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

For larger systems, due to the greatly increased number of components and branches, to do so manually would be very tedious and time consuming. However, part of the validation process for each version of the program, involves checking by inspection that the minimal path and cut set deduction is functioning correctly for at least one fairly large system.

Verification of the numerical algorithms is carried out during the program development by undertaking manual calculations, using the appropriate equations from Section 2.5.11 of this chapter, of busbar and system indices for a small system, and comparing the results with those obtained from using the computer program on the same system with the same component reliability data.

2.7 Typical applications

2.7.1 Example of the calculation and use of busbar indices

This section contains a specific example of the busbar indices evaluation techniques as they were used to answer a specific question relating the design of SESs for future nuclear power stations.

The higher voltage levels (down to 3.3 kV) of the SES shown in Fig 2.31 was the initial design proposal. It was put forward as part of an overall exercise to evolve a standard design of SES and grid connection interface arrangement, which would possibly be suitable for future nuclear power stations.

Depending on the exact siting of the power station, there can be a considerable variation in the reliability of the available grid connections.

The frequency of LOSP (loss of off-site power) contributes to the overall summated frequency of degraded core and hence forms part of the safety case.

The question raised was 'to what extent could the provision of additional on-site generation compensate for poor grid reliability?'

The procedure adopted was to assume a figure of 0.075 failures/year for the frequency of loss of all grid supplies for an average duration of 2 hours and to calculate the busbar indices for the II kV and 3.3 kV levels:

(a)For the basic system of Fig 2.31, which only has standby generators at the 3.3 kV level, designed to back up the SES.

(b)For the basic system, with additional standby generators on the 11 kV station boards.

Where: X n

X23

X123 rn

=Independent failure rate of component 'n' CMF rate for components 2 and 3

CMF rate for components 1, 2 and 3

=Repair time of component 'n'

(c)For the basic system, with additional standby generators on the 11 kV station and unit boards.

The following assumptions were made:

• The additional on-site generators provided at the 11 kV level would be standby generators and not run continuously..

•As normal practice in respect of the safety case, no claim is made for on-site generation from the main units.

Description of computer produced system diagrams

In all diagrams, the following busbar identification applies:

S6 and S13 — Generator main connections

S7 and 514 — Unit 11 kV switchboards

S8 and S15 — Unit 3.3 kV switchboards

S10 and S12 — Station 3.3 kV switchboards.

Note that the actual method of producing the systems and data for each of the cases studied was to draw the complete system only for case (c) and complete the reliability data entry. Case studies (a) and (b) were then undertaken as sensitivity studies, using the 'outage' facility of the GRASP2 computer program. The plant outaged for each particular case study is shown by dotted lines on the appropriate results diagrams.

Results

Only two of the busbar indices are of interest to permit a comparison to be made between the system with no additional on-site generation (case (a)) and the other two systems (cases (b) and (c)):

•The average failure rate (FR) is of interest, since every loss of supply to any of the four 11 kV busbars leads to a reactor trip.

Where: X n

X23

X123

r n

tc

=Independent failure rate of component 'n'

=CMF rate for components 2 and 3

CMF rate for components I, 2 and 3 Repair time of component 'n'

= Switching time of alternative (NO) path

•Average outage time (AOT) is of interest, since it gives an indication of the availability levels required of the SES to cater for the reactor post-trip (initiated by the electrical system) period.

The average failure rate for those events initiated by failures within the electrical system which cannot be recovered within 2 hours is also of interest. For the safety case, this indicates the improvement in the immediate reactor post-trip period that would be gained from providing the additional on-site generation.

The diagrammatic results for AOT and FR for case

(a) are shown in Figs 2.32 and 2.33 respectively. Those for cases (b) and (c) are shown in Figs 2.34 to 2.37.

Table 2.16 summarises both busbar indices and the (0-2 h) FR for each busbar for all three cases.

The (0-2 h) FR figures were obtained by manually sorting the list of failure events and combining only those events which had AOTs greater than 2 hours.

It can be seen from Table 2.16 that the effect of adding auxiliary standby generators at the 11 kV level would be to increase the average failure rates of the

11 kV and 3.3 kV boards, whilst only showing a marginal reduction in the corresponding average outage durations. A similar increase is shown in the (0-2 h) average failure rate.

Both these effects are predictable, since they are due mainly to the addition of the active failure rates of the 11 kV (NO) circuit-breaker associated with the additional standby generators, and these events are recoverable within the (0-2 h) period by switching/ isolation and the use of alternative sources of supply.

2.7.2 Example of the calculation and use of system indices

This section contains a specific example of the evaluation techniques for system indices as they were used to compare the performance of two alternative proposals for the design of a SES for the Coal-Fired Reference Design in terms of the availability of the main boiler/ turbine-generator unit.

It was also required to assess the cost of lost generation caused by failures within the SES over the

designed life of the station for use in the cost benefit exercise to assess whether the capital cost of providing the interconnection could be justified.

The basic design of SES proposed, is shown in Fig 2.38 with two variants:

•A system that is purely radial top-to-bottom, with

no switchboard interconnections at any voltage level.

•A system as shown in Fig 2.38, but having normally open interconnectors between corresponding switchboards of each train at each level within the unit system and also at the 11 kV level between each unit and station switchboard.

System conditions

Since the exercise was of a comparative nature, all cables (except those used to interconnect boards in the one system) were excluded from the studies to simplify the analysis.

It was assumed for the purpose of the study that the station was in the CMR condition. Thus, for example, all coal mills and fans were modelled as being in operation, whereas only one sootblower and two oil pumps were included, the remaining sootblower and oil pump being on standby.

One complete unit system (Unit 1 Trains A and B) and half of the station system (Station Train 1) were represented in the computer model.

Figures 2.39 and 2.40 show the computer-produced diagrams for the radial system and Figs 2.41 to 2.43 show those for the interconnected system.

Table 2.17 shows the correlation between the com- puter-generated busbar numbering system and the individual system board names.

A grid failure rate of 0.039 failures/year was used for the 400 kV and 132 kV systems and failure rate data accumulated for generators of 500 MW and above were used for the 900 MW unit.

It was recognised that plant maintenance policy would play an important role in this assessment and a logical maintenance scheme was assumed, which included a certain amount of in-line maintenance.

To calculate the system indices, a derating factor was applied to each of the main unit boards (i.e., those at 3.3 kV and above) of each system. For example, it was assumed that loss of supply to 11 kV Unit Board 1A1 would result in a reduction in output power from the main generator of 50%. In addition, combinations of various unit boards were considered; for example, loss of both 3.3 kV mill boards was assumed to result in 100 0/o loss of unit output, whereas loss of 3.3 kV mill

board IA and 11 kV fan board 1B would result in a loss of 50; output.

Loss of output due to maintenance of the main generator was not included in the system indices calculation, since this is usually a planned outage and is common to any auxiliary system. For the purpose of this analysis, loss of supply to unit boards at the 415 V level was not considered to cause loss (total or partial) of output, due to the difficulty of handling the large number of such boards and combinations of them with the GRASP computer program. However, since the analysis was comparative and the omission was made in both systems, the effects of the omission are negligible.

Results

The system indices calculated for the radial system ER and LOG are shown in Fig 2.44 and those for the interconnected system are shown in Fig 2.45.

The indices show that, although the frequency of encounter ER of the derated states is fractionally higher for the interconnected SES than for the radial system (0.28 encounters/year at 100% and 0.37 at 50% against 0.27 and 0.33, respectively), the loss of generation (LOG) is lower by approximately 25 GWh/year. With

replacement generation costs assessed at £25 per MWh, there would be a saving of £625 000 per unit per year or £37.5 million for a two-unit station over a 30 year life if the interconnected design of SES is used.

3 Power system performance analysis

3.1 Load flow analysis

3.1.1 Introduction

Load flow analysis is used to assist in planning, designing and operating power networks. The network or system is modelled in its steady state operating modes, then the voltage at each busbar or board and the power flow in each branch or circuit is calculated.

Particular attention is being paid here to the analysis of power station electrical systems. If a SES fails to provide sufficient power to motor drives or other equipment, then generating output may be lost completely or be significantly reduced. There are economic penalties associated with the loss of generation and there may be a hazard to plant safety. Thus, it is essential to have

well designed power station electrical systems, so their operating voltage and frequency limits are defined; if the auxiliary plant is specified to be supplied within these defined voltage and frequency limits, then its performance will be acceptable.

3.1.2 Program construction [4,51

General remarks

The equations defining load flow in a power network can be stated and digital computation then used to solve them. A great deal of research has gone into finding the best methods of doing this. Special numerical techniques are used, the most popular being based on nodal methods of network analysis, using Newton-Raphson based algorithms to solve the network equations. Gauss-Seidel based algorithms and Z-matrix methods have also been developed. These methods are discussed in detail in [6].

A set of complex simultaneous equations is set up relating currents and voltages within the network. Although the basic equations are linear, non-linearities arise for various reasons. Hence the need for an iterative numerical solution.

There are many ways of describing an electrical network or power system mathematically: all must satisfy Kirchoff's voltage and current laws. Nodal analysis has emerged as the method best suited to digital computation.

Assuming a balanced three-phase network it is sufficient to use the positive phase sequence impedances (and hence admittances) of circuit components such as transmission lines and cables, transformers, series and shunt capacitors. These are usually represented in perunit (p.u.) notation as lumped linear complex impedances at rated system frequency. Transmission circuits may be represented by their equivalent r-networks.

In nodal analysis an electrical system comprising transformers, lines, cables, inductors, series capacitors, shunt capacitors and loads is translated into a set of 'branches' expressed as impedances or admittances. Admittance values are normally used, because there are considerable advantages during computation in using admittance instead of impedance values for network branches. The busbars and switchboards are separately translated into a set of 'nodes' which serve as link points for the branches. All voltage sources (generators) are replaced by current injection at the appropriate node.

These techniques are employed to reduce the amount of computation needed to obtain the solution to the load flow problem.

Nodal analysis

Figure 2.46 illustrates how a voltage source may be replaced by an equivalent current source.

In Fig 2.46 (a) we have voltage source E with admittance Y connected to node I having voltage to ground of V. It follows that V = E — I/Y and I =

as shown in Fig 2.46 (b). If we define II = YE and 12 = YV, this is shown in Fig 2.46 (c) and the voltage source has been replaced by a current source.

In Fig 2.46 (d), we have a voltage source E and an admittance Y between nodes 1 and 2, then

E — i/Y. If now we define = —EY and 12 = + EY, this is shown in Fig 2.46 (e), and the voltage source has been replaced by two current sources.

To illustrate the formation of the basic equations used in nodal analysis, consider the simple network shown in Fig 2.47. Figure 2.47 (a) illustrates a simple power system which translates to the Fig 2.47 (b) network.

The network has a current injected into each node, each node is connected to at least one other node,

and at least one node is connected to ground (three nodes are connected to ground, in this example).

Using Kirchoff's first law at each node, we have the following equations:

expressing the admittance coefficients in matrix form, the voltages as a vector and the currents as a vector gives:

It will be seen that nodal admittance matrix Y can be written by inspection and that, for larger networks, the matrix will he highly sparse (i.e., contains a high proportion of zero elements). The properties of the matrix are:

•It is a square of order (n x n), where n is the number of nodes in the network.

• It is symmetrical (Yik = Yki, general element •th row, k'h column).

•It is complex, i.e., it may contain conductance and susceptance terms.

•Each diagonal element Ykk is the sum of the admittances connected to node k, including the branches to ground.

•Each off-diagonal element Y lk is the negative of the branch admittance between nodes i and k.

•In large networks, many off-diagonal elements will be zero, i.e., the matrix is sparse.

The matrix equation YV = I defines the injected currents in terms of network admittances and voltages. Mathematically speaking, the set of equations YV = I may or may not have a solution, depending on the characteristics of matrix Y. No solution is possible if matrix Y is singular and thus has no inverse. This happens if the system has no ground connections. If matrix Y is not singular, the ease of solution depends on whether the matrix is well conditioned; if it is, computational rounding errors will not accumulate during the numerical process. Fortunately, the admit-