Stability Analysis of PMSG Used in Micro-cogeneration System

STABILITY ANALYSIS OF PERMANENT MAGNET SYNCHRONOUS GENERATOR USED IN

MICRO-COGENERATION SYSTEMS

ION VONCIL, NICOLAE BADEA Electrical Engineering Department

Dunrea de Jos University of Galai no. 47, Domneasc Street, 800008, GALAI

ROMANIA Ion.Voncila@ugal.ro http://www.ugal.ro

Abstract: - This paper has a dual purpose: on the one hand the technical-economic analysis of cogeneration microplants (also emphasizing the producers preferences for certain classes of electric generators in terms of using the same type of prime mover, respectively the Stirling engine), on the other hand the functional stability analysis, in stationary regime, of permanent magnet synchronous generator at variations of mechanical and electrical parameters on both its access gates (the proposed solution). For stability analysis it has been used Matlab/Simulink programming environment. Key-Words: m-CHP; Stirling Engine; renewable energies, electrical generators. 1 Introduction In the past 120 years the synchronous generator has been widely used in alternative current (AC) power generation. Due to its existence were developed the centralized power systems of AC power transmission and distribution, systems that through integration achieved a global extension. Energy crisis by the end of the 20th Century, determined finding alternatives to the primary systems by which the electricity production can continue at the requirements of modern society. A conceptual and revolutionary change was the transition from centralized systems of electricity generation with low and medium power units, to decentralized systems. The change was claimed by the new "primary fuels", represented now by the kinetic energy of wind, solar energy, kinetic energy of water, etc. Irregular arrangement of the new primary energies also claimed the passing to a non-uniform distribution of conversion systems of these energies into electricity. Although various solutions have been tried for the new decentralized conversion systems, and for large power systems (centralized systems), using the synchronous generators adapted to the new power units, still turns out to be a viable solution. Indeed, adapting to new demands of decentralized systems determined a structural and overall change of synchronous generators, obtained by replacing the electromagnetic excitation with permanent magnets.

Similar to high power conventional synchronous generators with electromagnetic excitation, at new permanent magnet synchronous generators the functional stability problem arises in case of disturbances on the two access gates (mechanical and electrical) of the electric vehicle. Such solution was analyzed in this paper, for special case of low power synchronous generators excited by permanent magnets, used as mechanical-electrical converters in micro-cogeneration systems (m-CHPs). For these systems that operate in isolated sites, the functional stability is a vital problem to satisfy user requirements.

2 Types of cogeneration microplants (m-CHPs) and used generators particularities Generally the cogeneration and particularly micro-cogeneration were claimed by the domestic systems due to the following benefits, compared with conventional systems: energy losses reduction and efficiency increase; diminution of exhaust emissions (CO2, NO etc.) and so reducing environmental impact; the possibility of using the new prime movers and new fuels biogas, biomass, solar radiation etc.) fulfillment of local consumer needs (for the most exigent requirement). In Fig. 1 [1] it is comparatively presented the power diagrams for a domestic conventional system and a

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micro-cogeneration domestic system, on which the gas is the prime mover fuel. An important advantage of micro-cogeneration systems compared with centralized conventional systems, it is represented by their capability of being used in isolated sites.

Fig. 1. Power diagram for classic domestic systems

and micro-CHP systems

It is a hard struggle in the world to implement the new concepts, in order to find good solutions technically, economically and with reduced environmental impacts. Many companies try, year after year, to obtain prototypes for m-CHPs that allow rapid satisfying and implementation in the customer area. Over the years, among many reliable solutions proposed, were noted: Sunpower (USA), Sunmachine (Germany), Whisper Tech Limited (New Zeeland) etc.The heart of m-CHPs is represented by the prime mover, from which it is obtained - by intermediary converters- both thermal energy and electrical energy. Lately, has been strongly developed the class of external combustion prime movers to the detriment of internal combustion engines, and from this new class, the Stirling Engine has the place of honor. The issue of cogeneration with Stirling engines, in general and of micro-cogeneration in particular, is covered by many companies worldwide (Table 1). At the present day, the technical analysis it is not enough reason why it is necessary the doubling through the economic analysis. In case of cogeneration units (and m-CHPs) the costs per unit of power may be an important indicator for the user. Table 2 presents such an economic analysis for costs per unit of electric power in case of CHPs (cogeneration units) made by different companies. It is remarkable that for low power units, the costs supported by the companies to realize the prototypes are much higher (in relative values) than for medium and high power units. In the Fig. 2 it is shown a comparative analysis of unit costs of the main companies that produce CHP units.

Table 1. The technical-economic characteristics of the co-generation power stations for different construction companies [2]

Company Characteristics - electric part -

Characteristics - thermal part -

ADI Thermal Power Corp.

25 kWe -

BG Group 1,1 kWe 15-36 kWthBSR Solar Technologies

5-10 kWe -

External Power 15 kWe - Sigma Elektroteknisk

3 kWe 9 kWth

SOLO Kleinmotoren

2-10 kWe 8-24 kWth

Stirling Advantage

200 kWe 123 kWth

Stirling Energy Systems

25 kWe

Stirling Technology Company

350 We550 We

1,25 kWe3 kWe

-

STM Power 25 kWe 44 kWthSunpower 1 kWe - Sustainable Energy Systems

10 kWe -

Uwe Moch 900-950 We - Whisper Tech 950 We (AC)

1-1,1 kWe (DC)

6 kWth

Table 2. The costs per electric power unit of the co-generation power stations for different construction companies [2]

Company Product kWe $/demo $/ kWeSOLO Kleinmotoren

Integrated system

10 20000 2000

Stirling Technology Company

Integrated system

1,25 45000 36000

Stirling Energy Systems

Integrated system

25 250000 10000

STM Power Integrated system

25 60000 2400

Uwe Moch Integrated system

0,95 17000 17895

Whisper Tech Integrated system (AC)

0,95 13000 13684

According to this aspect, choosing an m-CHP must be made very carefully. For the Project RO 0054, that is the subject of this case study, were comparatively observed the m-CHPs, with Stirling engines, units that were offering technical and economic benefits and also

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environmental impact advantages (the Stirling motor is a noisy system, sometimes hard to accept in development of domestic systems).

Fig. 2. The comparative analysis of the unit costs for the integrated co-

generation systems [2]

It is interesting that in the m-CHPs are used squirrel cage induction generators and also permanent magnet synchronous generators, with generators with a tilt of balance for second category generators (recently, for the linear synchronous generators). This particularity is displayed in tables 3 and 4. Table 3. Technical-economic characteristics of the Sunpower micro power stations USA[2]

Product Cogeneration micro power station

Type of primary engine Stirling, with free movement of the piston

Number of pistons One Work fluid Helium Fluid exit emperature (for the heating part)

5500C

Fluid exit emperature (for the cooling part)

500C

Type of generator Synchronous, linear Power discharged 1 kWeTension delivered/frequency

240V/50 Hz

Fuel Natural gas, propane, biomass

Efficiency of the electric part

28 %

Distributor price 35 000$/kWe Due to this wide utilization of permanent magnet synchronous generators (both linear and rotary), in the project mentioned above was proposed the acquisition of a m-CHP equipped with a rotary permanent magnet synchronous generator (product of Sunmachine).

Table. 4 Technical-economic characteristics of the Whisper Tech Limited micro power stations from New Zeeland[2]

Product Integrated cogeneration system

Type of primary engine

Stirling (Beta type)

Number of pistons Four Work fluid Azoth Type of generator Asynchronous Power discharged 950 WeNumber of phases mono-phased Tension delivered/frequency

(230-240) V/(50-60) Hz

Thermal power available

6 kWth

Fuel Natural gas, propane Efficiency of the electric part

12 %

Total efficiency 90 % (Net) Weight 100 kg Noise level 48 dBA (no vibrations) Life expectancy 30000 ore Distributor price (2000-3000)$/system

The problem developed in this paper has the main purpose the verification of functional stability of this type of synchronous generator at variations of mechanical and electrical parameters on both access gates.

3 Modeling and simulation of permanent magnet synchronous generator used in m-CHP with Stirling motor Mathematical Modelling of classical synchronous machine, with cu electromagnetic excitation is well known worldwide [3], [4], [5]. Replacing the electromagnetic excitation with permanent magnets brings from the mathematical point of view, a model simplification [6], [7]. The mathematical model of permanent magnet synchronous generator in system (d,q), utilized for analysis in this paper, it is given by system (1). To implement the system (1) it was used programming environment Matlab/Simulink. At the voltage equations and electromagnetic torque expression - from system (1) it is also added the equation of movement (the last equation of system).

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dd

qmd

qd

d

d uL

ipLL

iLr

dtdi += 1

qqq

mmdm

q

dq

q

q uLL

pip

LL

iLr

dtdi = 1

(1)

( )[ ]qdqdqmem iiLLipT += 23 2

2

dtd

pJ

dtdJTT egmema

== where:

du , - the d and q axis stator voltages; qu

di , - the d and q axis stator currents; qir - the phase resistance of stator winding;

qd LL , - the d and q axis stator inductances;

m - the flux of permanent magnets (it is considered a constant value specific to each class of permanent magnets available on the market ;

emT - the electromagnetic torque developed by the generator;

aT - the active torque due to prime mover; J - the total moment of inertia of generator shaft, considered constant;

m - the mechanical angular velocity; m - the angular position (instantaneous mechanical

angle of the generator) eg - the instantaneous electrical angle of the

generator. The relationship between electric and mechanic angles is:

meg p = (2) where: p is the number of rotor pole pairs.

For simplicity and facile interpretation of the results, was used as a global task for generator, a three-phase receiver purely resistive (active power ). kWP 3=In Fig. 3 it is shown the block scheme for simulation, in selected programming environment, of permanent magnet synchronous generator operation and in Fig. 4 it is presented the window with parameters of studied generator. Block diagrams that allow implementation of the mathematical model of permanent magnet synchronous generator are shown in Figure 5 a, b.

Fig. 3. The Simulink block scheme for the simulation of the functioning of synchronous generators excited with permanent magnets

Fig. 4. The parameters of the modeled synchronous

generator with permanent magnets

a)

b)

Fig 5. The Simulink block schemes for the implementation of the mathematical model of the synchronous generator with permanent magnets:

a) implementation of the tension equations system; b) implementation of the movement equation

To obtain the generator regime of synchronous machine excited with permanent magnet, according to convention work specified in Simulink library [8] the mechanic torque input must have minus sign, thereby, specifying that the electric machine receive

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mechanic power from a prime mover (in our case, the Stiriling engine).

4 The obtained results

For functional stability analysis of permanent magnet synchronous generator, was considered parameters variation on mechanical access gate (the toque developed by the prime mover) and also the parameters variation on electrical access gate. The obtained results at load operation of chosen synchronous generator are shown in Fig.6.

Fig. 6. Simulation results for the functioning in resisting load of the chosen synchronous three

phased generator with permanent magnets (currents, delivered tensions and the primary engine couple

according to the specified signs convention)

The variation in stabilized mode of currents in the generator stator winding analyzed (reference) is presented in Fig. 7.

Fig. 7. Variation of statoric currents for the

generator analyzed in stabilized mode

In the case when the torque of prime mover (Stirling engine) has a variation of % at constant generator parameters, respectively at load, the variation of statoric currents in stabilized mode are as shown in Fig. 8 and 9.

10

In these processes, the delivered voltage recorded variations of 8,33 % compared to reference value and the current intensity varies between %, and % range , compared with reference value.

36,11+

6,8

Fig. 8. Variation of statoric currents for the generator analyzed in stabilized mode, at an increase of 10 % of the primary engine couple

Fig. 9. Variation of statoric currents for the generator analyzed in stabilized mode, at a

decrease of 10 % of the primary engine couple

There is a strong influence on the output values of the electric generator due to variations of the load connected at its terminals (electric access gate). In Fig.10 it is shown the output parameters variation of studied generator in case when the load, connected at terminals, increases by 10 % and in Fig. 11 it is presented the variation of the same parameters if the generator load decreases by 10 %.

Fig. 10. Variation of currents and tension delivered

by the synchronous generator with permanent magnets when the load increases by 10 %

Fig. 11. Variation of currents and tension delivered

by the synchronous generator with permanent magnets when the load decreases by 10 %

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Load increasing by 10 % leads to a decreasing of delivered voltage by 12,5 % and a current increasing only by 4,5 %. Reduction of the load by the same percentage will determine an increase of delivered tension by 12,5 % and will maintain practically constant the current compared with reference value. Also it is worth to mention that in these processes, the other parameters of electric generator (and of prime mover) were kept constant. The modification of generator internal parameters can have a major influence on functional stability The most expected phenomenon is the aging of permanent magnets in time and with temperature. Through aging, the flux of permanent magnets decreases; the consequences of flux weakening by 20 % compared with initial state, influence the variation of currents and tensions delivered as it is shown in Fig. 12.

Fig. 12. Variation of currents and tensions delivered

by the synchronous generator with permanent magnets when the flux of the permanent magnets

decreases by 20 %

Flux diminution determines the increase of voltage level by 27,5 % and the increase of current intensity by 18,18 % for the same load value. Such a situation is problematical for electrical installation first because can affects the electric machine insulation (leading to its rapid aging and to decreasing of electric generator lifetime), second because leads to Joule losses increasing (with a faster growth of temperature from inside and with causing an avalanche effect on the aging process of permanent magnets and insulation, and therefore a drastic reduction of the electric generator lifetime). 5 Conclusion From the accomplished functional stability analysis of permanent magnet synchronous generator result the following conclusions: - the variation of generator input parameters (in

principle, of prime mover torque) determines the variation of output parameters (voltage, current, power delivered to load);

- the value of output parameters (voltage, current) of generator it is also affected by the load variation while maintaining constant the other specific parameters;

- exists a strong influence on output parameters of electric generator due to aging phenomenon of permanent magnets (decreasing in time of permanent magnets flux);

The study achieved, through modeling and simulation, on electric generator indicated for m-CHPs, emphasizes that permanent magnet synchronous generator is a viable solution, with the advantages of constructive and functional simplicity, an inexpensive maintenance when high-performance permanent magnets are used (stabilized from thermic point of view and also stabilized against reaction magnetic fields, statoric and demagnetize and stabilized, while reaction against magnetic fields, stator field and demagnetizing field) . References: [1] C. Ghler, Micro-CHP with Stirling Engine,

Smart&Efficient Energy Council, Trento, 2009, PowerPoint Presentation

[2] D. Thimsen, EPRI Project Manager - Stirling Engine Assessment - Final Report, October, 2002; [3] A. Genon, W. Legros, Machines lectriques,

Hermes Science Europe, 2000 [4] M. Jufer, Trait dlectricit, Vol X, Machines

lectriques, Presses Polytechniques et Universitaires Romandes, Paris, 1995

[5] A. NASAR, I. BOLDEA, Electrical machines: dinamics and control, CRS Press, 1993

[6] C. GHI, Convertoare electromecanice, Vol. 2, Ed. ICPE, Bucureti, 1999

[7] C. GHI, Convertoare electromecanice, Vol. 3, Ed. ICPE, Bucureti, 2001

[8] ***MATLAB 7.0. Simulation software, MathWorks-licence, 2004

Acknowledgements The authors would like to acknowledge to EEA Financial Mechanism for financing the research on Integrated m-CCHPs Stirling Engine based on renewable energy sources for the isolated residential consumers from South-East region of Romania (m-CCHP-SE), under the contract No. RO-0054/2009.

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