POWERWORLD SIMULATOR University of Texas at Austin By: Mohammad Majidi Feb 2014
AGENDA Contingency Analysis OPF SCOPF Examples 2
START CONTINGENCY ANALYSIS Open case B7SCOPF from the Program Files/PowerWorld/Simulator/Sample Cases directory. Ensure Simulator is in Run Mode. Select Contingency Analysis from the Run Select Contingency Analysis from the Run Mode ribbon group on the Tools ribbon tab. Simulator opens the Contingency Analysis Dialog.
CONTINGENCY ANALYSIS
DEFINING CONTINGENCIES Different ways to define contingency: Load Contingencies from a File Auto Insert Contingencies Use the local menu to Insert contingencies Quick Insert of Single Element Contingency.
AUTO INSERT CONTINGENCIES Select Records>Auto Insert Contingencies
RUN CONTINGENCY ANALYSIS
OPTIMAL POWER FLOW OVERVIEW The goal of an optimal power flow (OPF) is to determine the best way to instantaneously operate a power system. Usually best = minimizing operating cost. OPF considers the impact of the transmission system We ll introduce OPF initially ignoring the transmission system 8
TWO BUS EXAMPLE Total Hourly Cost :8459 $/hr Area Lambda : 13.02 Bus A Bus B 300.0 MW 199.6 MW 400.4 MW AGC ON AGC ON 300.0 MW 9
MARKET MARGINAL COST IS DETERMINED FROM NET GEN COSTS Below are some graphs associated with this two bus system. The graph on left shows the marginal cost for each of the generators. The graph on the right shows the system supply curve, assuming the system is optimally dispatched. 16.00 16.00 15.00 15.00 14.00 14.00 13.00 13.00 12.00 0 175 350 525 700 Generator Power (MW) 12.00 Current generator operating point 0 350 700 1050 1400 Total Area Generation (MW) 10
OPTIMAL POWER FLOW (OPF) Minimize cost function, such as operating cost, taking into account realistic equality and inequality constraints Equality constraints bus real and reactive power balance Inequality constraints generator MW limits 11
SOLVING THE LP OPF All LP OPF commands are accessed from the LP OPF menu item. Go to Add Ons and click on OPF Options and Results 12
LP OPF OPTIONS: COMMON OPTIONS 13
LP OPF OPTIONS: COMMON OPTIONS Check it if you want to ignore transmission constraints. It will convert OPF to ED Cost of unenforceable line violations 14
UNENFORCEABLE CONSTRAINT COSTS If a constraint can not be enforced due to insufficient controls, the slack variable associated with enforcing that constraint can not be removed from the LP basis marginal cost depends upon the assumed cost of the slack variable this value is specified in the Maximum Violation Cost field on the LP OPF, Options dialog. 15
MODELING GENERATOR COSTS Generator costs are modeled with either a cubic cost or piecewise linear cost function Cost model is specified on the generator dialog The LP OPF requires a piecewise linear model. Therefore any existing cubic models are automatically converted to piecewise linear before the solution, and then converted back afterward. 16
COMPARISON OF CUBIC AND PIECEWISE LINEAR MARGINAL COST CURVES 16.0 16.0 12.0 12.0 / MWh $ 8.0 4.0 8.0 4.0 0.0 0 100 200 300 400 Generator Power (MW) Continuous generator marginal cost curve 0.0 0 100 200 300 400 Generator Power (MW) Piecewise linear generator marginal cost curve with five segments This conversion may affect the final cost. Using more segments 17 better approximates the original curve, but may take longer to solve
OPF CASE INFORMATION DISPLAYS Several Case Information Displays exist for use with the OPF OPF Areas OPF Buses OPF Lines and Transformers OPF DC Lines OPF Generators OPF Phase Shifters OPF Super Areas OPF Interfaces OPF Load Records OPF Transactions OPF Zones 18
OPF AREA RECORDS DISPLAY AGC (automatic generation control) status must be set to OPF to include this are in the OPF objective function 19
OPF AREA RECORDS DISPLAY Controls Types that are available XF Phase specifies if phase shifters are available Load MW Dispatch specifies if load can be moved DC Line MW -specifies if DC MW setpoint can be moved Constraint Types which should be enforced Branch MVA should branch limits be enforced Interface MW - should interface limits be enforced Include Marg. Losses Specifies if marginal losses are used in the OPF 20
OPF GEN RECORDS DISPLAY 21
OPF GEN RECORDS DISPLAY Fast Start Should the generator be available for being turned on/off by the OPF OPF MW Control (YES, NO, or If Agcable) Should the generator be made available for OPF dispatch IC for OPF The incremental cost of the generator used by the OPF (ma ybe different than actual IC for cubic cost curve generators) Initial MW, Cost The output and cost at the start of the OPF solution Delta MW, Cost The change in the output and cost for the last OPF solution 22
COST OF ENERGY, LOSSES AND CONGESTION Some ISO documents refer to the cost components of energy, losses, and congestion Open Bus7OPF case Go to the Add Ons ribbon tab and select OPF Case Info >OPF Areas Toggle Include Marg. Losses column of each area to YES Choose OPF Case Info >Primal LP to resolve. Now choose OPF Case Info >OPF Options and Results Go to the Results Tab Go the the Bus MW Marginal Price Details subtab Here you will find columns for the MW Marg Cost, Energy, Congestion and Losses Congestion and Losses 23
COST OF ENERGY, LOSSES AND CONGESTION The only value that is truly unique for an OPF so lution is the total MW Marginal Cost The cost of Energy, Losses, and Congestion are dependent on the reference for Energy and Losses 24
SCOPF : SECURITY CONSTRAINT OPF Click on Run Full security constraint OPF Make sure you have already added contingencies to your model before running SCOP. 25
26 EXAMPELS
TWO BUS EXAMPLE - NO CONSTRAINTS With no overloads the OPF matches the economic Dispatch(ED) Bus A Total Hourly Cost : 8459 $/hr Area Lambda : 13.01 Transmission line is not overloaded 13.01 $/MWh Bus B 13.01 $/MWh 300.0 MW 197.0 MW 403.0 MW AGC ON AGC ON 300.0 MW Marginal cost of supplying power to each bus (locational marginal costs) 27
TWO BUS EXAMPLE WITH CONSTRAINED LINE Total Hourly Cost : 9513 $/hr Area Lambda : 13.26 Bus A 13.43 $/MWh Bus B 13.08 $/MWh 380.0 MW 260.9 MW 419.1 MW AGC ON AGC ON 300.0 MW With the line loaded to its limit, additional load at Bus A must be supplied locally, causing the marginal costs to diverge. (Load at Bus A is increased from 300MW to 380MW) 28
THREE BUS EXAMPLE Consider a three bus case (bus 1 is system slack), with all buses connected through 0.1 pu reactance lines, each with a 100 MVA limit Let the generator marginal costs be Bus 1: 10 $ / MWhr; Range = 0 to 400 MW Bus 2: 12 $ / MWhr; Range = 0 to 400 MW Bus 3: 20 $ / MWhr; Range = 0 to 400 MW Assume a single 180 MW load at bus 2 29
B3 WITH LINE LIMITS NOT ENFORCED 60 MW 60 MW Bus 2 Bus 1 10.00 $/MWh 0 MW 10.00 $/MWh 0 MW 60 MW Total Cost 1800 $/hr 60 MW Bus 3 0 MW 120% 120 MW 180 MW 120 MW 120% 10.00 $/MWh 180 MW Line from Bus 1 to Bus 3 is overloaded; all buses have same marginal cost 30
B3 WITH LINE LIMITS ENFORCED 20 MW 20 MW Bus 2 Bus 1 10.00 $/MWh 60 MW 12.00 $/MWh 0 MW 80 MW Total Cost 1921 $/hr 80 MW Bus 3 0 MW 100 MW 80% 100% 80% 100% 180 MW 100 MW 14.01 $/MWh 120 MW LP OPF redispatches to remove violation. Bus marginal costs are now 31 different.
WHY IS BUS 3 LMP = $14 /MWH All lines have equal impedance. Power flow in a simple network distributes inversely to impedance of path. For bus 1 to supply 1 MW to bus 3, 2/3 MW would take direct path from 1 to 3, while 1/3 MW would loop around from 1 to 2 to 3. Likewise, for bus 2 to supply 1 MW to bus 3, 2/3MW would go from 2 to 3, while 1/3 MW would go from 2 to 1to 3. 32
WHY IS BUS 3 LMP = $ 14 / MWH? With the line from 1 to 3 limited, no additional power flows are allowed on it. To supply 1 more MW to bus 3 we need Pg1 + Pg2 = 1 MW 2/3 Pg1 + 1/3 Pg2 = 0; (no more flow on 1-3) Solving requires we up Pg2 by 2 MW and drop Pg1 by 1 MW -- a net increase of $14. 33
THREE BUS CASE View results using the LP OPF, OPF Areas, OPF Buses, OPF Gens and OPF Line/Transformer displays on the OPF Line/Transformer display, toggle the Enforce MVA field to enable/disable the enforcement of individual lines. verify that the marginal cost of enforcing the line overload is $ 6 / MVA/hr by changing the line limit and resolving. Why is it $6? 34
BOTH LINES INTO BUS 3 CONGESTED 0 MW 0 MW Bus 2 Bus 1 10.00 $/MWh 100 MW 12.00 $/MWh 0 MW 100 MW Total Cost 3201 $/hr 100 MW Bus 3 50 MW 100 MW 100% 100% 100% 100% 100 MW 20.00 $/MWh 250 MW 100 MW For loads above 200 MW on bus 3, the load must be supplied locally. Then what if the bus 3 generator opens? 35
MARGINAL COST OF ENFORCING CONSTRAINTS Similarly to the bus marginal cost, you can also calculate the marginal cost of enforcing a line constraint For a transmission line, this represents the amount of system savings which could be achieved if the MVA rating was increased by 1.0 MVA. 36
MVA MARGINAL COST Choose OPF Case Info >OPF Lines and Transformers to bring up the OPF Constraint Records dialog Look at the column MVA Marginal Cost 37
WHY IS MVA MARGINAL COST $6/MVAHR If we allow 1 more MVA to flow on the line from 1 to 3, then this allows us to redispatchas follows Pg1 + Pg2 = 0 MW 2/3 Pg1 + 1/3 Pg2 = 1; (no more flow on 1 3) Solving requires we drop Pg2 by 3 MW and increase Pg1 by 3 MW a net savings of $6 38
THREE BUS CASE Increase the bus 3 load to 250 MW. Resolve with line enforcement active. What are the new LMPs? Why? Open the generator at bus 3 and then resolve. Does this case have a solution? Why? Are the LMPs valid? 39
CASE WITH G3 OPENED UNENFORCEABLE CONSTRAINTS 53 MW 53 MW Bus 2 Bus 1 10.00 $/MWh 47 MW 12.00 $/MWh 0 MW 99 MW Total Cost 2594 $/hr 99 MW Bus 3 0 MW 151 MW 100% 152% 99% 151% 151 MW 1040.55 $/MWh 250 MW 203 MW Both constraints can not be enforced. One is unenforceable. Bus 3 marginal cost is arbitrary 40
UNENFORCEABLE CONSTRAINT COSTS Is this solution Valid? Not really. If a constraint cannot be enforced due to insuffici ent controls the slack variable associated with enforcing that constraint cannot be removed from the LP basis marginal cost depends upon the arbitrary cost of the slack variable the slack variable this value is specified in the Maximum ViolationCost field on the LP OPF, Options dialog 41
SEVEN BUS CASE Load the B7FlatLP case. What are the marginal costs of enforcing the line constraints? How do the system costs change if the line constraints are relaxed (i.e, not enforced)? For example, try solving without enforcing line 1 to 2. 42
SEVEN BUS CASE Modify the cost model for the generator at bus one. How does changing from piece-wise linear to cubic affect the final solution? How do the generation conversion parameters on the option dialog affect the results? Try resolving the case with different lines removed from service. 43
PROFIT MAXIMIZATION If the bus 7 generator has a marginal cost equal 7$/MWh and were paid its bus LMP * its output, its profit would be Profit = LMP * MW - 7 * MW The question then is what should they bid to maximize their profit? This problem can be solved using the OPF with different assumed generator costs. 44
45 QUESTIONS?