EE5721 FINAL EXAM MAY 11, 2011 NAME PLEASE DO NOT ENTER YOUR ID NUMBER

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1 Final Exam, EE5721, May 9, 2011 EE5721 FINAL EXAM MAY 11, 2011 NAME PLEASE DO NOT ENTER YOUR ID NUMBER Problem Max Points SCORE TOTAL 100

2 Final Exam, EE5721, May 9, 2011 Problem 1) 20 Points Power System Security Analysis Consider the six bus power system network below from the EE5721 textbook. Initially all loads are at 40 MW generators are each at 40 MW output. Bus 1 is the reference bus. The initial power flows are calculated with a DC Power Flow and result in the base flows below. The line flow limits are also shown with the percent loading. BASE TRANSMISSION LOADING Path From To Low Flow High Percent Loading

3 Final Exam, EE5721, May 9, 2011 The generator on bus 2 now agrees to sell an extra 50 MW to the load on bus 6. This requires adding 50 MW to the generation on bus 2 and adding an extra 50 MW to the load on bus 6. With this sale added to the original generation and load in operation, the power system must pass the (n-1) security test for line outages on lines 6-2, 6-3, and 6-5 a) In the base case there are no contingency outages which cause overloads. (You do not have to calculate this.) b) Do any of the line outages on lines 6-2, 6-3, and 6-5, taken one outage at a time, result in overloads when the additional 50 MW is being transferred? If so how much and what lines are overloaded. You only need to test for overloads on the same set of lines 6-2, 6-3, and 6-5. c) If there are overloads found, the generator at bus 2 will reduce its output and at the same time the load at bus 6 is going to reduce its load until there are no overloads due to the line outages found in part b above. How much should the generation on bus 2 and the load on bus 6 be reduced to eliminate all overloads. The PTDF factors, and the LODF factors for this system are on the next page.

4 POWER TRANSFER DISTRIBUTION FACTOR (PTDF) MATRIX Monitored Transaction Line From(Sell) - To(Buy) 1 to 4 1 to 5 1 to 6 2 to 4 2 to 5 2 to 6 3 to 4 3 to 5 3 to 6 1 to to to to to to to to to to to LINE OUTAGE DISTRIBUTION FACTOR (LODF) MATRIX Monitored Outage of one circuit Line From - To 1 to 2 1 to 4 1 to 5 2 to 3 2 to 4 2 to 5 2 to 6 3 to 5 3 to 6 4 to 5 5 to 6 1 to to to to to to to to to to to

5 Final Exam, EE5721, May 9, 2011 Problem 3 (30 points) Given the following power system: The network is to be modeled with a DC power flow with line reactances as follows: (assume 100 MVA base) x 12 = 0.1 pu x 23 = 0.05 pu The meters are all of the same type with a standard deviation of σ = 0.01 pu for each. The measured values are: m12 = 80 MW m21 = -75 MW m2 = 115 MW m23 = 150 MW m32 = -190 MW 1) Build the H matrix, label the rows and columns 2) Find the phase angles which result in a least squares fit to the measured values. 3) Do you suspect that any one of the measurements is a bad measurement? Just identify which you suspect is bad and say why.

6 Final Exam, EE5721, May 9, 2011 Problem 3) 20 Points Block Bidding of Generation in a Spot Price Auction You are to solve generation, load and pricing problems for a two bus power system. Each bus has a single generator and a single load as shown below: The generators are labeled G1 and G2 and the loads are labeled L1 and L2. The schedule of generation and load in this system is determined by an auction. The auction will consider the load to be variable in that the load shall submit a willingness to pay price to purchase blocks of energy. If the price of energy is below the load s willingness to pay price it is satisfied (assuming that there is sufficient transmission and generation capacity). If the price of energy from the generators is above the load s willingness to pay price - then the load is not satisfied (that is, the load block is not supplied). Draw the Supply Demand curves for this auction and show the clearing price. What is the flow on the line from 1 to 2 for each block sold, where flow from 1 to 2 is positive, from 2 to 1 is negative. The Generation and Load Prices are: Generator Blocks for sale: G1 Generator Blocks for sale: G2 Block Block Price Block Block Price Number MW $/MWh Number MW $/MWh G G G G Load bids to purchase: Load bids to purchase: L1 L2 Block Block Price Block Block Price Number MW $/MWh Number MW $/MWh L L L L

7 Final Exam, EE5721, May 9, 2011 Problem 4) 30 points You are asked to analyze the bilateral transaction versus a market auction for the three bus system below: Hydro Gen GEN 1 GEN 2 BUS 1 BUS MW max flow 700 MW max flow 600 MW max flow LOAD MW Green Load MW GEN 3 BUS 3 Green Load MW LOAD MW The Green Load Company owns loads at bus 2 and bus 3 and is trying to buy 300 MW at bus 2 from the Hydro Generator and 500 MW at bus 3 from the Hydro Generator. The Green Load Company s trading group calls up the Hydro Generator s trading group and asks for a price for 800 MW to be delivered 300 MW to bus 1 and 500 MW to bus 3. The Hydro Generator Trading Group has decided that it can get a high price from the Green Load and asks a price of 40 $/MWh. The traders at Green Load trading thinks that this price is much too high and says no thanks we will take our chances in the Market. Green Trading then puts in a bid to buy that is at $200/MWh so that they are assured of obtaining the 800 MW they need. We will solve this problem both ways and you will be asked to analyze the results. Bilateral Transaction Case: In this case the transactions are done completely outside the market and the MW transactions are superimposed onto the transmission system. The price for the MW sold by the hydro generator is 40 $/MWh. The generator has to pay any transmission charges determined by the results of the auction. You can treat this as two separate transactions 300 MW from the Hydro Generator on bus 1 to Green Load 1 on bus 2, and 500 MW from the same Hydro Generator on bus 1 to Green Load 2 on bus 3 with both transaction made at a price of 40 $/MWh. Next page

8 Final Exam, EE5721, May 9, 2011 Problem 4 continued: The results of the Bilateral calculations are: 700 MW max flow 700 MW 600 MW max flow ZERO MW FLOW Market case: Here the Hydro generator trading group places a bid to sell power into the market. This is done by giving a cost function to the auction operator of: C( P ) = P P 2 hydro hydro hydro The Green Loads both submit a bid to buy function of: C( P ) = 0 200P green _ load _1 green _ load _1 C( P ) = 0 200P green _ load _ 2 green _ load _ 2 Next page

9 Final Exam, EE5721, May 9, 2011 Problem 4 continued: The other generator cost functions and the cost functions of the loads are: Bid A B C Max (MW) Gen Gen Gen Load Load The market auction results with the hydro generator and the green loads as part of the market are: Hydro gen price = 40 $/MWh MARKET CASE 300 MW Hydro Gen GEN 1 Lambda= MW 1100 MW GEN 2 BUS 1 BUS MW max flow Lambda= MW Lambda= MW Green Load MW 700 MW max flow GEN MW LOAD MW BUS MW max flow ZERO MW FLOW LOAD MW Green Load MW MARKET CASE: No transactions Market participants are Gen 1, Gen 2, Gen 3 and Hydro Gen Load 2, Load 3, Green Load 1 and Green Load 2 Line 1-3 is at limit Note that the hydro generator only sells 300 MW and the Green Load Company still receives 300 MW at bus 2 and 500 MW at bus 3.

10 Final Exam, EE5721, May 9, 2011 Problem 4 continued: You are to find the following: 1) For the Bilateral case: The dollar income received by the Hydro generator, the transmission charges for each of the two bilateral transactions, and the net income of the Hydro Generator. 2) For the Bilateral case: The dollars paid by the Green Load Company for each of its loads. 3) For the Market Case: The dollar income received by the Hydro generator 4) For the Market Case: The dollars paid by the Green Load Company for each of its loads. 5) In this case we know that the Green Load had the opportunity to make direct transactions with the Hydro Generator and chose instead to go into the Market. Was this a good decision for the Green Load Company? 6) Was the Green Load s decision good or bad for the Hydro Generator? 7) If the Hydro Generating Company had purchased Financial Transmission Rights (FTRs) to insure against the transmission costs of the bilateral transactions: a. What are the FTRs it would need to have owned to pay off all transmission charges? Give details for all FTR contracts needed: i. From bus ii. To bus iii. MW amount b. What would be the Hydro Generation company s profits if it had owned the FTRs you specified in part a.

11 PROBLEM 1 Part b (n-1) Outage analysis Step 1: Calculate all flows with the 50MW added transaction fromula: Flow_ij_withtrans = flow_ij_start + PTDF_rs_ij * Mwtransaction_rs Line Flow_ii_withtrans flow_ij_start PTDF_rs_ij Mwtransaction_rs ij Step 2: Calculate all (n-1) contingency outage flows with the transaction of 50MW in place formula: Flow_ij_with_outage_nm = flow_ij_initial + LODF_ij_nm * flow_nm_initial Line flow_ij_with_outage_nm Flow_ii_withtrans outaged line nm LODF_ij_nm flow_nm_initial Limit ij initial flow OVERLOAD OVERLOAD OVERLOAD There are three overloads as shown above

12 PROBLEM 1 Part c) For this part it is best to reduce the transaction until the worst overload is eliminated, then check the remaining overloads. We will now use a formula that combines both the PTDF's and the LODF's so as to capture the transfer effect and the line outage effect in one place. formula: Flow_ij_withtrans_and_outage_nm = flow_ij_initial_withtrans + LODF_ij_nm * flow_nm_initial_withtrans = (flow_ij_start + PTDF_rs_ij * Mwtransaction_rs) + LODF_ij_nm * (flow_nm_start + PTDF_rs_nm * Mwtransaction_rs) = (flow_ij_start + LODF_ij_nm * flow_nm_start) + (PTDF_rs_ij + LODF_ij_nm * PTDF_rs_nm) * Mwtransaction_rs = flow_ij_with_outage_nm_notrans + adjusted_ptdf * Mwtransaction_rs where adjusted_ptdf = (PTDF_rs_ij + LODF_ij_nm * PTDF_rs_nm) line Flow_ij_withtrans_and_outage_nm flow_ij_start line LODF_ij_nm flow_nm_start flow_ij_with_outage_nm adjusted_ptdf wtransaction_rs ij nm _notrans OVERLOAD OVERLOAD OVERLOAD This obviously gives the same result, however, we can now solve for the amount to adjust the transaction to reduce any overloads. formula: for overloaded lines the needed change in flow is = flow_limit - flow with transaction and ourage then the formula for the required adjustment in transaction is: = ( (required adjustment in flow) - flow_ij_with_outage_nm)/adjusted_ptdf) line Flow_ij_withtrans_and_outage_nm Line Limits line required adjustment flow_ij_with_outage_nm adjusted_ptdf required adjustment ij nm in flow without transaction to transaction none none none Reduce the transaction by MW and all flows will be below limit and line 3-6 will be exactly at its limit of 45 MW when line 2-6 is opened.

13 Problem 2 solution H = θ2 θ 3 m m m m m R = H'*(R )*H = meas = Estimated values for bus phase angles in radians θ est 1 1 T 1 =(H'*(R )*H) *H *(R )*meas θ 2 = θ = Results Pflow 1-2 = Flow 2-3 = Pnet on bus 1 = Pnet on bus 2 = Pnet on bus 3 =

14 Problem 2 solution Errors: this is the error between measured value and calculated values using the estimated theta values: m12 error m21 error m2 error m23 error m32 error from this one would conclude that measurement m23 was in error because of the large MW error between m23 and its calculated value.

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18 EE 5721 Final Exam Problem 4 solution BILATERAL TRANSACTION CASE Bus Bus LMP Values Hydro Generator to Green Load MW Transaction separate from Market Hydro Generator Green Load Price MW Sold Income Transmission Charge Net Profit Price MW Purchased Cost $12,000 0 $12, $12,000 Transmission Charge = (LMPreceive - LPMsend)*Mwtransacted = -$4,650 since negative, count as zero Hydro Generator to Green Load MW Transaction separate from Market Hydro Generator Green Load Price MW Sold Income Transmission Charge Net Profit Price MW Purchased Cost $20,000 $28,000 -$8, $20,000 Transmission Charge = (LMPreceive - LPMsend)*Mwtransacted = $28,000 SUMMARY FOR HYDRO GENERATOR COMPANY: net profit is $ $8000 = $4000 SUMMARY FOR GREEN LOAD COMPANY: net cost of the 800 MW of load = $ $20000 = $32000 MARKET CASE Bus Bus LMP Values Hydro and Green Load are part of the Market Hydro Generator Green Load Price MW Sold Income Transmission Charge Net Profit Price MW Purchased Cost Expense $12,180 0 $12, $18, $41,000 Net cost $59,390 SUMMARY FOR HYDRO GENERATOR COMPANY: net profit is $32,480 SUMMARY FOR GREEN LOAD COMPANY: net cost of the 800 MW of load = $18,390 + $41,000 = $59,390 CONCLUSIONS: Hydro gen actually sells less MW but makes more money in the market Green Load Co. pays more in the market and would have been better with the bilateral transactions of 300MW and 500MW FTR Analysis: This is the from to and MW necessary to cover the Hydro Gen Co. From - To MW Payoff Bus 1 to Bus No transmission charges so no payoff Bus 1 to Bus $28,000 This would change Hydro Gen Co profits to $32,000 income Hydro Gen Co. still makes more in the market

19 There was an error in writing the exam, the LMP value at bus 3 should have been 54 not 10.5 $/MWh in the Bilateral Transactions case. All students were graded on how they calculated the results using the incorrect value of I have also included the correct set of values just to show what it should have been and of course students were not expected to get these answers. Professor Wollenberg

20 EE 5721 Final Exam Problem 4 solution CORRECTED LMP AT BUS 2 BILATERAL TRANSACTION CASE Bus Bus LMP Values Hydro Generator to Green Load MW Transaction separate from Market Hydro Generator Green Load Price MW Sold Income Transmission Charge Net Profit Price MW Purchased Cost $12,000 $8,400 $3, $12,000 Transmission Charge = (LMPreceive - LPMsend)*Mwtransacted = $8,400 since negative, count as zero Hydro Generator to Green Load MW Transaction separate from Market Hydro Generator Green Load Price MW Sold Income Transmission Charge Net Profit Price MW Purchased Cost $20,000 $28,000 -$8, $20,000 Transmission Charge = (LMPreceive - LPMsend)*Mwtransacted = $28,000 SUMMARY FOR HYDRO GENERATOR COMPANY: net profit is $ $36,400 = $-4400 SUMMARY FOR GREEN LOAD COMPANY: net cost of the 800 MW of load = $ $20000 = $32000 MARKET CASE Bus Bus LMP Values Hydro and Green Load are part of the Market Hydro Generator Green Load Price MW Sold Income Transmission Charge Net Profit Price MW Purchased Cost Expense $12,180 0 $12, $18, $41,000 Net cost $59,390 SUMMARY FOR HYDRO GENERATOR COMPANY: net profit is $32,480 SUMMARY FOR GREEN LOAD COMPANY: net cost of the 800 MW of load = $18,390 + $41,000 = $59,390 CONCLUSIONS: Hydro gen actually sells less MW but makes more money in the market Green Load Co. pays more in the market and would have been better with the bilateral transactions of 300MW and 500MW FTR Analysis: This is the from to and MW necessary to cover the Hydro Gen Co. From - To MW Payoff Bus 1 to Bus $8,400 No transmission charges so no payoff Bus 1 to Bus $28,000 This would change Hydro Gen Co profits to $32,000 income Hydro Gen Co. still makes more in the market