Engineering Essentials of the Electric Grid: Homework Solutions Vermont Law School, June 2014

Transcription

1 Engineering Essentials of the Electric Grid: Homework Solutions Vermont Law School, June Forms of Energy a. In your own words, explain the difference between power and energy, giving an appropriate unit of measurement for each. Please note: your response to this question may not exceed 100 words. Two or three brief sentences should suffice. Answer: Electric power, which takes units of watts, describes the rate at which electricity is instantaneously generated. Electric energy, which takes units of watt- hours, describes the total quantity of electric power produced over some time interval. b. Give one example each of chemical energy, mechanical potential energy, mechanical kinetic energy, electrical energy, radiant energy, and thermal energy from your immediate surroundings at this moment. Answer: I am writing this from my desk, so here goes. There are obviously a large number of correct answers here: Chemical energy: My body digesting the chocolates I just ate for lunch. Mechanical potential energy: There is mechanical potential energy embedded in the door, which happens to be open. Mechanical kinetic energy: As I close the door, I am releasing some of the door s kinetic energy as I engage it in movement. Electrical energy: My laptop computer is utilizing electrical energy to light up the screen and to allow me to type. Radiant energy: It s a cloudy day but radiant energy is still being absorbed from the sunlight by a tree outside my office. Thermal energy: As I am furiously typing these answers, my hands are getting warmer. c. From your immediate surroundings, give three examples of energy being converted from one form into another (either by natural or human- made process). State the type of energy in each case, whether it is being converted into a form of higher or lower quality, and what losses there are, if any. Answers: Again, there are a lot of different answers. Chemical energy is being converted to electrical energy by my computer. This is a conversion to high- quality energy but there are some losses as my computer battery heats up. The chemical energy in the chocolate I am eating is being converted to mechanical energy so I can type, and thermal energy. The thermal energy conversion (which makes my hands warm) is of lower quality. Because I am not typing that hard, there are minimal losses the additional heat that my body gives off. Electrical energy is being converted into thermal energy by the light bulb in my office. This is a conversion from high to low quality, and there are losses since the light bulb gets quite hot. 2. Power Plant A nuclear power plant has a rated electric capacity of 600 MW. It operates at 30% efficiency in converting thermal to electrical energy. a. What is the heat rate of the plant, in BTU per kwh?

2 Answer: The heat rate of the plant is equal to 3,412/0.3 = 11,373.3 BTU/kWh. b. State in your own words the relevance of the first and second laws of thermodynamics to this calculation. Answer: The calculation describes how much of the energy input to the power plant is lost as heat versus how much is captured to be useful electricity (this is the second law). The energy losses plus the energy captured in the form of electricity must add up to the total amount of energy input to the power plant (this is the first law). c. If the nuclear power plant generates 5 million MWh of electric energy per year, what is the plant s capacity factor? Note: please use exactly two decimal places in your answer, and give your answer in terms of a decimal rather than a percentage (e.g and not 40%). Answer: The capacity factor is 5,000,000/(600*8760) = 5,000,000/5,256,000 = Your Basic Toaster Oven a. A toaster oven has a resistance of 24 Ω. At a voltage of 120 V, what is the current through the toaster, and how many watts of power does it draw? Answer: From Ohm s Law (V=IR), we can calculate the current as 120V/24 Ω = 5 Amps. Power is thus P=IV = 5*120 = 600 Watts. b. How many kilowatt- hours of electric energy does this toaster oven consume in a 30- day month, if it operates for 20 minutes every day? Answer: If the toaster operates for 20 minutes per day over 30 days, it operates for a total of 20*30 = 600 minutes or 10 hours. At a power consumption of 600 Watts, it consumes 600 Watts * 10 hours = 6,000 Watt- hours or 6 kwh. 4. Your Basic Light Bulb a. An incandescent light bulb is rated 40 W at 120 V. What is the current, and what is the light bulb s resistance in ohms? Answer: From the P=IV equation, we calculate current as I = P/V = 40/120 = 1/3 Amps. The resistance, from Ohm s Law, is R = V/I = 120/0.333 = 360 Ω. c. Repeat for an incandescent light bulb rated 60 W. Answer: From the P=IV equation, we calculate current as I = P/V = 60/120 = 0.5 Amps. The resistance, from Ohm s Law, is R = V/I = 120/0.5 = 240 Ω. c. Explain in your own words why a load with lower resistance draws more power. Shouldn t it be the other way around? Answer: Resistance is simply a measure of how easy or hard it is for current to flow through some medium, and doesn t necessarily have anything to do with the power drawn by some load. That is determined by current and potential (voltage) quantities. Of course, Ohm s Law does relate resistance to current and voltage.

3 5. Your Basic Battery a. A battery can deliver 100 amp- hours (Ah) at 12 V. How much stored energy does it have, in kilowatt- hours? In joules? (1 watt = 1 joule/second, or 1 kwh = 3,600,000 J) Answer: The battery can deliver 100 * 12 = 1,200 Watt- hours or 1.2 kwh. In joules, this would be 1.2 * 3,600,000 = 4,320,000 Joules. b. Find an alkaline (not rechargeable or lithium ion) AA, AAA or C battery and note its voltage and (milli- ) amp- hour capacity. Calculate the stored energy in watt- hours. Based on the approximate retail price of such a battery, what is the cost of electricity from this battery in $/kwh? Answer: There isn t a single right answer for this question, but I expect to see enough work shown that I can follow your calculations. Below I provide my answers for each type of battery. I got all battery prices from the Home Depot web site, for alkaline (not lithium or NMH) batteries. AA battery: 3 Amp- hours (Ah) at 1.5V. The electric energy stored in the battery is thus = 4.5 Wh. The cost of a four- pack of AA batteries is $3.50, so each battery costs 88 cents. Thus, the electricity cost of the battery is 19.5 cents per Wh, or $195 per kwh. AAA battery: 1.2 Amp- hours (Ah) at 1.5V. The electric energy stored in the battery is thus = 1.8 Wh. The cost of a six- pack of AAA batteries is $5.00, so each battery costs 83 cents. Thus, the electricity cost of the battery is 46.1 cents per Wh, or $461 per kwh. C battery: 8.5 Amp- hours (Ah) at 1.5V. The electric energy stored in the battery is thus = Wh. The cost of a four- pack of C batteries is $6.50, so each battery costs 163 cents. Thus, the electricity cost of the battery is cents per Wh, or $ per kwh. Note that in Vermont you would pay about $0.14 per kwh, so batteries are very expensive by comparison. 6. Shocking Science a. While doing some wiring in my garage, I accidentally touched a hot wire at 220 V. What would the resistance of my shoes (which we assume to be the most significant resistance in the circuit) have to be so that the current through my body could not exceed 50 milliamps (ma)? Answer: From Ohm s Law, we can write R=V/I. If we want the current to be no more than 50 ma, then the resistance would need to be: R = 220/0.05 = 4,400 Ω. b. Why is it inadvisable to perform electrical work while standing in a puddle of water, and why are wooden ladders preferable to aluminum? Answer: Water and aluminum are both materials with low resistance i.e., they are good conductors of electricity so they would create a low- resistance circuit through your body. 7. Rip- off? Rumor has it that some time back in the 1980s, some European utility companies were accused of trying to increase their revenue by simply raising the service voltage for unsuspecting customers by a few percent. For example, instead of supplying 220 V as expected at the customer service drop, they might have supplied 230 V instead.

4 a. In general terms (equations for voltage, current and power), explain why the utility might expect to sell more kwh of electric energy if the service voltage were raised. Answer: Since P = IV, if the service voltage can be increased while other end- uses (i.e., demands for current) remain constant, this would increase the power consumption. b. Consider an electric heater that draws 2000 W at 220 V. How much power would the same heater use if the voltage were raised from 220 to 230 V? Answer: at 220V, the water heater would consume 2000/220 = 9.09 Amps of current. Holding that amperage constant, at 230V the water heater would consume 230*9.09 = 2,090.9 Watts. c. Suppose that this heater is operating on a thermostat (for example, we might be talking about an electric oven that is set to a particular temperature). Does the argument in a. still apply, and will the utility still make more money by raising the voltage? Answer: Since the heater is operating on a control device and is not constantly drawing power, the argument in part (a) probably would not apply. If the device was drawing more power because of the voltage increase then the heating element would get hotter and would hit its upper limit (based on the settings of the thermostat) more quicky. d. Extra Credit: Someone told me there was a lawsuit, as customers began to notice that their light bulbs burned out sooner and sued the utility for supplying too high a voltage. Alas, I can t find any records of such a case. Can you help me determine if this is a true story? 8. Grid Components For each of the following components, state their function and the locations where they might be found within an electric power system: Answers: A transformer is a device that adjusts voltage magnitudes in an a.c. circuit. Transformers may be found in a number of locations including substations, distribution poles and even on some end- use electronics. A circuit breaker is designed to open a circuit in response to overly high currents. Circuit breakers may be found in homes or on distribution systems. A fuse is a simple device that is designed to protect against overcurrent by melting when too much current passes through it. Older homes may have fuse boxes instead of circuit breaker boxes. Fuses can also be found on the radial feeders of distribution systems. Switchgear is generally installed at substations to open and close circuits. Unlike circuit breakers, switchgear is designed to operate during normal current conditions and is not specifically designed to protect against overcurrents. 9. AC/DC a. Explain in your own words why our legacy electric grid uses alternating current. Answer: AC power can have its voltage transformed in a relatively straightforward way, which reduces line losses associated with long- distance transmission and allows power to be generated and transmitted at high voltages (more efficient) while being utilized at lower voltages (safer).

5 b. In recent years, high- voltage d.c. lines are more commonly used in the grid, with special converter stations at each end connecting them to the a.c. system. These lines are quite efficient in that the losses are fairly small. Does this not contradict your explanation above? Answer: At the time that much of the legacy grid was built, these DC lines were not a feasible technological option. Although DC transmission is more technically feasible, it still entails higher construction costs (because the DC lines are made from more expensive materials and the inverters are also expensive). 10. Geographic Scale Explain in your own words why electric power systems are large and interconnected. Answer: There are two primary advantages to having transmission systems that are large (that cover a broad geographic scope) and highly interconnected. The first is that it allows generation resources to be shared across geographic areas and used more efficiently (it may also allow for greater economies of scale). The second is that it may increase reliability through increasing the number of redundant connections. 11. Your Basic Transformer The step- down transformer to my house connects my 120 V residential service to the 12 kv primary distribution line. Suppose the total load at my house is 2400 W. a. What is the current in the secondary distribution line to my service panel? Answer: From the P=IV equation, we can calculate current as I=2400W/120V = 20 Amps. b. What is the current attributable to my house in the primary distribution line? Answer: Again, we can calculate current as I=2400W/12,000V = 0.2 Amps. c. Which wire needs to have a greater diameter: the one from the transformer to the primary distribution line, or the one from the transformer to my house? d. Without knowing anything about transformer design, how can you visually determine which wires to or from a transformer connect to the higher voltage? 12. System Topology a. What is the main reason for the radial layout of most distribution systems? Answer: Radial distribution systems were designed to permit one- way flow (from substation towards load), though this is changing with more distributed generation (like rooftop PV) being added to the distribution system. The advantage to a radial system is that it makes the placement and operation of protection devices (like circuit breakers) easier and allows distribution system operators to isolate faulted areas of the distribution grid more easily. b. What is the main reason for the meshed network design of transmission or distribution systems? Answer: The meshed network design of transmission systems allows for more redundancy in connecting generation and loads.

6 c. Describe one scenario in which transmission or distribution operators would open and close switches to reconfigure how the lines are connected. Answer: There are many such scenarios, most of which involve isolating faulted sections of the distribution grid while avoiding or minimizing service interruptions to customers. A specific example would be a selective feeder system (see slide 51 and thereabouts of the Day 2 notes), where the distribution system operator may adjust the feeder serving a specific customer without interrupting other customers. 13. The Cholesterol of Power Lines a. Why is the term reactive power consumption a misnomer? Explain in your own words. Answer: The term is misleading because nothing on the power grid actually consumes reactive power. Reactive power transfers no net energy across a circuit, so there is literally nothing to consume! A more appropriate term would be reactive power circulation, which describes how reactive power winds up taking space on transmission lines without doing any useful work. b. State one specific end- use load that would involve little or no reactive power. State one specific end- use load that would involve the circulation of reactive power. Answer: Resistive loads, such as toasters or incandescent light bulbs, do not induce circulation of reactive power (or very little). Inductive or reactive loads, which would include motors; pumps; and electronics do induce reactive power to circulate in transmission grids. Since the induction that leads to reactive power circulation arises because of the electrical properties of end- uses, we often use the (inappropriate) c. State two types of costs that result from reactive power consumption by electric end users, and explain who incurs these costs. Answer: Reactive power circulation can lead to increased transmission losses (owing to increased circulating currents) and voltage degradation at the point of the customer. Costs associated with losses are generally shared throughout the system (since with more losses, more generation is needed to meet a fixed amount of load), while local voltage degradation would affect a smaller number of customers though the costs of the solution in the form of capacitors or other voltage support may be spread across the entire system. 14. Time Scales a. Explain what actions a system operator or automated system could take to meet additional electric demand Answers: (i) the next day: Additional generation or other resources could be scheduled on a 24- hour ahead basis. (ii) in an hour: Additional generation or other resources could be scheduled on a one- hour ahead basis. (iii) in the next minute: A one- minute- ahead basis is too fast to schedule additional generation resources, so imbalances at this time scale would likely be remedied through an automated system like automatic generation control. (iv) right this second: Automatic frequency regulation (through automated generator valve

7 response) is basically the only option at this point. (v) next year: Existing generation is generally not committed or scheduled at a time period of a year in advance. If you expected demand to increase a year from now then you would likely need to build additional generation or engage customers to reduce demands. b. For each time scale above, explain what would happen if these actions were to fail that is, if supply falls short of demand. Answer: With the exception of (v), if an intervention fails on one time scale then the system operator would need to resort to the action associated with the subsequent time scale. For example, if insufficient generation were to be scheduled on a one- hour ahead basis then the system operator would need to rely on automated systems on the sub- hourly level. If the automated systems fail at the last minute then supply will fall short of demand and there will be a blackout. If sufficient investments in new generation are not made, such that total generation capacity falls short of total demand, then the system operator would need to rely on voluntary consumption curtailments (also called rolling blackouts ) to avoid a larger blackout. 15. Power Flow In one paragraph, explain a situation in which understanding the basics of power flow analysis would help you to evaluate a legal or policy issue that you have discussed in a previous class; experienced in your professional life; or read about in a newspaper or magazine. In your response please identify how you first encountered this situation (e.g., in class or in professional capacity)