Load Flow Analysis
System Concepts
Power in Balanced 3-Phase S V I Systems *
1
LN LN
3
S 3 3
P
S 1 *
V LL LL I jQ
Inductive loads have lagging Power Factors. Capacitive loads have leading Power Factors. Lagging Power Factor
Leading Power Factor
Current and Voltage
Leading & Lagging Power Factors ETAP displays lagging Power Factors as positive and leading Pow er Factors as negative. The Power Factor is displayed in percent.
Leading Power Factor
Lagging Power Factor
P jQ
P - jQ
P + jQ
3-Phase Per Unit System IB
kVAB
S
3VI
3kVB
V
3ZI
(kVB )
ZB
2
MVAB
IB ZB
If you have two bases:
SB
Then you may calculate the other two by using the relationships enclosed in brackets. The different bases are:
3VB
•IB (Base Current)
VB2
•ZB (Base Impedance)
SB
•VB (Base Voltage) •SB (Base Power)
I pu Z pu
I actual IB Zactual ZB
V pu S pu
Vactual VB Sactual SB
ETAP selects for LF:
•100 MVA for SB which is fixed for the entire system.
•The kV rating of reference point is used along with the transformer turn ratios are applied to determine the base voltage for different parts of the system.
Example 1: The diagram shows a simple radial system. ETAP converts the branch impedance values to the correct base for Load Flow calculations. The LF reports show the branch impedance values in percent. The transformer turn ratio (N1/N2) is 3.31 and the X/R = 12.14 Transformer Turn Ratio: The transformer turn ratio is used by ETAP to determine the base voltage for different parts of the system. Different turn ratios are applied starting from the utility kV rating.
kVB1
To determine base voltage use: 1 B
kV 2 B
kV
N1 N 2
kVB2
Transformer T7: The following equations are used to find the impedance of transformer T7 in 100 MVA base.
Z pu X pu 1
X R X R
2
R pu
x pu X R
X pu
0.065(12.14) 1 (12.14)
2
0.06478
0.06478
R pu
12.14
0.005336
The transformer impedance must be converted to 100 MVA base and therefore the following relation must be used, where “n” stands for new and “o” stands for old.
n pu
o pu
Z
Z
o B n B
V
2
V
%Z 100 Z pu
SnB o B
S
(5.33 10
3
j0.06478)
13.8 13.5
2
100 5
(0.1115 j1.3538)
11.15 j135.38
Impedance Z1: The base voltage is determined by using the transf ormer turn ratio. The base impedance for Z1 is determined using the base voltage at Bus5 and the MVA base.
VB
kVutility
N1 N2
13.5 3.31
4.0695
Z B
VB2
(4.0695) 2
MVA
100
0.165608
The per-unit value of the impedance may be determined as soon as the base impedance is known. The per-unit value is multiplied by one hundred to obtain the percent impedance. This value will be the value displayed on the LF report.
Z pu
Zactual
(0.1 j1)
ZB
0.1656
%Z 100 Z pu
(0.6038 j6.0382)
60.38 j603.8
The LF report generated by ETAP displays the following percent impedance values in 100 MVA base
Load Flow Analysis
Load Flow Problem • Given – Load / Power consumption at all buses – Configuration / Network Topology – Power production for each generator
• Basic Calculation Requirements – Power Flow for each branch – Voltage Magnitude and Phase Angle at each bus
Load Flow Studies • Determine Steady State Operating Conditions – – – – – – – – – –
Voltage Profile Power Flows Current Flows Power Factors Transformer LTC Settings Voltage Drops
Generator’s Mvar Demand (Qmax & Qmin) Total Generation & Power Demand Steady State Stability Limits MW & Mvar Losses
Size & Determine System Equipment & Parameters • • • • • • • • •
Cable / Feeder Capacity Capacitor Size Transformer MVA & kV Ratings (Turn Ratios) Transformer Impedance & Tap Setting Current Limiting Reactor Rating & Imp. MCC & Switchgear Current Ratings Generator Operating Mode (Isochronous / Droop)
Generator’s Mvar Demand Transmission, Distribution & Utilization kV
Optimize Operating Conditions • Bus Voltages are Within Acceptable Limits • Voltages are Within Rated Insulation Limits of Equipment
• Power & Current Flows Do Not Exceed the Maximum Ratings
• System MW & Mvar Losses are Determined • Circulating Mvar Flows are Eliminated
Calculation Process • Non-Linear System • Calculated Iteratively – Assume the Load Voltage (Initial Conditions)
– Calculate the Current I – Based on the Current, Calculate Voltage Drop Vd
Assume VR Calc: I = Sload / VR Calc: Vd = I * Z Re-Calc VR = Vs - Vd
– Re-Calculate Load Voltage VR – Re-use Load Voltage as initial condition until the results are within the specified precision.
Load Flow Calculation Methods 1.
Accelerated Gauss-Seidel Method
•
2.
Low Requirements on initial values, but slow in speed.
3.
Fast-Decoupled Method
•
Two sets of iteration equations: real power – voltage angle, reactive power – voltage magnitude.
•
Fast in speed, but low in solution precision.
•
Better for radial systems and systems with long lines.
Newton-Raphson Method
•
Fast in speed, but high requirement on initial values.
•
First order derivative is used to speed up calculation.
Load Nameplate Data
kVA Rated FLA3 FLA1
kW Rated
HP 0.7457
PF Eff
PF Eff
kVA Rated 3 kV kVA Rated kV
Where PF and Efficiency are taken at 100 % loading conditions
kVA PF I3 I1
(kW )
2
( kVar )
kW kVA 1000 1000
kVA ( 3 kV) kVA kV
2
TYPE OF LOADS: TYPE OF LOAD
PHASOR
PHASE ANGLE
POWER ABSORBED BY THE LOAD P
Q
I V
I
R
Ф =
V
I
0
P>0
Q=0
V
V
Ф
L
Ф
= +90°
P=0
Q>0
Ф
= - 90°
P=0
Q<0
0 <Φ<+90
P>0
Q>0
I I
I
C
V
Ф
I
V
R
V
V L
Φ
I V
R
L
TYPE OF LOADS: TYPE OF LOAD
PHASOR
PHASE ANGLE
POWER ABSORBED BY THE LOAD P
Q
I R
V
C V
C
R
I Φ
V
-90°<Φ<0°
P>0
Q<0
90 <=Φ<=+9 0
P=0
Q=0
Tuned to Resonance IL = Ic
I V
L
C
PL = Pc Energy travels
Ic IL
Back & forth Between C&L
Constant Power Loads •
In Load Flow calculations induction, synchronous and lump loads are treated as constant power loads.
•
The power output remains constant even if the input voltage changes (constant kVA).
•
The lump load power output behaves like a constant power load for the specified % motor load.
Constant Impedance Loads • In Load Flow calculations Static Loads, Lump Loads (% static), Capacitors and Harmonic Filters and Motor Operated Valves are treated as Constant Impedance Loads.
• The Input Power increases proportionally to the square of the Input Voltage.
• In Load Flow Harmonic Filters may be used as capacitive loads for Power Factor Correction.
• MOVs are modeled as constant impedance loads because of their operating characteristics.
Constant Current Loads • The current remains constant even if the voltage changes.
• DC Constant current loads are used to test Battery discharge capacity.
• AC constant current loads may be used to test UPS systems performance.
• DC Constant Current Loads may be defined in ETAP by defining Load Duty Cycles used for Battery Sizing & Discharge purposes.
Constant Current Loads
Load Type Summary
Generic Loads
Exponential Load Polynomial Load Comprehensive Load
Generator Operation Modes
Feedback Voltage •AVR: Automatic Voltage Regulation •Fixed: Fixed Excitation (no AVR action)
Governor Operating Modes • Isochronous: This governor setting allows the generator’s power output to be adjusted based on the system demand.
• Droop: This governor setting allows the generator to be Base Loaded, meaning that the MW output is fixed.
Isochronous Mode
Droop Mode
Droop Mode
Droop Mode
Adjusting Steam Flow
Adjusting Excitation
In ETAP Generators and Power Grids have four operating modes that are used in Load Flow calculations.
Swing Mode •Governor is operating in Isochronous mode •Automatic Voltage Regulator Voltage Control •Governor is operating in Droop Mode •Automatic Voltage Regulator Mvar Control •Governor is operating in Droop Mode •Fixed Field Excitation (no AVR action) PF Control •Governor is operating in Droop Mode •AVR Adjusts to Power Factor Setting
• In the Swing Mode, the voltage is kept fixed. P & Q can vary based on the Power Demand
• In the Voltage Control Mode, P & V are kept fixed while Q & are varied
• In the Mvar Control Mode, P and Q are kept fixed while V & are varied
• If in Voltage Control Mode, the limits of P & Q are reached, the model is changed to a Load Model (P & Q are kept fixed)
Generator Capability Curve
Generator Capability Curve
Generator Capability Curve
Maximum & Minimum Reactive Power Machine Rating (Power Factor Point) Field Winding Heating Limit
Steady State Stability Curve Armature Winding Heating Limit
Generator Capability Curve Field Winding Heating Limit
Machine Rating (Power Factor Point)
Steady State Stability Curve
Generation Categories Generator/Power Grid Rating Page
Load Flow Loading Page
10 Different Generation Categories for Every Generator or Power Grid in the System
Power Flow
S
V*I V1*V2 X
P Q
P
X V1*V2 X
V1
V2
V2
1
2
jQ
*SIN(
V1*V2
V1
1
*SIN( *COS(
2
1
)
j
2
1
V1*V2 X
)
2
)
V2
2
X
*COS (
1
2
)
V2
2
X
Example: Two voltage sources designated as V1 and V2 are connected as shown. If V1= 100 /0 , V2 = 100 /30 and X = 0 +j5 determine the power flow in the system.
I
V1
I
V2
100 j0 (86.6 j50)
X
j5
10 j2.68 I
V1I*
100( 10 j2.68)
V2 I*
(86.6 j50)( 10 j2.68)
| I |2 X
10.352 5
1000 j268
536 var
1000 j268
The following graph shows the power flow from Machine M2. This machine behaves as a generator supplying real power and absorbing reactive power from machine M1.
1
( V E) X ( V E) X
Power Flow 1
0
si n 2
cos
V
X 1
2 2 0
Real Power Flow React ive Power Flow
S
Bus Voltage ETAP displays bus voltage values in two ways
•kV value •Percent of Nominal Bus kV For Bus4:
k V Calculated V %
13.5 kV No min al 13.8
k V Calculated k V No min al
100
97.83%
For Bus5:
k V Calculated V %
4.03
k V Calculated k V No min al
kV No min al
100
4.16
96.85%
Lump Load Negative Loading
Exercise Time • Open LF-Example-A1 • Follow instructions in LF-Example-A1.PDF
Load Flow Adjustments • Transformer Impedance – Adjust transformer impedance based on possible length variation tolerance
• Reactor Impedance – Adjust reactor impedance based on specified tolerance
• Overload Heater – Adjust Overload Heater resistance based on specified tolerance
• Transmission Line Length – Adjust Transmission Line Impedance based on possible length variation tolerance
• Cable Length – Adjust Cable Impedance based on possible length variation tolerance
Load Flow Study Case Adjustment Page Adjustments applied
•Individual •Global
Temperature Correction
• Cable Resistance • Transmission Line Resistance
Allowable Voltage Drop NEC and ANSI C84.1
Load Flow Alerts
Equipment Overload Alerts Bus Alerts
Monitor Continuous Amps
Cable
Monitor Continuous Amps
Reactor
Monitor Continuous Amps
Line
Monitor Line Ampacity
Transformer
Monitor Maximum MVA Output
UPS/Panel
Monitor Panel Continuous Amps
Generator
Monitor Generator Rated MW
Protective Device Alerts Protective Devices
Monitored parameters %
Condition reported
Low Voltage Circuit Breaker
Continuous rated Current
OverLoad
High Voltage Circuit Breaker
Continuous rated Current
OverLoad
Fuses
Rated Current
OverLoad
Contactors
Continuous rated Current
OverLoad
SPDT / SPST switches
Continuous rated Current
OverLoad
If the Auto Display feature is active, the Alert View Window will appear as soon as the Load Flow calculation has finished.
Exercise Time • Open LF-Example-B1 • Follow instructions in LF-Example-B1.PDF
Load Flow Example B1 Part 1
Load Flow Example B1 Part 2
Voltage Control • Under/Over Voltage Conditions must be fixed for proper equipment operation and insulation ratings be met.
• Methods of Improving Voltage Conditions: – Transformer Replacement – Capacitor Addition – Transformer Tap Adjustment
Under-Voltage Example • Create Under Voltage
• Method 2 - Shunt
Condition
Capacitor
– Change Syn2 Quantity to 6.
– Add Shunt Capacitor to Bus8 – 300 kvar 3 Banks – Voltage is improved
(Info Page, Quantity Field)
– Run LF – Bus8 Turns Magenta (Under Voltage Condition)
• Method 1 - Change Xfmr – Change T4 from 3 MVA to 8 MVA, will notice slight improvement on the Bus8 kV
– Too Expensive and time consuming
• Method 3 - Change Tap – Place LTC on Primary of T6 – Select Bus8 for Control Bus – Select Update LTC in the Study Case
– Run LF – Bus Voltage Comes within specified limits
Advanced LF Topics Voltage Control Mvar Control Load Flow Convergence Load Flow vs. Optimal Power Flow
Mvar Control • Vars from Utility – Add Switch to CAP1 – Open Switch – Run LF
• Method 2 – Add Capacitor – Close Switch – Run Load Flow
– Var Contribution from the Utility reduces
• Method 1 – Generator – Change Generator from Voltage Control to Mvar Control
– Set Mvar Design Setting to 5 Mvars
• Method 3 – Xfmr MVA – Change T1 Mva to 40 MVA – Will notice decrease in the contribution from the Utility
Advanced LF Topics Voltage Control Mvar Control Load Flow Convergence Load Flow vs. Optimal Power Flow
Load Flow Convergence • Negative Impedance • Zero or Very Small Impedance • Widely Different Branch Impedance Values • Long Radial System Configurations • Bad Bus Voltage Initial Values
Exercise Time LF-Example-A2 • Open LF-Example-A2 LF-Example-A2.PDF • Follow instructions in LF-Example-A2.PDF
Advanced LF Topics Voltage Control Mvar Control Load Flow Convergence Load Flow vs. Optimal Power Flow
Review of Load Flow Solution • Given generation, loading and control settings (Mwgen, Vgen, LTC, Capacitor
Bank, …) • Solve bus voltages and branch flows • Check over/under voltage, device overloading conditions
• Reset controls and run Load Flow again • Iterative process
Optimal Power Flow Approach • Given control setting ranges • Specify bus voltage and branch loading constraints
• Select optimization objectives (Min. P Losses, Min. Q Losses, …) • Solve bus voltages, branch flows and control settings
• Direct solution
Control Variables • • • • • • • • •
Load Tap Changer (LTC) Settings Generator AVR Settings Generator MW Generation Series or Shunt VAR Compensator Settings Phase Shift Transformer Tap Positions Switched Capacitor Settings Load Shedding DC Line Flow
…
Objective Functions • Minimize Real Power Losses - To minimize real power losses in the system
• Minimize Reactive Power Losses - To minimize reactive power losses in the system
• Minimize Swing Bus Power - To minimize real power generation at the swing bus(s)
Objective Functions • Minimize Shunt var Devices - To minimize var generation from available shunt var control devices
• Minimize Fuel Cost - To minimize total generation fuel cost
• Minimize Series Compensation - To minimize var generation from available series var control devices
Objective Functions • Minimize Load Shedding - To minimize load to be shed from the available bus load shed schedule
• Minimize Control Movement - To minimize total number of controls
• Minimize Control Adjustment - To minimize overall adjustment from all controls
Objective Functions • Maximize Voltage Security Index AllBuses
V i V i ,avg
i
dV i
Voltage Security Index
2n
Where, V i ,avg
V i ,max
V i ,min 2
dV i
V i ,max
V i ,min
2
Objective Functions • Maximize Line Flow Security Index AllB ra nche s
Line Flow Security Index i
S i
2n
S i
Where, d S i is the line rating
• Flat Voltage Profile - Voltage Magnitude difference between all buses is minimum
Other Constraints • Bus Voltage Constraints • Branch Flow Constraints • Interface Flow Constraints • …
Exercise Time • Open LF-Example-A3 • Follow instructions in LF-Example-A3.PDF
Comparison of LF and OPF
Panel Systems
Panel Boards • They are a collection of branch circuits feeding system loads
• Panel System is used for representing power and lighting panels in electrical systems
Click to drop once on OLV Double-Click to drop multiple panels
Representation A panel branch circuit load can be modeled as an internal or external load Advantages: 1. Easier Data Entry 2. Concise System Representation
Pin Assignment Pin 0 is the top pin of the panel ETAP allows up to 24 external load connections
Assumptions • Vrated (internal load) = V rated (Panel Voltage) • Note that if a 1-Phase load is connected to a 3Phase panel circuit, the rated voltage of the panel
circuit is (1/√3) times the rated panel voltage • The voltage of L1 or L2 phase in a 1-Phase 3-Wire panel is (1/2) times the rated voltage of the panel
• There are no losses in the feeders connecting a load to the panel
• Static loads are calculated based on their rated voltage
Line-Line Connections Load Connected Between Two Phases of a 3-Phase System A
A
B
B
C
C IB = IBC
IBC
IC = -IBC
Load LoadB
Angle by which load current IBC lags the load voltage = θ Therefore, for load connected between phases B and C:
For load connected to phase B
SBC = VBC.IBC PBC = VBC.IBC.cos θ QBC = VBC.IBC.sin θ
SB = VB.IB
PB = VB.IB.cos (θ - 30) QB = VB.IB.sin (θ - 30) And, for load connected to phase C SC = VC.IC
PC = VC.IC.cos (θ + 30) QC = VC.IC.sin (θ + 30)
Info Page
NEC Selection A, B, C from top to bottom or left to right from the front of the panel Phase B shall be the highest voltage (LG) on a 3-phase, 4wire delta connected system (midpoint grounded)
3-Phase 4-Wire Panel 3-Phase 3-Wire Panel 1-Phase 3-Wire Panel 1-Phase 2-Wire Panel
Rating Page Intelligent kV Calculation If a 1-Phase panel is connected to a 3-Phase bus having a nominal voltage equal to 0.48 kV, the default rated kV of the panel is set to (0.48/1.732 =) 0.277 kV For IEC, Enclosure Type is Ingress Protection (IPxy), where IP00 means no protection or shielding on the panel
Select ANSI or IEC Breakers or Fuses from Main Device Library
Schedule Page
Circuit Numbers with Standard Layout
Circuit Numbers with Column Layout
Description Tab First 14 load items in the list are are based on NEC 1999 Last 10 load types in the Panel Code Factor Table Table are user-defined Load Type Type is used to determine the Code Factors used in calculating the total panel load External loads are classified as motor load or static load according to the element type For External links the load status is determined from the connected load’s demand factor status
Rating Tab
Enter per phase VA, W, or Amperes for this load. For example, if total Watts for a 3-phase load are 1200, enter W as 400 (=1200/3)
Loading Tab For internal loads, enter the % loading for the selected loading category For both internal and external loads, Amp values are calculated based on terminal bus nominal kV
Protective Device Tab Library Quick Pick LV Circuit Breaker (Molded Case, with Thermal Magnetic Trip Device) or
Library Quick Pick – Fuse will appear depending on the Type of protective device selected.
Feeder Tab
Action Buttons Copy the content of the selected row to clipboard. Circuit number, Phase, Pole, Load Name, Link and State are not copied.
Paste the entire content (of the copied row) in the selected row. This will work when the Link Type is other than space or unusable, and only for fields which are not blocked.
Blank out the contents of the entire selected row.
Summary Page Continuous Load – Per Phase and Total Non-Continuous Load – Per Phase and Total Connected Load – Per Phase and Total (Continuous + Non-Continuous Load)
Code Demand – Per Phase and Total
Output Report
