2. Generator-Generator Attraction Region • AGG YGG YGLYLL1YLG • 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 .... Impact of Generator-Generator Attraction Region • Now, 1 GG VG A [ IG KGL I L ] • Decompose with AGG WW r w j 1 j j w*j as appropriate eigenvalues r • Yielding * VG j 1 * j wj w j [ I G K GL I L ] 3. Generator Affinity • Re-write VG Z GG H GL I G I W C V L LG LL L Z GG YGG1 ,WLG YLG YGG1 H GL YGG YGL1 CLL YLL YLG YGG1 YGL ... Generator Affinity • represents the influence of generators over load buses and is termed the “generator affinity” HGL YGGYGL1 • The absolute value of the summation of each row of this matrix is approximately equal to unity 4. Load-load Electrical Attraction • CLL YLL YLGYGG1YGL 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. .... Structural Impact of Load Electrical Attraction Region • Now, 1 LL VL C [ I L WLG I G ] • Decompose with C LL MM r m m i 1 i i * i as appropriate eigenvalues n • Yielding * VL i 1 * i mi m i [ I L WLG I G ] 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 APPLICATIONS Southwest England 40 bus network Device Location Number of Compensators Proposed method bus number bus number Classical Q-V sensitivity bus number bus number 1 33 29 2 33, 36 29, 37 3 33, 36, 38 4 33, 36, 38, 25 29, 37, 33 29, 37, 33, 35 Standard Deviation of Voltages Number of SVCs 1 2 Proposed method Classical 0.0193 0.0122 Q-V sensitivity 0.0235 0.0198 3 0.0123 0.0121 4 0.0120 0.0118 Example • Topologically strong versus topologically weak networks IEEE 30 bus network Eigenvalue • The Y matrix has a zero eigenvalue ( actually, less than a given precision value) S?N Bus Number Ranking 1 0 1st 2 0.7370 2nd 3 1.5385 3rd 4 2.3619 4th 5 3.1080 5th • Eigen vectors Not Easily Improved Southwest England 40 bus network .... • The smallest eigenvalue (in absolute value) is greater that the precision defined for this test network and it is 0.0045. Eigen vector