41.2.1 Characteristics of system components

41.3.1 The flow of power and vars

Electricity supply networks have predominantly inductive series impedances. Figure 41.3(a) shows an elementary circuit in which a load is supplied from a generator via inductance, X. The generator output voltage, V_s, is constant; the voltage at the load is V_R. When there is no load, the voltages V_s and V_R are equal in magnitude and phase. When a load is connected it will draw a current, I, through X.

Figure 41.3(b) shows the vector diagram for a resistive load; I is in phase with V_R and φ = 0. If the value of the load resistance is R, the power is P = V_R · I = I²·R = V_R²/R. The voltage drop through the reactance X, is ΔV = I · X and is in quadrature with V_R. It causes a phase angle difference, δ, between V_s and V_R. Also, V_R is smaller than V_s because of the vars (Q = I²X) consumed in X.

Figure 41.3(c) shows the vector diagram for a purely inductive load, with I lagging by φ = 90° behind V_R. The voltage drop through X is in now in phase with V_R, which therefore remains in phase with V_s but is appreciably smaller. Figure 41.3(d) is the general case, with a lagging power factor load that causes differences both of phase angle and magnitude between V_s and V_R.

These examples illustrate that, when power flows through inductive impedance from one point to another, it is accompanied by a difference in the phase angles of the voltage at those points. Var flow between two points is accompanied by a difference in the voltage magnitudes at those points. It is important to bear in mind that these features may be expressed in the converse way. Thus, when a difference in phase angle is enforced between the voltage vectors at two points in a network, power will be transmitted from one point to the other; by enforcing a difference between the voltage magnitudes at the two points; var flow will take place. Put simply, differences in phase angle control the flow of power and differences in voltage magnitude control the flow of vars. This is a highly simplified, but crucial, description of the principles of a.c. power transmission; reference should be made to Chapters 3 and 35 for the theoretical background.

41.3.2 Voltage instability

Figure 41.3(e) plots the relationships between power, vars and current supplied by the generator, together with the load voltage, V_R for the purely resistive load illustrated by Figure 41.3(b). As the magnitude of load resistance, R, is reduced, the current, power and vars each increase at different rates, but V_R decreases. When R is equal to X, P = Q, and δ = 45°. For this load resistance, the power has its maximum value, given by . Any further reduction of resistance will cause a further reduction of V_R and also of P whereas Q continues to increase. Figure 41.3(f) plots the relationship between voltage V_R and power P and shows how important it is, for the stable operation of a system, that voltages at load points should not be allowed to drop below certain limits. If the load voltage falls too far, the condition can become progressively worse, leading to a complete collapse of voltage. Such voltage instability is more prone to occur in systems with large inductive impedances and can be exacerbated by loads that tend to consume constant power and vars irrespective of the magnitude of their supply voltage. Loads of this kind include those that are supplied by transformers with on-load tap-changers, when the tap-changers have an automatic control which attempts to maintain a constant secondary voltage.

Figure 41.3(g) shows a family of voltage-load curves for different power factor loads, including the unity pf case of Figure 41.3(f). When the load current has a lagging component, i.e. is at less than unity pf, the maximum power capability will be smaller and the voltage for a given load will be reduced compared with Figure 41.3(f). For a particular power factor curve and for any power less than the maximum there are two operating points; points A, A₁, etc., are stable (i.e. dV_R/dP is negative) and points D, D₁, etc., are unstable. The upper, stable, values represent possible system operating conditions; however, if the load is increased, or the load pf is decreased, the operating point moves towards the ‘nose’ of the curve, accompanied by a progressive reduction in voltage, which tends towards a complete collapse of the system.

Figure 41.3(g) includes the interesting result for a load with a leading pf. This increases both the load voltage and the maximum load that may be transferred.

The phenomenon of voltage instability has been the cause of, or a contributory factor in, a number of major system failures. The adequate provision and the correct control of the network var resources can play a vital role in preventing voltage instability.

41.3.3 Var balancing for steady state conditions

It is clear from the previous sections that there are significant benefits in local balancing of load vars by power factor correction. In addition to the improvement in load voltage conditions, the magnitude of the load current is reduced, which reduces transmission losses and releases circuit capacity for increased power transfer. Capacitors draw a reactive current that leads the voltage across their terminals and shunt capacitor banks provide a relatively economic means of improving the power factors of loads connected to a power supply system especially if the load is constant, or almost constant. When there is a slow variation of the load, shunt capacitors may be switched into or out of service to provide an approximate balance of the load vars. When the load varies quickly, it can no longer be regarded as ‘steady state’ and a compensating system that can be quickly controlled to counteract the load fluctuations must be used, as will be described later.

It is also clear that, if the vars absorbed in the supply inductance were to be reduced by series var balancing, the effective inductance of the supply would be reduced. The adverse effects of both active and reactive currents would then be lessened and the stability margin could be increased.

41.3.4 Power transmission over long distances

The use of reactive compensation to improve transient stability and so increase the amount of power that can be transmitted over given transmission lines is discussed next. In contrast to the example of a simple load discussed above, it is usual for machines to be present and to provide voltage sources within the systems at each end of the line.

41.3.5 Transmission characteristics

A number of performance features are associated with long distance transmission.

At light loads which are only a small fraction of SIL, or at energisation of the line from one end only, the distributed inductance and capacitance of the line can cause a large over-voltage due to the Ferranti effect; this must be countered by either (a) reducing the vars from the line capacitance by shunt reactive compensation, or (b) cancelling part of the line inductance by series reactive compensation.

The maximum power that can be transmitted down a long uncompensated line is limited by its series inductance and by the line surge impedance. Increase in transmitted power can be achieved by series or shunt reactive compensation.

Figure 41.4(a) represents a long transmission line, with a total series inductive impedance X; to simplify this illustration, the effect of the line shunt capacitance is ignored. In Figure 41.4(b) the voltages V_s and V_R at the two ends of the line are assumed to be maintained constant and equal for all values of current, I. As the current increases, so does the angle, δ, between the voltages. The voltage at the midpoint of the line will be

and, with V_s = V_R, will be in phase with the line current.

The power flowing through the line will be

As shown in Figure 41.4(c) the transferred power rises to a maximum (given by ) as the angle δ reaches 90°. The power decreases as δ increases beyond 90°. It may be noted that control of the load voltage has doubled the power obtainable in the simple case illustrated in Section 41.3.2 where V_R is not controlled.

The shunt capacitance of a practical line will have the effect of increasing the voltage at all intermediate points along the line, including the mid-point, and consequently will give a corresponding increase in the maximum power. However, the voltage rise must not be allowed to exceed the maximum operating voltage of the system under no load or light load conditions.

Owing to the inertia of the rotating machines connected within the networks at either end of transmission lines, any system operating near its steady-state stability limit (corresponding to the phase angle of 90°) is bound to become unstable following a major disturbance, due to the ensuing increase of phase angles. It is therefore necessary to design a line to be able to transmit more than pre-fault power up to the point of maximum angular swing. Consequently, sufficient var generation must be available to compensate for the increased var consumption by the line current at increased phase angles. Thus, for transient stability to be secured, some excess var generation must be available. This can be achieved either by operating the line sufficiently below its surge impedance power before the fault or by adding var generation transiently for the period in which the line phase angle will be abnormally increased. However, without adequately fast voltage control along the line, either solution can lead to dangerous overvoltages, particularly under the condition of a severe ‘back-swing’ (i.e. a transient phase condition when the power transmitted is much less than the pre-fault level) or during a load rejection situation consequent to loss of stability.

Then the total vars Q to be absorbed from the line when operating at a voltage V and power P approximates to Q = Q₀ [V²-(P/V)²] where Q₀ is the vars generated by the line shunt capacitance, C, at rated voltage V₁. Here P, Q, and Q₀ are expressed in per-unit of the SIL, P_s, and V is expressed in per-unit of V₁.

For V = 1 p.u., Q is equal to go at P = 0, and falls to zero for P = 1, i.e. for a power equal to P_S. Power can be increased above P_S, if Q can be made negative, i.e. if var generation is added.

41.3.6 Transient instability

There has been a tendency to increase the distance over which power is transmitted for the following typical requirements:

Transient instability can occur in a transmission system following a sudden disturbance such as a short-circuit. The power output of a generator located near a fault may be greatly reduced, thereby allowing its speed to increase, while the output of a remote generator may be hardly affected by the event. As the acceleration of the two generators will differ, the phase angle between their internal emfs will change. In a simple system the two generators will drop out of synchronism if the fault persists long enough to allow the phase angle between their emfs to swing too far above 90°. The loss of synchronism takes place usually within 1 s of the disturbance. It is clear that the larger the series inductive reactance of the transmission lines and system transformers in the network interconnecting the generators, the greater attention must be paid to the possibility of phase-angle instability. In a well-interconnected system that does not have long distances between generators, transient and dynamic instability is rarely a difficult problem because fast clearance times can be obtained by using modern relays and circuit breakers.

On the other hand, slow swings or oscillations may develop between two parts of the system (or perhaps between one remote generator and the rest of the system), possibly initiated by minor disturbances, and these may build up to unacceptable levels after perhaps 20 or 30 seconds. Modern automatic controllers for generator excitation, with auxiliary stabilising signals, can exert some damping on such oscillations. Shunt or series dynamic compensation may be used alternatively or in addition to generator excitation control.

41.3.7 Var balancing for dynamic conditions

Figure 41.4(d) represents the same transmission line as Figure 41.4(a) but with the assumption that the mid-point is connected to a virtual infinite bus-bar, which will always keep the magnitude of V_M constant and equal to the voltages at the ends of the line. In this context, the ‘infinite busbar’ is not required to supply active power, (i.e. it will not control the phase angle of V_M) but must behave as an ‘ideal’ FACTS controller to supply the vars required to control the voltage at the mid-point.

Figure 41.4(e) shows that this additional voltage support effectively divides the line into two equal sections, each with a reactance of X/2 and operating at an angle, δ/2. Each line section now has an independent stability limit which is reached when δ/2 = 90°. Thus the theoretical total angle between V_S and V_R can now be 180°, i.e. double the conventional critical value of 90°, with a resultant increase in power transfer capability.

Without any voltage support at the mid-point the power will be as in curve 1 of Figure 41.4(f) (repeated from Figure 41.4(c)).

With voltage support at the mid-point, the condition will be as in curves 2 and 3. If the vars were to be supplied instantaneously, the power transfer would be doubled (curve 2),

In practice it is not possible for the theoretical maximum to be achieved, owing to losses and the response delay of a practical controller (curve 3). However, it is possible to provide voltage support at several places along the line and so make up, to some extent, for the lack of the ‘ideal controller’.

Figure 41.5 illustrates an example of conditions to be expected on a very long high-voltage transmission line with voltage support, provided for example by SVCs (static var compensators) at two intermediate substations, Figure 41.5(a).

For each of the three sections there are two conditions that can be responsible for limiting the maximum power that is reached.

Assume that the controllers can hold the voltage rigidly constant irrespective of load. In this case the stability limit will theoretically be reached if the phase angle between two adjacent voltage controlled bus-bars reaches 90°. In practice, even with controllers, the resistance of the line and the controller response delays limit the total angle at maximum power to less than the theoretical maximum of 3 × 90°, e.g. to 175° in Figure 41.5(b). Figure 41.5(c) illustrates the phase angles of the line at this steady-state power limit.

The second limiting condition might be that any one of the controllers reaches the limit of its var generation capacity; the required vars from the controller are illustrated in Figure 41.5(b) by the curve Q (generation or absorption). When the power P and angle δ reach the condition of this limit, as for point ‘a’ in Figure 41.5(b), the controller ceases to be effective in controlling the line voltage at its point of connection and the stability limit is reached even if the total angle has not reached the expected limit (e.g. 175°).

The action of a shunt controller in improving the transmission capacity of a line can be thought of in terms of its effect on the natural surge impedance of the line; the shunt C is controlled so that the effective surge impedance matches the load being transferred. For heavy loads the shunt C is increased and the surge impedance is decreased, thereby increasing the value of SIL.

An alternative way of reducing the surge impedance in order to provide extra margin for a long transmission line is to reduce the series inductive reactance; this can be done by inserting a controller with a negative inductive reactance (usually in the form of capacitive reactance). Series compensation inserted in one or two locations along a transmission line has the following important characteristics.

Even when a long h.v. or e.h.v. line is series compensated, shunt reactors are normally needed to absorb part of the shunt vars of the line. Typically between 40% and 100% of line shunt capacitive power may be compensated at light load to prevent overvoltages on the line. To restrict insulation stresses caused by overvoltages following sudden load rejection, a substantial part of the shunt reactive compensation is usually left permanently connected; clearly, this reduces the maximum power limit of the line.

Figure 41.6(a) shows an illustrative theoretical example of the power–angle characteristic of a line including its terminal impedances; the line is represented as three π sections of about 200 km length each, with shunt reactors (R) at each line section terminal and series capacitors (C) at two intermediate locations. The curves in Figure 41.6(b) were calculated neglecting power losses, and the values are given in per-unit terms on the base of the surge impedance load (P_S).

As the degree of shunt compensation is increased, the line requires a greater amount of series compensation to maintain the power–angle characteristics of the line. A comparison of curves 1 and 6 and the table in Figure 41.6(c) shows that with 100% shunt-reactor compensation the line requires almost 50% series compensation to reach the same maximum stable power limit as for the case without any shunt or series compensation. The maximum allowable limit of series capacitor compensation and choice of its location are governed not only by economic considerations, but also by various practical aspects, such as subsynchronous resonance (SSR, described later) and by the series capacitor short-circuit overcurrent protection needs. The latter requires spark gaps or non-linear resistors. The line distance protection relaying must be co-ordinated with these features.

41.4.1 Objectives

Traditionally, a single organisation was responsible for all aspects of generation, transmission and distribution but, increasingly, these functions are being separated and allocated to organisations that are independent of each other. This subdivision of responsibilities usually results in competition between generating companies to supply power to the transmission network and often between distribution companies to supply power to customers, but the responsibility for transmission sometimes rests with a single organisation. The transmission company must then ensure that an adequate supply of energy is called up from the generators and that satisfactory levels of voltage exist throughout the transmission system in order to satisfy the moment by moment demands of the distribution companies; this requires the effective management of vars at the points where the energy is received and delivered, as well as within the transmission system itself. Adequate provision of vars at all times can be crucial for the security of a system.

It is necessary to balance various factors to arrive at an optimum solution for the management of vars. The objectives in such management must be both economic and technical.

41.4.2 Tools for var management

To attain the above objectives of efficient var management, system designers, operators and consumers can use some or all of the following types of plant or procedures: generators; on-load tap-changing transformers; switching of transmission circuits; various types of FACTS controller. Later sections provide information on the development and application of these controllers, which include shunt reactors and capacitor banks, switched or unswitched; series compensation; synchronous compensators; static var compensators; STATCOM; other FACTS controllers.

41.4.3 Var management by the supply authorities

The benefit of good var management by the supply authority can be significant. Three areas of management can be identified.

The first is in the system planning and design stage, where a choice must be made on the rating and type of any reactive compensation equipment to be used, where it should be connected in the network, and when is the optimum time for installation. The characteristics of any power system, particularly the proportion of generation connected at the different transmission voltage levels and the ratio between the system maximum and minimum loading, greatly influence the decisions to be made.

Most transmission networks, even at peak demand, operate below their surge impedance load and hence generate more vars than they absorb, i.e. they have a positive var balance. However, under emergency conditions following a loss of one or more lines, the positive balance may turn into a deficit which under extreme conditions can give problems of voltage instability as well as possible loss of synchronism due to the network’s low power-transfer capability.

A var planning study involves the balancing of the vars in the complete network. Then, after allocating an amount of var production to generating plant, it is necessary to decide on the best method to deal with the resultant surplus or deficit. For a large system this can require a protracted and major design exercise, and over the last two decades much effort has gone into the development of mathematical and computational techniques to aid system designers in this task.

The second area of var management is in system operation, where the facilities provided must be used in the most efficient manner to maximise system operational security and minimise system losses. Again much work has been done on the development of both off-line and on-line computer programs. Various studies have shown that, in general, minimising network losses also gives maximum security and minimum unnecessary circulation of vars in the network.

The third area is the commercial one of tariff policy, in which financial incentives are adopted to persuade consumers to maintain a power factor close to unity.

41.4.4 Var management by consumers

The induction motor is by far the most common driving machine and, in consequence, the natural power factor of most industrial loads is in the 0.7–0.8 lagging region in the absence of reactive compensation. Such a load requires a var supply of between 75 and 100% of its power, increasing the loading on the plant (e.g. transformers and cables) and causing significant losses and voltage drops. By generating the required vars close to the loads, these disadvantages can be largely overcome and for this reason supply authorities impose tariffs on industrial consumers to encourage them to install power-factor correction plant within their systems. This can often be achieved in a relatively inexpensive way by shunt capacitors, either direct on the motor terminals or as larger banks on supply voltage bus-bars. Often a combination is the optimum solution.

Fixed capacitors or switched banks may not always be adequate where the var requirements fluctuate widely and rapidly and cause greater voltage variations at a point of common coupling with other consumers than the supply authority allows. Such loads are found, for example, in the steel industry where, with thyristor driven rolling mills, the sudden impact of the billet meeting the rolls produces a rapid increase in low-power-factor current; and with electric arc furnaces, where frequent and random short-circuits occur between electrodes, producing short bursts of high current, again at a very low power factor.

Most supply authorities have regulations covering allowable limits for voltage fluctuations, particularly in respect of lamp flicker; as the human eye is most sensitive to fluctuation frequencies in the region of 8–10 Hz, these limits vary with frequency. Typically they might allow only 0.25% voltage dips at 10 Hz but 1–2% at 1 Hz. To compensate for such conditions requires a fast and continuously variable reactive source such as some types of static var compensator.

Thyristor power conversion equipment (which is increasingly being used in large ratings) and electric arc furnaces generate harmonic currents that flow into the supply network. These can affect other plants, causing losses, possible overheating or interference with electronic and telecommunication circuits. Supply authorities must therefore limit the harmonic distortion on their networks and many authorities stipulate maximum permissible values. To avoid exceeding these, it may be necessary to prevent a proportion of the harmonic currents generated by the consumer from penetrating the supply system. It is common to bypass these currents into harmonic filters. It is often possible to convert capacitor banks for power-factor correction into harmonic filters, giving significant cost savings. In any case the harmonic filters will generate vars at the power supply frequency and these must be accounted for in the system var balance.

41.5.1 Synchronous compensators

All synchronous machines can give continuously variable var compensation and, in industrial systems where large synchronous motors are installed, they are frequently used in this way to provide power factor correction of the local load in addition to their main driving duty. Self-driven synchronous machines not connected to any mechanical load (synchronous compensators) can be used anywhere in a system either to generate or to absorb vars on a balanced three-phase basis. The synchronous compensator directly generates a voltage at its terminals. The magnitude of this voltage is controlled by a high-speed excitation system, which is often arranged to provide control of the voltage at another point, usually at the high voltage side of the compensator transformer. When overexcited, the machine generates vars and operates in a stable condition; when underexcited, it absorbs vars but its stability decreases as the excitation falls towards zero. Because of this tendency towards unstable operation, the var absorption rating of a synchronous compensator is typically only 50% of its var generation rating. Most machines operate with an automatic excitation control that needs to have a rapid response to assist the machine in maintaining stability through system disturbances or to follow rapid reactive load changes. The control time constant is normally in the range from 5–10 cycles.

Figure 41.7(a) illustrates the voltage–current characteristics of a synchronous compensator. The rated excitation voltage corresponds to the rated voltage of the system. If the system voltage falls below its rated value to V_d and the field current remains unchanged, the var generation will initially follow the sub-transient characteristic to point B but it will finally settle to point A on the synchronous reactance characteristic. In practical applications of synchronous compensators, the machine excitation will usually be controlled either to maintain a nominally constant Mvar output or to maintain a nominally constant ‘target voltage’ on the system, subject to a defined ‘droop’, or slope characteristic. Thus, for 5% droop, and starting from the float condition with zero output, a reduction of 5% of terminal voltage will provoke an increase in excitation sufficient to generate rated leading current. Conversely, a voltage rise of about 2.5% will cause the synchronous compensator to absorb its rated lagging current. When there is a sudden disturbance, the output will initially follow the sub-transient characteristic as before, but after a few cycles the fast excitation control will cause the output to settle at the appropriate point C on the controlled characteristic. As shown in Figure 41.7(b) the slope of this characteristic is equivalent to a reactive impedance, X_m, such that a voltage change, ΔV_m, at the controlled bus-bar will cause a reactive current change ΔI_m in the synchronous compensator, i.e.

Synchronous compensators have several limiting or disadvantageous features; costs are relatively high and losses significant; they need good foundations, buildings, complex auxiliary systems and regular maintenance and refurbishment that detracts from availability. These drawbacks prompted the development of alternative types of equipment, using static components, with the synchronous compensator acting as the initial benchmark for dynamic response.

41.5.2 Sign convention for vars and reactive current

There are standard sign conventions for power and vars when current flows from a system bus-bar into a load. Power is positive for the component of current that is in phase with the voltage; vars are positive for a load operating at lagging power factor, i.e. when the current flowing into the load lags the voltage on the bus-bar. By this convention, when treated as loads as in Figure 41.7, shunt reactors will draw positive vars from the system, shunt capacitors will draw negative vars and generators will draw negative power. However, a reversed sign convention has been adopted to define the ratings of var compensation equipment for the following reason.

Generators supply both the power and the vars to satisfy the demands of the system and its loads. The sign convention for generators is that both power and vars are positive when current is flowing from the generator into the system bus-bar to supply a lagging power factor load. A synchronous compensator behaves in the same way as a generator operating at zero power and therefore it uses the same sign convention for vars. Thus, vars are positive when the synchronous compensator is over-excited, acting as a shunt capacitor and supplying an inductive (positive var) load and negative when it is under-excited, supplying a capacitive (negative var) load.

The same sign convention has become the norm for defining and specifying the var duties and output ratings of shunt static var plant and is thus consistent with that for rotating plant, i.e. shunt capacitive vars are designated as positive and shunt inductive vars are designated as negative. Note, however, that as shown in Figure 41.7, which treats the compensating plant as a load, the corresponding currents have opposite signs to those for vars.

41.5.3 Basic features of static compensation

The main elements of the traditional type of static var compensator (SVC) are a capacitor to generate vars and an inductor to absorb vars. To provide operation in both the generation and absorption modes, both elements must be used; at least one of them must be rapidly variable, Figure 41.8(a), in order to replicate the dynamic characteristic of a synchronous compensator shown in Figure 41.7(b). A capacitor element cannot give a stepless variation: therefore, if a smooth continuous variation is needed over the whole range A-A′ in Figure 41.8(b), a capacitor bank having a rating to give at least the current I_C must be connected and the variable element must be inductive, with a rating to give a current at least equal to I_C + I_L.

Although a SVC does not generate a real voltage, its dynamic voltage–current (V–I) characteristic enables it to be represented in studies of the system behaviour as if it were a synchronous compensator. The reference parameters for the SVC’s characteristic are a target voltage, V_ref, equivalent to the excitation voltage of a synchronous compensator, and an equivalent slope reactance, X. The SVC inductive current, I, (or capacitive current if I is negative) at an actual system voltage, V, is given by the function

The equivalent machine can be controlled to generate and absorb vars over a defined range of system voltage variation, but has no inertia. At the limits of the linear range, the SVC representation is changed to that of a simple shunt capacitor or reactor, as appropriate.

In some system applications the SVC must be capable of operating under different system conditions at the extremes of its range (i.e. at A and A′), but it need not be capable of swinging in a continuous manner from one extreme to the other. Its ‘dynamic’ or ‘swing’ range, which is the range over which it can give a very fast response, may be only a proportion of its total range. In such a design the size of the variable element, which is the most expensive item in per unit of rating, can be reduced to deal only with the required swing; mechanically switchable L and/or C elements, Figure 41.8(c), can then be controlled automatically to adjust the position of the dynamic range within the total range. The overall cost of the SVC is then reduced. Sometimes the total range of a SVC is extended by using its control system to control the switching of shunt capacitors or reactors connected elsewhere in the substation.

The first commercial application of a SVC was in 1964. It used a self-saturated reactor to reduce the lamp flicker caused by an electric arc furnace. The first static var compensator for a transmission system was installed in 1967, followed by another in 1969: both used saturated reactors (SRs) as the continuously variable inductive component, the first was a d.c.-controlled transductor and the second a self-saturated reactor with harmonic-compensation and slope correction.

During the next decade many SVCs were commissioned, particularly on industrial systems where SVCs were installed to reduce voltage disturbances and to suppress disturbing lamp flicker caused by the var fluctuations of loads such as arc furnaces, large converter-fed drives in rolling mills and, in some cases, particle accelerators. The first thyristor-controlled reactor (TCR) for a transmission system entered service in 1978 and this coincided with a rapid growth in such applications of both thyristor and SR types of compensator, Figure 41.9. This growth resulted mainly from two factors. First, the rapid increase in the cost of power made utilities more conscious of the need to minimise transmission losses. Second, the growing opposition in industrialised countries to the construction of new transmission lines encouraged the maximisation of power transfer down existing rights of way. The 1990s saw the advent of a completely new type of static controller, the ‘STATCOM’, which uses voltage sourced converter technology.

41.5.4 Harmonic-compensated self-saturated reactor

The saturated reactor (SR) is the original type of SVC; it gives an inherent variation of reactive current with voltage and its response does not depend on an imposed control system. The variable element comprises an iron-cored inductor whose core becomes saturated during each half cycle of the supply voltage and this core saturation results in a r.m.s. voltage–current characteristic as shown in Figure 41.10. This voltage–current characteristic resembles the controlled characteristic of a synchronous compensator. A saturated reactor can only absorb vars from the system but not generate vars; its saturation voltage is the ‘excitation voltage’ of an equivalent machine and its slope reactance is the ‘droop’. The operating current of the saturated reactor automatically adjusts itself to the point at which its characteristic intersects the system load line. If the terminal voltage falls below the saturation voltage, the SR current becomes negligibly small. Shunt capacitor banks are used to enable a SR type of SVC to generate vars.

An iron-cored inductor with a simple winding is rarely used on a power network, as it generates large magnitudes of odd harmonic currents. However, by interconnecting sections of all three-phase windings it is possible to cancel out most of these harmonics in normal operation. The twin-tripler and treble-tripler harmonic compensated SRs (invented and developed by Dr E. Friedlander of the former General Electric Company, England) use this principle and have, respectively, six and nine active iron-cored limbs with inter-star connected windings and ratings up to 170 MVA for a treble-tripler saturated reactor, Figure 41.11. In addition to reducing the harmonic content of the reactor current to negligible proportions the designs give a voltage-current characteristic with a sharp knee point and a slope that remains linear to within about 1%, for currents from about 10% to more than 300% of rated load. The slope reactance is normally within the range 8–15% on the basis of nominal full-load rating.

41.5.5 Thyristor switches

In the 1960s, the demand for thyristors in industrial applications led to the very rapid development of devices with high withstand voltages and also capable of operating at high currents. Thyristor pairs with inverse-parallel connection Figure 41.12(a) are suitable for use as static switches, capable of extremely fast and frequent switching operation without the time delays, wear and tear and maintenance requirements of mechanical switchgear. A.c. thyristor switches were at the heart of most of the SVCs supplied during the 1980s and 1990s.

For a practical application, thyristors are assembled in a modular way into an ‘a.c. thyristor valve’. An a.c. valve is made up of inverse-parallel connected thyristors, which are themselves connected in series (and occasionally in parallel) to obtain the necessary rating, with voltages up to 40 kV and currents up to about 6kA. The cost of a thyristor valve is influenced not only by the ratings of the thyristors, but also by the number of voltage levels in series. Thyristors are available with voltage ratings up to about 8 kV (peak), although derating factors of 2 or more need to be applied in a series string of thyristors to determine the actual rms operating voltage of each thyristor.

Differences in the thyristor leakage currents, stray capacitances and stored charge all tend to cause an uneven voltage distribution between series-connected thyristors. A resistor–capacitor a.c. grading network is used in parallel with a d.c. grading resistor across each thyristor level, Figure 41.12(b). These grading networks reduce the voltage unbalance, and the R–C network also serves to damp the transient overshoots in the reverse voltage that occur when thyristors come out of conduction (twice per cycle per valve). Individual thyristor levels within a module are protected against overvoltage by breakover diodes or similar devices, which provide a gate pulse for forward firing of the thyristors above a pre-set overvoltage level. Special care must be taken in the design of the gating electronics and the signal transmission circuits to ensure coherent (simultaneous) firing of all the series-connected thyristors.

Most thyristor valves are indoor installations, with air insulation and water cooling. Only pure demineralised water having very high resistivity is allowed to flow through the thyristor heat sinks, which are at high voltage with respect to ground. The water cooling plant is mounted separately at ground potential and the pipework from ground to the thyristor stacks includes some sections made of insulating material. Air cooling is much simpler than water cooling, but it limits utilisation of the current capability of the thyristors and is rarely used for SVC applications. Figure 41.13 shows one type of thyristor valve used in a SVC installation in a transmission network.

The thyristor-controlled reactor (TCR) comprises an a.c. thyristor valve connected in series with a linear reactor. One phase of a TCR is shown in Figure 41.14. Variation of the current in the TCR is obtained by control of the thyristor conduction duration in each half-cycle, from a 90° firing angle delay (as measured from the applied voltage zero) for full conduction to 180° delay for no conduction.

A.c. thyristor valves consisting of inverse-parallel connected thyristors, very similar to those used for the TCR, are used to enable rapid and frequent switching of blocks of capacitors, Figure 41.15. The thyristor-switched capacitor (TSC) gives directly the effect of a variable capacitance, although for reasons given below the variation is in steps.

Once gated, the thyristor valve will conduct for a half-period and unless again gated the current will then cease. A TSC, therefore, can only give a variation of capacitance between two states, on and off, for a discrete period of an integral number of half-periods. The kind of point-on-wave control used to give variable output with a TCR is not a practicable option for a TSC.

At the end of each half cycle of conduction, the capacitor current through the thyristor reaches zero; unless re-gating occurs the capacitor will remain charged at peak voltage while the supply voltage peaks in the opposite polarity after a half-period. This imposes a doubled voltage stress on the non-conducting thyristor, so that a TSC valve usually needs approximately twice the number of thyristors in series compared with a TCR valve of equivalent voltage. Ideally, gating is arranged to take place when the voltage across the thyristor is zero and the supply voltage is at its peak (i.e. dv/dt = 0); this results in a transient-free energisation. Except when continuous conduction is achieved by repetitive re-gating, such ideal switching conditions are rarely achieved, owing to mismatch between the capacitor voltage (which normally slowly loses its charge from its previous energisation) and the system voltage (which may have changed its value during the same interval).

The TSC control system is normally arranged to choose the gating instant that gives the minimum transient. Nevertheless, quite large transients occur during initial energisation of an uncharged capacitor and current limiting reactors must normally be installed to reduce the magnitude of the inrush current to a value within the thyristor capability. With the exception of these switching transients the TSC does not produce harmonics.

It is possible to arrange for a very rapid discharge of the capacitors after each period of conduction; this can reduce the voltage stress on the non-conducting thyristor and provide more consistent conditions for the next energisation. With a delta-connected three-phase TSC, current zero is reached sequentially in the three phases. By connecting a suitably designed three-phase transformer across the capacitors, most of the energy stored in the capacitors can be commutated back into the system, and into discharge resistors, by transformer action. Core saturation effects supplement this transformer action.

41.5.6 Convertor-based FACTS controllers

41.6.1 General

The load carried by a power system is continuously changing. Major variations in total load occur quite slowly, over a period of tens of minutes or longer in a daily cycle see Figure 41.24, which itself changes with a weekly and yearly variation. Normally any very rapid changes of load are only a small proportion of the total and do not affect the overall pattern.

For a system operating under normal conditions the overall var compensation requirements also change relatively slowly. In a well-proportioned system the var flows are not sensitive to small load changes and it is generally possible to use fixed shunt reactors or capacitor banks to balance the vars for average load conditions. Often, however, it is advantageous to arrange that some or all of these shunt compensation elements are switchable, so as to give better control and to reduce unnecessary losses. These discretely variable devices are the simplest and the most common var compensators.

Many power systems now take advantage of the benefits offered by continuously variable var compensators. These can be used for particular categories of application such as:

These different applications call for different characteristics of the variable var compensator. The types of compensator are reviewed in this section, with particular reference to their operating characteristics and applications, a comparative summary of which is given in Table 41.1.

41.6.2 Mechanically switched reactors and capacitors

Mechanically switched reactors and capacitors are used at all voltage levels, from the highest voltage transmission systems down to the correction of power factor on a works distribution system. Both technical and economic factors influence the decision to install switched reactive compensation. In many cases, operational considerations would permit the units to be permanently connected, but at the expense of continuous losses. The losses can be reduced by the installation of a switch suitable for fairly frequent operation, but this entails additional capital and maintenance costs.

If the compensation unit is permanently connected to other equipment (e.g. to a load or to a line), that equipment’s protective circuit-breaker will also serve for clearing faults in the compensation plant. In assessing the economics of var balance it is desirable to know for what proportion of the time a unit could be switched out, but this data is often difficult to obtain from the existing loading information and even more difficult to predict for the future.

41.6.3 Synchronous compensators

The synchronous compensator has a more positive action than most types of compensator in supporting a weak system, as it has both a generated voltage and inertia that enable it to act transiently as if it were coupled to a prime mover. The synchronous compensator can maintain full rated current independent of its terminal voltage and may be arranged to increase its var output temporarily to provide transient assistance to the system. This has been of value in certain applications; for example, where power is supplied by h.v.d.c. to a system having minimal generation, the receiving system has usually been strengthened by a synchronous compensator.

When synchronous compensators have been used for dynamic compensation of high voltage systems it has been necessary either to provide a dedicated transformer or, in some cases, to utilise a tertiary winding on a transformer which links two voltage levels within a system. With tertiary connection, the inter-winding reactance distribution of the transformer determines the high voltage bus-bar to which the compensator is most closely coupled.

The main limitations of synchronous compensators compared with static alternatives are a notably slower speed of response, typically 0.2 s, higher losses, inertia that can cause underdamped oscillations or loss of stability in some transient conditions, higher maintenance requirements (and lower availability) and higher capital costs. Because of their inherent limitations, synchronous compensators have now been almost completely superseded by static controllers.

41.6.4 Static var compensators

41.6.5 STATCOM

41.6.6 STATCOM applications

41.7.1 Series capacitor compensation

Series capacitors have, for many years, provided the only practicable means of compensating the series inductance of transmission lines. Nevertheless, the application of series capacitors in large power systems requires caution at the system design stage, because series capacitors always introduce natural frequencies below the power frequency. Series capacitors resonate with the generator and line inductances at subharmonic frequencies and the subharmonic oscillations which follow any transient disturbances can lead to self-excitation of generators, to rotor hunting and to shaft oscillations. The possible danger of this phenomenon was illustrated in the early 1970s when the shaft of a large turbo-generator was twice damaged in service, owing to subsynchronous resonance (SSR) excited by series capacitors in the transmission system.

The SSR phenomenon is now well understood as being due to near coincidence of a shaft torsional resonance frequency and the complement of an electrical subharmonic frequency. It can be fully analysed using non-linear differential equations of the complete electrical–mechanical system. For studying such phenomena more economically, however, digital computer programs have been developed, based on either eigenvalue analysis or frequency-response analysis of the complete system of linearised machine and network equations, including any shaft torsional equations of the turbine prime movers.

41.7.2 Controllable series compensation

41.7.3 Buffering of loads from system disturbances

There are many industries and industrial processes that are intolerant to voltage dips and even brief interruptions. If critical drive motors are shut down because the voltage falls below about 85% of rated voltage, or inverters suffer commutation failures because of voltage dips or distortion in one phase, the disruption can result in a serious loss of production. There may be an extended shut down of the plant while the rescue and re-start processes are undertaken. A device that sustains the voltage on the load bus-bar in the face of disturbances on the system has great potential value for protecting the sensitive loads.

41.73.2 Dynamic voltage restorer (DVR)

The advent of voltage-sourced converter technology has enabled another buffering technique to be applied, which avoids the disadvantages of series capacitors and does not rely on local generation being present, the Dynamic Voltage Restorer (DVR), Figure 41.40. This can be designed to be effective for voltage dips down to about 50% of rated voltage, which is sufficient for most dips caused by lightning. Energy to maintain the level of the source voltage is usually derived from a simple rectifier on the input side. In order to deal with larger, prolonged voltage dips, it would be necessary to use an energy source of sufficient capacity to supply the load demand for the duration of the voltage dip.

41.8.1 Quadrature booster transformer (QBT)

One of the simplest types of phase shifting transformer is the quadrature booster transformer; Figure 41.42(a) shows the basic arrangement. One transformer is connected with its primary winding in series with the transmission line, its secondary being fed from the secondary winding of a transformer connected in shunt to the system. The magnitude and polarity of the injected voltage is usually controlled by means of an on-load tap-changer.

The phase angle of the injected voltage is in quadrature with the system voltage, Figure 41.42(b), and therefore the magnitude of the voltage at the output terminals of the QBT is slightly different from that at the input terminals. For a typical maximum injected voltage equal to 20% of the shunt voltage, the difference will be about 2%; the phase shift is about 11°. The NGC has installed about a dozen QBTs, with ratings up to 2750 MVA, at critical points within the transmission network on England and Wales. Phase shifting transformers are commonly used by utilities in the US to control power flow in parallel, long distance, circuits.

QBTs are usually connected in substations where they can control the power flow in one or more circuits to prevent thermal overloading. As thermal time constants of lines are measured in minutes, a conventional mechanical tap-changer can be operated quickly enough to prevent such overloads.

If there were a requirement to improve transient stability with the aid of a phase shifting transformer, the injected voltage would have to be changed much more rapidly, for example, using a thyristor-based tap-changer instead of a mechanical tap-changer.

41.8.2 Unified power flow controller (UPFC)

The UPFC, Figure 41.43(a), is a combination of a STATCOM and an SSSC and offers great flexibility of operation. In this case the secondary winding of each transformer is connected to a three phase voltage-sourced converter. The two converters are connected back-to-back as a d.c. link with their d.c. capacitors acting as a common d.c. voltage source so that, with an appropriate co-ordination between the control systems for the two converters, power can be exchanged in either direction between the shunt and series systems. In addition, each converter can be controlled to supply or absorb Mvar independently to the series and shunt systems.

Thus, whereas a series impedance device, such as SSSC can only develop a voltage in quadrature with the current, the UPFC can generate a voltage in the series circuit with a phase angle that is controllable throughout the full range of 360°, as shown in Figure 41.43(b). When the voltage is not in quadrature with the current, power will flow out of or into the series connected converter, via the d.c. link, into or out of the power system through the STATCOM. The series converter can therefore provide impedance compensation and/or phase shifting. The STATCOM can provide voltage regulation at its point of connection independently of the power being transferred, subject only to its limits of rating.

A UPFC was commissioned in 1998 at the Inez substation of American Electric Power (AEP) in Kentucky, USA. The series and shunt units can be operated together as a UPFC or may be operated independently as STATCOM and SSSC respectively. The converters are rated at ±160 MVA and use GTOs; they are identical. A spare shunt transformer has been provided so that the converter provided for the series application is also capable of being operated as a STATCOM.

41.9.1 Lamp flicker compensation

The spectral density of voltage fluctuations produced by an arc furnace is approximately in inverse proportion to the square root of the frequency. People experience a subjective response to lamp flicker; generally, human sensitivity peaks just below 10 Hz for 230 V filament lamps. As can be seen from Figure 41.44, a weighted combination of these characteristics shows that the frequencies most liable to cause visual annoyance lie in a band from about 2 to 25 Hz. If the voltage fluctuations at 10 Hz are greater than about 0.2%, then they are likely to cause a noticeable flicker on the luminous output of a 230 V filament lamp. A 110 V lamp of the same wattage has a heavier filament with a greater thermal capacity, which results in a smaller response to voltage fluctuations and the most disturbing frequency is reduced to about 5 to 6 Hz.

A circuit supplying an arc furnace can be simplified to that shown in Figure 41.45, where the point of common coupling (pcc) is the point in the network at which other consumers are connected. The resistance of the supply is usually small compared to the reactance, X_s, and the voltage dip at this point, V_p, is predominantly due to the variation of arc furnace var demand. If there is no SVC installed, the reactive current, I_s, in the supply is the same as the furnace reactive current, I_q, and we get:

It is thus relatively easy to estimate the magnitudes of the voltage dips caused by var fluctuations, but the annoyance caused by a sequence of rapid voltage dips is difficult to assess. In order to assess and quantify the effects of fluctuating voltage dips on the human eye and brain, a flicker meter has been developed by the International Union for Electroheat (UIE) and has been accepted by the IEC. The flickermeter measures the successive voltage fluctuations and, by means of algorithms worked out from first principles, converts them into numerical values that are compared with what 50% of the population would regard as the threshold of perceptibility for lamp flicker. For this threshold level of lamp flicker, the UIE flickermeter would give a numerical output of 1.0 for ‘short term flicker severity’ (Pst).

A flickermeter can only be applied when a furnace comes into service and cannot be used directly to predict flicker levels. However, a simple estimating procedure for planning purposes, has been derived empirically from records of complaints of flicker on many installations. This procedure evaluates the ‘short-circuit voltage depression’ (SCVD) for a proposed arc furnace; this is the change of voltage at the pcc that would be caused by a change in furnace var demand from no-load to a steady three-phase short-circuit on the electrodes. If the SCVD is greater than about 2%, consumers are likely to suffer sufficient annoyance to complain about lamp flicker. For an arc furnace installation with an SCVD of about 1.3%, the UIE flickermeter would typically indicate a maximum Pst value of about 1.

The SCVD criterion can be used to assess the maximum furnace rating that should be connected to a given system, but it can only be used to determine the rating of a compensator for flicker reduction provided that the compensator is capable of reducing all flicker frequencies in the visual annoyance range reasonably equally. Where a compensator has an acceptably linear fluctuation frequency versus speed of response characteristic up to about 25 Hz, then, if connected as shown in Figure 41.45, a steady state calculation of SCVD can be used to estimate its rating, i.e. the compensator current jI_c makes up the difference between the allowable −jI_s and the value of −jI_q. A high speed of response is essential for flicker reduction. It has been shown that if the compensator has a control-time delay of 10 ms, no matter what its rating, it can give very little reduction of flicker; with a time delay of 20 ms or greater, a range of frequencies within the visual annoyance range will be strongly accentuated. A thyristor switched capacitor compensator, for example, cannot achieve the necessary speed of response to reduce the arc-furnace flicker in the frequency range above 5 Hz, where the human eye is most sensitive.

The harmonic-compensated saturated reactor without a slope-correction circuit has been used to give flicker reduction of up to 3:1. It has been employed successfully in many installations as a bus-bar compensator (Figure 41.46(a)), having been designed on the basis of the SCVD criterion. The tapped-reactor/saturated-reactor scheme (Figure 41.46(b)) has been used to obtain a flicker reduction of up to 7:1 for a single arc-furnace. In this scheme the saturated reactors are single-phase devices and the slope correction is achieved by the tapped reactor winding ratios; this compensator inherently compensates for the unbalance loadings of the arc furnace and gives an instantaneous response. It produces considerable harmonic distortion and requires substantial filtering.

The TCR used as a bus-bar compensator can be made suitable for arc-furnace compensation with a flicker reduction of about 2:l. Voltage-sourced converters, because of their lower reactances and capability for much faster response, can outperform conventional TCRs; present indications point to a flicker reduction of about 4:1 being obtainable.

41.9.2 Phase balancing

Three-phase a.c. systems are intended to operate in a balanced mode. Unbalance can have detrimental effects on equipment connected to the system; rotating plant is particularly sensitive due to additional losses and consequent excessive heating. Most rotating plant is able to accept only 1 % of negative phase sequence voltage continuously and 2% for short periods.

Most loads of significant size are 3-phase and operate in a balanced manner. The main exceptions are arc furnaces, mentioned above, and substations supplying a.c. traction loads. Unbalance is also caused by the physical asymmetry of transmission lines; on long lines it is usual to minimise this unbalance by regular transposition of the conductors. In rural distribution systems, unbalance is sometimes caused by unequal distribution of the many single-phase loads between the three phases.

Arc furnaces are unlikely to cause adverse unbalance effects without first causing complaints of lamp flicker. The corrective action of any flicker suppression equipment will normally also limit unbalance contributions to acceptable levels.

The unbalance caused by traction systems has sometimes been corrected by means of conventional thyristor controlled equipment with one phase providing conventional power factor correction and the other two acting as a controllable Steinmetz circuit, Figure 41.47, for balancing the power component of traction load. The asymmetrical operation of the three phases of the SVC requires the shunt capacitors to be arranged to filter low order harmonics.

Converter technology now provides an alternative method of phase balancing with a nominally lower rating of equipment. A voltage (or current) sourced converter is used to generate an nps current which is equal in magnitude but in phase opposition to the nps current of the traction load. It thus acts as an active filter for unbalance.

41.9.3 Switched resistors

Switched resistors do not come under the strict heading of reactive power plant but have been used in certain situations to complement such plant. In situations where system transient stability is threatened by loss of synchronism due to the acceleration of a suddenly unloaded generator, switched braking resistors can provide a temporary substitute load for the generators and prevent excessive acceleration. By using thyristor switches instead of mechanical switches, fast repetitive switching can be used to aid in damping system swings.

Thyristor switched resistors have also been used with an arc furnace which comprised a significant proportion of the load on a set of gas turbine generators. In order to reduce maintenance requirements, it was desirable to operate the generators at a fairly steady load and to smooth out the rate of change of load when the furnace was suddenly switched off. This was done by thyristor switching of shunt resistors.

41.9.4 Harmonic currents and harmonic filter design

Many types of plant draw a distorted, non-sinusoidal current from the supply system, as, for instance, large rectifiers (aluminium smelters), controlled converters (traction drives, mine winders, rolling mills) and discharge lamps. The millions of low power, harmonic-producing devices used in the home and workplace, such as light dimmers, television receivers and personal computers also make a surprisingly large contribution to the total voltage distortion on many systems. Power transformers (due to magnetising currents), h.v.d.c. converter stations, SVCs and many other FACTS controllers are sources of waveform distortion in the network itself. These currents and the consequent voltage waveform distortions can be described in terms of fundamental and harmonic frequency components using Fourier analysis.

The harmonic content of voltages and currents can have undesirable disturbing effects on the system and its loads and on adjoining telecommunication circuits. Inductive or capacitive coupling between telephone and power lines induces harmonic interference over the audio-frequency range, and appropriate weighting factors are applied to the individual frequencies when assessing total distortion effect using measures such as telephone interference factor (TIF). The increased use of fibre-optic communication circuits has reduced the extent of this telephone interference.

Rotating generators and induction motors experience increased power loss due to the flow of harmonic currents. Waveform distortion can sometimes cause maloperation of electromagnetic as well as static protective relaying equipment. Shunt capacitor banks primarily for power factor correction are particularly affected by harmonics, as their impedance falls inversely with frequency so that they tend to act as ‘sinks’ for high frequency harmonic currents and may overload due to increased losses. Shunt capacitors form a resonant circuit with respect to the rest of the system at some frequency above the fundamental (i.e. at a super-synchronous frequency); if the resonant frequency is close to that of a local source (or sometimes even a remote source) of harmonic current, large and potentially damaging harmonic overvoltages and current magnifications can occur. For these reasons, harmonic distortion must be limited to acceptable levels by careful system design and, where necessary, by installation of shunt harmonic filter equipment at appropriate system bus-bars.

In order to minimise adverse harmonic effects, supply authorities apply harmonic current and voltage distortion limits, based on observed disturbances and on a desire to protect other consumers and telecommunication services. Compliance with the limitations at the point of common coupling with other loads may require reduction of system impedance by addition of lines or transformers, or the connection of the distorting load to a different point in the network. In case of converter loads the pulse number may have to be increased from 6 to 12, or even 24.

Connection of a properly designed harmonic filter consisting of a combination of inductive, capacitive and resistive elements at a suitable bus-bar will provide a low-impedance shunt path to the flow of harmonic currents generated by the distorting loads. The filter and the system will share the harmonic current injected by the load in the inverse ratio of their respective impedances. The desired impedance pattern of the filter circuit can usually be achieved by an appropriate combination of single-frequency tuned arms and broadband damped arms, Figure 41.48.

The system impedance varies with harmonic frequency in a complex manner, as most systems are not purely inductive. Systems have intrinsic resonant frequencies and, at these frequencies, there are dramatic changes in impedance from inductive to capacitive for only a few per cent variations in frequency. The supply system will, in general, have many different operating configurations and, to take account of the worst conditions, the system impedance vector is sometimes assumed to lie within a circular segment limited by maximum impedance angles. In simpler industrial circuits, the supply impedance is usually dominated by transformer impedance; this transformer impedance is assumed to increase in proportion to frequency to give the system harmonic impedance. This simplifying assumption can also be made (in the absence of other data) if the system up to the point of connection of the filters is not primarily composed of long lines or cables.

The system may contain several harmonic sources other than the particular known loads, or SVCs, or h.v.d.c. converters; in the assessment of the voltage distortion levels and filter component current ratings the effects of such ‘preexisting’ harmonics must be included.

The high-pass damped filter shown in Figure 41.48 is sometimes advantageous compared with sharply tuned arms if the filter is to be satisfactory over a wide range of system operating frequency (e.g. from 49 to 51 Hz); but such damped arms can have greater losses. The modified damped filter is of particular use if the frequencies of the harmonics to be passed are low, as the loss in the resistor can then be excessive at the fundamental frequency unless it is shunted by the series L–C circuit tuned to the fundamental frequency. Such a filter is specifically useful for suppressing unintended resonances at ‘non-characteristic’ frequencies (e.g. second harmonic) which are inherently low in current magnitude and thus would not give large loss in the resistor at these harmonic frequencies.

The optimum design of a combination of different filter arms (tuned, damped, etc.) to achieve a particular harmonic impedance pattern requires an economic assessment of the effects of choosing different relative proportions (in terms of fundamental Mvar) of the filter arms. The choice is governed not only by the harmonic performance requirements, but also by the fundamental plus harmonic ratings of the filter components—in particular, the capacitor banks. The effects of variations in the filter impedance with system frequency, temperature and component tolerances should be taken into account. The choice of the filter combination should also ensure that the non-characteristic harmonics (e.g. second, third or fourth order), which may be relatively small, are not excessively magnified by unintended resonances between the filter itself and the system. The need to minimise fundamental plus power–frequency losses in the filters also plays an important role in the final choice of the design.

41.10.1 Recent progress

There has been considerable progress in the field of var control during the last few years. A number of ‘future prospects’ of only 10 years ago have now been developed into practical FACTS controllers. In the field of shunt var compensation, several different types of voltage-sourced converter are being used in the various STATCOMs that are now in service in transmission systems. TCSCs are being used to provide series compensation of long transmission lines. The concept of the SSSC combined with a STATCOM to form a UPFC has been realised in a unit rated at ±160MVA and progress has been made towards the installation of an IPFC. In distribution systems there are a number of DVRs providing protection against voltage dips for sensitive loads. Several active filters have been put into service.

41.10.2 Further advances

41.10.3 Future applications of FACTS controllers