EE 521 Analysis of Power Systems
Fall 2012
C.C. Liu
Midterm Examination I
Print Your Name: SOLUTIONS
Instructions:
This is an open-book, 1-hour-15-min test. All problems will be graded. Describe the procedures that you use to obtain the answer.Calculators are allowed but not laptops.
Grading:
Problem 1: System Security Concepts ______(20 Points)
Problem 2:Update Zbus Matrix ______(20 Points)
Problem 3: Contingency Ranking ______(30 Points)
Problem 4: State Estimation ______(30 Points)
Total: ______(Max 100 Points)
Total Number of Pages Including the Cover Sheet:
Problem 1: System Security Concepts (20 Points)
Circle only the most appropriate item between parentheses.
Dispatcher Jane at the Control Center of Northwest Power Grid (NPG) regularly performs security assessment of the system condition. For NPG, the critical operating constraints are the bus voltage limits. At this time all bus voltages satisfy the operating limits and all loads are served. Therefore, the power system is in a (secure, normal, restorative) state. Dispatcher Jane uses a list of next contingencies and performs on-line (economic dispatch, automatic generation control, power flow) for the next contingencies. For one of the contingencies, Dispatcher Jane finds that the system violates the low bus voltage limits at some substations. She concludes that the system is in an (emergency state, insecure, secure, normal) state. Dispatcher Jane should take (emergency control, preventive control, restorative control) actions to improve the system operating condition.
NPG assigns John to analyze the power grid’s transmission capability to accommodate the market transactions. John has to calculate the Available Transfer Capability (ATC) between Area A and Area B linked by tie lines. He starts with a base case that already has 1,000 MW power transfer from Area A to Area B. John then identifies the critical contingencies so that he can ensure that(Security Assessment, Automatic Generation Control, Economic Dispatch) is incorporated in the ATC calculation. John performs power flow calculations and check the (System Frequency, Total Area Load, Operating Constraints) each time he increases the power transfer amount from A to B by (Increasing Generation in A and Decreasing Load in B, Decreasing Generation in A and Decreasing Load in B, Increasing Generation in A and Increasing Load in B).
When John identifies the power transfer level where (Pre-Contingency System Meets All Constraints and Post-Contingency System Hits At Least One Constraint, Pre-Contingency System Violates Some Constraints but Post-Contingency System Meets All Constraints, Pre-Contingency System Violates Only One Constraint and Post-Contingency System Meets All Constraints), he decides that the transfer level in addition to the base case 1,000MW is the (First Contingency Total Transfer Capability, First Contingency Incremental Transfer Capability, Optimal Dispatch). John then reduces the amount by the Transmission Reliability Margin and the non-recallable reservation amounts of the transmission capability to obtain the (Recallable ATC, Non-recallable ATC, Capacity Benefit Margin).
Problem 2: Update Zbus Matrix (20 Points)
A 4-bus power system is shown below. It is desired to obtain the Zbus(inverse of Ybus) matrix after the line from the reference node to bus 3 is eliminated.
(a) Find the Zbusbefore the line from the reference node to bus 3 is eliminated.
(a) Find the new Zbus from the old Zbus for the system before the line is eliminated. You must use the rank 1 update formula.
Solution:
a)
b)
Problem 3: Contingency Ranking (30 Points)
A 3-bus power system is shown below:
All quantities are in per unit. Use the DC load flow method for this problem. The angles shown above are the base case values. The performance index for the contingencies is defined by
Where L is the total number of lines (=3). The line flow limit for all lines is Bus 3 is the reference bus for the DC load flow. Note that the flow Plis a function of the angle difference.
Suppose the line outages are being evaluated by the ‘Adjoint Network’ method.
Solution:
(a)Calculate the PI value for the base case.
b) Solve the adjoint network DC load flow to find
Problem 4: State Estimation (30 Points)
The one-line diagram of a power system is shown below.
All transmission lines have the same reactance X = j0.1pu, and the standard deviation of all meters is given by σ = 0.01. Assume that the state vector is and θ1 = 0.
a) Write down the measurement matrix H with the 3 meters.
Solution:
b) Calculate the best estimates of bus angles. Assume that Z measure is given by:
Solution:
c) Due to the failure of a remote terminal unit at Bus 2, meter M2 is out of service. Is the system observable with the two remaining meters? Justify your answer step-by-step.
Solution:
Rank of H is 2 so H has full row rank.
However,
Since is 3 by 3 matrix and has a rank of 2.
So it is singular, i.e. det(HTR-1H)=0.
Therefore,the state estimation cannot be solved and the system is unobservable.
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