A Synchronization of Permanent Magnet Synchronous Generator Dedicated for Small and Medium Hydroelectric Plants

Abstract

This article presents the simulation results of synchronization of a permanent magnet synchronous generator (PMSG) dedicated for a hydroelectric plant without power converter devices. The proposed machine design allows to connect a generator to the grid in two different ways. With the first method, the machine is connected to the grid in a similar way as in the case of an electrically excited synchronous generator. The second method is a direct line-start process based on asynchronous torque—similar to asynchronous motor start. Both methods can be used alternately. The advantages of the presented design are elimination of converter devices for starting the PMSG, possibility of use in small and medium hydroelectric power plants, operation with a high efficiency and high power factor in a wide range of generated power, and smaller dimensions in comparison to the generators currently used. The described rotor design allows for the elimination of capacitor batteries for compensation of reactive power drawn by induction generators commonly used in small hydroelectric plants. In addition, due to the high efficiency of the PMSG, high power factor, and appropriately selected design, the starting current during synchronization is smaller than in the case of an induction generator, which means that the structural elements wear out more slowly, and thus, the generator’s service life is increased. In this work, it is shown that PMSG with a rotor cage should have permanent magnets with an increased temperature class in order to avoid demagnetization of the magnets during asynchronous start-up. In addition, manufacturers of such generators should provide the number of start-up cycles from cold and warm states in order to avoid shortening the service life of the machine. The main objective of the article is to present the methods of synchronizing a generator of such a design (a rotor with permanent magnets and a starting cage) and their consequences on the behavior of the machine. The presented design allows synchronization of the generator with the network in two ways. The first method enables synchronization of the generator with the power system by asynchronous start-up, i.e., obtaining a starting torque exceeding the braking torque from the magnets. The second method of synchronization is similar to the method used in electromagnetically excited generators, i.e., before connecting, the rotor is accelerated to synchronous speed by means of a water turbine, and then, the machine is connected to the grid by switching on the circuit breaker. This paper presents electromagnetic phenomena occurring in both cases of synchronization and describes the influence of magnet temperature on physical quantities.

1. Introduction

Synchronization is the process of connecting a generator to the power system, which must be performed very carefully. Electrical, mechanical, and human components have a significant impact on the dynamic synchronization process. In the electrically excited synchronous generators commonly used in the many of power systems, the frequency and voltage of the disconnected generator must be closely matched to the frequency and voltage occurring on the power system side [1,2,3,4]. The instantaneous value of voltage induced in the opened stator terminals must be close to the instantaneous value of the voltage on the grid. The connection of many synchronous generators operating in parallel creates a power system. These generators are hydrogenerators (with the salient pole rotors) and turbogenerators (with cylindrical rotors). These machines are connected by transmission lines supplying power system receivers. The disconnected generator can be connected in parallel with the grid by driving the rotor at synchronous speed, e.g., by a turbine and adjusting its excitation current so that the voltage at opened stator terminals is equal to the grid voltage. In addition, the phase sequence must be maintained.

Failure of the synchronization procedure causes out-of-phase synchronization, mainly caused by: wiring failure during start-up, delay during breaker closure, flash-over in the breaker’s contacts, wrong setting of the synchronous system, and a problem in manual synchronization [5].

A special case of synchronization is connecting a permanent magnet synchronous generator to the power system. The frequency of the electromotive force induced at the opened stator terminals is matched by regulating the rotational speed of the hydroturbine. Conversely, the value of the back electromotive force (back EMF) depends on the type and dimensions of the permanent magnets in the rotor. At the rated speed, the back EMF value is determined by the temperature and magnetic properties of magnets. The higher the temperature, the lower the back EMF value. The selection of the type and size of permanent magnets is determined by obtaining the desired operating parameters of the generator, such as induction in the airgap, power factor values in the entire load range, and overload (work stability).

During synchronization, before the circuit breaker between the generator terminals and the power system is closed, the frequency of the voltage induced in the open armature terminals is regulated by the speed of the rotating magnetic field (rotor speed), while after synchronization, the power system frequency regulates the speed of the rotating magnetic field (the breaker is closed).

The rotor position and speed must be closely matched when the hydrogenerator is connected to the power system to eliminate the transient torque required to synchronize the rotor [5]. If the frequency of the voltage induced on the opened armature (derived from the angular velocity) differs significantly from the frequency in the power system, a big transient torque will occur.

The most important consequences of incorrect synchronization are the following: damage to stator winding and the step-up transformer due to high currents, damage to the generator rotor and water turbine due to mechanical stresses caused by rapid acceleration or deceleration of the rotating masses, and reduced service life of the generator components [6].

IEEE standards [7,8] clearly describe the limits of voltage, frequency, and phase shift fluctuations on the generator and power system sides that guarantee correct synchronization:

• Phase shift angle difference between generator-side voltage and the power system: ±10 deg;
• Generator-side voltage relative to the power system: 1.0–1.05 U_N;
• Frequency fluctuations: ±0.067 Hz.

In the hydroelectric plants, asynchronous generators are common due to their availability and quick delivery from the manufacturers. Another type of machine that is increasingly used is the permanent magnet synchronous generator. Induction machines operating in hydroplants are induction motors operating in generator mode. This is associated with a nonoptimal number of stator winding turns per pole and phase, low power factor (0.7–0.85), and low efficiency. Low power factor requires the use of capacitor banks to compensate for reactive power. Synchronization of the induction machine with the network takes place as an asynchronous start-up in motor operation. During start-up, there are currents 5–8 times greater than the rated current flows through the stator winding. In addition, the starting torque generated exceeds the rated torque by two times (the smaller the motor, the greater the starting torque). Due to the high moment of inertia of the water turbine, the start-up time may be prolonged, which may result in a reduction of the voltage on the hydroelectric plant’s supply bus and negatively affect adjacent generating units. Manufacturers are able to supply induction motors with a synchronous speed range of 600–3000 rpm. For lower speeds, gears are used. This adds another element, reducing the efficiency of the entire hydrounit and adding another element that wears out and requires frequent inspections [9,10,11].

PMSGs do not have many of the above disadvantages. They have high efficiency and a high power factor (close to 1) in a very wide range of torque on the shaft (0.3–1 T_N). They are characterized by smaller dimensions than induction machines. In many cases, high efficiency, and consequently, a small amount of heat released, favors the complete elimination of the fan or reducing its diameter, which helps reduce the mechanical losses. A particularly large gain in efficiency is especially visible for a larger number of poles (2p > 10), i.e., in a range that exceeds the number of machines in the portfolio of most manufacturers of induction motors. Therefore, the use of PMSGs eliminates the use of gears and allows the construction of a hydrounit with only one shaft.

There are many types of turbines that exist in hydroelectric plants, depending on the level of water fall and the amount of its flow [12]. In the case of water turbines, optimal electrical generator solutions are sought that meet a number of requirements, such as high efficiency, operational stability, reliability, resistance to centrifugal forces during turbine run-up, and relatively low cost.

Common machines used in hydroelectric plants are synchronous generators with magnets inside the rotor or with magnets glued to the cylindrical surface of the rotor and without a damping cage [13,14,15].

Synchronization of these machines is quite difficult. Despite bringing the rotor speed to the grid frequency, during synchronization, quite significant unsteady states are created that generate large torsional torques and huge stator currents. This is the result of the difference in voltage levels on the generator and grid side (which mainly depends on the temperature of the permanent magnets). Most often, however, PMSG generators work with frequency converters, which significantly help in synchronization and at the same time allow the generator to work with different rotor speeds [16], which significantly improves the work of the hydrounit with a variable flow of water flowing into the turbine. However, they affect the increase in investment costs by adding a converter.

Another new, innovative type of generator is the modular generator [17]. There are many stator and rotor modules on one shaft, each with the same power. The number of segments depends on the turbine power, which can be added and subtracted at will. This significantly simplifies the design and its cost. In the case of small machines, the cost of documentation is the largest part of the price of the entire machine. In addition, this generator can operate in a wide range of rotational speeds: 50–519 rpm. Different configurations of stator winding connections allow the generator to operate with different power, rotational speed, and voltage. The honeycomb structure and standardization of bearing sizes and bearing discs allow for production dedicated to a given customer regardless of the type of mounting (feet or flange). The disadvantage of this solution is the use of a dedicated converter for this solution.

Another interesting design solution for a generator in a hydroelectric power plant is a hybrid excitation synchronous generator (HESG) [18]. This type of machine combines the advantages of permanent magnets synchronous machines and electrically excited synchronous machine (EESM). In this solution, permanent magnets create the main flux of the generator, whereas current flowing by excitation winding is used to regulate the back EMF during the synchronization process and to control the generation of reactive power during the generating mode. The use of permanent magnets in the rotor reduces the excitation current and reduces losses in the rotor winding, thus significantly increasing efficiency. The excitation current regulation enables the power factor to be adjusted in the range of 0.95 (cap.) to 0.8 (ind.). Unfortunately, this machine design significantly increases the cost of production, because there are two types of salient pole rotors on one shaft—one containing magnets and a damping cage and the other containing only the excitation winding. The salient pole rotor requires winding the coils on the edge of the stump, which requires many man-hours.

There are many solutions for generators in small hydropower plants. In the case of PMSGs, most of them are connected to the power system using a converter, which provides smooth synchronization. However, there are no articles in the literature describing the electromagnetic phenomena occurring during connecting PMSG to the power system without a converter. There is a lack information of maximum current and torque on the shaft, which has a huge impact on the life time of the hydrounit.

There is a lack of publications in the literature describing the operation of PMSG with a rotor cage. Most of the works focused on PMSG machines with magnets placed on the rotor surface [19]. These machines do not have a large rotor diameter, and therefore, the effect of the centrifugal force on permanent magnets is not critical. In the case of hydrosets with power above 500 kW, electrically excited synchronous generators are commonly used (with cylindrical and salient pole rotors). On the other hand, induction machines are commonly used up to 500 kW. For power up to 100 kW, PMSG with magnets on the rotor surface are increasingly common. This is clearly visible in the case of a hydrounit with adjustable rotational speed depending on the amount of water [20,21]. Adding a cage to the rotor in PMSG improves the operating properties of the generator. This cage generates an asynchronous torque, enabling the start-up of the machine, and dampens the swinging of the rotor during generator operation during disturbances in the power system. This increases the cost of manufacturing the machine itself by adding rotor bars and segments containing these bars. In addition, it adds technological processes such as soldering the aforementioned structural elements. The expanded design does not significantly increase the weight of the generator or its external dimensions compared to PMSG with magnets on the rotor surface. There are many scientific papers describing permanent magnet synchronous machines with magnets inside the rotor (interior PMSMs and PMSGs). They often do not have a cage and must be powered by an inverter. Most often, these studies concern small electrical machines [22,23,24,25]. Rotor cages are mainly used in line-start permanent magnet synchronous motors (LSPMSMs). In such a case, they allow the motor to start with a load, generating a starting torque greater than the loading torque and the braking torque from the permanent magnets (the braking torque is particularly strong at low rotational speeds) [26,27,28].

The paper presents the results of the PMSG synchronization simulation with the power system. The advantages of LSPMSMs were used during the generator design. The rotor contains permanent magnets and a cage. This solution enabled the generator to be synchronized with the power system by asynchronous start-up, i.e., obtaining a starting torque exceeding the braking torque from the magnets. The second method of synchronization is in a similar way to that used in electromagnetically excited generators, i.e., before connecting, the rotor was accelerated to synchronous speed by means of a water turbine, and then, the machine is connected to the grid by switching on the circuit breaker. The paper presents electromagnetic phenomena occurring in both cases of synchronization and describes the influence of magnet temperature on physical quantities.

Therefore, for the purposes of this article, a two-dimensional field-circuit model of the PMSG generator was built, adapted to perform the analysis of synchronization with the power system in two ways. The first is the synchronization of the hydrogenerator by asynchronous start-up, and the second is the classic synchronization that is performed in electrically excited synchronous generator. The new machine design was chosen to enable synchronization identical to that of asynchronous generators and electrically excited synchronous generator (with salient pole and cylindrical rotor). This procedure allows for replacing machines at the workstation with an existing state in the hydropower plant and a new one. In this way, the existing state can be modernized and its reliability and efficiency can be increased. This article presents the design solution of the PMSG and describes the electromagnetic phenomena occurring during synchronization with the power system.

2. Description of Field-Circuit Model of Investigated PMSG

The numerical calculations are based on the field-circuit model of the hydrogenerator. The circuit equations for the rotor and stator windings based on Kirchhoff’s laws are coupled with the field equations used to describe the time-spatial distribution of the electromagnetic field [29]. Field and circuit equations are solved in each time step. The magnetic field distribution is used to determine the flux–voltage relationship. The solution of the part of the electric circuit are the values of the currents, which are the source of the magnetic field.

By solving Ampere’s law and expressing the magnetic flux density by the circulation of the potential of the magnetic vector A, the distribution of the magnetic field can be determined.

$$rot(v\cdot rotA)=J_t$$

(1)

where J_t is the total current density, A is the magnetic vector potential, and ν is the reluctivity.

The total current density vector J_t takes into account all sources of magnetic field in the model face. The current density vector includes eddy currents induced due to changes in the magnetic field in time and velocity of the conducting parts and magnetizing currents expressing the presence of a permanent magnet in the system. Solving the voltage–flux equations of the two-dimensional model uses the scalar potential V [29].

$$curl(\nu \cdot curlA)=J_t+J_m$$

(2)

$$div(\sigma \cdot gradV)=div\left(\sigma {\displaystyle \frac{\partial A}{\partial t}}\right)$$

(3)

where σ is the conductivity.

$$J=-\sigma \left({\displaystyle \frac{\partial A}{\partial t}}+gradV\right)$$

(4)

$$J_m=curlM$$

(5)

where J_m is the magnetization current density vector in the region with the permanent magnet of magnetization vector M.

In the two-dimensional field-circuit model, the field equations are extended by the equations describing windings. For the stator winding, the equation is presented as follows:

$$u_s=R_s{i}_s+{\displaystyle \frac{\partial }{\partial t}}{L}_s{i}_s+{\displaystyle \frac{\partial }{\partial t}}\Psi$$

(6)

where u_s is the vector of stator winding supply voltages, R_s is the matrix of stator winding resistance, i_s is the vector of stator winding currents, L_s is the inductance of stator winding ends, and Ψ is the vector of stator winding flux linkage, defined by magnetic potential A.

The simulations were performed using a two-dimensional model of the hydrogenerator (Figure 1) created in Ansys Electronics software (2023/R1). This software is designed to analyze the electromagnetic field distribution utilizing the finite element method The ratings of the generator are presented in

Table 1. Rated data of investigated PMSG.

Parameter Name	Symbol	Value	Unit
Generated active power	PN	800	kW
Terminal voltage	UN	690	V
Stator current	ISN	669	A
Synchronous speed	nN	250	rpm
Power factor	cos φN	0.97	-
Frequency	fN	50	Hz
Rated torque on the shaft	TN	30.56	kNm
Efficiency at rated load	ηN	97.5	%
Generator moment of inertia	JG	2210	kg m2

. This generator is placed in a vertical position on the flange. The cooling system is IC411, i.e., the machine is cooled by air washing the ribs of the casing generated by the fan on the shaft. The machine has rolling bearings. The bearing discs are adapted to transfer the forces from the water turbine. In addition, the construction is adapted to withstand a run-up speed of 2.5 times the synchronous speed.

The field-circuit model of the hydrogenerator reflects the magnetic circuit for the magnetic flux path. This model takes into account nonlinear magnetization curves of the rotor and stator cores, the possibility of inducing eddy currents in the rotor cage, rotor movement, and permanent magnets (type: N45SH) in the rotor. The field model is extended by the circuit model containing voltage sources, resistances, and inductances of the end-winding part of stator winding and the rotor cage short-circuiting segments. The model neglects skin effects in the stator coils and eddy currents in the stator and rotor laminations. The rotor bars are short-circuited by a short-circuiting ring surrounding all the rotor bars. The bars and ring-shaped segments are made of copper.

The numerical model is based on verified material properties obtained from designed and implemented PMSGs for small hydroelectric power plants (first type: GZMV-1528S, S = 300 kVA, n = 214 rpm, η = 96.4%, cos φ = 0.97; second type: GZMV-1112S, S = 200 kVA, n = 500 rpm, η = 96.6%, cos φ = 0.98). These generators have magnets and a cage in the rotor, similar to the presented machine. The mentioned generators collect positive reviews and do not cause any operational problems. They were launched in 2022.

Figure 2 shows a fragment of the model with a visible finite element grid. The considered model contains 15,712 finite elements and 22,038 nodes (one third of the model). The electromagnetic field equations are solved utilizing tow boundary conditions. The first Dirichlet boundary condition is located on the outer diameter of the stator core (edge Γ2), where the magnetic potential vector was set at the level of 0. The periodic magnetic potential condition was set on the edge Γ1. It allows the construction of only one third of the model (the number of parallel branches is 3), which contributes to reducing the computation time.

3. Technical Data of Investigated PMSG

Synchronization of PMSG without rotor cage and without a suitable converter system is almost impossible. This is due to the lack of a damping cage in the rotor, in which eddy currents would be induced during the transient state and would create the torque of falling into synchronism. In addition, synchronization is hindered by the magnetic properties of permanent magnets, which are strongly dependent on temperature. The higher the temperature, the lower the induced electromotive force on the stator terminals. The greater the difference between the voltage on the grid and generator side, the greater the currents flow and greater torques are created on the hydrogenerator shaft in the transient state. In order to eliminate the converter system and enable synchronization of PMSG with the power system, the rotor design was modified—a rotor cage was added. A proper arrangement of magnets allows to provide a high power factor in a wide load range. Therefore, the value of the electromotive force with open armature terminals during generator operation is higher than the recommended value of 1.05 U_N [7,8] and equals 1.07 U_N (Figure 3a). An appropriately selected layout of stator and rotor slots and permanent magnets allows obtaining low values of higher harmonics (Figure 3b). The total harmonic distortion (THD) coefficient equals 0.32%, which should be considered as a very good result.

Optimization of the electromagnetic circuit allowed to obtain low cogging torque. Figure 4 shows the cogging torque curve for two stator slot pitches. Cogging torque is an unfavorable torque, which causes undesirable pulsations of the electromagnetic torque, additional power losses, vibrations, and noise, resulting in reduced efficiency. It is created as a result of the interaction of the magnetic field from the permanent magnets placed in the rotor and the uneven air gap between the stator and the rotor. The stability of PMSG operation is ensured by the appropriate overload capacity, which equals 1.8 (Figure 5).

The water turbine rarely operates at its rated power. In the annual cycle, the amount of power generated for the system depends on the amount of water available. Therefore, the PMSG has been designed to achieve high efficiency (Figure 6) in a wide range of generated power. In addition, the power factor should have a high value in a wide range of generated power. Small hydroelectric plants with PMSGs operate with a low power factor, which is why they generate or consume quite a lot of reactive power. It is common for owners of such plants to add capacitor banks or inductive chokes.

Adding a cage in the generator’s rotor enables synchronization with the grid through asynchronous starting—similar to the case of induction motors. During the starting process, the flux of permanent magnets contributes to the generation of a braking torque that reduces the resulting asynchronous torque coming from the rotor cage. This phenomenon is particularly noticeable in the low rotor speed ranges. The electromagnetic circuit has been selected so that the resultant torque is large enough to set the generator in motion and achieve synchronous speed with an appropriately high synchronism entry torque (Figure 7).

4. Calculation Results

Using the described numerical model of PMSG, two types of synchronization were investigated: similar to what occurs in electrically excited synchronous generators and by direct start-up. During stimulation, the generator is coupled to the water turbine on a common shaft (Figure 8). Synchronization is achieved by switching on the breaker.

4.1. Synchronization Similar to That of Electrically Excited Synchronous Generators

The studied hydrogenerator is modeled in a single-machine system. In the simulation, the generator is connected to the power system at instant t = 0.02 s for a phase shift close to 0 deg. The moment of water turbine inertia is similar to the generator moment of inertia and equals 2210 kg m². During the simulation, the following physical quantities are obtained: speed, electromagnetic torque, stator current, currents in rotor bars, and currents in the segments of the short-circuiting rotor cage between bars. The grid frequency during the simulations is 50 Hz. Before synchronization the rotor speed equals 250 rpm and is adjusted to grid frequency. During the calculations, two cases are considered: the temperature of the windings and magnets equals 20 °C and the temperatures of the stator windings and magnets correspond to the thermal conditions established during the rated load.

The temperature of permanent magnets significantly affects the operation of permanent magnets machines. This is particularly visible in generator operation with open stator terminals. For a temperature of 20 °C, the induced electromotive force equals 1.07 U_N, and for a thermally steady state, the induced electromotive force equals 1.02 U_N (stator winding temperature is 95 °C and permanent magnets 60 °C).

The obtained results (Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14) show that the temperature of the magnets strongly influences the course of synchronization. The electromagnetic torque, stator currents, currents in the rotor bars, and currents in the short-circuited rotor segments are two times smaller for the temperature in the thermally steady conditions (Figure 10b, Figure 11b, Figure 12b and Figure 13b) for rated load than in the case of 20 °C, corresponding to the ambient temperature (Figure 10a, Figure 11a, Figure 12a and Figure 13a). Permanent magnet temperature does not affect rotational speed fluctuation during synchronization (Figure 9).

In the first synchronization period, the highest values of currents in the rotor cage appear (Figure 12). In the next time period, the values of these currents decrease by half. After a time of about 0.2 s, they stabilize. The highest observed current density in the rotor bar is about 20 A/mm² (Figure 14).

The current density in the segment short-circuiting the rotor cage is about 8 A/mm². The currents in the rotor cage stabilizing in such a short time do not pose a threat to the studied generator. The currents in the segments shorting the rotor cage strongly depend on the temperature of the magnets (Figure 13). The higher the temperature, the lower the current values.

4.2. Synchronization as an Asynchronous Start Similar to Induction Machines

The tested generator was designed to enable synchronization of the machine with the power system by direct start-up. Such a procedure was possible by means of a rotor cage. The reserve of asynchronous torque over the braking torque from permanent magnets is so large that the machine enters synchronism within a few seconds, despite the high moment of inertia of the generator and turbine. During start-up, the driving torque from the turbine equals zero. The tested machine has better starting properties at an increased temperature of permanent magnets. This is the effect of shielding the field generated by the magnets for a higher operating temperature. A higher temperature of the magnets shortens the duration of start-up (Figure 15), reduces the starting torque (Figure 16), and does not affect the maximum values of stator currents (Figure 17), which depend on the number of series-connected turns in the stator winding, the materials, and the distribution of the rotor cage. The computed torque of entering synchronism is 12.4 Nm.

During asynchronous start-up, significant eddy currents are induced in the rotor cage (Figure 18 and Figure 19). These currents contribute to the temperature increase of the cage. The heat released in this way radiates to the permanent magnets, increasing their temperature. The determined time of strong heat release lasts no longer than 5 s for the tested turbine-generator system. This time is short enough that the heat released in the stator winding and rotor cage will not cause the temperature of the magnets to rise above their temperature class. The rotor cage has a shielding effect, which minimizes the risk of demagnetization of the permanent magnets. Despite this, it is recommended that the permanent magnets used in the machine construction have an increased temperature class—similarly to the case of line-start permanent magnet synchronous motors (LSPMSMs). The highest recorded eddy current densities in the rotor cage are approximately 260 A/mm² (Figure 20). Conversely, the highest current density in the short-circuited rotor between selected segments reach a value of 113 A/mm². The temperature of the magnets does not significantly affect the value of the rotor cage currents during start-up; therefore, in this work, the focus was only on the temperature of 20 °C.

5. Conclusions

This article presents the possibility of using a PMSG to work with a water turbine without using a converter system to work with a single rotational speed. The field-circuit model of electromagnetic phenomena in the generator has been implemented in the Ansys Electronics package and employed in the conducted research. Two cases of connecting the generator to the grid are studied. In the first case, the machine is connected to the grid in a similar way as in the case of electrically excited synchronous generator. In the second case, a direct line-start process is used based on asynchronous torque, similar to asynchronous motor start. In addition, the influence of the magnet temperature on the transient states is investigated.

During the first case, the magnets temperature has an important impact on the electromagnetic phenomena in the generator. The lower the temperature of the magnets, the worse the effects on the generator. In this state, there is no risk of damaging the generator because the computed electromagnetic torque and stator current do not exceed the rated value.

During asynchronous start-up, significant values of currents in the stator winding and eddy currents in the rotor cage were noted. In the case of the tested generator, the start-up lasts less than 5 s. The strongly heating rotor cage has a thermal effect on the permanent magnets, increasing their temperature. Therefore, it is recommended to use an increased temperature class of magnets in order to minimize the risk of their demagnetization.

In order to minimize the risk of magnet demagnetization, the influence of the start-up time should be taken into account in the design process, taking into account the moments of inertia of the generator together with the water turbine. The number of start-up cycles should be clearly defined in the technical and operational documents in order to avoid inadvertent damage to the machine.

It is not permissible to resynchronize the machine when the induced electromotive forces can be in close to counter-phase the power system voltage, as there is a great risk of demagnetizating the permanent magnets in the rotor [30,31].