Literature Survey
CHAPTER 2. LITERATURE SURVEY 13
(2.15) This has one lead term and one washout term. Comparing the frequency response of the original electrical transfer function
922
(s) with the compen- sated electrical transfer function 922(S)+P(S)912(S), the effect of the inverted notch characteristic of the P88 is to dominate the "switchback" character- istic and by doing so, alleviates its effect on the system. This approach is effective at different loading conditions. Thus the system, with the P88 in place, can be treated as a pseudo 8180 system loop where the governor loop is first closed and the AVR-excitation loop is treated as a 8180 system for the sole purpose of providing voltage disturbance rejection.The use of QFT as a viable tool for designing power system stabilisers was gaining momentum, and Boje and Jennings [6] presented a tutorial on how such a design should be undertaken. A third order model was used and relates the inputs to the outputs as shown in Equation 2.15. The tutorial was used to examine existing P88 design for a system with the AVR and speed governor already in place.
[6W(S)] _p [6Tm(S)]
6vt(s) - 6Efd(S) P
=
_1_[~ll ~12]
6s P21 P22
The design was done with decoupled S180 speed and voltage loops. The specification was twofold:
1. to guarantee robust stability for all likely operating conditions, and 2. to improve the performance of the system in a structured manner.
The performance can be specified as tracking performance and regulation performance. Details of the derivation of these specifications are found in the paper. Itis important to note, however, that the behaviour of the system when meeting these performance specifications is significantly influenced by shaping the loop transmission function. The design procedure is summarised as follows
1. draw the locus of the plant elements as the plant parameters vary.
This will result in plant templates,
2. choose a nominal fixed plant to use as a handle on the design process.
Such a handle is used to generate nominal boundaries, which meet the design specifications, and
3. design the controller to satisfy the nominal boundaries at the discrete frequency points.
The design specifications are used as an initial starting point. The QFT method offers insight for design improvement, and this means that the re- sulting trade-offs can be clearly seen during the design procedure.
CHAPTER 2. LITERATURE SURVEY
2.5 1999
14
A useful insight into how power system stabilisers are designed and tuned in industry is found in the paper byLakmeeharan and Coker [23]. The study was to damp electromechanical oscillations, which might be induced on the E8KOM system by interconnections within the 80uth African Power Pool.
The phase lead required was determined by measuring the phase response from the voltage reference to the airgap torque. No mention is made of the operating condition at which the measurement was made. Of interest is the way the P88 gain was determined. Two methods were given. One method used the root locus to determine the gain that will result in maximum damp- ing. The other method sets the initial value of the gain equal to the inverse of the compensator's time constant. Values above and below this are then tried to see which value would give the best performance.
Clearly a quantitative method is required which will allow convergence to a compensator that meets the design specifications.
Boje, Nwokah, and Jennings [7] describe such a quantitative method in de- tail. The design is approached from a control engineering rather than a power system viewpoint. Historically, P88 have been designed after the speed and terminal voltage loops have been closed. Boje et al suggest de- signing a forward path decoupler (to reduce the interaction between the speed and voltage) before the loops are closed, and then performing 8180 QFT designs on the speed and voltage loops. The reason for this becomes apparent when it is realised that the initial control loops may destabilise the system before the addition of a P88. Fadlalmoula [12] showed that one of the reasons a P88 is applied, is to reduce to the coupling between the speed and voltage loops. Boje, Nwokah expand on this fact by using the Perron root R as a measure of the interaction between the loops to design a P88 that guarantees robust stability.
The resulting QFT stability specification is of the form
I ~(jw) + gpS~b(jw! I
< R w c(]w)+
gpss(]w)d(]w) - () The 7th individual loop sensitivity is given bys - - -
, - 1+
11*(2.16)
(2.17) If ISlS2RI :::; 1, then stability for the individual design of the torque-speed and field-terminal voltage loops will result in a stable design. If
Vl
SlS2RI :::;0.5, then the two loops will not be strongly coupled even when the loop gains are low.
The speed and voltage loops are then designed using 8180 QFT methods
CHAPTER 2. LITERATURE SURVEY
25 20 15 10 5 0 -5 -10 -15 -20
-25-10 -5 0 5
Figure 2.6: The D contour showing z
=
10% and a=
0.5.15
such that the controllers do not destabilise the existing system.
Rao and Sen [34] showed the application of QFT to PSS design from the power system perspective. The method used differed slightly from the one proposed by Horowitz. Instead of achieving robust stability of the closed loop with discrete complex frequency points on the imaginary axis, the closed loop poles are now chosen to lie within a modified D contour (Figure 2.6).
The D contour is determined from the damping factor and the constraint that the real part of the dominant closed loop rotor eigenvalues is less than some value, a. Ifthe designed PSS places the closed loop poles to the left of the contour for the given range of operating conditions, then the system achieves robust stability, and the damping requirements are met.
The closed loop will be robustly stable for all plants G of the plant set 9 if 1. the templates of the compensated plants K(s)G(s) do not contain the
point (-180°,OdE) on the Nichols chart for allW E R, and 2. the nominal closed loop is stable.
The procedure for designing the robust controller is
1. choose a set of points on the D contour for which robust stability is desired,
2. compute the plant templates as G is varied over 9 for each of the chosen point, and
CHAPTER2. LITERATURE SURVEY 16