Energy Optimization of Ship’s Shaft Generator with Permanent Magnet Synchronous Generator Energetska optimizacija brodskog osovinskog generatora sa sinkronim generatorom s permanentnim magnetima

With the development of power electronic systems, the use of a shaft generator in ship power plant systems is becoming more widespread. The use of the Permanent Magnet Synchronous Generator (PMSG) in these systems instead of the commonly used Electrically Excited Synchronous Generator (EESG) results in increased propulsion effi ciency and reliability of the ship’s power plant. The lack of a voltage regulator in PMSG requires the use of an electronic power converter to maintain constant voltage parameters in the ship’s network, consisting of an active rectifi er (AR) and an active network inverter (AI). The article presents AR tests in the PMAG-AR system, whose task is to maintain a constant voltage of the DC circuit when the shaft speed and load changes, as a result of which the selection of AI remains a simple choice. Energy optimization of the shaft generator system was also carried out, which allows reducing losses in AR and PMSG by limiting reactive power in the PMSG-AR system, which is particularly important in high power plants.


INTRODUCTION / UVOD
The ship's power plant is the most important system on the ship, determining the correct operation of the other systems. Economic production of electric energy is important to the economics of ship exploitation.
Shaft generators (SG) have been in use for a long time because they can produce electricity that can cover the energy demand of the entire ship. The use of a shaft generator allows using the reserve power of the main engine of a ship and is therefore the most economical system of an electricity generation on board, while giving up the work of diesel generators (DG).
The main problem of variable shaft speed and variable load has been solved by the evolution of power electronic devices.
The main benefi ts of using ship's shaft generators can be presented as follows: -energy production using a shaft alternator reduces air pollution, as opposed to other traditional methods of energy production on the ship (e.g. DG). Noise and vibration levels are also reduced, -the use of the SG for electricity production is more costeff ective because it does not require expensive fuel, as the main engine is mostly fueled by residual fuel, -the Specifi c Fuel Oil Consumption (SFOC) for slow-running engines (main engine -ME) is lower than for mediumrunning engines (DG) and the operating point for slowrunning engines is located near the minimum characteristic of SFOC = f(Load) (Fig. 1.) [18], -the amount of wear and, consequently, the overhaul of Maintenance is reduced for SG, -the cost of spare parts and the cost of man-hour are low, as the maintenance period of the SG schedule has a higher time interval compared to a DG, -the installation costs of the shaft generator are also low because they do not require a separate fundament or exhaust system, -the installation time is shorter for SG, -low spare parts and man-hour costs, because the maintenance period of the SG schedule has a greater time interval compared to a DG, -developments in mechanical engineering and the development of semiconductor technologies have allowed engineers to increase the effi ciency of ship propulsion by using a generator with PMSG in place of the commonly used EESG. Developments in mechanical engineering and the development of semiconductor technologies have allowed engineers to increase the effi ciency of ship propulsion by using a generator with PMSG in place of the commonly used EESG.
The main advantages of the PMSG compared to the EESG are: -higher effi ciency (over the range of load) (from 3 to 6%depending on the load [11]), -easy to obtain a large number of pole pairs, PMSG slow speed) can be installed without gearboxes (loss from the gearbox -about 2% [11]), -lower weight and dimensions, -high operational reliability and simple construction, -higher power density, -low vibration level.
In order to eliminate problems with maintaining constant parameters of the voltage generated by the PMSG with the change of the shaft speed and load, it is necessary to use power electronic converters. Figure 2 shows a diagram of the SG system with PMSG, which can be identifi ed: -ME -Main Engine, -PMSG-Permanent Magnet Synchronous Generator, -AR -is an active rectifi er, -ARC -is an active rectifi er control system, -C -DC circuit capacitor.
Generators set with permanent magnet synchronous machine are widely used in the construction of power plants for autonomous objects in hybrid vehicles, wind turbines, aircraft and ship installations [2,4,15,16]. In recent years, when building energy systems, more and more preference has been given to DC power grids [1,5,9,10,14,17].
In this article the mechatronic system containing PMSG and active rectifi er (AR) is investigated. This system makes it possible to build the DC network in which the direct voltage of the load is supported by AR. Appropriate AR control allows to maintain constant voltage in the DC circuit of the converter together with the change of SG shaft speed and load (within specifi ed limits) [20]. As a consequence, the control of the network inverter is known and simple to implement.

MATHEMATICAL DESCRIPTION OF PMSG / MATEMATIČKI OPIS PMSG-a
Electromagnetic processes in the system are investigated on the basis of the equivalent scheme. The scheme is presented in Figure 2 [6]. In this equivalent circuit AR is represented by a controlled voltage source (U 1 ) that is connected in parallel to the stator windings of PMSG with E 1 . The inductive and active resistance in the equivalent circuit are internal parameters of the machine. The mathematical description of PMSG is carried out in the synchronously rotating coordinate system (x,y) using the generalized (resulting) vector method [9,12,16] and the "main component " method [3,8]. This mathematical description looks like: Where: -spatial vector of electromotive force (emf ) on the stator windings; ù -angular frequency of PSC voltage.
Below we consider the way of controlling the machine, in which the active rectifi er acts as a control current source. Similar analysis has been conducted for PMSG with the parameters presented in the Table 1: In the rotated coordinate system dq (d -actual axis, qimaginary axis) equation (1) is presented as: To fully describe the system of equations (2) should be supplemented by the energy balance equation and the Kirchhoff equation in the DC circuit. Where: The basic physical properties of the considered system can be found without the solution of diff erential equations (2, 3), considering only the established modes of operation.
In the steady state operation, the systems of equations (2, 3) are transformed to form:

ELECTROMAGNETIC AND ENERGY CHARACTERISTICS OF THE SHAFT GENERATOR WITH PMSG / Elektromagnetske i energetske značajke osovinskog generatora s PMSG-om
In the mathematical description (4, 5) the vectors of state variables are used in a vector diagram to estimate the electromagnetic and energy properties of PMSG. When constructing a vector diagram according to equation (4,5), electromagnetic processes in the PMSG are considered in the system of rotating coordinates (d,q) related to the construction of the machine [9,12,16], and electromagnetic processes in the AR are considered in the rotating coordinate system x,y related to the voltage and current in the load. In this case, the fl ow vector 0  is combined with the zero state of the rotor position sensor (RPS) and is directed along the real axis (d) rotating at the speed of the coordinate system. In this case, the EMF rotation is 90 degrees ahead of the 0  and will be directed along the imaginary q-axis. Therefore, when building a vector diagram, it is necessary to take into account the fact that the direction of one of the state vectors (voltage or current) is determined by the initial installation of DPR. Vector diagram refl ects the physical operation of PMSG and allows you to qualitatively assess the properties of the generator, which depends on both the parameters of the machine itself and the way of construction and the algorithm of active rectifi er control.
In the general case for control of the current source the vector diagram of PMSG in the generator mode is shown in Figure 3.

Figure 3 Vector diagram of the generator with PMSG Slika 3. Vektorski dijagram generatora s PMSG-om
The main static characteristic, which represents the dependence of the output voltage AR on the modulation factor m and phase of modulation m  , is determined on the basis of the joint solution of equations (4,5). 1  1  1  0  2  2   2  2  1  1  2  2  1  1   3  3  cos  sin  cos  sin  4  4  3  3  1  1  8 8 where R L -load resistance, -full resistance of PMSG and AR on the AC side. Figure 4 shows the dependencies of output voltage AR on the modulation factor and modulation phase for the two speeds of the machine shaft 100 rad/s and 150 rad/s. Projections of these surfaces on the main plane are lines of constant voltage at the output of the AR.
The areas of allowable values of modulation factor and phase of modulation lie above the specifi ed values of the output voltage AR.
If the power semiconductor converter uses current control [2,8], the control signals are currents * d I and * q I the longitudinal and transverse components of the voltage are determined from equations: Energy characteristics of PMSG are calculated by equations: Figure 5 shows the results of calculation of energy characteristics, which are presented by the dependencies of active and reactive power at the PMSG output on control signals. Power surface projections on the main plane represent the dependencies between these control signals, at which the power is constant.  / s (b).
The received power characteristics of the current control of PMSG allow estimating of properties of the system which are reduced to the following: -the active power in the PMSG load in the generator mode depends mainly on the current component q I and insignifi cantly on the component d I , -the reactive power in the PMSG load is comparable with the active power, which causes an increase in the total current and losses in semiconductor AR devices and PMSG windings, -in order to maintain zero reactive power in the PMSG load, it is necessary to maintain a certain nonlinear dependence between q I and d I , -the range of control signal change at the zero reactive power in the PMSG load for the selected machine is limited by the value

ENERGY CHARACTERISTICS OF AN OPTIMIZED SHAFT GENERATOR WITH PMSG / Energetske značajke optimiziranog osovinskog generatora s PMSG-om
For the optimal control of the AR, the voltage and current at the PMSG output coincide in the phase ( Figure 6). Figure 6 Vector diagrams in the system at zero reactive power in the PMSG load. Slika 6. Vektorski dijagrami u sustavu s nula jalove snage u PMSG opterećenju.
Then from geometrical constructions (Figure 6), it is possible to defi ne longitudinal and transverse components of currents at which reactive power at the PMSG output is equal to zero.  Calculation of energy characteristics of the generator at such control is carried out by equations (7,8,9).
Calculated and constructed energy characteristics of the system are presented in Figure 6, from which it follows that: -while maintaining the dependence (9), the reactive power at the PMSG output is equal to zero in the whole range of control signals change; -while maintaining the dependence (9), active power at the PMSG output can be maintained constant at essentially nonlinear dependence between modulation phase and shaft speed of the machine; -with the increase of power at the PMSG output, the permissible range of changes in the control signals is reduced.

MODEL STUDY OF PSMG / Studija mod ela za PSMG
Experimental study of the closed-loop generator control system was carried out in Matlab-Simulink environment. The model of the generator with PMSG is shown in Figure 8. In the structure under consideration, the internal combustion engine is controlled by a speed regulator. In this mode, the speed of the PMSG shaft is specifi ed and the main requirement to its electrical part is to maintain a constant voltage in the DC link when changing the electrical load. Voltage stabilization is carried out in a classical system control with a PID regulator. The signal from the output of the PID regulator is fed to the functional converters (Fcn6, Fcn7 - Figure 8). In converters the reference currents according to the equation are calculated (9). Modulation phase is defi ned in block Fcn10 (Figure 8)  The system with independent current control, which is described by equation (4), and the system with optimized current control, described by equation (5), are compared. Figure  9 and Figure 10 show the results of modelling of both systems in transient and steady-state modes of operation of the generator set with PMSG.
In the steady-state mode of operation under load in the system with independent current control ( * * 0, var d q ) the reactive power of PMSG is approximately one third of the active power (Figure 9,a). In the optimized system ( Figure 10,a), shortterm changes in reactive power are observed at the time of load shedding. In the steady-state mode this power is practically equal to zero. Electromagnetic processes in both systems are shown on the Figure 9,b, Figure 10,b , they are rep resented by currents in the stator of the machine, the load current in the DC link AV (I dc ) and the voltage in the DC link AV (U dc ). The processes presented on Figure 10 show that in the optimized system the change in the generator electrical load does not aff ect the voltage.
Curves (Figure 11, a, b) demonstrate energetics and electromagnetics processes in the optimized system with PMSG when changing the speed from 150 to 100 rad/s of generator shaft.
The results of the modeling show that the generator set with PMSG provides the basic requirements -to maintain a constant voltage at changing the current (power) in the load and changing the speed of rotation of the shaft. In addition, with the optimal control according to the equation (5), the reactive current in the machine is reduced to zero, which reduces the losses in the active resistances of the machine and the active rectifi er.

CONCLUSION / Zaključak
The study of the electromagnetic and electromechanical properties in a steady state of the PMSG-AR system allowed assessing the performance of the SG system in the case of shaft speed and load change.
The proposed AR control allowed the optimization of the SG system by reducing the reactive power in the PMSG-AR system. Reactive currents and, accordingly, losses in the converter and the machine may be several times lower with a certain ratio between the amplitude and the phase of the voltage (current) on the AC side of the AR. Optimization of energy properties of generating sets acquires special importance in the construction of powerful hybrid transport systems and systems with full electric propulsion. These systems have diff erent, as compared in terms of power, sources of electrical energy operating on the total variable load. Examples of such objects are land-based, sea, river and air transport, and examples of such sources of electrical energy -diesel generators, shaft generators, steam and turbo generators, batteries, supercapacitors, etc.