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

In this approach, I I and fk have to be recalculated at each iteration, but the nodal matrix is easier to formulate and remains symmetrical, even in the case of out-of-phase taps, because it contains no turns-ratio terms.

Representation of transformers with on-load tapch angers

On-load tapchangers are provided to regulate voltage or, sometimes, reactive power flow.

When used for voltage regulation, it is usual for the voltage at the lower voltage side of a transformer to be monitored and compared with a reference or target setting. An error signal is then used to activate a change in the transformer tap position to restore the monitored voltage to the reference setting. Because tappings are discrete steps, it is not possible to match the reference setting exactly, so a tolerance is applied to the reference setting. For example, if tappings are in 2% steps, a tolerance of ± 1% is used and no automatic tap change takes place if the re-

ference voltage is within the range 99% to 101% of its setting.

To represent on-load tapchanging transformers within the load flow solution program, it is necessary to provide logic to compare target voltage with calculated voltage, then to alter tap position to correct the voltage. It is also necessary to check that the transformer tapping range is not violated during this process. This can be done between iterations until the solution converges.

Practical experience has shown it is best to leave tap adjustments until towards the end of the solution process. During early iterations, voltage levels can oscillate and vary considerably. Tap changing at this stage does not speed convergence, especially with slowly converging algorithms, such as Gauss-Seidel. Because the Gauss-Seidel algorithm converges slowly, intuitively it suggests that tap changes should also be made small.

An algorithm of the form an w = a id + a (Vr _

Yr) a e o

can be used, where is a small constant, typically 0.05 and aoid is the transformer turns ratio at iteration p.

In the Newton-Raphson method, convergence is rapid at later stages and a higher value of a can be used, or a different algorithm. When calculated from the above expression, a new requires adjusting to match the nearest discrete tap, and needs checking to ensure that the tapping range is not violated.

Representation of reactive power limitation on synchronous plant

Generators have defined MVAr output limits for a given MW output. The upper limit is imposed by heat dissipation or exciter capability and the lower limit by stability considerations. A synchronous compensator has maximum and minimum VAr output ratings.

When a generator or group of generators is set to control voltage at a busbar during a load flow solution, the busbar is designated a PV busbar. A check is made during the solution that the VAr output limits of the plant have not been violated. If the limits are exceeded, the busbar is redesignated as a PQ busbar and the generating plant VAr output is fixed at its

limit of operation. The solution then continues until convergence at a feasible result is reached.

Experience shows that checking of VAr output being outside the designated range is best left until rough convergence is reached.

General analytical considerations

There are many methods of solving a set of simultaneous linear differential equations by numerical methods (Reference [7] is recommended to the reader who wishes to pursue this topic). The efficiency of these methods varies and a method which may be acceptable in solving one type of problem may be inefficient in solving a different type.

The physical structure of the problem is very important. The set of equations describing an electrical power system network produces an admittance matrix which is highly sparse. Typically, the matrix associated with a network having 100 nodes will have about 3% of its coefficients non-zero. To process the other 97% is very inefficient and a method which only stores,

identifies and processes the non- zero terms has clear advantages.

Use is also made of methods original set of data into a set

which may be easier to solve. Triangular decomposition of matrices — the coefficient matrix is factorised into a set of upper and lower triangular matrices — can speed the solution process and is used in many programs (Reference [8j provides an introduction to matrix manipulation), Ordered elimination — to keep calculation processes to near minimum — is also used extensively, and advantage is taken of the symmetry of the coefficient matrix. Reference [9] provides further reading on power system modelling.

3.1.3 Use of programs

Typical electrical auxiliary supply systems

Figure 2.52 shows an analysis diagram of the SES in an oil-fired power station and Fig 2.53 shows an

analysis diagram of the SES in an advanced gas-cooled reactor nuclear power station,

Unless there are differences between generating units and their respective electrical auxiliary systems within a power station, it is sufficient to represent one Unit with its supply systems.

The diagram is drawn by the analyst onto a computer terminal screen. To avoid unnecessary detail and to limit the size of the diagram, the analyst decides what plant he wants to represent prior to drawing the network. He will include any plant which has a significant effect on system performance; for example, he will represent all 11 kV motor drives as separate motors, but only represent a limited number of 415 V motor drives as separate motors. The remainder will be lumped together for analysis purposes.

A convenient starting point in drawing the analysis diagram is the high voltage busbar to which the power station is connected. In Fig 2.52 this busbar is named '400 kV'. Later, it will be nominated as the 'slack' busbar. A 'reference' or 'source' generator is then drawn

connected to this busbar. This nominal generator, for present purposes, represents a tie to the grid system to be used as a power source or power sink.

The power station system voltages are 11 kV, 3.3 kV and 415 V in both examples (Figs 2.52 and 2.53). The choice of voltages is based on engineering needs, economic grounds and consideration of the hardware available at the time of ordering plant.

Design operating limits

The normal voltage operating range of the 400 kV supergrid is 0.95 per-unit (380 kV) to 1.05 per-unit (420 kV), with a short term (15 minutes) upper limit of 1.10 per-unit (440 kV). The normal voltage operating range of the 132 kV grid is 0.90 per-unit (119 kV) to 1.10 per-unit (145 kV). Frequency, nominally 50 Hz, is normally regulated between 49.9 Hz and 50.1 Hz. System faults may give rise to variation between 49.5 Hz and 51 Hz, with exceptional variation between 47 Hz and 52 Hz for a period not exceeding 15 minutes. System faults can also lead to

step changes in voltage of 6% at 132 kV grid supply points.

A station electrical system is normally designed to have an upper voltage limit of 1.06 per-unit and a lower voltage limit of 0.94 per-unit during steady state operation.

When a motor starts, the transient voltage dip at the motor terminals should not fall to less than 0.80 per-unit and the remainder of the electrical system must remain stable and recover from the transient dip in voltage.

The station electrical systems are designed to withstand the effects of electrical faults, internal and external. The worst credible disturbance normally considered is that produced by a transient fault having a clearance ti me of 0.2 second.

Except for some special applications, such as PWR power station essential systems, the motors are specified to run at any load within rating over the voltage range 0.94 per-unit to 1.06 per-unit, to operate for five minutes at 0.75 per-unit voltage and be capable of running up to speed from a transient starting voltage dip as low as 0.80 per-unit.

All other AC electrical and electronic equipment must be capable of operating continuously under such actual steady state and transient service conditions without malfunctioning or suffering damage.

Design operation mode — transformer outages

The SES is designed to permit any one transformer except the generator transformer to be out of service, yet maintaining full station output within voltage design operating limits.

Load flow analysis of the power station electrical system

Having set the voltage limits in which the SES is to operate, the system is examined in its normal steady state operating modes, and during the transition between modes. These modes are:

•Unit shut down.

•Unit generating its rated output at any power factor between maximum rated lag and maximum rated lead.

• Unit post-trip.

The system is also examined with designed plant outages.

The effects of starting large motors are important and strongly influence the design of the system. The large starting current drawn by an induction motor when it is switched on, causes a sharp reduction in voltage at its terminals and at its supplying board. The voltage continues to fall for a short period as other motors, fed from the same supply, draw more current to maintain their outputs at the reduced voltage. The switched-in motor must run up successfully; this means the electrical torque produced must always exceed the mechanical torque of the drive. It is particularly important in nuclear stations that some specific motors must (also) run up within a specified time after a reactor trip. The other motors subject to the lowered voltage must be able to remain stable and maintain their outputs until the switched-in motors run up and the voltage rises.

The magnitude of the voltage drop is a function of the current taken at the supplying board, and the impedance between that board and its effective supply source. Table 2.18 shows typical impedances and other data of transformers feeding and within a SES. Column 5 of Table 2.18 shows that the transformer closest to any motor drive being considered, has a much higher impedance than that of the (larger) transformers nearer to the effective supply source. It follows that the impedance of this transformer strongly influences the voltage drop at the motor terminals, and must be chosen with this in mind.

Optimisation of transformer off-load tapchanger tap Positions

Once a transformer tap is set to a specific position, the

voltage range at the transformer LV terminals is determined by:

•The voltage at the transformer [-IV terminals.

•The transformer impedance.

• The load on the transformer.

It follows that, where 11 kV/3.3 kV transformers have off-load tapchangers and 3.3 kV/415 V transformers also have off-load tapchangers, the voltages at the 415 V boards of the SES are operationally determined by:

•The voltages at the 11 kV boards.

•The loads on the transformers between the 11 kV,

3.3kV and 415 V boards.

When a power station is shut down, the load on the SES is usually at its minimum. This provides a convenient starting point in deciding which tap positions to adopt on transformers with off-load tapchanging arrangements. The system is modelled with its electrical load at minimum value, and 11 kV boards' voltages set to nominal value (1.00 per-unit). The offload taps of the transformers are then set, within the model, such that the 415 V (and 3.3 kV) board voltages are close to, but do not exceed, the maximum permitted voltage (usually 1.06 per-unit).

Using these off-load tap settings, the system is then modelled at its predicted maximum load condition.

Any permitted outage, or combination of outages, is also modelled and the supply system voltage must remain within the permitted voltage range under steady state and transient (motor start or fault) conditions. The steady state and transient voltage conditions must both be attainable with the voltages at the 11 kV boards set to nominal value (1.00 per-unit).

If it is shown that the system is inadequate to supply plant within design criteria, then it is necessary to identify the cause and correct this by changing system and plant parameters.

Analysis of a SFS will identify the relative strengths and weaknesses of the system.

Figures 2.54 and 2.55 show voltage profiles of an oil - fired power station electrical system at minimum and maximum loads, without plant outages.

Loss of grid supplies

It is essential to maintain cooling supplies to nuclear

power station reactors. Supplies to motors providing reactor cooling are normally derived from the grid system. In the event of grid failure, gas turbines or diesel generators provide power for these motors. Analysis is performed to demonstrate that a SES functions correctly in this isolated mode. A small, isolated system like this does not have the built in inertia of the grid system. This is not important in load flow studies but is a very important consideration in transient stability analysis.

Figure 2.56 shows a network voltage profile with a 3.3 kV diesel generator supplying an isolated part of an electrical supply system.

Reactor and turbine start sequence — voltage profile studies

Figures 2.57 to 2.64 show a series of load flow/voltage profile studies for an AGR nuclear power station simulating a reactor and turbine start sequence.

On the network diagram, only one reactor unit is represented. B1 is a 400 kV busbar and 83 a 132 kV

busbar. The main generator U is connected to B4 (23.5 kV). B5A, B5B, B5C and B5D are 11 kV boards. B6* are 3.3 kV boards and B7* are 415 V boards (where * represents alphanumeric symbol(s)). The 132 kV/11 kV/11 kV station transformer is a three-winding transformer. This is represented by three separate transformers connected to a common point, shown as 3W on the diagram.

Figure 2.57 shows the turbine and reactor off-load. Figure 2.58 shows load flows and voltage profiles at the next stage in the start sequence. The generator is off-load and the gas circulators at 56% of their full load power (corresponding to 75 07o gas flow in the reactor). All the remaining loads, except the standby feed pumps, are assumed to be running at the generator continuous maximum rating (CMR) condition.

The next study, shown in Fig 2.59, illustrates the 11 kV starting/standby feed pump on the station board (B5A) being started. In these load flow studies, the standby feed pump is represented by a shunt. The shunt impedance is set equal to the effective impedance of the motor at its start. The voltage profile shown is the lowest during the motor run-up; the increased current drawn by other motors is taken into account during the load flow algorithm solution. This study also identifies any induction motor instability — the load flow algorithm solution will not converge if the mechanical torque required by a motor drive exceeds the electrical torque available.

In practice, the results given by this study would be considered satisfactory. Voltage at the board where the motor is being started is 0.867 per-unit, the lowest

voltage at any other board is 0.876 per-unit and the highest at any board is 1.034 per-unit.

The next study in the sequence, Fig 2.60, shows the starting/standby feed pump up to speed and running at full load. The minimum voltage at any board is 0.975 per-unit. Physically, the next event in bringing the generator and reactor to power is to synchronise and load the generator, and increase the gas circulator loads to full power. The next study in the start sequence, shown in Fig 2.61, shows the main generator in service delivering 264 MW (40% of its 660 MW full load rating). The voltage profile is satisfactory. Figure 2.62 shows the 11 kV starting/standby feed pump on the unit board (B5C) being started and Fig 2.63 shows this pump up to speed and running at full load.

Figure 2.64 is the last in this sequence of studies. It shows the voltage profile and load flows with the unit at CMR delivering maximum lagging VAr, gas circulators at full power rating and the turbine boiler feed pump running instead of the station and unit starting/standby electric boiler feed pumps.

Similar sequences of studies are performed with plant outages, e.g., a station transformer outage, to show that the system functions correctly under outage conditions.

Network drawing and data entry

Modern analysis programs are interactive in design and allow the user to represent power system network diagrams on a screen. Mnemonic codes are available to draw and modify network diagrams. Examples are:

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