SVC Control Components and Models
4.3 THE VOLTAGE REGULATOR .1 The Basic Regulator
4.3.2 The Phase-Locked Oscillator (PLO) Voltage Regulator
Phase-locked oscillators (PLOs) are extensively employed in the control of HVDC converters [39], [40]. A similar closed-loop control of SVCs using PLOs was proposed by Ainsworth [28] in 1988 and is now used in many applications.
The PLO-based control does not involve any control filter or other lead-lag circuits and provides immunity from instabilities at harmonic frequencies in addition to generating a fast response. The main features of this control are as follows:
1. The feedback signal must possess a mean dc component proportional to the quantity to be controlled.
2. The PLL incorporates the integral control. The TCR firing angle and, consequently, the TCR current are so controlled that in the steady state, the error between the controlled quantity and its reference value becomes zero.
3. The control reacts only to the mean value of the measured signal averaged over half-cycles. It does not respond to harmonics or transient impulses, thereby imparting a strong immunity from the instability at harmonic and other supersynchronous frequencies. However, special measures need to be taken to preclude the 2nd and 3rd harmonic instabilities discussed in Chapter 5.
4. The PLO does not also respond to spurious harmonic components hav- ing frequencies that are integral multiples of (system frequencyf0 . pulse number p). Thus a single-phase (2-pulse) PLO will ignore the frequen- cies 2f0, 4f0, 6f0, and so on, in the control signal. Similarly, a 3-phase, 6-pulse or 3-phase, 12-pulse PLO will ignore harmonic components of frequencies 6p f0 or 12p f0, respectively, wherepc1, 2, 3, . . . This spe- cial characteristic of the PLO obviates the need for installing any delay- introducing filters into the input-measurement system.
5. The process of integration extends in time to the very firing instant in each half-cycle. The control is thus of a “zero-delay” type, with the only unavoidable delay caused by the half-cycle integrations. A rapid response, combined with a good stability characteristic, is the key feature of the PLO.
4.3.2.1 The Basic Single-Phase Oscillator The principle of operation
THE VOLTAGE REGULATOR 119
Σ +
−
Σ
∫
Reset PT
V
+V1
+V2 +
+
−
PG ÷2
G 1
Vc Vref
V2
3 2
4 5 6
Voltage-Controlled Oscillator (VCO)
7
Valve 1 Fire
Valve 2 Fire
Figure 4.18 Phase-locked oscillator control for a single-phase TCR with (voltage)2 feedback.
of a PLO in a 3-phase system can be explained based on its control perfor- mance in a single-phase (2-pulse) TCR. The control system for a single-phase TCR involving (voltage)2 feedback is illustrated in Fig. 4.18. The output of this squarer transducer contains a dc component proportional to square of the voltage (in addition to a 2nd harmonic component that is ignored by the PLO).
This signal is compared with a reference signalVref, and the error signalVc is added to a fixed-bias voltageV1 in the summer 3 of the figure. The combined signal is integrated, and the output is compared with a constant-voltage V2 in a comparator. As soon as the integrator output becomes equal to V2, a short- duration output pulse activates the pulse generator (PG). The PG, acting through the divide-by-two counter, releases two firing pulses spaced 1808 apart that are appropriately amplified and transmitted to the anti-parallel–connected set of thyristors. The PLO thus effectively operates at twice the system frequency.
The relevant waveforms are depicted in Fig. 4.19. The positive- and negative- cycle TCR-current pulses are denoted by i1 and i2; the conduction period is denoted by 2b.
For an integrator-transfer function ofK
/
s, the magnitudes of V1 andV2 are chosen to reduce the error voltage Vc to zero in the steady state. The required magnitudes ofV1 andV2 are obtained from the relation [28]:K1V1 c2f0V2 (4.41)
where K1 is the constant.
The PLOs for multiphase SVC systems can be realized in two configurations:
individual-phase control and equidistant-pulse control (also known as common- oscillator control).
120 SVC CONTROL COMPONENTS AND MODELS
0
0
0 Integrator
Output Firing-Pulse
Valve 1 Firing-Pulse
Valve 2 V2
V2
b b V
i1 i2
2
p p 2p
p + ∝
∝ ω0t= 0
Figure 4.19 Waveforms for a single-phase TCR.
4.3.2.2 The 3-Phase Oscillator
Individual-Phase Control (6-Pulse Operation) This requires three sets of 2- pulse oscillators, one for each phase. Each set operates on the basis of the corresponding phase voltage. In case of load compensation or voltage bal- ancing (where such a scheme is most commonly employed), unequal currents flow in the three TCR phases, resulting in the generation of noncharacteristic harmonics—among which a predominant 3rd harmonic component exists for which adequate filtering must be provided.
Equidistant-Pulse Control (Common-Oscillator Control) Only one common PLO is needed in this configuration. The layout is the same as shown in Fig.
4.18, except that a divide-by-6 or -12 ring counter is employed for the 6- or 12- pulse operation, respectively, instead of a divide-by-2 ring counter. The 6-pulse PLO is impervious to harmonics of order 6, 12, 18, and so on; hence, even if the feedback signal is derived from the output of a 6-pulse rectifier, instead of a (voltage)2 measurement there is no need to filter out the 6-pulse ripple.
Other closed-loop control applications and features of PLOs are described in ref. [28].
THE VOLTAGE REGULATOR 121 4.3.3 The Digital Implementation of the Voltage Regulator
The dramatic evolution of microprocessor technology in recent times, together with the availability of powerful software tools, has opened up new dimensions in the digital control of power-system controllers, such as FACTS [16], [33].
The digital technology offers the following advantages:
1. Enhanced flexibility and amenability to different system requirements.
2. Control functions synthesized in software. This hardware can implement different control schemes; for instance, controllers with variable param- eters, as well as adaptive and nonlinear controller. Controller parameters are not subject to variation with age and environmental conditions, and their performance is completely repeatable.
3. Graphical, friendly, and interactive user interface. Operator interface can be both local and remote.
4. Improved alarm and protection functions.
5. Advanced autodiagnostics, internal supervision, and debugging facilities.
6. Data communication with supervisory controls.
7. On-line monitoring and recording of variables affected by transient phe- nomena.
8. Ease in testing and commissioning.
9. High resolution and accuracy.
10. Adequate bandwidth for FACTS controller applications, even though it is somewhat limited in extremely fast, complex control loops.
11. Steadily declining costs of digital controllers.
Most modern FACTS installations are equipped with digital controllers. The details of the application of digital control to SVCs in practical installations are provided in refs. [16] and [33]. The SVC controller is implemented on a MACH 2computer. The high-speed functions, such as the regulator and firing controls, are realized in digital signal processors (DSPs), whereas the other regular fea- tures, such as the operator interface, are provided in a main computer’s central processing unit (CPU). The other control features of SVCs that are implemented on the main computer are
1. closed-loop PI voltage regulator with variable gain, which responds to the positive-sequence component of the measured voltage;
2. voltage measurement;
3. gain supervisor;
4. gate-pulse generation;
5. power oscillation damper;
6. control of external reactive-power sources;
7. undervoltage-control strategy;
122 SVC CONTROL COMPONENTS AND MODELS
8. sequence control of breakers; and 9. TCR direct-current control.
These functions are explained later in this chapter, as well as in Chapter 5.
4.3.3.1 Digital Control The concept of digital control of SVCs is based on the Z-transform technique [19], [20]. In a digital controller, a new transfer function,G(z), is derived that corresponds to the continuous-transfer function, G(s), which provides the same output at discrete time instants in response to sampled values of the input. The Ztransform is subsequently expressed as a difference equation of the general form:
Ync
M
冱 冱
k冱c0
AkXn−k−
L
冱 冱
k冱c1 BkYn−k (4.42) where Yn c the present output values
Yn−1,Yn−2 c the past output values
Xn,Xn−1,Xn−2 c the present and past input values
Ak,Bk c the constant coefficients that are dependent on the poles and zeroes of the continuous-transfer function G(s) and the sampling frequency
L,M c the positive integers that depend on G(s) For instance, let a pure integral SVC controllerG(s) be expressed as
G(s)c K
s (4.43)
The corresponding Ztransform is given by G(z)c KTz−1
1−z−1 (4.44)
where K c the controller gain Tc the sample period z−1 c a delay ofTseconds
The transform G(z) is step-invariant, that is, it has a similar response as G(s) corresponding to a step change in input. Then,G(z) is expressed as a difference equation:
YncK T Xn−1+Yn−1 (4.45)
GATE-PULSE GENERATION 123 where Yn c the present output at t seconds
Yn−1 c the past output att −T seconds Xn−1 c the past input att −T seconds
For an SVC controller,Xand Ycorrespond to the error signalVe and desired susceptanceBref, respectively. Thus, Eq. (4.45) can be rewritten as
Bref(n)cK T Ve(n−1)+Bref(n−1) (4.46) A general difference equation corresponding to a third-orderG(s) having three poles is expressed as
Bref(n)cK[A1Ve(n−1)+A2Ve(n−2)+A3Ve(n−3)]
+B1Bref(n−1)+B2Bref(n−2)+B3Bref(n−3) (4.47)