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1. INTRODUCTION
This section describes three main areas of transmission and distribution network analysis, namely load flow, system stability and short circuit analysis. Such system studies necessitate a thorough understanding of network parameters and generating plant characteristics for the correct input of sys tem data and interpretation of results. A background to generator characteristics is therefore included in Section 3.
It’s now recognized that harmonic analysis is also a major system study tool. This is discussed separately in Section 24. Reliability studies are considered in Section 23.
The analysis work, for all but the simplest schemes, is carried out using tried and proven computer programs. The application of these computer methods and the specific principles involved are described by the examination of some small distribution schemes in sufficient detail to be applicable to a wide range of commercially available computer software. The more general theoretical principles involved in load flow and fault analysis data collection are explained in Section 28.
2. LOAD FLOW
2.1 Purpose
A load flow analysis allows identification of real and reactive power flows, voltage profiles, power factor and any overloads in the network. Once the network parameters have been entered into the computer database the analysis allows the engineer to investigate the performance of the network under a variety of outage conditions. The effect of system losses and power factor correction, the need for any system reinforcement and confirmation of economic transmission can then follow.
2.2 Sample Study
2.2.1 Network Single-Line Diagram
Fig. 1 shows a simple five busbar 6 kV generation and 33 kV distribution network for study. Table 1.1 details the busbar and branch system input data associated with the network. Input parameters for cables and overhead lines are given here in a per unit (pu) format on a 100 MVA base. Different pro grams may require input data in different formats, for example per cent impedance, ohmic notation, etc. Please refer to Section 28, for the derivation of system impedance data in different formats from manufacturers' literature.
The network here is kept small in order to allow the first-time user to become rapidly familiar with the procedures for load flows. Larger networks involve a repetition of these procedures.
Above: Fig. 1 Load flow sample study single-line diagram.
TABLE 1 Load Flow Sample Study Busbar and Branch Input Data
2.2.2 Busbar Input Database
The busbars are first set up in the program by name and number and in some cases by zone. Bus parameters are then entered according to type. A 'slack bus' is a busbar where the generation values, P (real power in MW) and Q (reactive power in MVAr), are unknown; there will always be one such busbar in any system. Busbar AO in the example is entered as a slack bus with a base voltage of 6.0 kV, a generator terminal voltage of 6.3 kV (1.05 pu) and a phase angle of 0.0 degr. (a default value). All load values on busbar AO are taken as zero (again a default value) due to unknown load distribution and system losses.
A'P, Q generator bus' is one where P and Q are specified to have definite values. If, for example, P is made equal to zero we have defined the constant Q mode of operation for a synchronous generator. Parameters for busbar BO in the example may be specified with base voltage 6.0 kV, desired voltage 6.3 kV, and default values for phase angle (0.0 degr ), load power (0.0 MW), load reactive power (0.0 MVAr), shunt reactance (0.0 MVAr) and shunt capacitance (0.0 pu). Alternatively, most programs accept generator busbar data by specifying real generator power and voltage. The program may ask for reactive power limits to be specified instead of voltage since in a largely reactive power network you cannot 'fix' both voltage and reactive power _ something has to 'give way' under heavy load conditions. Therefore, busbar BO may be specified with generator power 9.0 MW, maximum and minimum reactive power as 4.3 MVAr and transient or subtransient reactance in per unit values.
These reactance values are not used in the actual load flow but are entered in anticipation of the need for subsequent fault studies. For the calculation of oil circuit breaker breaking currents or for electromechanical protection relay operating currents, it’s more usual to take the generator transient reactance values. This is because the subtransient reactance effects will generally disappear within the first few cycles and before the circuit breaker or protection has operated. Theoretically, when calculating maximum circuit breaker making currents subtransient generator reactance values should be used. Likewise for modern, fast (say 2 cycle) circuit breakers, generator breakers and with solid state fast-relay protection where accuracy may be important, it’s worth checking the effect of entering subtransient reactances into the database. In reality, the difference between transient and subtransient reactance values will be small compared to other system parameters (transformers, cables, etc.) for all but faults close up to the generator terminals.
A 'load bus' has floating values for its voltage and phase angle. Busbar A in the example has a base voltage of 33 kV entered and an unknown actual value which will depend upon the load flow conditions.
2.2.3 Branch Input Database
Branch data is next added for the network plant (transformers, cables, over head lines, etc.) between the already specified busbars. Therefore, from busbar A to busbar B the 30 km, 33 kV overhead line data is entered with resistance 0.8 pu, reactance 1.73 pu and susceptance 0.0 pu (unknown in this example and 0.0 entered as a default value).
Similarly for a transformer branch such as from busbar AO to A, data is entered as resistance 0.0 pu, reactance 0.5 pu (10% on 20 MVA base rating550% on 100 MVA base or 0.5 pu), susceptance 0.0 pu (unknown but very small compared to inductive reactance), load limit 20 MVA, from bus AO voltage 6 kV to bus A voltage 33.66 kV (1.02 pu taking into account transformer 65% taps). Tap ranges and short-term overloads can be entered in more detail depending upon the exact program being used.
2.2.4 Saving Data
When working at the computer it’s always best to regularly save your files both during database compilation and at the end of the procedure when you are satisfied that all the data have been entered correctly. Save data onto the hard disk and make backups for safe keeping to suitable alternative media (e.g. CD, USB flash drive). Fig. 2 gives a typical computer printout for the bus and branch data files associated with this example.
Above: Fig. 2 Load flow sample study busbar and branch computer input
data files.
Above: Fig. 3 Load flow sample study base case busbar and branch computer
report.
Above: Fig. 4 Load flow sample study. Base case load flow results superimposed
upon single-line diagram.
2.2.5 Solutions
Different programs use a variety of different mathematical methods to solve the load flow equations associated with the network. Some programs ask the user to specify what method they wish to use from a menu of choices (Newton_Raphson, Gauss_Seidel, Fast decoupled with adjustments, etc.).
A full understanding of these numerical methods is beyond the scope of this guide. It’s worth noting, however, that these methods start with an initial approximation and then follow a series of iterations or steps in order to eliminate the unknowns and 'home in' on the solutions. The procedure may con verge satisfactorily in which case the computer continues to iterate until the difference between successive iterations is sufficiently small. Alternatively, the procedure may not converge or may only converge extremely slowly. In these cases it’s necessary to re-examine the input data or alter the iteration in some way or, if desired, stop the iteration altogether.
The accuracy of the solution and the ability to control round-off errors will depend, in part, upon the way in which the numbers are handled in the computer. In the past it was necessary to ensure that the computer used was capable of handling accurate floating-point arithmetic, where the numbers are represented with a fixed number of significant figures. Today these can be accepted as standard. It’s a most important principle in numerical work that all sources of error (round off, mistakes, nature of formulae used, approximate physical input data) must be constantly borne in mind if the 'junk in equals junk out' syndrome is to be avoided. A concern that remains valid in selecting computing equipment is the need to ensure that the avail able memory is adequate for the size of network model under consideration.
Some customers ask their engineering consultants or contractors to prove their software by a Quality Assurance Audit which assesses the performance of one software package with another for a single trial network.
Fig. 3 gives typical busbar and branch reports resulting from a load flow computation. It’s normal to present such results by superimposing them in the correct positions on the single-line diagram as shown in Fig. 4.
Such a pictorial representation may be achieved directly with the more sophisticated system analysis programs. Alternatively, the network single line diagram may be prepared using a computer graphics program (Autocad, Autosketch, GDS, etc.) and the load flow results transferred using data exchange files into data blocks on the diagram.
2.2.6 Further Studies
The network already analyzed may be modified as required, changing loads, generation, adding lines or branches (reinforcement) or removing lines (simulating outages).
Consider, For example, removing or switching off the overhead line branches running either from busbars A to C or from B to C. Non-convergence of the load flow numerical analysis occurs because of a collapse of voltage at busbar C.
If, however, some reactive compensation is added at busbar C _ for example a 33 kV, 6 MVAr (0.06 pu) capacitor bank _ not only is the normal load flow improved, but the outage of line BC can be sustained. An example of a computer generated single-line diagram describing this situation is given in Fig. 5. This is an example of the beauty of computer aided system analysis.
Once the network is set up in the database the engineer can investigate the performance of the network under a variety of conditions. Refer to Section on Fundamentals regarding Reactive Compensation principles.
Above: Fig. 5 Load flow sample study. Computer generated results superimposed
upon single-line diagram-reactive compensation added.