PowerFlow provides basic models and a general connector for the electrical side of power plant systems. Currently it allows to treat symmetrically loaded three phase systems and direct current lines in one framework. PowerFlow is used to investigate the test case "Stabilization of wind power" in the Eurosyslib work package 5.3.

The PowerFlow connector is motivated by the SPOT library and by the concept of replaceable Modelica.Media packages for fluid models. The aim is to support different single and polyphase systems and different mathematical formulations in one framework. This may cover applications like:

- Three phase AC transmission lines, using natural or modal coordinates,
- Single phase AC applications,
- Variable freqency systems, e.g. to control the power of a motor with a frequency converter, and
- Direct current lines, like HVDC

A general terminal for electrical power systems can be defined as:

connector Terminal "General power terminal" replaceable package PhaseSystem = PhaseSystems.PartialPhaseSystem "Phase system"; PhaseSystem.Voltage v[PhaseSystem.n] "voltage vector"; flow PhaseSystem.Current i[PhaseSystem.n] "current vector"; PhaseSystem.ReferenceAngle theta[PhaseSystem.m] "vector of phase angles"; end Terminal;

The replaceable PhaseSystem defines the number

of independent voltage and current components
and their representation in the connector. Moreover it defines
types for the physical quantities so that terminals of different
phase systems cannot be directly connected.**n**

The vector of reference angles

allows the definition of a rotating reference system for the
description of AC systems with modal components. It is known from
the SPOT library that this simplifies the treatment of sinosodial
quantities in the time domain. The power Terminal is overdetermined
with the reference angles though and the operators
Connections.root, Connections.potentialRoot, Connections.isRoot and
Connections.branch are used for their implementation. A Modelica
tool needs to analyze connection graphs and eliminate redundant
equations.**theta[m]**

**Modelica.Electrical** describes voltages and currents using
natural coordinates in the time domain, i.e. m=0. It defines a
distinct MultiPhase sublibrary for multi phase systems
(n>=1, default: 3). This has the drawback that sinusoidal
quantities of AC systems with frequencies of e.g., 50 Hz complicate
the numerical analysis as electrical quantities vary with a period
of 20 ms while the system dynamics of interest may be in the order
of seconds to minutes.

**ObjectStab** uses complex current and voltage phasors for
the analysis of symmetrically loaded three phase systems with
constant frequency, i.e. n=2, m=0. The freqency is a global
property. This complicates the analysis of power/frequency control
and of drives with frequency converters.

**Complex** combines the concepts of Modelica.Electrical and
ObjectStab. It uses complex voltage and current phasors with
constant frequency (m=0). Similar to Modelica.Electrical it defines
different sublibraries for one phase systems (n=1) and three phase
systems (n=3).

**AC** uses complex voltage and current phasors for
SinglePhase systems (n=1, m=1).

**SPOT** allows the detailed and efficient analysis of three
phase systems. It provides the most comprehensive collection of
models for power electronics currently available in Modelica. SPOT
provides three sublibraries for three phase systems with modal dq0
coordinates (n=3, m=2), natural abc coordinates (n=3, m=2) as well
as for DC systems (n=1, m=0).

It is the hope that the valuable concepts of different existing
libraries can be combined into one and that at least basic
interfaces and components can be shared. The current version of the
PowerFlow library concentrates on the not yet available
symetrically loaded three phase systems with modal coordinates.
This is provided by the `ThreePhaseSymmetric`

phase
system (n=2, m=1). Moreover the `DirectCurrent`

phase
system (n=1, m=0) is provided to investigate the sharing of
connectors and component models.

A PhaseSystem is a package that provides types, functions and constants. A generic steady-state impedance model, which is independent of the phase system in use, can be formulated as:

model GenericImpedance replaceable package PhaseSystem = PackagePhaseSystem "Phase system"; function j = PhaseSystem.j; Terminal terminal_p(redeclare package PhaseSystem = PhaseSystem); Terminal terminal_n(redeclare package PhaseSystem = PhaseSystem); PhaseSystem.Voltage v[:] = terminal_p.v - terminal_n.v; PhaseSystem.Current i[:] = terminal_p.i; PhaseSystem.Frequency w = der(PhaseSystem.angle(terminal_p.theta)); parameter Modelica.SIunits.Resistance R = 1 "active component"; parameter Modelica.SIunits.Inductance L = 1/50 "reactive component"; equation v = R*i + w*L*j(i); zeros(PhaseSystem.n) = terminal_p.i + terminal_n.i; terminal_p.theta = terminal_n.theta; Connections.branch(terminal_p.theta, terminal_n.theta); end GenericImpedance;

The examples NetworkLoop and NetworkOpened are taken from the textbook Oeding, Oswald: Elektrische Kraftwerke und Netze, section 14.2.5: Leistungsfluss in Ringnetzen. The example NetworkControlled additionally investigates frequency/power control in conjunction with the Modelica.Rotational library and a basic EMF (Electro-Motoric Force).

The PowerWorld example models a control area for power distribution in island mode. It is used to investigate the test case "Stabilization of wind power" in the Eurosyslib work package 5.3. See Examples.PowerWorld.

The component tests are taken from the textbook Oeding, Oswald: Elektrische Kraftwerke und Netze, section 14: Leistungsfluss im Drehstromnetz.

Copyright © 2007-2009, Modelica
Association.

This Modelica package is Open Source software; it can be redistributed and/or modified under the terms of the Modelica license, version 2.0.

Partial financial support of ABB for this work within the ITEA2 EUROSYSLIB project is highly appreciated (BMBF Förderkennzeichen 01IS07022F).

*26 Feb 2009*by Rüdiger Franke:

Version 0.3-
- Generalize power Terminal with n voltages/currents and m reference angles
- Add PowerWorld example

*21 Oct 2008*by Rüdiger Franke:

Version 0.2-
- Replace balanced, non-minimal connector with overdetermined minimal connector
- Remove instance variables BaseProperties from PhaseSystems and introduce member functions instead

*15 Aug 2008*by Rüdiger Franke:

Version 0.1

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