Power Formulas for Various Energy Resources and Their Application

Transcription

1 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 1 UNIT 2.2 Energy Cnversin and Efficiency Purpse Once energy resurces are effectively utilized, cnversin t ther frms f energy is necessary t satisfy the needs f humanity. A variety f factrs cntribute t these energy cnversins being less than 100% efficient. The purpse f this lessn is t explre sme cntemprary examples f energy transfer and t analyze their respective limitatins and efficiencies. Prcedure During this activity, yu will: Explre the pwer frmulas fr varius energy resurces. Examine a simplified representatin f where nnrenewable and renewable energy resurces are typically cnnected t the pwer grid. Explre classrm scale energy cnversin systems and dcument the assciated energy cnversins. Create yur wn energy cnversin system and dcument the assciated energy cnversin(s). Analyze tw cntemprary energy cnversin systems: Garvin Falls Pwer Generatin Statin (in Bw, NH) and a hybrid vehicle (Chevrlet Vlt) Create yur wn energy cnversin system. Then dcument the assciated energy cnversin(s) and determine the verall efficiency f yur system, based upn direct measurements made while yur system is perating. Pwer Frmulas fr Varius Energy Resurces and Their Applicatin Imprtant Definitin Reminders: Energy A measure f an bject r substances ability t affect change in itself r the envirnment. Typical Units: Jule (J), Watt-Secnd (W-sec), Kilwatt-Hur (KW-Hur), Electrnvlt (ev), British Thermal Unit (BTU) Pwer The rate at which energy is transferred with respect t time. Typical Units: Watt = Jule/Secnd, BTU per hur, Hrsepwer Pwer Equatins fr Varius Energy Resurces: The frmulas listed belw can be used t determine the rate f energy prductin via varius methds. In the margin t the left, use the factr label methd t illustrate that the frmula yields the crrect units fr each methd. Nte: The calculatin has been dne fr yu fr the first and last resurce. Electricity Fssil and Bi-fuels P = VI V = vltage ( jules culmb ) I = electrical current ( culmbs secnd ) Q = V E g V = vlumetric burn rate ( gal ) hur E g = energy released per galln ( BTU ) gal = 140,000 BTU fr #2 hme heating il gal Date Cmpleted:

2 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 2 Nuclear Hydrelectric Q = R f E f R f = fissin rate ( fissins secnd ) E f = energy released per fissin ( MeV = 202 P = ρv gh MeV fissin fr U 235 fissin ) g ρ = water density = 1.0 cm 3 V = vlumetric flwrate ( m3 ) sec g = gravitatinal acceleratin = 9.81 h = hydraulic head (m) m sec 2 (n earth) Gethermal: Thermal energy that is available due t the fact that there are high temperature water reservirs near the earth s surface Q = m c p (T H T C ) m = mass flwrate ( Kg hur ) c p = specific heat = 1000 Jules Kg K T H, T C = ht, cld reservir temperatures (K) Wind P = 1 2 ρav3 ρ = air density = 1.0 Kg m 3 A = area f turbine blades (m 2 ) v = air velcity ( m sec ) Hydrgen Fuel Cell: A device that thrugh an electrchemical prcess cnverts hydrgen and xygen directly int water. In this prcess energy is released in the frm f electricity and heat. Q = n H t n = mles f hydrgen cnverted (mles) KJ H = mlar energy = t = time interval (hur) mle Date Cmpleted:

3 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 3 Slar: Radiatin Heat Transfer resulting frm the temperature difference between tw bdies. Especially ntewrthy due t the amazing prperty that the energy can travel thrugh a vacuum (that is it des nt require a medium t travel thrugh): Q = σa(t 1 4 T 2 4 ) σ = W m 2 K 4 A = surface area (m 2 ) T 1, T 2 = Temperatures f bdies (K) Simplified Pwer Grid Representatin: The fllwing schematic was fund at the website indicated at the bttm f the schematic. Explain the differences between where nnrenewable and renewable energy surces typically cnnect t the pwer grid: Date Cmpleted:

4 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 4 Classrm-Scale Energy Cnversin System: Belw is a phtgraph f an energy cnversin system that Mr. Wawrzyniak has created. Indicate the fllwing: Original Energy Resurce Intermediate Frms f Energy Frm f Energy Date Cmpleted:

5 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 5 Efficiency: The verall effectiveness f an energy cnversin system is indicated by its efficiency. In fact, we can talk abut the efficiency f the varius steps in an energy cnversin prcess and relate the efficiency f the verall system t thse values. Cnsider the wind pwer generatin system illustrated belw: Surce: We can identify a number f specific steps in the energy cnversin prcess: Rtr: cnverts wind energy t mechanical energy Generatr: cnverts mechanical energy t electrical energy Cnverter: cnverts electrical energy frm ne frequency t anther Transfrmer: adjusts electrical energy (vltage increase/current decrease) while maintaining the same frequency Distributin System: adjusts electrical energy (vltage decrease/current increase in steps) while maintaining the same frequency Each f these energy cnversin steps will have an efficiency assciated with it, whereby the utput pwer f that step will be less than the assciated input pwer. Fr each f these steps, the efficiency is a measure f hw well that step transfers energy frm ne frm t anther. This can be visualized using the fllwing diagram: Surce: The equatin fr efficiency can be written in terms f either energy r pwer: efficiency (%) = (useful energy ut ttal energy in) x 100 r efficiency (%) = (useful pwer ut ttal pwer in) x 100 Date Cmpleted:

6 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 6 When energy is transferred, sme f the energy turns int frms we dn't want. This energy is called wasted energy. Wasted energy takes the frm f heat and smetimes sund r light. During any energy transfer, sme energy is changed int heat. The heat becmes spread ut int the envirnment. This dispersed energy becmes increasingly difficult t use in future energy transfers. In the end, all energy is transferred int heat. Example: Cnsider the wind pwer generatin system illustrated n the prir page a. The first step in ur analysis will be t create a diagram with bxes that represent the different frms f pwer alng the way with arrws that represent the pwer passed between the cmpnents (black utline) and the pwer lsses (slid gray) alng the way (this is dne fr yu): ROTOR GENERATOR CONVERTER TRANSFORMER DISTRIBUTION b. The secnd step is t illustrate the pwer assciated with the different arrws if the input pwer is W and the efficiencies f the varius cmpnents g frm 90.0% t 50.0% in steps f 10.0% as the energy flws thrugh the system (perfrm the calculatins and label the diagram): ROTOR GENERATOR CONVERTER TRANSFORMER DISTRIBUTION c. ly, calculate the verall efficiency f the system and cmpare that t the prduct f the efficiencies fr the five cnversin steps alng the way. Date Cmpleted:

7 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 7 Garvin Falls Analysis: Overarching Questin: Is the rated capacity f PSNH s lcal hydrelectric statin (Garvins Falls, Bw, NH) sufficient t satisfy the maximum pwer requirements fr the residents f Bw? Imprtant Data: Typical Hydraulic Head at Garvins Falls: 20.0 ft Typical Hydrelectric Plant Efficiency: 80% Rated Electrical Pwer Output f Garvins Falls: 12.4 MW Vltage Output prvided by Garvins Falls: 345kV Estimated verall transmissin lsses between Garvins Falls and husehlds: 7% Vltage f husehlds: 110V Estimated maximum current fr husehld in Bw: 200 Amps Bw Ppulatin/Husing Infrmatin: 7,100 peple/2,300 husehlds Fur interesting slides frm: Date Cmpleted:

8 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 8 Steps t answer Overarching Questin: a. Estimate the ttal electrical current that wuld need t be prvided (at 110V) if all husehlds in Bw required maximum electrical current at the same time. b. Estimate the ttal pwer at the custmer end f the transmissin line that crrespnds t yur answer t a. c. Estimate the ttal pwer requirement at Garvins Falls and cmpare it t the rated pwer f Garvins Falls Useful Equatins: P = VI η = 100 P utput P input P = pwer (watts = jules V = vltage (vlts = ) secnd jules ) culmb I = current (ampheres = culmbs secnd ) η = efficiency (%) Other related questins: d. Estimate the ttal electrical current that wuld need t be prvided by Garvins Falls (at 345KV) in rder t meet the pwer requirement in part a. e. Estimate the necessary flwrate f water in the Merrimack River t meet the requirement f part a. Nte that the Hydraulic Pwer available in the river is given by the fllwing equatin P = ρv gh ρ = water density = 1.0 g/cm 3 V = vlume flwrate (m 3 /sec) g = gravitatinal accelaratin = 9.81 m/sec 2 h = hydraulic head (m) Imprtant ntes regarding slutins: Submit yur answers n the Engineering Ntebk Paper prvided. All equatins, units, and algebraic manipulatin must be shwn t receive maximum credit. All answers must be bxed t receive maximum credit. Date Cmpleted:

9 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 9 Understanding EPA Fuel Ecnmy Ratings fr a Hybrid Vehicle In March f 2011, Ppular Mechanics published an article that included an analysis f the infrmatin prvided in the EPA s 2011 Fuel Ecnmy and Envirnmental Cmparisn sticker fr hybrid vehicles (see fllwing page). Yur bjective is t demnstrate that the numbers in small print (that is within and belw the table labeled Examples: Charging Rutines ) are cnsistent with the MPG, Energy Per 100 Miles, and Cst Per Year numbers that are in large print. 1. Small Print Calculatins Using Electrical Energy in All Electric mde: a. What value was used fr the cst per KW-hr f electrical energy fr charging purpses? b. Shw that the cst per mile listed fr perating the Vlt in All Electric mde (4 /mile) is cnsistent with the value that can be calculated by cmbining ther values listed. c. Estimate the annual cst f perating the Vlt in All Electric mde. 2. Small Print Calculatins Using Chemical Energy in Gas Only mde: a. Estimate the cst per KW-hr f the chemical energy stred in gasline. b. Shw that the cst per mile listed fr perating the Vlt in Gas Only mde (9 /mile) is cnsistent with the value that can be calculated by cmbining ther values listed. c. Estimate the annual cst f perating the Vlt in Gas Only. 3. Cmparing All Electric and Gas Only mde: a. Estimate the cst per galln f gasline that wuld necessary fr the annual csts in All Electric and Gas Only mdes t be equivalent. Cncrd Mnitr Article (see fllwing pages): Use the data frm the Ppular Mechanics Article t calculate the Equivalent MPG fr the case where a Chevy Vlt is perated in All Electric mde and travels 28.9 miles n 9.3 Kilwatt-Hurs and cmpare the number yu get t the Equivalent MPG claimed in the Cncrd Mnitr article. Imprtant ntes regarding slutins: Submit yur answers n the Engineering Ntebk Paper prvided. All equatins, units, and algebraic manipulatin must be shwn t receive maximum credit. All answers must be bxed t receive maximum credit. Date Cmpleted:

10 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 10 Date Cmpleted:

11 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 11 Date Cmpleted:

12 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 12 Date Cmpleted:

13 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 13 Thery t Practice Prject: Energy Cnversin The gal f this prject is t perfrm the fllwing fr a self-designed energy cnversin system Identify the initial energy resurce t be utilized fr yur energy cnversin system Identify the final type f energy desired Create a sketch f the cnversin yu plan t cnstruct Obtain apprval frm yur teacher t begin cnstructin (iterate as necessary) Build yur system (iterate as necessary) Make apprpriate measurements and determine the verall efficiency f yur cnversin system Utilize the space belw fr dcument yur design prcess, cnstructin f yur system, measurements made, and the analysis f yur system s efficiency. Include additinal pages as necessary. Initial Data: Team: Input Energy Resurce: Apprved by Teacher: Output Energy Type: Apprved by Teacher: Dcumentatin f prgress: Date Cmpleted:

14 2: Energy, UNIT2.2: Energy Cnversin and Efficiency Page 14 Date Cmpleted: