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Question 1 Economic dispatch: A power system includes two generators serving load demand \(d=1\) per unit (pu). Their generation costs and limits (in pu and \$/pu) are shown below:\begin{align*}c_1(p_1)&=300p_1^2+200p_1, &&\underline{p}_1=0,~\bar{p}_1=0.9.\\c_2(p_2)&=200p_2^2+300p_2, &&\underline{p}_2=0,~\bar{p}_2=0.8.\end{align*} (a) Formulate the economic dispatch and find the optimal generation dispatch. (b) What is the price of electricity for this system? Calculate the net gain for each generator. (c) How much money does the independent system operator (ISO) collect from the load, and how much money does the ISO distribute to GENs? (d) Compute the participation factors for the two generators.   Question 2 Power flow: Consider the 3-bus power system shown below. Line impedances are given as \(x_{12}=0.2\) and \(x_{23}=x_{31}=0.1\) pu. Bus 1 is set as the reference and slack bus and we adopt the linearized (DC) PF model. (a) Find matrices \(\mathbf{X}\), \(\mathbf{A}\), \(\mathbf{B}\) and the reduced matrix \(\mathbf{B}_r\), involved in the DC-PF model.  (b) The vectors of power flows \(\mathbf{f}\) and power injections \(\mathbf{p}\) are related as\[\left[\begin{array}{c}f_{12}\\f_{23}\\f_{31}\end{array}\right]=\mathbf{S}\left[\begin{array}{c}p_{1}\\p_{2}\\p_{3}\end{array}\right]\quad \quad \text{where}\quad \quad\mathbf{S}=\left[\begin{array}{ccc}0 & -0.5 & -0.25\\0 & +0.5 & -0.25\\0 & +0.5 & +0.75\end{array}\right].\] Find the bus voltage angles for injections \(\mathbf{p}=[+0.7~+0.3~-1]^\top\). Question 3 Network-constrained optimal power flow: Using the generation/load data of Q1) and the network data of Q2), the ISO solves a DC-OPF. Line capacities are given as \(\bar{f}_{12}=0.4\),  \(\bar{f}_{23}=0.4\), and \(\bar{f}_{31}=0.8\) pu. The optimal dispatch is \(\mathbf{p}=[+0.7~+0.3~-1.0]^\top\). The marginal energy component is $620. Among the three lines, line \((2,3)\) gets congested and reaches its upper limit. The corresponding Lagrange multiplier is $400. (a) Find the vector \(\boldsymbol{\pi}\) of locational marginal prices at all buses. (b) How much money does the ISO pay each generator? How much money does the ISO collect from the load? Calculate the congestion surplus. Question 4 Contingency analysis: For the system of Q3) and power injections \(\mathbf{p}=[+0.7~+0.3~-1.0]^\top\), find the post-contingency flow on line \((2,3)\) if line \((3,1)\) trips.  Is the system in this post-contingency state secure? Question 5 For each of the following statements related to the (lossless) DC-OPF model, mark if they are true or false: (a) Building more transmission lines can only decrease the total generation cost.  (b) Building more generators can only decrease the total generation cost. (c) LMPs are equal across all buses only if there is no congestion. (d) The power injections obtained from the DC-OPF are also feasible for the AC-OPF. (e) The corrective security-constrained SC-DC-OPF yields a lower total generation cost compared to the preventive SC-DC-OPF. (f) The corrective SC-DC-OPF may yield lower total generation cost compared to the plain DC-OPF. Question 6 Unit commitment: The generators of Q1) are given the price of $500/pu to generate power for the next hour. (a) If GEN1 is currently off and its start-up cost is $50, what would be the self-dispatch for GEN1? (b) If GEN2 is currently off and its start-up cost is $100, what would be the self-dispatch for GEN2? Congratulations, you are almost done with this exam.  DO NOT end the Honorlock session until you have submitted your work to Brightspace.  When you have answered all questions:  Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible.  Submit your PDF as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.).  Click this link to go to submit your work: Midterm exam Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam.  End the Honorlock session.   

Please match the following to into either positives symptoms and negative symptoms.

In a cross between an organism pure-breeding for a dominant trait & an organism expressing the recessive trait, what portion of the F1 generation should phenotypically resemble the parent with the dominant trait (simple dominance/recessive)?  

You are orientating a new psychiatric nurse practitioner. He asks you what SSRI discontinuation is. Which of the following statements regarding SSRI discontinuation syndrome is true?

Some antipsychotic medications can increase the prolactin level. Which of the following medication has the highest risk of hyperprolactemia?

You started a patient on lithium. The patient asks about side effects of lithium. Which of the following statements about its use is true?

A 30-year-old pregnant patient with a history of bipolar I disorder presents to the ER in labor. She is at 39 weeks gestational age. Her water soon breaks, and she gives birth to a healthy baby boy; however, the baby has Ebstein’s anomaly. Which of the following medications was the child most likely exposed to in utero?

A 26-year-old man was recently diagnosed with schizophrenia. He has  a body mass index of 30, fasting glucose of 114 and fasting triglycerides of 230. Which of the following is least likely to worsen his metabolic profile?

You are treating a patient with a history of medication-controlled bipolar disorder who presents with complaints of new onset of bilateral hand tremor. She reports the tremor started about 1 week ago, a few days after a minor motor vehicle accident. The patient denies hitting her head, any loss of consciousness, or altered mental status after the accident. She reports that since the accident, she has experienced some minor neck pain that has been responding well to OTC NSAIDs. She takes NSAID medication as recommended on the bottle. Her review of systems is otherwise negative except for recent nausea and vomiting. What is the most likely explanation for the patient’s presentation?

Which of the following instruments offers most direct and efficient inflation protection?