ER100/PP184/ER200/PP284, Fall 2022Problem Set #5Total Points: 100 for ER110/PP184; 125 for ER200/PP284Show your work for complete credit. Online submissions must be a single PDF document,otherwise points will be deducted.1) Electric grid (25 points) The Trans Bay Cable is a 53 mile long, underwater high-voltagedirect current (HVDC) line connecting PG&E's Potrero Substation in San Francisco toPG&E’s Pittsburgh Substation in Pittsburgh, CA. The cable can transmit 400MW of power toSan Francisco at +/- 200kV DC.a. With a difference in voltage of 400kV (+200kV - (-200kV)), what is the total currentof the Trans Bay Cable? Assume no losses. [3 points]P = IV → I = P/V = 400MW/400kV = 1*103A or 1 kA (1 sig fig)b. Assume the Trans Bay Cable has a resistance of 0.0375844Ω/mile per conductor.Typically, the current flowing through an HVDC power line is evenly split across itstwo conductors, ½ on the positive voltage line and ½ on the negative voltage line.Assuming this is the case for the Trans Bay Cable, calculate the power lost to heatfrom a single conductor of the cable using the current calculated in part a. [6 points]1*103A / 2 = 500A per conductor 0.0375844Ω/mile * 53 miles = 1.9919732 ΩP = I2R = (500 A)2* 1.9919732 Ω = 497993.3W = 500 kW We are modeling the DC current here flowing through the both positive and negative side ofthe DC line to ground because of the design of the circuit. In reality, the power is still splitacross the lines but the splitting is coming from the voltage. A single DC line at 200kV wouldconsume 2000A and by using the +/- 200kV, we only need to use 1000A. To avoid confusionwith +/- voltages, we chose to half the current in this problem. We are able to do this becauseof the symmetrical pole design of the HVDC system. In fact, the Trans Bay Cable was thefirst Symmetric Monopole VSC HVDC line built. This type of design is now a popular designfor point-to-point HVDC. For students looking for a more advanced discussion on HVDC,take a look at this review of HVDC technology from 2014 (For information on symmetricmonopole designs and their cables, see section 2.2.2 starting on page 13, section 2.2.4 on page22, and section 4.2 on page 53):http://www.eirgridgroup.com/site-files/library/EirGrid/Grid-West-HVDC-Technology-Review-Report-PSC.pdfc. The engineers that built the Trans Bay Cable believe they could modify the line tooperate at 700kV (+350kV - (-350kV)). What would be power lost to heat from asingle conductor of the cable at this new voltage? [7 points]P = IV → I = P/V = 400MW/700kV = 571.429A 571.429 A / 2 = 285.714A per conductorP = I2R = (285.714 A)2* 1.9919732 Ω = 162609.73W = 200kW (1 sig fig) In reality this wouldn’t happen because the equipment is rated a specific voltage (importantlythe cables). However, notice the significant reduction in losses here. This is why we like totransmit power at higher voltages.d. NextEra Energy, the company that now owns the Trans Bay Cable, claims the cablehas enough power to provide 40% of San Francisco’s peak power needs. Based onthis claim, what is San Francisco’s peak power consumption? [3 points]400MW/0.4 = 1000MW = 1GW (1 sig fig)You do not need to include losses in this calculation because the size of the losses is less thanyour significant figures. At one sig fig, you’re on the order of magnitude of GWs, the lossesare in kW. Based on the date you were given; you may have rounding errors or measurementerrors bigger than those losses.e. According to the California Energy Commission, the County of San Franciscoconsumed 5631.8615 GWh of electricity in 2019. If San Francisco consumedNextEra’s claimed peak power for 2 hours every day, what was the average off-peakpower consumption in 2019? Assume power is constant over any given hour [6points]1GW*2 hours/day*365 days/year=730GWh peak5631.8615-730=4901.8615GWh off-peak 4901.8615GWh off-peak*1 day/22 hours*1 year/365 days=610.4435MW = 610.MW3 sig figs because of the rules of subtractionWe assume electricity consumption occurs only as peak and off-peak consumption. In reality,this fluctuates every minute of the day. However, on average you can identify peak hours ofconsumption. For pricing electricity, some utilities charge different prices throughout the dayto incentivize customers to consume electricity in off-peak hours. This is called time-of-usepricing. PG&E, the utility for San Francisco, has some residential pricing schemes with “peakhours” and “off-peak hours”. So, a similar approach as this problem could be used todetermine the average amount a residential customer would pay in peak vs off-peak electricityin a year.For commercial customers, PG&E has pricing schemes where prices change three differenttimes during the day. In the summer they call these “peak hours”, “part-peak hours”, and“off-peak hours”. In the winter they call the hours “peak hours”, “off-peak hours”, and“super-off-peak hours”. For additional information on electricity pricing, take a look atEnergy Regulation and Public Policy in GSPP or Energy Markets in Haas.2) Natural Gas and Fracking [25 points]: Answer the following questions with a shortparagraph each. Rely on course materials including lecture, section notes, and readings. Citeyour sources where appropriate. a. Hydraulic fracturing has revolutionized the energy industry in the United States, whatare the consequences of this change, positive and negative? Consider impacts to theenvironment, public health, marginalized communities, land use, the economy, andpolitics. [5 points]● Positive: source of jobs, increased economic activity in rural areas● Negative: pollution of water resources, can cause unintended seismic activity,boom/bust of economic activityb. What are the benefits to using natural gas as an energy source and what are thedrawbacks? Think about its impact on the electric grid, carbon emissions, energyaccess, and energy prices. [10 points]● Benefits: lower emissions than coal/oil, fast cycling to meet rapidly changingdemand/renewable generation, utilizes existing infrastructure, lowers oil/gas prices,domestic energy source● Drawbacks: non-renewable resource, still emits GHG’s, potential for methaneleakage, low price crowds out some zero carbon resources (including nuclear)c. Natural gas is sometimes called a “transition fuel.” What does this mean and what arethe implications for energy policy? [10 points]● It is a lower carbon fuel that society can utilize to