FLOWC RE

technical report SR 95/###### p. 1
Technical report of FLOWC program

technical report SR 95/###### p. 2
INDEX
1. GENERALS......................................................................................................................4
1.1 Network models .......................................................................................................5
1.2 Algorithm of solution................................................................................................6
1.3 Functional possibilities..............................................................................................6
1.4 Limits of the program ...............................................................................................7
2. LOAD-FLOW solution......................................................................................................8
2.1 Generals ...................................................................................................................8
2.2 Scope and validity of the model.................................................................................8
2.3 Description of the model...........................................................................................8
2.4 Other algorithms of solution in the program............................................................11
2.5 References..............................................................................................................12
3. LOAD-FLOW SOLUTION THROUGH THE LOAD ANALYSIS METHOD................14
3.1 Generals .................................................................................................................14
3.2 Scope and validity of the model...............................................................................14
3.3 Description of the model.........................................................................................14
3.4 References..............................................................................................................16
4. MODEL OF THE NETWORK COMPONENTS.............................................................17
4.1 Model of the lines...................................................................................................17
4.2 Model of the transformers and LTC (on load tap-changer)......................................18
4.2.1 Model of the transformers with the ratio out of the rated value in p.u.............18
4.2.2 LTC model - Derivatives of the parameters with respect to the
regulation variables........................................................................................20

technical report SR 95/###### p. 3
4.6.1 Generals ........................................................................................................30
4.6.2 Scope and validity of the model .....................................................................30
4.6.3 Description of the model................................................................................31
5. MODELS FOR THE REACTIVE POWER CONTROL..................................................33
5.1 Generals .................................................................................................................33
5.2 Scope and limits of the model .................................................................................33
5.3 Description of the models .......................................................................................34
5.4 References..............................................................................................................37
6. MODEL FOR THE HVDC SYSTEM .............................................................................38
6.1 Description of the model.........................................................................................38
6.2 References..............................................................................................................44
7. CONTINGENCY CALCULATION IN THE FLOWC PROGRAM ................................45
7.1 Generals .................................................................................................................45
7.2 Scope and validity of the model...............................................................................45
7.3 Description of the model.........................................................................................45
7.4 References..............................................................................................................48
8. CALCULATION OF THE DISTANCE FROM THE VOLTAGE COLLAPSE...............49
8.1 Generals .................................................................................................................49
8.2 Definition of the sensitivities and of the distance from the collapse ..........................49
8.3 Implementation of the method in the FLOWC program...........................................52
8.4 References..............................................................................................................53

technical report SR 95/###### p. 4
1. GENERALSErrore. Il segnalibro non è definito.
The scope of FLOWC program is the solution of the steady state power flow distribution and of
the voltage profiles in electrical power systems; these systems can be AC transmission network
or integrated AC-DC networks.
Exploiting the main characteristics of the solution algorithm it's possible, without any loss of
precision, to analyze the steady state of electrical distribution systems and, more in general, of
industrial plants.
In the following some of the most interesting aspects of the load-flow analysis are synthetized:
1) The generation must satisfy the load plus the transmission losses, so this generation must be
optimally distributed among the generation groups from an economic point of view.
2) The connections can transmit a certain power and then it's necessary that the working point
isn't near to the stability limit or to the thermal limit.
3) It is necessary to verify that the voltage levels of some busbars are within the limits. This
control can be performed by an adequate reactive power dispatching.
4) If the power system is part of an interconnected system it is necessary that the scheduled
power exchanges among the areas are respected.
5) The network disturbances due to faults may cause the out of service of some components;
the effects of these emergency situations may be reduced through proper load-flow
simulations in n-1 conditions (contingency analysis).
As said before the scope of the load-flow is the calculation of the power flows and voltage
profiles of the network.
A single-line representation of the network can be considered advantageous since electrical
systems are generally symmetric. Four quantities are associated to each busbar: the active and
reactive power and the voltage module and phase. In the load-flow calculation three different
busbar types are represented and in each busbar two of the four quantities are fixed. One of

technical report SR 95/###### p. 5
1.1 Network modelsErrore. Il segnalibro non è definito.
The models available for transmission networks components are:
### AC lines, represented by lumped or distributed parameters models or by
generalized ### model;
### two or three winding transformers with or without tap-changer;
### quadrature booster (phase-shifter) with the on-line control of the angle or power;
### DC multiterminal connections with different transmission schemes (mono-phase,
bi-phase, with grounded return, etc.); converter representation through a base module
foreseeing a completely controlled bridge connected to the AC system through a conversion
transformer. The transformer is represented with a tertiary winding to which a synchronous
compensator, AC filters or other devices for reactive power control may be connected.
### FACTS (Flexible AC Transmission System) devices as: Phase-Shifter,
Tap-Changer (LTC or TCUL), series controlled reactance (RANI) and controlled
compensator (SVC).
The models available to represent loads are:
### constant power load;
### constant impedance load;
### voltage dependent load through exponential law;
### voltage dependent load through tabular data defined by the user or through the
point defined by POWASY (this last type is useful for asynchronous machine simulation).
The models available for generators are:
### generation busbar with controlled voltage and active power (P,V type). The user
has available an analytical equation that allows the simulation of the capability curve of the
machine to define the relevant limits;