A modular simulation system for synchronous generators utilizing ...

Transactions on Engineering Sciences vol 22 © 1999 WIT Press, www.witpress.com, ISSN 1743-3533

A modular simulation system for synchronous generators utilizing simulink M. Vilaragut, A. Costa. Electrical Tests and Research Center (Centra de Investigaciones y Pruebas Electroenergeticas, CIPEL), Ciudad Habana, Cuba E-mail: miriamv@electrica. ispjae. edu. cu cipel@electrica. ispjae. edu. cu

Abstract The synchronous generator is one of the most important components of a Power Plant. Then, it is necessary to be able to predict its dynamic or transient behaviour when it is submitted to any disturbance, such as: a sudden short circuit, load rejection, loss of excitation, etc. in order to evaluate the stability of the generator operating in a power system, synthesize the control algorithms for automatic voltage regulators, protect adequately the generator and to detect incipient faults. A modular simulation system for synchronous generator supported in SIMULINK is proposed. One of the most outstanding features of this proposal is the consideration of the complex nature of the generator rotor. Three different synchronous generator models are utilised: the so-called standard model, which neither considers the unequal mutual inductance of the rotor nor the turbogenerator solid rotor, the hydrogenerator model or the turbogenerator model. The simulation results demonstrate the necessity of considering the characteristics of the rotor. 1. Introduction The research aims at elaborating a Modular Simulation System for Synchronous Generator operating against a constant bus voltage. The proposed system is useful for determining the generator electrical transient behavior when the most important perturbations and parameters changes occur, such as: short-circuits, sudden load and excitation variations and field resistance excitation changes due to internal faults. This simulation system could also be utilized as a convenient


298

Software for Electrical Engineering Analysis and Design

tool for synthesizing the control algorithm of synchronous generator voltage regulators, and for the identification of the whole generator excitation system utilizing neural networks. This simulation approach considers the complex nature of the generator rotor. In the second paragraph, the different types of mathematical models are explained. The necessity of elaborating an adequate model taking into account the rotor characteristic is emphasised. The third paragraph concerns to the writing of the state space equations of synchronous generators. These are the equations solved by the simulink numerical method. The next paragraph explains the modular system elaborated. The functions of the different modules are detailed. Finally, the last paragraph shows a particular example with its simulation results. Here, the standard model is compared with the turbogenerator one, that considers the unequal mutual inductances and the necessity of this consideration is demonstrated. 2. Synchronous generator mathematical models There are two different types of large synchronous machines: the salient pole hydrogenerator and the non-salient pole turbogenerator, e.g. Adkins [4]. The former is characterized by a low synchronous speed, a great number of poles and a damper winding attached to the pole faces, while, the latter is a high speed machine with a solid rotor that plays the role of the damper windings. In order to adequately state the mathematical model of the synchronous generator, it is better to employ a reference frame rotating at generator speed, e.g. Kovacs [7]. Thus, the stator is represented, in both types of machines, by a two set of windings system: the direct axis windings (d-axis) and the quadrature axis windings (q-axis). The difference between the two types of machines is in the rotor windings. The rotor of the salient pole machines with the damper windings in the poles can be represented fairly well by a three winding system: two corresponding to the direct axis, -the field winding and the direct axis damper winding-, and one corresponding to the quadrature axis damper winding. On the other hand, the rotor circuits consideration in a turbogenerator is a more complicated issue because the only real winding at the rotor is the field winding and the current circulates in the solid rotor through its whole body, not at specific windings. It has been demonstrated that this phenomena can be represented with a good degree of approximation provided there exists two damper windings in the direct axis and three damper windings in the quadrature axis, e.g. Canay [1], Dandeno [2 y 6], Umans [5], Keyhani [8],Lozano [10]. Traditionally, the so-called standard model has been used. This approach considers that the mutual inductance between the stator and the rotor equivalent windings are the same, and supposes that there exists only two rotor circuits at the direct axis and one rotor circuit at the quadrature axis. Since 1969, it has been demonstrated that this approximation leads to an erroneous solution of the field winding current. However, as I. M. Canay stated [9], in spite of that, unfortunately, this circuit is still being used for the synchronous machine, as shown in many recent publications, e.g. Lozano [11]. Consequently, an



299

important issue to be considered is the different mutual couplings between the stator and the rotor windings and the rotor windings between them. Taking into account all these facts, three machine models have been established: one for the standard model, one for the salient pole hydrogenerator, and another one for the solid rotor turbogenerator. In all cases, the model considers the existence of windings at the machine symmetry axis: the direct current axis and the quadrature one, e.g. Adkins [4], Umans [5] and Kovacs [7], Figure 1 shows the coupled circuit equivalent circuit for the turbogenerator (the most complicated one). There are four windings at the direct axis: the stator direct axis winding d, the field winding / and two equivalent rotor damper windings kdl and kd2 and four windings at the quadrature axis: the stator quadrature axis winding q, and three equivalent rotor damper windings: kql, hq2 and kq3.

Figure 1. Turbogenerator coupled circuit model 3. State space equations of synchronous generators Initially, the order of the state space equation has to be considered. It can be appreciated that there are eight degrees of freedom corresponding to each of the windings. On the other hand, the mechanical system must be considered as well. It has been demonstrated that the equation of mechanical motion of the synchronous generator is a second order one, e.g. Adkins [4], Kovacs [7]. As a result, there are two mechanical degrees of freedom. Summarizing, turbogenerator state space model is of tenth order. A similar analysis leads to the conclusion that the state space standard and salient pole model are of seventh order.


300


The next step is to choose the state variables. The electrical state variables are of two types: current variables or flux linkages variables. The second type was selected because the equations are easier to be stated. A direct approach consists of selecting the five winding flux linkages. In order to facilitate the consideration of magnetic saturation, one direct axis damper winding flux linkage and one quadrature axis damper winding flux linkages were eliminated, and substituted by the direct axis magnetizing flux linkage and the quadrature axis magnetizing flux linkage, associated to the direct axis magnetizing inductance and the quadrature axis magnetizing inductance. Concerning the mechanical state variables the angular speed and the power angle were chosen. The state space equations of the turbogenerator are then: ["11 "21 "31 _"41 ""51 "61 "n lq ["81

"14 "24 "34 "44 "54 "64 "74 "84

"15 "25 "35 "45 "55 "65 "75 "85

"16 "26 "36 "46 "56 "66 "76 "86

31 41 51

^52

21

\fd Vm ' qm

"13 "23 "33 "43 "53 "63 "n "83

14 12 13 24 22 23 ^25 34 ^35 ^32 ^42 ^43 ^44 245

' *V

"12 "22 "32 "42 "52 "62 "72 "82

^53 ^54

"17 "27 "37 "47 "57 "67 "77 "87

^36

,3 "18 VTJ "28 UJ "38 >32 43 "48 \d "58 V dm + 51 "68 "78 &72 &73 "88 * qm

M7 ^27 ^37 ^47 ^57

*18 ^28 38 '48

, dm

^58 qm

R

1

The coefficients of these equations are function of the circuit parameters. In these equations, all the parameters and variable are in the per unit system. The parameters needed for solving these state equations are: the stator armature resistance, the stator leakage inductance, the direct and quadrature axis magnetizing inductance, the field winding leakage inductance and internal



301

resistance, the damper windings leakage inductance, and internal resistance and the so called Canay reactance that consider the unequal mutual inductance between stator and rotor windings. These parameters can be directly obtained by means of the Standstill Frequency Response Tests, e.g. Umans [5] or by means of any parameter identification method such as the Maximum Likelihood, e.g. Keyhani [8] Sometimes, this set of parameters is not known a priori, and the short circuit test parameters are the only information available, In this case, the state space equations parameters can be deduced employing, for example, the method of Canay [9] The direct and quadrature axis magnetizing inductances depend upon the magnetic circuit saturation. In order to consider this variation, a three zone magnetic saturation curve is utilized, an initial linear nosaturated zone, the knee region zone (simulated employing the arctangent function), and a final linear saturated zone. The concepts of static and differential inductance are also employed. As it can be seen, these equations are strongly nonlinear, and the utilization of a powerful non linear dynamic simulator is required. The SIMULINK of MATLAB software was chosen because is a friendly and very well known system compatible with all MATLAB toolboxes. 4. Simulink modular simulation system for synchronous generators The modular system proposed takes advantages of the facilities bringing about by SIMULINK. The state space model described above is divided into separate functions; each one gives rise to a different module. These modules are: 1. The Initial Setup Saturation Module (ISSM) 2. The Voltage Module (VM) 3. The Standard Model Module (GS). 4. The Hydrogenerator Module (HG). 5. The Turbogenerator Module (TG) and 6. The Mechanical Module (MM) The Initial Setup Saturation Module establishes the steady state conditions considering the magnetic saturation. It calculates the initial flux linkage values in order to be utilized by the simulation program. If no saturation is included, this module does not exist as such, because this calculation is included in the specific generator module. The user must supply the initial per unit values of the active and the reactive power. The Voltage Module gives entrance to the field voltage and calculates the direct and quadrature axis voltage as a function of power angle, a variable calculated at each simulation stage, and the bus voltage. These voltages may be constant or may be changed at a specific time instant. In the Generator Model Modules the equations of the specific model are solved. It is the dynamic module which uses a numerical method to obtain the flux linkages with the state space equations. It is possible to select the variables the user wishes to know by means of the simulink facilities.


302


Lastly, the Mechanical Module is concerned with the prime mover and the dynamic equation of motion of the machine; the outputs of the mechanical state variables are: the power angle and the rotor speed. In this module, the mechanical torque of the prime mover is considered a function of time. The modular system is called GESINC and has an initial entrance window (figure 2) that allows the user to select any one of three models, i.e.: the standard one, the hydrogenerator, and the turbogenerator. This window has the voltage module (composed by the excitation voltage and the stator voltage), the mechanical module, and the help entrance. Each model module has its own window that contains separate modules (see, for instance, the excitation voltage dialogue box in figure 3) in order to be able to build the overall simulation model. Each separate module has a dialog box for selecting the required parameters. File Edit View Simulation Format Tools

GESINC: A modular simulation system for synchronous generators.

Voltages

Standard Model

Hydro Generator

Ttnbo Generator

Miriam I/Saras** Uanex. A*$ef Costa Mottief. CUPEL 199$. Version l.ff Figure 2- GESINC Entrance Window Block Parameters: Uf Excitation (mask) With this block, the time variation of excitation voltage can be selected. Parameters Uf will be: Distuibance time: 150 % of Ufd variation: Rio Apply |

Revert

Help

|

Close

Figure 3- Excitation Voltage Dialogue Box

|



303

5. Simulation results As it has been explained above, this modular system can be used to analyze the synchronous generator transient behavior submitted to different disturbances. As an example of such disturbances, a turbogenerator symmetrical sudden shortcircuit was considered. The machine was delivering 0,8 per unit active power and 0,3 reactive power before the occurrence of the fault. The electromagnetic torque (M), power angle (deltag), field current (If), and stator current (la) variations were analyzed. Firstly, the overall system must be built utilizing the appropriate modules and introducing all the parameters and associated data as shown in figure 4. The selected variables time response can be observed in figure 5. In order to demonstrate the necessity of including the unequal mutual couplings and the effect of the solid rotor, the same disturbance was simulated utilizing the standard model. The variables time responses are shown in figure 6. If this result is compared to the one in figure 5, the field current time response is quite different. The time variations of the power angle, the electromagnetic torque, and the stator current components are very similar.

Figure 4- Turbogenerator System for Analyzing a Sudden Short-circuit. Conclusions A synchronous generator modular system for analyzing its transient behavior has been obtained. It has several important advantages: 1. It considers the different type of rotors, obtaining in this way, a better field current simulation. 2. A recognised professional program as SIMULINK from MATLAB supports it. 3. The input data needed from the user is very simple, only the active and reactive power and the bus voltage. 4. It is an adequate educational tool for undergraduate and postgraduate programs as well as for training courses in the Electric Utility Industry and in research centers. This modular system will be expanded in the near future by introducing the following steps: 1. The possibility of introducing a random noise. 2. The simulation of the excitation system permitting the voltage regulator adjustment. 3. The simulation of an isolated generator against an electric load. 4. The simulation of a limited number of parallel generators.


304

Software for Electrical Engineering Analysis and Design BEE3I 300 200 100

0 Time offset: 0

50

100

150

200

0 0 Time offset: 0

50

100

150

BEE

0 Time offset: 0

50

100

150

200

200 BED

0 Time off set: 0

50

100

150

200

Figure 5- Selected variables time response with the turbogenerator model: a) Electromagnetic torque, b) Power angle, c) Field current and d) Stator current.