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DIgSILENT Technical Documentation
General Load Model
DIgSILENT GmbH Heinrich-Hertz-Strasse 9 D-72810 Gomaringen Tel.: +49 7072 9168 - 0 Fax: +49 7072 9168- 88 http://www.digsilent.de e-mail: mail@digsilent.de
General Load Model Published by DIgSILENT GmbH, Germany Copyright 2008. All rights reserved. Unauthorised copying or publishing of this or any part of this document is prohibited. TechRef ElmLod V4 Build 507 30.10.2008
General Load Model
Table of Contents
Table of Contents
1 General Description........................................................................................................................... 4 1.1 Load-Flow Analysis ................................................................................................................................... 4 1.1.1 Balanced Load-Flow ............................................................................................................................. 5 1.1.2 Unbalanced Load-Flow ......................................................................................................................... 5 1.1.2.1 3-phase loads ................................................................................................................................. 6 1.1.2.2 2-Phase Loads ................................................................................................................................ 7 1.1.2.3 1-phase loads ................................................................................................................................. 8 1.1.3 DC loads ............................................................................................................................................. 9 1.1.4 Voltage dependency........................................................................................................................... 10 1.1.5 Load Scaling factors ........................................................................................................................... 12 1.2 Short-Circuit Analysis .............................................................................................................................. 14 1.3 Harmonic Analysis................................................................................................................................... 15 1.3.1 Passive Load...................................................................................................................................... 15 1.3.2 Harmonic Current Injections ............................................................................................................... 17 1.4 RMS Simulation (Transient Stability) ........................................................................................................ 18 1.5 EMT Simulation....................................................................................................................................... 21 2 Input/Output Definition of the Dynamic Model .............................................................................. 22 2.1 Three-Phase Load................................................................................................................................... 22 2.1.1 RMS-Simulation ................................................................................................................................. 22 2.1.2 EMT-Simulation ................................................................................................................................. 23 2.2 Single-, Two-Phase Load and DC-Load ..................................................................................................... 23 3 Parameter Definitions ..................................................................................................................... 24 3.1 General Load Type (TypLod) ................................................................................................................... 24 3.2 General Load Element (ElmLod)............................................................................................................... 25
General Load Model
1 General Description
In power systems, electrical load consists of various different types of electrical devices, from incandescent lamps and heaters to large arc furnaces and motors. It is often very difficult to identify the exact composition of static and dynamic loads in the network. This load composition can also vary depending on factors such as the season, time of day etc. Additionally, the term load can be used for entire MV-feeders in case of an HV-system or LV-feeders if an MVsystem is in the centre of interest. The PowerFactory model “General Load” can therefore represent: • • A complete feeder A combination of dynamic and static loads
The general load model diagram is shown in Figure 1 below.
Figure 1: DIgSILENT General Load Model
1.1 Load-Flow Analysis
In the element window for the load, the user is free to choose whether the load is balanced or unbalanced. Furthermore the user can specify the input parameters for the load using the Input Mode drop down menu as shown in Figure 2 below. Based on the available data, the user can select the relevant combination of parameters from S (apparent power), P (real power), Q (reactive power), cos(phi) (power factor) and I (current). For load-flow analysis, it suffices to only specify the load's electrical consumption. Other data characterizing a load, such as the number of phases or voltage dependency factors (see also 1.1.3) are defined in the Load Type. If no load type is specified, a balanced, three-phase load is assumed having default parameters for voltage dependency kpu=1.6 and kqu=1.8 (see also section 1.1.4).
General Load Model
Figure 2: Specifying the input parameters for the load model
1.1.1 Balanced Load-Flow
Depending on the selected input mode, the user needs to specify two input parameters. Figure 3 shows the load model used for balanced load-flow analysis, where only P0 and Q0 are specified. All loads specified as 2-phase and/or 1-phase loads are only considered in unbalanced load flow calculations. They are ignored when a balanced load-flow is performed.
Figure 3: Load model used for balanced load-flows.
1.1.2 Unbalanced Load-Flow
When running a load flow with a complete ABC-network representation, network unbalances resulting from either unbalanced loads or unbalanced branch elements can be considered. Additional data for unbalanced load flow analysis is: • Technology
Figure 4 shows the input dialog window for specifying the type data for General loads.
General Load Model
Figure 4: General load type data input window
1.1.2.1 3-phase loads (3PH-‘D’, 3PH PH-E, 3PH-’YN’)
The actual load per phase is entered in the input dialogue-box of the load element. The user has the choice between: • Balanced load, only specifying the sum of all phases. In this case, it is assumed that the load is shared equally amongst the phases. Unbalanced load, specifying the individual phase loads.
•
Figure 5: 3-phase, Technology 3PH ‘D’ load model diagram
General Load Model
Figure 6: 3-phase, Technology 3PH PH-E load model diagram
Figure 7: 3-phase, Technology 3PH ‘YN’ load model diagram
1.1.2.2 2-Phase Loads (2PH PH-E, 2PH-’YN’)
Such a load type can be used for modelling loads in two-phase or bi-phase systems.
General Load Model
Figure 8: 2-phase, Technology 2PH PH-E load model diagram
Figure 9: 2-phase, Technology 2PH-‘YN’ load model diagram
1.1.2.3 1-phase loads (1PH PH-PH, 1PH PH-N, 1PH PH-E)
The “1PH PH-PH” load model can be used for representing loads connected between two phases, which is in fact a single-phase load between two phases (see Figure 10).
Figure 10: 1-phase, Technology 1PH PH-PH load model diagram
The “1PH PH-N” load model can be used for a load connected between one phase and the neutral phase (see Figure 11).
General Load Model
Figure 11: 1-phase, Technology 1PH PH-N load model diagram
The “1PH PH-E” load model can be used for a load connected between one phase and earth (see Figure 12).
Figure 12: 1-phase, Technology 1PH PH-E load model diagram
1.1.3 DC loads
DC-loads are always “single-phase”, as shown in Figure 10. For load flow analysis, the load is characterized by the active power flow P. Inductive effects are only considered in transient simulations.
Figure 13: 1-phase DC load model diagram
General Load Model
1.1.4 Voltage dependency
Voltage dependency of loads can be modelled using a potential approach, as shown in (1) and (2). In these equations, the subscript 0 indicates the initial operating condition as defined in the input dialogue box of the Load Element.
e _ aP e _ bP e _ cP ⎛ ⎞ ⎛v⎞ ⎛v⎞ ⎜ aP ⋅ ⎛ v ⎞ ⎟ ⎜ ⎟ + bP ⋅ ⎜ ⎟ P = P0 + (1 − aP − bP ) ⋅ ⎜ ⎟ ⎜v ⎟ ⎜v ⎟ ⎜v ⎟ ⎜ ⎟ ⎝ 0⎠ ⎝ 0⎠ ⎝ 0⎠ ⎝ ⎠
(1)
where
1 − aP − bP = cP
e _ aQ e _ bQ e _ cQ ⎛ ⎞ ⎛v⎞ ⎛v⎞ ⎛v⎞ ⎟ Q = Q0 ⎜ aQ ⋅ ⎜ ⎟ + bQ ⋅ ⎜ ⎟ + (1 − aQ − bQ ) ⋅ ⎜ ⎟ ⎜v ⎟ ⎜v ⎟ ⎜v ⎟ ⎜ ⎟ ⎝ 0⎠ ⎝ 0⎠ ⎝ 0⎠ ⎝ ⎠
(2)
where
1 − aQ − bQ = cQ
By specifying the respective exponents (e_aP/e_bP/e_cP and e_aQ/e_bQ/e_cQ ) the inherent load behaviour can be modelled. Table 1 provides the value for the exponents required to achieve constant power, current and impedance behaviour. However, the relative proportion of each coefficient can be freely defined using the coefficients aP, bP, cP and aQ, bQ, cQ. See Figure 11.
Table 1: Selection of exponent value for different load model behaviour
Exponent Constant
0 1 2
power current impedance
General Load Model
Figure 14: Specification of the voltage dependency factors NOTE: These factors are only considered if the “Consider Voltage Dependency of Loads” is checked in the Load-flow Calculation window, as shown in Figure 15 below.
Figure 15: Load-flow Calculation window indicating the use of voltage dependency terms for loadflow calculations
General Load Model
1.1.5 Load Scaling factors
Loads can be scaled individually by setting the “Scaling Factor” s of the Load Element (see also Figure 16). Together with the scaling factor, the actual load is calculated as follows:
P = scale ⋅ P0 Q = scale ⋅ Q0
If voltage dependency of loads is considered then (3) and (4) become;
e _ aP e _ bP e _ cP ⎛ ⎞ ⎛v⎞ ⎛v⎞ ⎜ aP ⋅ ⎛ v ⎞ ⎟ ⎜ ⎟ P = scale ⋅ P0 + bP ⋅ ⎜ ⎟ + (1 − aP − bP ) ⋅ ⎜ ⎟ ⎜v ⎟ ⎜v ⎟ ⎜v ⎟ ⎜ ⎟ ⎝ 0⎠ ⎝ 0⎠ ⎝ 0⎠ ⎝ ⎠ e _ aQ e _ bQ e _ cQ ⎛ ⎞ ⎛v⎞ ⎛v⎞ ⎛v⎞ ⎟ Q = scale ⋅ Q0 ⎜ aQ ⋅ ⎜ ⎟ + bQ ⋅ ⎜ ⎟ + (1 − aQ − bQ ) ⋅ ⎜ ⎟ ⎜v ⎟ ⎜v ⎟ ⎜v ⎟ ⎜ ⎟ ⎝ 0⎠ ⎝ 0⎠ ⎝ 0⎠ ⎝ ⎠
(3) (4)
(5)
(6)
Alternatively to explicit scaling factors, loads in radial feeders can be scaled based on the total inflow into the feeder, as illustrated in Figure 17. For considering a load in the feeder-load-scaling process, the option “Adjusted by Load Scaling” (see Figure 16) has to be enabled. In this case, the individual “Scaling Factor” of the load is not considered but overwritten by the feeder-scaling factor. The feeder-load-scaling function can be enabled or disabled globally using the corresponding load-flow option (see also Figure 15).
General Load Model
Figure 16: Scaling factor specification
Figure 17: Diagram indicating load scaling (adjustment) in order to maintain the feeder settings specified in the Feeder Definition
General Load Model
1.2 Short-Circuit Analysis
Short circuit calculations according to IEC 60909, VDE102/103 or ANSI C37 generally neglect loads. Only motor contributions are considered here. The COMPLETE short circuit method utilises constant impedance (Z) or constant current I0 models. Z and I0 are calculated from a preceding load-flow analysis. Figure 18 shows the type data window used to select whether the load is constant current or constant impedance. See notes on Harmonic Analysis for further explanation of the models.
Figure 18: Selection of load type of either constant current or constant impedance for consideration in short circuit calculations using the Complete Method.
Figure 19 shows a 3-phase representation of a Y connected constant impedance and Figure 20 shows the 3phase representation of the D connected constant current model.
Figure 19: 3-phase constant impedance model, in Y and D connection, used for short circuit calculations using the Complete method.
General Load Model
Figure 20: 3-phase constant current load, in Y and D connection, used load for short circuit calculations utilising the Complete method
1.3 Harmonic Analysis
In the type data of the general load model, the harmonic load model can be specified as either constant impedance or current source. Figure 21 shows the selection of the harmonic load model type.
Figure 21: Selection of the load model type for harmonic analysis
1.3.1 Passive Load
Passive loads can be represented as purely inductive or capacitive or a mixture of inductive and capacitive. Figure 22 shows the single-phase representation of a purely inductive and capacitive load.
General Load Model
Figure 22: Purely inductive/capacitive load models used for harmonic analysis
The parameters R,L (G,C) are calculated from a preceding load-flow. Figure 23 shows the single-phase load model for mixed inductive/capacitive load models (e.g. cables), used during harmonic analysis.
Figure 23: The single phase equivalent for mixed inductive/capacitive load model
NOTE: Figure 22 and Figure 23 are single phase representations of the passive load. The 3-phase presentation is similar to that shown in Figure 6 and Figure 5, and with either Y or D connections. The inductive/capacitive portion of the load is specified by (7) and (8);
Qc QC 1 = = Q QL + QC QL +1 QC
(7)
ω nC =
y ⎛ QL ⎜1 − ⎜ Q C ⎝
⎞ ⎟ ⎟ ⎠
(8)
General Load Model
1.3.2 Harmonic Current Injections
Nonlinear loads are described by their harmonic current spectrum. A requirement for modelling current injecting loads is to set the corresponding parameter on the harmonics page to current source. For balanced loads, only characteristic harmonics can be specified. Figure 24 shows the specification of the characteristic harmonic spectrum in the element data window of the load. The angles of harmonic currents are defined with reference to the fundamental frequency phase angle (cosine reference). This way of entering phase angles allows defining the current waveform independent from the power factor at fundamental frequency. Figure 24 shows the current spectrum of an ideal 6-pulse rectifier. Absolute current angles will be adjusted by
PowerFactory according to (10).
Figure 24: Specification of the harmonic current spectrum for balanced loads
The harmonic currents are defined by (9) and the phase angle of the harmonic currents is defined by (10).
I ( f ) = k( f ). I ( f )
n
(9)
General Load Model
ϕ( f ) = ϕ +
f ϕ1 fn
(10)
where fn is the nominal frequency and ϕ1is phase angle of the fundamental current. In case of unbalanced loads, frequency, phase angle and magnitude of harmonic currents can be entered individually for each phase. Figure 25 shows the input window for entering such data.
Figure 25: Specification of the harmonic current spectrum per phase for unbalanced loads
1.4 RMS Simulation (Transient Stability)
For RMS simulations a three-phase load can be modelled as a percentage of static and dynamic load. The static portion is modelled as constant impedance whereas the dynamic load can be modelled as either a linear load or a non-linear load. Two-phase, single-phase- and DC loads are generally modelled as constant impedance.
General Load Model
Figure 26: Diagram indicating the mixture of static and dynamic loads used for stability studies.
The background of the dynamic, voltage- and frequency dependent load model according to Figure 24 and Figure 25 is a motor-load in parallel to a static, non-linear load. The parameters of the block diagrams in Figure 24 and Figure 25 can either be calculated from such a configuration, but they are usually identified from load measurements. The model according to Figure 24 is a small signal approximation of the model according to Figure 25. Parameters with equal names correspond to each other.
Figure 27: Model used to approximate the behaviour of the linear dynamic load.
General Load Model
Figure 28: Model used to approximate the behaviour of the non-linear dynamic load.
Since the block diagrams according to Figure 27 and Figure 28 represent small signal models, they are only valid in a limited voltage range. This voltage range is defined by the variables umin and umax. Outside this voltage range, the power is adjusted according to Figure 29.
Figure 29: Low/High voltage approximations used in the non-linear dynamic load model.
With reference to the outputs of the block diagrams according to Figure 24 and Figure 25, the load equations representing the full voltage range can be expressed as follows:
General Load Model
P = k .Pout Q = k .Qout k =1 k= 2u u min
2 2
: u min < u < u max : 0

__u max 1.5 EMT Simulation In EMT type simulations, all the loads are modelled as passive loads using the equivalent circuits shown in the harmonics-section. NOTE: The use of negative active power leads in EMT simulations to unstable behaviour, since negative P is interpreted as negative resistance. General Load Model 2 Input/Output Definition of the Dynamic Model 2.1 Three-Phase Load 2.1.1 RMS-Simulation Pext Qext Figure 30: Input/Output Definition of General Load Model (RMS-Simulation) Table 2: Input Variables (RMS-Simulation) Parameter Description Unit Pext Qext Active Power Input Reactive Power Input MW Mvar Table 3: State Variables (RMS-Simulation) Parameter Description Unit xu xf cosphiu sinphiu Delayed Voltage (Time constant T1) Delayed Frequency (Time constant T1) cosine of voltage angle sine of voltage angle p.u. p.u Table 4: Additional Parameters and Signals (RMS-Simulation) Parameter Description Unit fe scale Electrical Frequency Scaling Factor p.u. General Load Model 2.1.2 EMT-Simulation Table 5: State Variables (EMT-Simulation) Parameter Description Unit curLA curLB curLC Inductive Current, Phase A Inductive Current, Phase B Inductive Current, Phase C p.u. p.u p.u. 2.2 Single-, Two-Phase Load and DC-Load Constant impedance load models. No input or output variables. General Load Model 3 Parameter Definitions 3.1 General Load Type (TypLod) Table 6: Input parameters of Load - Type Parameter Description Unit loc_name systp nlnph cnm kpu kqu i_csrc i_pure pgrd qcq xt Prp lodst loddy i_nln t1 kpf kpu tpf tpu kqf kqu tqf tqu udmax udmin i_nln Name System Type Phases Connection Static Voltage Dependence: Volt. Dependence on P Static Voltage Dependence: Volt. Dependence on Q Current Source/Impedance Load model Capacitive/Inductive Reactive Power: QL/QC Capacitive/Inductive Reactive Power: QC/Q Transformer Short Circuit Reactance Power of parallel Resistance/Total Active Power Percentage: Static (const Z) Percentage: Dynamic Percentage: Nonlinear Model Dynamic Load Time Constant Dynamic Active Load: Frequ. Dependence on P Static Voltage Dependence: Volt. Dependence on P Dynamic Active Load: Transient Frequency Dependence Dynamic Active Load: Transient Voltage Dependence Dynamic Reactive Load: Frequ. Dependence on Q Static Voltage Dependence: Volt. Dependence on Q Dynamic Reactive Load: Transient Frequency Dependence Dynamic Reactive Load: Transient Voltage Dependence Voltage Limits: Upper Voltage Limit Voltage Limits: Lower Voltage Limit Percentage: Nonlinear Model p.u. p.u. s s s s s % % % % % % General Load Model 3.2 General Load Element (ElmLod) Table 7: Input parameters of Load - Element Parameter Description Unit loc_name outserv mode_inp i_sym plini qlini slini ilini coslini pf_recap u0 scale0 i_scale plinir qlinir slinir ilinir coslinir pf_recapr plinis qlinis slinis ilinis coslinis pf_recaps plinit qlinit slinit ilinit coslinit pf_recapt i_rem p_cub NrCust pSCDF OptCost OptMeth pStoch pCurve Name Out of Service Input Mode Balanced/Unbalanced Operating Point: Total Active Power Load Operating Point: Total Reactive Power Load Operating Point: Total Apparent Power Operating Point: Current Operating Point: Power Factor Operating Point: Power Factor Operating Point: Voltage Operating Point: Scaling Factor Operating Point: Adjusted by Load Scaling Phase a: Active Power Phase a: Reactive Power Phase a: Apparent Power Load Phase a: Current Phase a: Power Factor Phase a: Power Factor Phase b: Active Power Phase b: Reactive Power Phase b: Apparent Power Phase b: Current Phase b: Power Factor Phase b: Power Factor Phase c: Active Power Phase c: Reactive Power Phase c: Apparent Power Phase c: Current Phase c: Power Factor Phase c: Power Factor Remote Control Controlled Branch (Cubicle) (StaCubic Number of connected customers Interruption costs (ChaVec,ChaOut) Interruption costs Characteristic Stochastic model Area Model (StoChalod) StoLod MW Mvar MVA kA MW Mvar MVA kA MW Mvar MVA kA p.u. MW Mvar MVA kA General Load Model i_prty shed trans pTrans Load shedding/transfer: Load priority Load shedding/transfer: Shedding steps Load shedding/transfer: Transferable Load shedding/transfer: Node to Transfer to (ElmTerm,StaBar) % General Load Model__