HIGH VOLTAGE TRANSMISSION TOWERS

Background

The towers support one or more overhead lines serving the energy distribution. Most frequently three-phase AC circuits are used requiring three live conductors each. To provide safety against lightning, earthed conductors are placed at the top of the tower, see Figures 1 and 2.

The live conductors are supported by insulators, the length of which increases with increasing voltage of the circuit. To prevent short circuit between live and earthed parts, including the surrounding environment, minimum mutual clearances are prescribed.
Mechanically speaking, the conductors behave like wires whose sag between their points of support depends on the temperature and the wire tension, the latter coming from the external loads and the pre-tensioning of the conductor. As explained in Section 2.4, the size of the tension forces in the conductor has a great effect upon the tower design.

2.2 Types of Towers

An overhead transmission line connects two nodes of the power supply grid. The route of the line has as few changes in direction as possible. Depending on their position in the line various types of towers occur such as (a) suspension towers, (b) angle suspension towers, (c) angle towers, (d) tension towers and, (e) terminal towers, see Figure 1. Tension towers serve as rigid points able to prevent progressive collapse of the entire line. They may be designed to serve also as angle towers.
To the above-mentioned types should be added special towers required at the branching of two or more lines.
In Figure 2 examples of suspension tower designs from four European countries are presented. Note similarities and mutual differences.

2.3 Functional Requirements

Before starting the design of a particular tower, a number of basic specifications are established. They are:
a. voltage.
b. number of circuits.
c. type of conductors.
d. type of insulators.
e. possible future addition of new circuits.
f. tracing of transmission line.
g. selection of tower sites.
h. selection of rigid points.
i. selection of conductor configuration.
j. selection of height for each tower.
The tower designer should notice that the specifications reflect a number of choices. However, the designer is rarely in a position to bring about desirable changes in these specifications. Therefore, functional requirements are understood here as the electrical requirements which guide the tower design after establishment of the basic specifications.
The tower designer should be familiar with the main features of the different types of insulators. In Figure 3 three types of insulators are shown. They are all hinged at the tower crossarm or bridge.

Figure 4 shows the clearances guiding the shape of a typical suspension tower. The clearances and angles, which naturally vary with the voltage, are embodied in national regulations. Safety against lightning is provided by prescribing a maximum value of the angle v. The maximum swing u of the insulators occurs at maximum load on the conductor.

2.4 Loads on Towers, Loading Cases

The loads acting on a transmission tower are:
a. dead load of tower.
b. dead load from conductors and other equipment.
c. load from ice, rime or wet snow on conductors and equipment.
d. ice load, etc. on the tower itself
e. erection and maintenance loads.
f. wind load on tower.
g. wind load on conductors and equipment.
h. loads from conductor tensile forces.
i. damage forces.
j. earthquake forces.
It is essential to realize that the major part of the load arises from the conductors, and that the conductors behave like chains able to resist only tensile forces. Consequently, the dead load from the conductors is calculated by using the so-called weight span, which may be considerably different from the wind span used in connection with the wind load calculation, see Figure 5.

The average span length is usually chosen between 300 and 450 metres.
The occurrence of ice, etc. adds to the weight of the parts covered and it increases their area exposed to the wind. Underestimation of these circumstances has frequently led to damage and collapse. It is, therefore, very important to choose the design data carefully. The size and distribution of the ice load depends on the climate and the local conditions. The ice load is often taken as a uniformly distributed load on all spans. It is, however, evident that different load intensities are likely to occur in neighbouring spans. Such load differences produce longitudinal forces acting on the towers, i.e. acting in the line direction.
The wind force is usually assumed to be acting horizontally. However, depending on local conditions, a sloping direction may have to be considered. Also, different wind directions (in the horizontal plane) must be taken into account for the conductors as well as for the tower itself. The maximum wind velocity does not occur simultaneously along the entire span and reduction coefficients are, therefore, introduced in the calculation of the load transferred to the towers.
The tensile forces in the conductors act on the two faces of the tower in the line direction(s). If they are balanced no longitudinal force acts on a tower suspending a straight line. For angle towers they result in forces in the angle bisector plane, and for terminal towers they cause heavy longitudinal forces. As the tensile forces vary with the external loads, as previously mentioned, even suspension towers on a straight line are affected by longitudinal forces. For all types of towers the risk of mechanical failure of one or more of the conductors has to be considered.
The loads and loading cases to be considered in the design are usually laid down in national regulations.

2.5 Overall Design and Truss Configuration

The outline of the tower is influenced by the user's functional requirements. However, basically the same requirements may be met by quite different designs. In general, the tower structure consists of three parts: the crossarms and/or bridges, the peaks, and the tower body.
Statically speaking, the towers usually behave like cantilevers or frames, in some cases with supplementary stays. For transmission lines with 100 kV voltage or more, the use of steel lattice structures is nearly always found advantageous because they are:

• easily adaptable to any shape or height of tower.
• easily divisible in sections suitable for transport and erection.
• easy to repair, strengthen and extend.
• durable when properly protected against corrosion.

By far the most common structure is a four-legged tower body cantilevering from the foundation, see Figure 6. The advantages of this design are:

• the tower occupies a relatively small area at ground level.
• two legs share the compression from both transverse and longitudinal loads.
• the square or rectangular cross-section (four legs) is superior to a triangular tower body (three legs) for resisting torsion.
• the cross-section is very suitable for the use of angles, as the connections can be made very simple.

The following remarks in this section relate mainly to a cantilever structure. However, many features also apply to other tower designs.
For a cantilever structure, the tower legs are usually given a taper in both main directions enabling the designer to choose the same structural section on a considerable part of the tower height. The taper is also advantageous with regard to the bracing, as it reduces the design forces (except for torsional loads).
The bracing of the tower faces is chosen either as a single lattice, a cross bracing or a K-bracing, possibly with redundant members reducing the buckling length of the leg members, for example see Figure 6. The choice of bracing depends on the size of the load and the member lengths. The most common type is cross bracing. Its main advantage is that the buckling length of the brace member in compression is influenced positively by the brace member in tension, even with regard to deflection perpendicular to the tower face.
Generally, the same type of bracing is chosen for all four tower body faces, most frequently with a staggered arrangement of the nodes, see Figure 7. This arrangement provides better space for the connections, and it may offer considerable advantage with respect to the buckling load of the leg members. This advantage applies especially to angle sections when used as shown in Figures 10 and 11, since it diminishes the buckling length for buckling about the 'weak' axis v-v. For further study on this matter see [1].

Irrespective of the type of bracing, the tower is generally equipped with horizontal members at levels where leg taper changes. For staggered bracings these members are necessary to 'turn' the leg forces. Torsional forces, mostly acting at crossarm bottom levels, are distributed to the tower faces by means of horizontal bracings, see Figure 8.

Cross arms and earthwire peaks are, in principle, designed like the tower itself. However, as the load on the cross arms rarely has an upward component, cross arms are sometimes designed with two bottom chords and one upper chord and/or with single lattice bracings in the non-horizontal faces.

2.6 Structural Analysis

Generally, the structural analysis is carried out on the basis of a few very rough assumptions:

• the tower structure behaves as a self-contained structure without support from any of the conductors.
• the tower is designed for static or quasi-static loads only.

These assumptions do not reflect the real behaviour of the total system, i.e. towers and conductors, particularly well. However, they provide a basis from simple calculations which have broadly led to satisfactory results.
Generally speaking, a tower is a space structure. It is frequently modelled as a set of plane lattice structures, which are identical with the tower body planes together with the planes of the cross arms and the horizontal bracings mentioned in Section 2.5.
In a simplified calculation a four-legged cantilevered structure is often assumed to take the loads as follows:
a. centrally acting, vertical loads are equally distributed between the four legs.
b. bending moments in one of the main directions produce an equal compression in the two legs of one side, and equal tension in the two legs of the other side. The shear forces are resisted by the horizontal component of the leg forces and the brace forces (thus, the leg taper has a significant influence on the design of the bracing).
c. torsional moments broadly produce shear forces in the tower body faces, i.e. in the braces.
A classical analysis assuming hinges in all nodes leads to very simple calculations. However, the effect of redundancies should be considered, especially concerning the forces and moments in the brace members.
Although this approach is satisfactory in most cases attention must be drawn to the function of redundant members, which in some cases may change the load distribution considerably. In addition, the effect of fixed connections (as opposed to hinged connections) must be considered, since they produce moments in the bracing members. The effect of eccentricities in the joints should also be taken into account, see Section 2.7.
Finally, the distribution of an eccentric horizontal load is studied. In Figure 9 the force H is acting at the cross arm bottom level. Without horizontal bracing in the tower, three tower body planes are affected by H. The deflections of the plane lattice structures of the tower body deform the rectangle ABCD to a parallelogram A¢B¢ C¢ D¢ . By adding member AC or BD this deformation is restricted and all four tower body planes participate in resisting the force H.

2.7 Detailing of Joints

The detailed design is governed by a number of factors influencing the structural costs once the overall design has been chosen, such as:

• simple and uniform design of connections.
• simple shaping of structural components.
• details allowing for easy transportation and erection.
• details allowing for proper corrosion protection.

As an introductory example of design and calculation, a segment of a four-legged tower body is discussed, see Figure 10. All members are made of angle sections with equal legs. The connections are all bolted without the use of gussets, except for a spacer plate at the cross bracing interconnection. This very simple design requiring a minimum of manufacturing work is attained by the choice and orientation of the leg and brace member sections.
By choosing the design described above, some structural eccentricities have to be accepted. They arise from the fact that the axes of gravity of the truss members do not intersect at the theoretical nodes. According to the bending caused by the eccentricities they may be classified as in-plane or out-of-plane eccentricities. In Figure 11, the brace forces C and T meet at a distance e_o from the axis of gravity. The resultant force DS produces two bending moments: M_e = DS´ e_o and M_f=DS´ e₁. These moments are distributed among the members meeting at the joint according to their flexural stiffness, usually leaving the major part to the leg members. As z-z is the 'strong' axis of the leg section, a resultant moment vector along axis v-v will be advantageous. This is achieved, when e_o=-e_1¢ . In this case C and T intersect approximately at the middle of the leg of the section. Usually this situation is not fully practicable without adding a gusset plate to the joint.
Additional eccentricity problems occur when the bolts are not placed on the axis of gravity, especially when only one bolt is used in the connection (eccentricities e_cand e_t).
The out-of-plane eccentricity causing a torsional moment, V = H´ e₂, acting on the leg may be measured between the axes of gravity for the brace members (see Figure 11). However, the torsional stiffness of the leg member may be so moderate - depending on its support conditions - that V cannot be transferred by the leg and, consequently, e₂ must diminish. The latter causes bending out-of-plane in the brace members.
The leg joint shown in Figure 10 is a splice joint in which an eccentricity e₃ may occur. In this case there is a change of leg section, or the gravity axis for the four (or two) splice plates in common does not coincide with the axis of the leg(s). For legs in compression the joint must be designed with some flexural rigidity to prevent unwanted action as a hinge.
The joint eccentricities have to be carefully considered in the design. As the lower part of the leg usually is somewhat oversized at the joint - this is, in fact, the reason for changing leg section at the joint - a suitable model would be to consider the upper part of the leg centrally loaded and thus, let the lower part resist the eccentricity moment. The splice plates and the bolt connections must then be designed in accordance with this model.
The bolted connections might easily be replaced by welded connections with no major changes of the design. However, except for small structures, bolted connections are generally preferred, as they offer the opportunity to assemble the structural parts without damaging the corrosion protection, see Section 2.8.
This introductory example is very typical of the design with angle sections. Nevertheless some additional comments should be added concerning the use of gussets and multiple angle sections.
The use of gussets is shown in Figure 12. They provide better space for the bolts, which may eliminate the in-plane eccentricities, and they allow for the use of double angle sections. In the latter case out-of-plane eccentricities almost vanish.

For heavily loaded towers it might be suitable to choose double or even quadruple angle sections for the legs. Figure 13 shows some possibilities.

Towers designed with other profiles than anglesIn principle any of the commercially available sections could be used. However, they have to compete with the angle sections as regards the variety of sections available and the ease of designing and manufacturing simple connections. So far only flat bars, round bars and tubes have been used, mostly with welded connections. The use is limited to small size towers for the corrosion reasons mentioned above.
In other contexts, e.g. high rise TV towers, circular sections may be more interesting because their better shape reduces wind action.
Construction joints and erection jointsThe tower structure usually has to be subdivided into smaller sections for the sake of corrosion protection, transportation and erection. Thus a number of joints which are easy to assemble on the tower site, have to be arranged. Two main problems have to be solved: the position and the detailing of the joints.
In Figure 14 two examples of the joint positions are shown. The framed structure is divided into lattice structure bodies, each of which may be fully welded, and stays. The cantilevered structure usually is subdivided into single leg and web members.

The two types of joints are lap (or splice) joints and butt plate joints. The former is very suitable for angle sections. The latter is used for all sections, but is mostly used for joints in round tube or bar sections. Figure 15 shows some examples of the two types.

2.8 Corrosion Protection

Today, corrosion protection of steel lattice towers is almost synonymous with hot-galvanising, possibly with an additional coating. The process involves dipping the structural components into a galvanic bath to apply a zinc layer, usually about 100 m m thick.
No welding should be performed after galvanizing, as it damages the protection. The maximum size of parts to be galvanized is limited by the size of the available galvanic bath.

3. CONCLUDING SUMMARY

• The overall design of a lattice tower is very closely connected with the user's functional requirements. The requirements must be studied carefully.
• A major part of the design loads on the tower results from the wind force on tower and equipment.
• The occurrence of an ice cover on the tower and equipment must be considered in the design.
• For towers supporting wires, differential loads in the wire direction must be taken into account.
• For systems of interconnected towers it must be considered that the collapse of one tower may influence the stability of a neighbouring tower.
• In most cases a cantilevered tower with four legs is preferred, as it offers structural advantages and occupies a relatively small ground area.
• The type of bracing greatly affects the stability of both legs and braces. K-bracings and/or staggered cross bracings are generally found advantageous.
• Horizontal braces at certain levels of the tower add considerably to its torsional rigidity.
• Angle sections are widely used in towers with a square or rectangular base, as they permit very simple connection design.
• Both in-plane and out-of-plane eccentricities in the connections must be considered.
• A proper, long lasting corrosion protection must be provided. The protection method influences the structural design.

Phasors Tutorial

Phasors

The generator at the power station which produces our AC mains rotates through 360 degrees to produce one cycle of the sine wave form which makes up the supply. In the next diagram there are two sine waves. They are out of phase because they do not start from zero at the same time. To be in phase they must start at the same time. The waveform A starts before B and is LEADING by 90 degrees. Waveform B is LAGGING A by 90 degrees. The next left hand diagram, known as a PHASOR DIAGRAM, shows this in another way. The phasors are rotating anticlockwise as indicated by the arrowed circle. A is leading B by 90 degrees. The length of the phasors is determined by the amplitude of the voltages A and B. Since the voltages are of the same value then their phasors are of the same length. If voltage A was half the voltage of B then its phasor would be half the length of B. All this has nothing to do with "set your phasors on stun". \ The voltages A and B cannot be added together directly to find the resulting voltage, because they are not in phase. The result of the two voltages can be found by completing the phasor diagram as shown on the right. The resulting voltage is slightly greater in amplitude than A or B, and leads B by 45 degrees and lags A by 45 degrees. Since the two voltages are 90 degrees apart, then the resultant can be found by using Pythagoras, as shown. Capacitance in AC Circuits Tutorial Here the ac current through the circuit leads the voltage by 90 degrees. Ohm's Law cannot be applied because current and voltage are not both at maximum at the same time. You need to find the capacitive reactance to be able to use Ohm's Law. In Fig. 1 above,  the two phasors are 180 degrees out of phase. The resultant voltage is found by subtracting B from A. The result is a voltage in phase with A but slightly smaller in amplitude. In Fig. 2 the two voltages are in phase and are added to find the result, which is in phase with A and slightly greater in amplitude. In Fig.3 a parallelogram must be constructed to find the resulting voltage.

R, C and L in an AC Circuit

Resistance in an AC Circuit

A resistor in an ac circuit behaves as it does in a dc one. It opposes the flow of current.The higher the resistance, the lower the current. The higher the voltage across the resistor, the higher the current through it. We can apply Ohm's Law. Voltage and current must both be rms or peak, not a mixture of the two. Inductive Reactance  The coil opposes the flow of ac current, as a resistor does in a dc circuit. This opposition is called inductive reactance, XL.  It is measured in ohms.  Ohm's Law can be applied, as in the top formula.  The bottom formula shows how inductive reactance is calculated.  f is the frequency of the applied voltage, and L is the value of the coil in     Henries.  It can be seen from this formula that the value of XL goes up as the frequency increases.  It also goes up if the value of the coil increases.  This means that as the value of L or f increases, the opposition to the flow of ac current increases, and the lamp will glow less. Capacitive in an AC Circuit  The capacitor opposes the flow of ac current, as a resistor does in a dc circuit.This opposition is called capacitive reactance, Xc. It is measured in ohms. Ohm's Law can be applied, as in the top formula. The bottom formula shows how capacitive reactance is calculated. f is the frequency of the applied voltage, and C is the value of the capacitor in Farads. It can be seen from this formula that the value of Xc goes down as the frequency increases. It also goes down if the value of the capacitor increases. This means that as the value of C or f increases, the opposition to the flow of ac current decreases,  R, C and L in an AC Circuit  The resistor, the capacitor and the coil all oppose the flow of ac current.Their combined opposition is called impedance, Z. Ohm's Law can be applied, as shown in the top formula. The higher the impedance, the lower the current. The resistor has resistance. The capacitor has capacitive reactance. The coil has inductive reactance. All of these values are measured in ohms. However, impedance is not calculated by adding these values. The bottom formula must be used. If you are familiar with Pythagoras, this is another application of it. When coupling one device to another, such as an amplifier to a loudspeaker, the output impedance of the amplifier and  the input impedance of the speaker must be the same, to give optimum transfer of power from one to the other.

Zener Diode Tutorial

Zener Diode

The Zener diode is operated in reverse bias mode (positive on its cathode). It relies on the reverse breakdown voltage occurring at a specified value. This value is printed on it.It has two main applications. 1. as a reference source, where the voltage across it is compared with another voltage. 2. as a voltage regulator, smoothing out any voltages variations occurring in the supply voltage across the load. When being used a voltage regulator, if the voltage across the load tries to rise then the Zener takes more current. The increase in current through the resistor causes an increase in voltage dropped across the resistor. This increase in voltage across the resistor causes the voltage across the load to remain at its correct value. In a similar manner, if the voltage across the load tries to fall, then the Zener takes less current. The current through the resistor and the voltage across the resistor both fall. The voltage across the load remains at its correct value.

Half Wave Rectifier

The voltage at point A does the opposite of that at point B. When A is increasing in a positive direction, B is increasing in a negative direction. It is rather like the two ends of a see-saw. During the first half cycle of the waveform shown on the left, A is positive and B is negative. The diode is forward biased and current flows around the circuit formed by the diode, the transformer winding and the load. Since the current through the load, and the voltage across the load are in the same proportions, then the voltage across the load is as shown in the right hand diagram, during the first half cycle. During the second half cycle, A and the anode are negative, B and  the cathode are positive. The diode is reverse biased and no current flows. This is indicated by the horizontal line in the right hand diagram. The diode only conducts on every other half cycle. There is one pulse for every cycle in. i.e 50 pulses per second (in the UK) The diode only conducts during half the cycle. Hence, HALF-WAVE RECTIFICATION. The rectified voltage is DC (it is always positive in value). However, it is not a steady DC but PULSATING DC. It needs to be smoothed before it becomes useful. If the diode is reversed then the output voltage is negative.

Torque versus Speed(Steper Motor)

Torque versus Speed

An important consideration in designing high-speed stepping motor controllers is the effect of the inductance of the motor windings. As with the torque versus angular position information, this is frequently poorly documented in motor data sheets, and indeed, for variable reluctance stepping motors, it is not a constant! The inductance of the motor winding determines the rise and fall time of the current through the windings. While we might hope for a square-wave plot of current versus time, the inductance forces an exponential, as illustrated in Figure 2.10: Figure 2.10 The details of the current-versus-time function through each winding depend as much on the drive circuitry as they do on the motor itself! It is quite common for the time constants of these exponentials to differ. The rise time is determined by the drive voltage and drive circuitry, while the fall time depends on the circuitry used to dissipate the stored energy in the motor winding. At low stepping rates, the rise and fall times of the current through the motor windings has little effect on the motor's performance, but at higher speeds, the effect of the inductance of the motor windings is to reduce the available torque, as shown in Figure 2.11: Figure 2.11 The motor's maximum speed is defined as the speed at which the available torque falls to zero. Measuring maximum speed can be difficult when there are resonance problems, because these cause the torque to drop to zero prematurely. The cutoff speed is the speed above which the torque begins to fall. When the motor is operating below its cutoff speed, the rise and fall times of the current through the motor windings occupy an insignificant fraction of each step, while at the cutoff speed, the step duration is comparable to the sum of the rise and fall times. Note that a sharp cutoff is rare, and therefore, statements of a motor's cutoff speed are, of necessity, approximate. The details of the torque versus speed relationship depend on the details of the rise and fall times in the motor windings, and these depend on the motor control system as well as the motor. Therefore, the cutoff speed and maximum speed for any particular motor depend, in part, on the control system! The torque versus speed curves published in motor data sheets occasionally come with documentation of the motor controller used to obtain that curve, but this is far from universal practice! Similarly, the resonant speed depends on the moment of inertia of the entire rotating system, not just the motor rotor, and the extent to which the torque drops at resonance depends on the presence of mechanical damping and on the nature of the control system. Some published torque versus speed curves show very clear resonances without documenting the moment of inertia of the hardware that may have been attached to the motor shaft in order to make torque measurements. The torque versus speed curve shown in Figure 2.11 is typical of the simplest of control systems. More complex control systems sometimes introduce electronic resonances that act to increase the available torque above the motor's low-speed torque. A common result of this is a peak in the available torque near the cutoff speed.

Half Stepping and Micro Stepping

So long as no part of the magnetic circuit saturates, powering two motor windings simultaneously will produce a torque versus position curve that is the sum of the torque versus position curves for the two motor windings taken in isolation. For a two-winding permanent magnet or hybrid motor, the two curves will be S radians out of phase, and if the currents in the two windings are equal, the peaks and valleys of the sum will be displaced S/2 radians from the peaks of the original curves, as shown in Figure 2.2: Figure 2.2 This is the basis of half-stepping. The two-winding holding torque is the peak of the composite torque curve when two windings are carrying their maximum rated current. For common two-winding permanent magnet or hybrid stepping motors, the two-winding holding torque will be: h2 = 20.5 h1 where: h1 -- single-winding holding torque h2 -- two-winding holding torque This assumes that no part of the magnetic circuit is saturated and that the torque versus position curve for each winding is an ideal sinusoid. Most permanent-magnet and variable-reluctance stepping motor data sheets quote the two-winding holding torque and not the single-winding figure; in part, this is because it is larger, and in part, it is because the most common full-step controllers always apply power to two windings at once. If any part of the motor's magnetic circuits is saturated, the two torque curves will not add linearly. As a result, the composite torque will be less than the sum of the component torques and the equilibrium position of the composite may not be exactly S/2 radians from the equilibria of the original. Microstepping allows even smaller steps by using different currents through the two motor windings, as shown in Figure 2.3: Figure 2.3 For a two-winding variable reluctance or permanent magnet motor, assuming no saturating magnetic circuits, and assuming perfectly sinusoidal torque versus position curves for each motor winding, the following formula gives the key characteristics of the composite torque curve: h = ( a2 + b2 )0.5 x = ( S / (/2) ) arctan( b / a ) Where: a -- torque applied by winding with equilibrium at 0 radians. b -- torque applied by winding with equilibrium at S radians. h -- holding torque of composite. x -- equilibrium position, in radians. S -- step angle, in radians. In the absence of saturation, the torques a and b are directly proportional to the currents through the corresponding windings. It is quite common to work with normalized currents and torques, so that the single-winding holding torque or the maximum current allowed in one motor winding is 1.0.

Stepper Motor Types

Variable Reluctance Stepper Motor

There are basically three types of stepping motors; variable reluctance, permanent magnet and hybrid. They differ in terms of construction based on the use of permanent magnets and/or iron rotors with laminated steel stators. The variable reluctance motor in the above illustration has four "stator pole sets" (A, B, C,), set 15 degrees apart. Current applied to pole A through the motor winding causes a magnetic attraction that aligns the rotor (tooth) to pole A. Energizing stator pole B causes the rotor to rotate 15 degrees in alignment with pole B. This process will continue with pole C and back to A in a clockwise direction. Reversing the procedure (C to A) would result in a counterclockwise rotation. Permanent Magnet Stepper Motor The permanent magnet motor, also referred to as a "canstack" motor, has, as the name implies, a permanent magnet rotor. It is a relatively low speed, low torque device with large step angles of either 45 or 90 degrees. It's simple construction and low cost make it an ideal choice for non industrial applications, such as a line printer print wheel positioner. Unlike the other stepping motors, the PM motor rotor has no teeth and is designed to be magnetized at a right angle to it's axis. The above illustration shows a simple, 90 degree PM motor with four phases (A-D). Applying current to each phase in sequence will cause the rotor to rotate by adjusting to the changing magnetic fields. Although it operates at fairly low speed the PM motor has a relatively high torque  Hybrid Stepper Motor Hybrid motors combine the best characteristics of the variable reluctance and permanent magnet motors. They are constructed with multi-toothed stator poles and a permanent magnet rotor. Standard hybrid motors have 200 rotor teeth and rotate at 1.80 step angles. Other hybrid motors are available in 0.9ºand 3.6º step angle configurations. Because they exhibit high static and dynamic torque and run at very high step rates, hybrid motors are used in a wide variety of industrial applications.