**The stator of a hydro generator is usually designed and constructed with open slots. Windings (bars or coils) are inserted into the stator core and then fixed with the non-magnetic slot wedges. Open slots result in slot harmonics which have an effect on some of the characteristics of the generator, such as total harmonic distortion, power losses, reactances, and excitation currents. One of the ways for reducing the negative effects of slot harmonics is the utilisation of magnetic wedges.**

The windings of a synchronous generator designed for power exceeding 1 MVA are usually made from rectangular conductors in the form of coils or bars and are placed into the open stator slots. Slot ripple occurs in the air gap flux density, as a result of changing reluctance due to the wide stator slot openings [1]. Pulsation frequency of the magnetic flux density in the air gap is determined by the number of stator slots Q and by synchronous rotating speed of the magnetic field fundamental wave ns in accordance with the equation:

(1)

Fig. 1 shows air gap flux density distribution along the air gap periphery of a salient pole hydro generator, calculated by means of finite elements methodology for two different stator voltages at no load operation, and Fig. 2 presents analysis of higher harmonics.

Due to magnetic induction pulses in the generator’s air gap, so called “surface losses” occur in a thin surface layer of the hydro generator’s rotor pole shoes. The thickness of that layer is determined by the electromagnetic wave penetration depth and is calculated in accordance with the following equation:

(2)

where:

*ρ* = pole iron resistance Ωm

*ω* = angular pulsation frequency s^{-1}

*μ* – pole iron permeability H/m

Surface losses due to magnetic induction pulsations occur in the damper winding placed in the rotor pole shoes as well. An increase of these pulsations results in an increase in current and power losses in the damper winding.

Analytical calculation of surface losses is very complex and is usually performed using more or less accurate equations which are supplemented by empirical coefficients. Due to the slotted stator core, geometric air gap between stator and rotor increases to a higher equivalent value calculated by means of the Carter coefficient [2]. An increase of the geometric air gap leads to a rise of the air gap excitation current by the same amount. Due to an increase of excitation current, power losses in the field windings also increases. Embedding magnetic wedges into stator slots decreases the equivalent slot opening, the Carter coefficient and the equivalent air gap.

The utilisation of slot wedges made of magnetic material in a synchronous generator gives the possibility to increase the efficiency of the machine. These wedges are used in order to reduce rotor pole surface and damper winding losses as well as losses due to magnetising current. Reduction of all these losses increases the generator’s efficiency by a value which is generally dependent on the optimisation of generator air gap parameters.

When considering the application of magnetic wedges, it is important to emphasise that wedge material can influence generator reactances as well. Therefore, optimising wedge properties should be carried out in such a way that the losses shall be minimised, while at the same time causing minimum possible change in reactance. By installing magnetic instead of non-magnetic wedges, the transverse (leakage) magnetic conductivity of the slot section, where the wedge is placed, increases.

The leakage magnetic flux through the magnetic wedge increases the stator winding’s leakage reactance. Due to the increase of the stator winding’s leakage flux, tooth saturation excitation current and its losses also increase. Taking into consideration all the above-mentioned consequences occurring due to the embedding of magnetic instead of non-magnetic slot wedges, each case should be optimised individually during the generator’s design, with an aim to minimise the losses and to keep the generator’s reactances as low as possible.

**Embedding technology of magnetic wedges in 34 MVA generators**

The first patents related to magnetic wedges were registered as early as from the turn of the 19th to 20th century. Although the basic theoretical benefits were known, application was almost negligible, as the key issues had not been solved, as well as installation technology and operational reliability of the selected concept. Embedding costs and installation related risks were more significant than the contribution of magnetic wedges to energy savings by means of increased efficiency of rotating electrical machines. The major drawback of most of the previous concepts of a stator with magnetic laminated wedges [3, 4] is unreliable mechanical connection between the wedge and the core sheets. This causes wedges to become loose and fall out of the slots during long time operation, particularly in the case of vertically placed machines.

There have been recent developments in the application of iron putty or composite materials based on soft iron laminates [5] and polyester resins for the embedding of magnetic wedges into the slot of a large electrical rotating machines. Iron putty is a dense plastic substance, made from specially shaped soft iron particles containing filling and compacting additives, mixed with epoxy resins. That substance, of relative permeability within the range of µ = 5 to 10, is used for filling the slots of high-voltage machines. Wedge embedding is followed by the process of curing and drying in the furnace, at a temperature of approximately 130°C, depending on material insulation class.

The diameter of the stator of a typical 34 MVA generator is 5,67 m. Performing total vacuum pressure impregnation (VPI) of the whole stator is usually not possible for such dimensions. In such VPI systems, the embedding of magnetic as well as non-magnetic wedges is performed prior the impregnation. The wedges during impregnation get stuck to the stator core and to the winding. The cohesion forces among the wedges, stator core and winding bar are therefore considerably higher than the electromagnetic forces which act on pulling the wedge out of the slot.

In the case of these generators, the stator winding bars are impregnated by VPI processes and tested prior to their insertion into the slots. The insertion and fixing of bars and wedges requirea simple and reliable procedure. It is expected that the magnetic wedges will have a lifetime equal to non-magnetic ones, i.e. that they will last during the generator’s entire operational lifetime. Based on the experience related to the application of magnetic wedges, the magnetic wedges made from laminate, that consists of a glass fibre as carrier, iron powder and epoxy resin as a binding agent, all in insulation class F, have been selected.

The bars are fixed in the slots with magnetic wedges by hard wedging, using the under-wedge strips of different thicknesses. The magnetic wedges are additionally fixed to the iron core by means of a two-component epoxy glue. A slot detail of these generators with the magnetic wedge is shown in Fig. 3.

The composition of the wedge material is: Glass fibre 7,8%, iron powder 74,9%, and epoxy resin 17,3%.

Prior to the embedding, tests of the electromagnetic, mechanical and thermal properties of the wedge material are performed in the laboratory.

Testing the temperature influence on mechanical and electromagnetic properties of magnetic wedges (accelerated ageing) was performed. Results of tests performed at a temperature of 200˚C during 500, 1000 and 1500 hours are shown in Table 1. No significant changes of properties were registered. Therefore it can be concluded that the embedded wedges could be able to withstand the designed operating conditions for a sufficient period of time.

Property | Standard | Unit | As delivered | Tested at 200ºC | ||

500 h | 1000 h | 1500 h | ||||

Thickness | mm | 6,01 | 5,98 | 5,95 | 5,92 | |

Density | ISO 1183 | g/cm^{3} |
3,508 | 3,492 | 3,485 | 3,478 |

Bending strength (at 23 ºC) | ISO 178 | MPa | 171 | 170 | 162 | 148 |

Electrical resistance | IEC 60167 | Ω cm | 5,7 x 10^{6} |
7,9 x 10^{6} |
8,2 x 10^{6} |
9,4 x 10^{6} |

Relative magnetic permeability µr at T |
Internal | – | 1,65 | 1,52 | 1,5 | 1,49 |

So far, experience based on one or two generators cannot be considered a sufficient reference for more than 25 years of generator operation. That is why the actual condition of the wedges is monitored and operation data is collected for these generators.

**Influence of magnetic wedges to losses and reactances**

Within the design process of hydro generator with magnetic and non-magnetic slot wedges, in house developed computer program for analytical electromagnetic calculation of synchronous generators with salient poles was used, as well as the FEM analyses. Rated and main data of the hydro generator are:

*S _{n}* = 34 MVA (rated power)

*Reactances and excitation current: Calculation*

When magnetic wedges, instead of non-magnetic ones, are embedded in the same generator’s stator slots, the reactance, rotor surface losses, excitation current under no-load condition and field winding losses will change. In this report, only the final results of analytical calculations are provided.

When performing the reactance calculation for magnetic and non-magnetic wedges, the only variable geometric value is a slot aperture width. The actual slot aperture dimension is replaced by a certain fictive, lower value, whereas the reduction amount depends on relative permeability of the wedge, the saturation of the leakage path through the stator slot and magnetic conditions in the generator. Accuracy of an analytical calculation depends on the estimation of wedge influence, of which the permeability is known, to the fictive reduction of the slot aperture.

In this specific calculation case, related to wedges which have a permeability value of µr = 2,8, the Carter factor decreased from 1,068 (non-magnetic wedges) to 1,011 (magnetic wedges) which is equivalent to a 5,4% reduction of the air gap.

The calculated excitation current at the generator’s rated load decreased by 2,88%, whereas the field winding losses decreased by 5,7%. The actual field winding loss reduction will be somewhat greater, as the temperature of the winding decreases, as a result of a total decrease in losses.

In accordance with the results of a conventional analytical calculation, the leakage reactance of the generator’s stator winding is 0,156 p.u. if the wedges are non-magnetic, (0,180 p.u. if the wedges are magnetic), which is an increase of approximately 15%. Due to the reduction of excitation current under no-load conditions, synchronous direct- and quadrature-axis reactances increase by approximately 5% for magnetic wedges. If the change of leakage reactance is taken into consideration, the total increase of synchronous reactance is approximately 8%.

The calculated value of unsaturated direct-axis transient reactance X’d increased from 0,294 to 0,306 p.u., whereas the saturated value increased from 0,28 to 0,293 p.u. As there is no excitation in the quadrature axis, quadrature-axis transient reactance X’q is equal to synchronous reactance Xq , i.e. it is increased by approximately. 8%. The sub-transient reactances in directand quadrature-axes also increased, due to increasing of the stator winding leakage reactance. Unsaturated direct-axis sub-transient reactance X”d is increased from 0,20 to 0,22, and the saturated value increased from 0,19 to 0,21 p.u.. Unsaturated quadrature-axis sub-transient reactance X”q is increased from 0,25 to 0,27, and the saturated value is increased from 0,24 to 0,26 p.u.

*Power losses*

Installing magnetic wedges reduces surface losses due to induction pulsations in the thin iron layer at the surface of rotor pole shoes. In this specific case, the wave penetration depth of the fundamental magnetic induction slot harmonics into the steel sheets at the rotor surface is 0,312 mm.

Total iron losses under no-load conditions were calculated by means of conventional analytical equations and thereafter were measured on the generator with magnetic wedges, and also on the generator with non-magnetic wedges. The only differences which were observed were in the surface losses on the rotor poles. In the design with non-magnetic wedges, total calculated iron losses are 121,7 kW, whereas the total losses with magnetic wedges are 106,4 kW. Loss reduction is about 15,3 kW, (12,6%), and is mostly related to the rotor surface losses.

A decrease of excitation current due to the installation of magnetic wedges is reflected in a decrease of losses in the field winding, from 107,8 to 102,3 kW, which is a reduction of 5,5 kW (5,1%).

The total reduction of losses as a result of the installation of magnetic wedges is 20,8 kW.

**Test results**

*Power losses*

On one out of the two 34 MVA generators, 10,5 kV, 187,5 min-1, cosϕ = 0,8, measurements were performed in a power plant, firstly with non-magnetic wedges, then with magnetic wedges. Power losses, reactance and other properties which might be affected by installation of magnetic wedges were measured.

Table 2 shows the results of the analytical calculation performed and the measurements of the power losses in iron at no-load and in the field winding at the rated operating conditions of the generator. Reductions of measured losses are 14,3% in iron at no load and 7,8 % in the field winding at rated operating conditions. The total reduction of measured power losses due to magnetic wedges is 26,15 kW. The main goal of their installation into the generator was achieved.

Power losses | Calculated (kW) | Measured (kW) | ||||

Non-magnetic wedge | Magnetic wedge | Difference | Non-magnetic wedge | Magnetic wedge | Difference | |

Iron at no-load | 121,7 | 106,4 | 15,3 | 124,9 | 107 | 17,9 |

Field winding at rated o. c. | 107,8 | 102,3 | 5,5 | 105,7 | 97,45 | 8,25 |

**Reactances**

The measured stator core leakage reactance with non-magnetic wedges is 0,12 p.u, whereas it amounts 0,16 p.u. with magnetic wedges, which is an increase of 33%. Synchronous reactance in direct axis (saturated value) obtained from the ratio of the short circuit and no-load excitation current is 1,04 for non-magnetic and 1,07 for magnetic wedges.

*Excitation currents*

The excitation current values for the rated load were obtained from the regulation curves, as the rated load conditions were not fulfilled during measuring. The measured excitation current is 655,4 A with non-magnetic wedge and 630,4 A with magnetic wedges.

**Analysis of the obtained testing results on the generators**

The measured excitation currents at rated load with non-magnetic and magnetic wedges match the calculated values quite well. The measurement difference is 3,8 %, whereas the calculation difference is 2,88%. Due to the reduced excitation current, the measured losses in the excitation winding are lower by approximately 8%, whereas the calculated losses are lower by about 6%.

Based on the results obtained by the measurement of iron losses performed with magnetic and with non-magnetic wedges, it cannot be precisely stated what the actual contribution of magnetic wedges to reduction of losses is due to different core temperatures during the tests with magnetic and non-magnetic wedges.

The generators with non-magnetic wedges had a leakage stator reactance of 0,12 p.u. (measured), whereas the calculated reactance was 0,16 p.u. The generators with magnetic wedges had a leakage reactance of 0,17 (measured), whereas the calculated reactance was 0,18 p.u. These differences might be caused by inaccuracy of analytical calculation and by discrepancies between the actual and assumed wedge permeability.

The synchronous reactance in direct axis, saturated value, for the generator with non-magnetic wedges, obtained by measurement, is 1,05 p.u.; and for the generator with magnetic wedges is

1,075 p.u. This is an increase is approximately 2,5%, whereas the assumed increase as per the calculation is 8%.

As per the calculation, subtransient direct-axis reactance X»d is 0,19 p.u. for non-magnetic and 0,21 p.u. for magnetic wedges. The generator with magnetic wedges, 0,34 p.u. was determined from the three phase sudden short circuit oscillograph and 0,30 p.u. was measured in the phase-pair power supply test. The difference between the subtransient reactance values of the generator with magnetic wedges is also caused by measuring which was performed with reduced voltage. Therefore it was not possible to determine the subtransient reactance at rated voltage. In general, it is to conclude that subtransient, transient and synchronous reactances increase when magnetic wedges are applied. Due to that, static and dynamic stability of generator might decrease, which have to be analysed separately for each specific case.

**Operation experience on generators with magnetic wedges**

The first one of the two 34 MVA, 10,5 kV, 187,5 min-1 generators, with the magnetic wedges, has been in commercial operation since September 2005, and the second one since November 2007. Since the first synchronisation, both generators have operated without any difficulties under the designed operating conditions. No user complaints related to generator operation have been received since installation.

**Conclusions**

The experiences acquired in design, installation, testing and exploitation of the magnetic slot wedges on two hydro generators of rated output 34 MVA, 10,5 kV, 50 Hz, 187,5 min-1, cosϕ = 0,8, vertical form, are presented. The fixation of magnetic wedges in the stator winding slots is described in detail. The results obtained in the design stage and the comparison of on-site testing results of the generator with non-magnetic wedges and the same generator with magnetic wedges show an increase in efficiency.

By installing the described magnetic wedges the surface losses in the generator rotor pole shoe iron were reduced by approximately 14%, whereas the losses in the field winding were reduced by approximately 8% due to the reduced excitation current by about 3,8%. The wedge permeability significantly influences rotor surface losses and slot leakage reactance. Influence of magnetic wedges to increasing of sub-transient, transient and synchronous reactances has been calculated and measured.

**References**

[1] CAM Weber and FW Lee: “Harmonics due to slot openings”, A.I.E.E. Trans., vol. 43, 1924.

[2] FW Carter: “The magnetic field of the dynamo-electric machine”, The Journal of the I.E.E., vol.64, 1926.

[3] FE Fisher: “Winding slot wedge”, US Patent 2386673, 1945.

[4] G Katz: “Powdered iron magnetic core materials”, US Patent 2783208, 1957.

[5] LB Simmonds: “Magnetic wedge and the process of making said wedge”, US Patent 3976902, 1976.

[6] Magnet: “Magnetostatic/Time-harmonic/Transient/Transient with Motion”, 2D&3D Tutorials, Infolytica Corporation, 2007.

[7] W Schuisky: “Berechnung elektrischer Maschinen”, Springer-Verlag, Wien, 1960.

[8] TA Lipo: “Introduction to AC machines design”, University of Wisconsin, 2004.

[9] PS Sergeev, et al: “Proektirovanie elektriceskih maschin”, Energia, Moscow1960 (in Russian).

[10] BJ Chalmers, et al: “Performance of some magnetic slot wedges in an open slot induction motor”. PROC.IEE, Vol. 114, 1967.

[11] H Keuth: “Magnetischer PROTOFER-Nutverschlus fur elektrische maschinen”, Siemens Zeitschrift, 1970.

[12] W Nurnberg, R Hanitsch, and J. Woelken: “Magnetische Nutverschlusskeile in elektrischen Maschinen”, VDE/IEC Symposium: Eigenschaften elektrisch leitender magnetischer Materialien 1971.

[13] D Ban, D Rodinis, and N Knezović: “Improvement of induction motor performances by closing the stator slots with magnetic material”, Koncar-stručne informacije1-2/87, page 18-21.

**Acknowledgement**

This article was published in *Electra* No. 274, June 2014, and is republished here with permission.

Contact Rob Stephen, Eskom, Tel 031 563-0063, rob.stephen@eskom.co.za