ObjectStab.Generators

Information

The generator subpackage contains definitions of 
the various generator types.

ObjectStab.Generators.Slack

Information

The slack node acts as angle and frequency reference. Presently, all networks must 
contain at least one slack node.

Parameters

Name	Default	Description
Vref	1.0	Voltage Amplitude [p.u.]
deltaref	0	Voltage Angle [rad]

Modelica definition

model Slack "Slack Node" 
  extends Partials.Generator;
  
  parameter Base.VoltageAmplitude Vref=1.0 "Voltage Amplitude";
  parameter Base.VoltageAngle deltaref=0 "Voltage Angle";
  
equation 
  1 + T.va = Vref*cos(deltaref);
  T.vb = Vref*sin(deltaref);
end Slack;

ObjectStab.Generators.GovExc3rdGen

Information

The 3rd order Generator model with first order governor and exciter 
extend the DetGen3 class with voltage and frequency regulation capabilities.

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

model GovExc3rdGen 
  "3rd order Generator model with first order governor and exciter" 
  extends Partials.DetGen3;
  ObjectStab.Generators.Controllers.Governor Gov(Pgref=Pgref);
  ObjectStab.Generators.Controllers.Exciter Exc;
equation 
  // connection equations for governor and exciter
  Exc.u = V;
  Exc.y = Efd;
  Gov.u = w;
  Gov.y = Pm;
end GovExc3rdGen;

ObjectStab.Generators.NoCon6thGen

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

model NoCon6thGen 
  extends Partials.DetGen6;
  ObjectStab.Generators.Controllers.ConstPm Gov(Pgref=Pgref);
  ObjectStab.Generators.Controllers.ConstEf Exc;
equation 
  
  // connection equations for governor and exciter
  Exc.u = V;
  Exc.y = Efd;
  Gov.u = w;
  Gov.y = Pm;
end NoCon6thGen;

ObjectStab.Generators.PVNode

Information

The PV node with Q-limits models a load-flow PV node with unlimited reactive
power generation resources.

Parameters

Name	Default	Description
Vref	1.0	Voltage Amplitude [p.u.]
Pgref	0	Generated Active Power [p.u.]

Modelica definition

model PVNode "PV Node" 
  extends Partials.Generator;
  
  parameter Base.VoltageAmplitude Vref=1.0 "Voltage Amplitude";
  parameter Base.ActivePower Pgref=0 "Generated Active Power";
  
equation 
  V = Vref;
  Pg = Pgref;
end PVNode;

ObjectStab.Generators.PVNodeLim

Information

The PV node with Q-limits models a load-flow PV node with limited reactive
power generation resources. The node is turned into a PQ-node when Q-limits 
are reached.

 

Parameters

Name	Default	Description
Vref	1.0	Voltage Amplitude] [p.u.]
Pgref	0	Generated Active Power] [p.u.]
Qgmax	10	Generated Reactive Power Limit [p.u.]
Qgmin	-10	Generated Reactive Power Limit [p.u.]

Modelica definition

model PVNodeLim "PV Node with Q Limitation" 
  extends Partials.Generator;
  constant Boolean DymolaCompatibility=true;
  parameter Base.VoltageAmplitude Vref=1.0 "Voltage Amplitude]";
  parameter Base.ActivePower Pgref=0 "Generated Active Power]";
  parameter Base.ReactivePower Qgmax=10 
    "Generated Reactive Power Limit";
  parameter Base.ReactivePower Qgmin=-10 
    "Generated Reactive Power Limit";
  Boolean up_limit(start=false);
  Boolean low_limit(start=false);
equation 
  0 = if up_limit then (Qg - Qgmax) else if low_limit then (Qg - Qgmin) else (
    V - Vref);
  Pg = Pgref;
  new(up_limit) = (up_limit and V < Vref) or not up_limit and (Qg > 
    Qgmax);
  new(low_limit) = (low_limit and V > Vref) or not low_limit and (Qg < 
    Qgmin);
end PVNodeLim;

ObjectStab.Generators.DetGen0

Information

Static implementation of the detailed generator model. Assumes voltage and 
governor controllers that regulate without frequency or voltage droop.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].

Parameters

Name	Default	Description
ra	0	Armature Resistance [p.u.]
xd	0.8948	Direct Axis Synchronous Reactance [p.u.]
xq	0.84	Quadrature Axis Synchronous Reactance [p.u.]
Vref	1.05	Reference Voltage Amplitude [p.u.]
Pgref	0.6	Reference Active Power Generation [p.u.]
rt	0	Step-up Transformer Resistance [p.u.]
xt	0	Step-up Transformer Reactance [p.u.]

Modelica definition

model DetGen0 "Static Detailed Generator" 
  extends Partials.Generator;
  
  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.VoltageAmplitude Vref=1.05 
    "Reference Voltage Amplitude";
  parameter Base.ActivePower Pgref=0.6 
    "Reference Active Power Generation";
  parameter Base.Resistance rt=0 "Step-up Transformer Resistance";
  parameter Base.Reactance xt=0 "Step-up Transformer Reactance";
  Base.VoltageAngle delta(start=1) "Rotor Angle";
  Real[2, 2] KronMatrix;
  Base.CurrentRealPart Eq "q-axis EMF";
  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.VoltageRealPart vap;
  Base.VoltageImagPart vbp;
  
equation 
  // voltage eqs
  Pg = Pgref;
  V = Vref;
  
  vd + ra*id + xq*iq = 0;
  // = Ed
  vq + ra*iq - xd*id = Eq;
  
  // 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];
  //  transformer eqs
  [T.va - vap; T.vb - vbp] = [rt, -xt; xt, rt]*[T.ia; T.ib];
end DetGen0;

ObjectStab.Generators.GovExc6thGen

Information

The 6th order Generator model with first order governor and exciter 
extend the DetGen6 class with voltage and frequency regulation capabilities.

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

model GovExc6thGen 
  "6th order Generator model with first order governor and exciter" 
  extends Partials.DetGen6;
  ObjectStab.Generators.Controllers.Governor Gov(Pgref=Pgref);
  ObjectStab.Generators.Controllers.Exciter Exc;
equation 
  
  // connection equations for governor and exciter
  Exc.u = V;
  Exc.y = Efd;
  Gov.u = w;
  Gov.y = Pm;
end GovExc6thGen;

ObjectStab.Generators.NoCon3rdGen

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

model NoCon3rdGen 
  extends Partials.DetGen3;
  // connection equations for governor and exciter
  ObjectStab.Generators.Controllers.ConstPm Gov(Pgref=Pgref);
  ObjectStab.Generators.Controllers.ConstEf Exc;
equation 
  Exc.u = V;
  Exc.y = Efd;
  Gov.u = w;
  Gov.y = Pm;
end NoCon3rdGen;