ObjectStab.Generators.Partials

ObjectStab.Generators.Partials.Generator

Information

The complex power a generator delivers to the network is given by:

S = Pg+jQg = -v * conj(i)

The variables Pg and Qg corresponds to the actual active and reactive power 
delivered to the network.

Modelica definition

partial model Generator "Shell model for generator" 
  extends Base.OnePin;
  
  Base.ActivePower Pg "Generated Active Power";
  Base.ReactivePower Qg "Generated Reactive Power";
  Base.VoltageAmplitude V(start=1);
  
equation 
  V = sqrt((1 + T.va)*(1 + T.va) + T.vb*T.vb);
  T.ia = -(T.vb*Qg + Pg + Pg*T.va)/(1 + 2*T.va + T.va*T.va + T.vb*T.vb);
  T.ib = -(Pg*T.vb - Qg - T.va*Qg)/(1 + 2*T.va + T.va*T.va + T.vb*T.vb);
end Generator;

ObjectStab.Generators.Partials.DetGen3

Information

The 3rd order detailed generator model corresponds to Model 3 in [1, pp 348], 
and extends the DetGen class. It adds a single transient EMF source in 
the quatradure axis and the field voltage input. This model neglects the effect 
of damper windings and the damping produced by rotor eddy-currents.
The effect of this damping is usually included in the damping coefficient D.


---
[1] J. Machowski, J.W. Bialek, and J.R. Bumby, Power System Dynamics and 
Stability, Number ISBN 0-471-97174. Wiley, 1993.

Parameters

Name	Default	Description
H	6	Inertia Constant [s]
D	0	Damping Coeficient [1]
Pgref	0.60	Active Power Generation Reference [p.u.]
rt	0	Step-up Transformer Resistance [p.u.]
xt	0	Step-up Transformer Reactance [p.u.]
ra	0	Armature Resistance [p.u.]
xd	0.8948	Direct Axis Synchronous Reactance [p.u.]
xq	0.84	Quadrature Axis Synchronous Reactance [p.u.]
xdp	0.30	Direct Axis Transient Reactance [p.u.]
Td0p	7	Open-circuit Direct Axis Transient Time Constant [s]

Modelica definition

partial model DetGen3 "3rd Order Detailed Generator" 
  extends DetGen;
  
  parameter Base.Resistance ra=0 "Armature Resistance";
  parameter Base.Reactance xd=0.8948 
    "Direct Axis Synchronous Reactance";
  parameter Base.Reactance xq=0.84 
    "Quadrature Axis Synchronous Reactance";
  parameter Base.Reactance xdp=0.30 
    "Direct Axis Transient Reactance";
  parameter Base.Time Td0p=7 
    "Open-circuit Direct Axis Transient Time Constant";
  
  Base.VoltageRealPart Eqp(start=1);
  Base.VoltageAmplitude Efd(start=1);
equation 
  // Transient EMF equation
  Td0p*der(Eqp) = Efd - Eqp + id*(xd - xdp);
  
  // stator equations 
  vd = -ra*id - xq*iq;
  vq = Eqp + xdp*id - ra*iq;
  
  // electrical power 
  Pe = Eqp*iq + (xdp - xq)*id*iq;
end DetGen3;

ObjectStab.Generators.Partials.DetGen6

Information

The 6th order detailed generator model extends the DetGen class and 
corresponds to Model 6 in [1, pp 347], and adds subtransient EMF voltage sources
in both the direct quatradure axes and the field voltage input. 

This model includes the damping introduced by damper winding and eddy-currents in
the rotor, and the damping coefficient D should only model the damping
due to friction.

---
[1] J. Machowski, J.W. Bialek, and J.R. Bumby, Power System Dynamics and 
Stability, Number ISBN 0-471-97174. Wiley, 1993.

Parameters

Name	Default	Description
H	6	Inertia Constant [s]
D	0	Damping Coeficient [1]
Pgref	0.60	Active Power Generation Reference [p.u.]
rt	0	Step-up Transformer Resistance [p.u.]
xt	0	Step-up Transformer Reactance [p.u.]
ra	0	Armature Resistance [p.u.]
xd	0.8948	Direct Axis Synchronous Reactance [p.u.]
xq	0.84	Quadrature Axis Synchronous Reactance [p.u.]
xdp	0.30	Direct Axis Transient Reactance [p.u.]
xqp	0.10	Quadrature Axis Transient Reactance [p.u.]
xqpp	0.20	Direct Axis Subtransient Reactance [p.u.]
xdpp	0.10	Quadrature Axis Subransient Reactance [p.u.]
Td0p	7	Open-circuit Direct Axis Transient Time Constant [s]
Tq0p	0.44	Open-circuit Quadrature Axis Transient Time Constant [s]
Td0pp	0.02	Open-circuit Direct Axis Subtransient Time Constant [s]
Tq0pp	0.03	Open-circuit Quadrature Axis Subtransient Time Constant [s]

Modelica definition

partial model DetGen6 "6th Order Detailed Generator" 
  extends DetGen;
  
  parameter Base.Resistance ra=0 "Armature Resistance";
  parameter Base.Reactance xd=0.8948 
    "Direct Axis Synchronous Reactance";
  parameter Base.Reactance xq=0.84 
    "Quadrature Axis Synchronous Reactance";
  parameter Base.Reactance xdp=0.30 
    "Direct Axis Transient Reactance";
  parameter Base.Reactance xqp=0.10 
    "Quadrature Axis Transient Reactance";
  parameter Base.Reactance xqpp=0.20 
    "Direct Axis Subtransient Reactance";
  parameter Base.Reactance xdpp=0.10 
    "Quadrature Axis Subransient Reactance";
  parameter Base.Time Td0p=7 
    "Open-circuit Direct Axis Transient Time Constant";
  parameter Base.Time Tq0p=0.44 
    "Open-circuit Quadrature Axis Transient Time Constant";
  parameter Base.Time Td0pp=0.02 
    "Open-circuit Direct Axis Subtransient Time Constant";
  parameter Base.Time Tq0pp=0.03 
    "Open-circuit Quadrature Axis Subtransient Time Constant";
  
  Base.VoltageAmplitude Efd(start=1);
  Base.VoltageRealPart Eqp(start=1);
  Base.VoltageImagPart Edp(start=0);
  Base.VoltageRealPart Eqpp(start=1);
  Base.VoltageRealPart Edpp(start=0);
equation 
  
  // transient and subtransient equations
  Td0pp*der(Eqpp) = Eqp - Eqpp + id*(xdp - xdpp);
  Tq0pp*der(Edpp) = Edp - Edpp - iq*(xqp - xqpp);
  Td0p*der(Eqp) = Efd - Eqp + id*(xd - xdp);
  Tq0p*der(Edp) = -Edp - iq*(xq - xqp);
  
  // stator equations 
  vd = Edpp - ra*id - xqpp*iq;
  vq = Eqpp + xdpp*id - ra*iq;
  
  // electrical power 
  Pe = (Edpp*id + Eqpp*iq) + (xdpp - xqpp)*id*iq;
end DetGen6;

ObjectStab.Generators.Partials.DetGen

Information

Common definitions for detailed generator models, includeing generator step-up
transformer. The terminal voltage used by the voltage regulator is the
voltage on the network side of the step-up transformer.

Each generator has it's own dq coordinate system, and its stator equations
must therefore be related to the network (global) coordinate system using the 
so called Kron's transformations [1, pp. 90].

 


---
[1] J. Machowski, J.W. Bialek, and J.R. Bumby, Power System Dynamics and 
Stability, Number ISBN 0-471-97174. Wiley, 1993.

Parameters

Name	Default	Description
H	6	Inertia Constant [s]
D	0	Damping Coeficient [1]
Pgref	0.60	Active Power Generation Reference [p.u.]
rt	0	Step-up Transformer Resistance [p.u.]
xt	0	Step-up Transformer Reactance [p.u.]

Modelica definition

partial model DetGen "Common Definitions for Detailed Generator" 
  extends Generator;
  
  parameter Base.InertiaConstant H=6 "Inertia Constant";
  parameter Base.DampingCoefficient D=0 "Damping Coeficient";
  parameter Base.ActivePower Pgref=0.60 
    "Active Power Generation Reference";
  parameter Base.Resistance rt=0 "Step-up Transformer Resistance";
  parameter Base.Reactance xt=0 "Step-up Transformer Reactance";
  
  Base.VoltageAngle delta "Rotor Angle [rad]";
  Base.MechanicalPower Pm(start=Pgref) "Mechanical Power";
  Base.ActivePower Pe(start=Pgref) "Electrical Power";
  Base.CurrentImagPart id 
    "Direct axis component of Armature Current";
  Base.CurrentRealPart iq 
    "Quatrature axis component of Armature Current";
  Base.VoltageImagPart vd 
    "Direct axis component of Armature Voltage";
  Base.VoltageRealPart vq 
    "Quadrature axis component of Armature Voltage";
  Base.AngularVelocity dw(start=0) 
    "Deviation from Synchronous Angular Speed";
  Base.AngularVelocity w(start=Base.ws) "Angular Speed";
  Real[2, 2] KronMatrix;
  Base.VoltageRealPart vap;
  Base.VoltageImagPart vbp;
  
equation 
  
  //   swing equations 
  dw = w - Base.ws;
  der(dw) = Base.ws/(2*H)*(Pm - Pe - D/Base.ws*dw);
  der(delta) = dw;
  
  // Kron's transformation, see fig 3.30 in Machovski 
  KronMatrix = [-sin(delta), cos(delta); cos(delta), sin(delta)];
  [1 + vap; vbp] = KronMatrix*[vd; vq];
  -[T.ia; T.ib] = KronMatrix*[id; iq];
  
  // step-up transformer eqs
  [T.va - vap; T.vb - vbp] = [rt, -xt; xt, rt]*[T.ia; T.ib];
end DetGen;