reading / British practice / Vol D - 1990 (ocr) ELECTRICAL SYSTEM & EQUIPMENT

manipulation) techniques. There are many internal number systems used in the program which are not displayed to the user.

There are, however, two important number systems, namely component and branch numbering, which are displayed and provide the user interface. They are both automatically applied to the system and can (at the user's option) be included in the graphic display on the VD U.

Component numbering

A component numbering system is used to identify every component of the SES uniquely. As well as providing a user interface, the component numbering system provides the interface with the component reliability database in which is stored the reliability data to be used in the evaluation.

Since numbering of all components by the user would be a very tedious task (there can be upwards of 300 components in a single system), it has been

arranged that the numbering is automatically carried out by the program. The component numbers can be displayed at any stage of the drawing process, the numbering sequence being continually updated as drawing proceeds.

The individual component number consists of a prefix which, in general, is the mnemonic code used to draw the component (see Fig 2.4), followed by a number representing the order in which components of that particular type were drawn. Figure 2.5 is an example of a small system as it would appear on the VDU, complete with its component and branch numbering.

Branch numbering

In addition to providing a user interface (branch numbers can be displayed in the same way as component numbers), the branch numbering system plays a part in improving the efficiency of the program. Certain types of component are defined within the program as being 'branch terminators', as follows:

•Source — a start component.

•Generator — a start component.

•Limited energy source (LES) — a start component.

•Busbar or node — a start or finish component.

•Three-winding transformer — a start or finish component.

•Induction motor — a finish component.

According to the network topology, components electrically positioned between two terminating components are automatically assigned branch numbers. The branch numbers are shown in parentheses in Fig 2.5. Branches are numbered upwards from (1). The lower order numbers in the sequence are assigned to the unidirectional branches (in the order they were drawn), followed by the bidirectional branches (in the order they were drawn). A definition of unidirectional and bidirectional branches is given in the following section.

2.5.3Branch definition

A branch is a group of components electrically connected in series between any pair of terminating components, as listed in the previous section.

Branches which are terminated at one end with either a source, a generator, or an LES symbol are referred to as source branches.

Branches which are terminated at one end with an induction motor symbol are referred to as load branches.

A unidirectional branch is one through which, as an acceptable operating condition, the flow of power is normally in one direction only. By definition, a source branch is unidirectional FROM the source and a load branch is unidirectional TO the load.

A bidirectional branch is one through which the flow of power can be in either direction as an acceptable system operating condition.

With a knowledge of the system and its normal and abnormal operating configurations, the engineer defines

each branch of the system as uni or bidirectional as part of the system drawing routine.

On the graphic display unidirectional branches are distinguished by a small arrow just before the branch termination (finish) component. Bidirectional branches have no special symbolic notation. In Fig 2.5, branches

(1) and (2), are unidirectional.

2,5.4 Criteria of failure

In performing a reliability analysis of a SES in terms of its load point busbar indices, the criterion of failure is regarded as the complete loss of supply to each load point being evaluated. A for a particular load point busbar, is any event that leads to loss of continuity between the busbar and any source of supply. The failure events are therefore identified from the Minimal Cut Sets (MCS) associated with the Minimal Paths between the load point and all sources of supply (sources, generators or LESs):

•A Path is a set of components that connects any input node to the load point being considered.

•A Minimal Path is a path in which no node or branch is included more than once.

•A Cut Set is a set of components that, when failed, causes loss of supply to the load point under consideration.

•A Minimal Cut Set is a cut set that causes failure of supply to the load point but, when any one component of the set has not failed, does not cause failure of supply to the load point.

2.5.5 Analysis control procedures

In performing a quantitative reliability analysis of a SES the engineer, in addition to ensuring that the SES has been correctly modelled from a topological viewpoint, has to ensure that the subsequent reliability calculations reflect any operational constraints and will be performed with the required precision.

This optional control of the analysis is achieved through engineer/program interaction in the form of a series of questions put to the engineer by the program at the point where calculation of load point (nodal) or system indices is about to commence.

A basic set of control questions is displayed in respect of both load point and system indices calculation. These, together with the default (most commonly used) answers, are illustrated in Fig 2.6.

For calculation of the system indices, it is necessary for the engineer, from his knowledge of the system, to provide supplementary data prior to commencement of the calculation stage. These data relate to the continuous maximum rating of the turbine-generator unit or station (according to the basis on which it is desired to calculate the system indices) and the impact that the loss of supply to each load point busbar in

the SES would have on the output of the associated generator unit or station.

2.5.6 Deduction of minimal paths

The initial stage of the topological part of the analysis consists of the deduction of the minimal paths associated with each load point to be included in the evaluation.

Digital techniques are used to deduce all the minimal paths between each load point being analysed and all sources of supply to the SES. All paths are deduced and, when displayed on the VDU screen or listed in a printed output, the normally closed (NC) and normally open (NO) paths are listed separately.

Each minimal path is listed first in terms of node and secondly in terms of branch numbers, commencing at the load point being considered and working back towards the source or input node.

It should be noted that the designation (with due regard to any system operational constraints) of certain branches as unidirectional leads to greater efficiency of the path deduction process. Paths containing branches where the direction of power flow would be opposite to that specified by the engineer during the system drawing stages are ignored or excluded. This, in turn, leads to reduced data storage requirements within the program. Smaller arrays are set up and manipulated, which result in enhanced execution time.

Alternatively, the designation of some branches as unidirectional can be regarded as a means of allowing larger SESs to be evaluated within the existing set program array dimensions.

As an illustration of the path deduction process, Fig 2.7 shows the list of minimal paths for the small system of Fig 2.5. It should be noted that all loop paths, and also paths involving the flow of power in the reverse direction through a unidirectional branch, have been eliminated.

By answering Y (yes) to the sixth control parameter question (Fig 2.6), it is possible to specify sets of incompatible components and thereby preclude the deduction of unrealistic or impractical paths.

2.5.7 Deduction of minimal cut sets

The next stage of the topological part of the analysis is the deduction of the minimal cut sets for each load point under consideration.

A full treatment of the minimal cut set theory as applied in the reliability assessment of general electrical networks is provided in [2].

A minimal cut set of order 'n' is a set consisting of n components. As the order increases, its significance with regard to its contribution to the load point or system reliability indices decreases. Using cut set analysis techniques, it is possible to deduce minimal cut sets of any order but the algorithm developed for, and implemented in, the GRASP computer programs

OPTIONS:-

1-REDISPLAY

2-PREPOTTE0 ANSWERS

3-HELP

9-EXECUTE

5-RETURN

only considers cut sets up to and including third order.

For a particular study, the order of cut sets included, and hence the precision to which the reliability indices are calculated, is controlled by entering a 1, 2, or 3 against the control parameter 'Maximum Number of Overlapping Outages' in Fig 2.6.

The algorithm for the deduction of minimal cut sets from the (NC) minimal paths for each load point works as follows:

Step 4 Deduce the second order cut sets by considering all combinations of two branches. If any of these combinations is found to break all minimal paths, the combination is a second order cut set.

Step 5 Expand each branch of each combination that is found to be a second order cut set into its constituent components to determine the second order cut sets in terms of pairs of components.

Step 6 Eliminate any duplicated second order cut sets.

Step 7 Deduce the third order cut sets in the same way, by repeating Steps 4 to 6 and considering all combinations of three branches.

Figure 2.8 lists the cut sets up to second order deduced for the system of Fig 2.5. There is only one first order

cut set (the load point busbar itself) and 60 second order cut sets.

Figure 2.9 lists the cut sets up to third order for the same system. It can now be seen that, in addition to the 61 first and second order cut sets, there are 60 third order cut sets.

Whilst the contribution of an individual cut set of order greater than one to the overall reliability indices may be insignificant, the total effect of all higher order cut sets cannot be ignored.

It can be shown that for power station electrical systems in general, a very large number of higher order cut sets are deduced and second order cut sets contribute significantly to the overall indices.

The simulation of realistic failure events during the calculation stage requires that failure events where recovery is from standby or alternative sources, via (NO) paths, are separately identified.

2.5.8 Types of failure/restoration event

The following realistic failure/restoration events are included in the evaluation as appropriate to the system topology and the operational effects to be considered:

(a)Overlapping forced outages due to component (independent and common mode) failures involving repair or replacement.

(b)Forced outages due to component active failure (independent and common modes) and their switching effects on healthy components. The primary protection zones can either be automatically de-

tected by an algorithm within the program or be specified by the engineer, using his knowledge of the actual system protection arrangements.

(c)Forced outages due to component (independent and common mode) failures overlapping a maintenance outage.

(d)Forced outages due to component active failures (independent and common mode) overlapping the malfunction of primary protection equipment (stuck breakers). The back-up protection zones are detected automatically by the program.

The GRASP program has been developed to simulate five basic types of failure/restoration event. They are categorised according to the component failure mode and the procedure adopted for the restoration of supply to the load point being evaluated:

TYPE 1 A cut set where all components of the set are outaged or failed in passive mode, e.g., for maintenance or repair. Supply can only be restored to the load point being evaluated by returning to service at least one of the components of the cut set.

TYPE 2 A cut set with the same component failure mode as for TYPE 1, but with at least one normally open path available which can be used to restore supply to the load point being evaluated.

TYPE 3 A cut set where supply is lost to the load point being evaluated due to one component actively failing whilst the remaining components of the set are out of service. Supply is restored by isolating the actively failed component and closing the circuit-breakers that were opened due to the active fault.

TYPE 4 A cut set similar to TYPE 3, but including one stuck (NC) circuit-breaker in the protection zone of the actively failed component (i.e., failing to operate on demand).

TYPE 5 A cut set with the same component failure modes as for TYPE 1, but where the supply is restored to the load point being evaluated from an LES, via a (NO) path.

Figures 2.8 and 2.9 provide separate lists of cut sets on which failure events of TYPE 2 are based. It can be seen that, of the total of 61 first and second order minimal cut sets, 49 are of TYPE 1 and 12 are of TYPE 2. Of the total of 121 first, second and third

order minimal cut sets, 73 are of TYPE 1 and 48 are of TYPE 2.

One or more of the following restoration procedures are included in the calculation of the AOT index for the load point being evaluated. The selection of the appropriate restoration mode(s), from those available, is on the basis of shortest time for restoration of supply to the load point from a normal (unlimited energy) source. Only where an alternative path leading to an unlimited energy source is not available is restoration from an LES considered.

These restoration procedures are:

•Repair.

•Replacement.

•Switching or isolation.

•Reclosing of circuit-breakers.

•Closing of (NO) circuit-breakers to provide an alternative source of supply, which may include standby plant.

The alternative (NO) paths may subsequently be considered to fail, or not to fail, according to the

requirements of the engineer or the purpose of the evaluation.

2.5.9 Switching effects of component active

failure

The evaluation of TYPE 3 and TYPE 4 failure events requires the determination of the switching effects of component active failures (see Section 2.4.1 of this chapter).

To calculate the effect of the active failure of each component that can actively fail on the indices of the load point of interest, it is first necessary to determine he extent of the network outage that would be a consequence of each component active failure.

There is an algorithm in the GRASP2 computer program which, by the use of digital search techniques, identifies and provides a listing of the protective circuitbreakers that would trip for active failure of each system component that has been specified as likely to suffer an active failure. The algorithm is based on the assumption that the nearest (NC) circuit-breakers in all branches adjacent to the actively failed component would trip to clear the fault.

Since this facility would obviously not be appropriate for all the different designs of SES and their associated protection arrangements, a facility is provided whereby the protective circuit-breakers to trip on active failure of each component can be specified manually. For large systems, this can be a very tedious operation.

The choice of manual or automatic specification of 'breakers which trip' is controlled by the answer to question number 7 of Fig 2.6.

On selection of the manual facility, the engineer is presented with a display on the VDU, as shown in Fig 2.10. He then specifies the appropriate component numbers of the 'breakers which trip' against each actively failed component listed.

The automatic deduction of 'breakers that trip' results in the listing shown in Fig 2.11 for the system of Fig 2.5. This listing is optionally available for viewing on the VDU or for printing with the full study results output (see Section 2.5.13 of this chapter).

2.5.10 Markov state - space models

A state-space model is a diagrammatic representation of: