Transcript Lecture #21
ECE 333 Renewable Energy Systems Lecture 21: Photovoltaic Systems, Water Pumping Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign [email protected] Announcements • • Exam 2 Average: 78 Read Chapter 8 1 Amortizing PV Costs • Simple payback is the easiest analysis, which assumes there is no cost for money and no inflation. Annual cost is just total cost divided by lifetime This can give a quick ballpark figure – • Example: Assume 5 kW system with a capacity factor of 18%, an installed cost of $ 5/W (after tax credits), and a lifetime of 20 years with no maintenance costs. What is $/kWh? $5/W×5000 W 20 yrs $1250/yr = =$0.158/ kWh 5 kW×0.18×8760 7884 kWh/yr 2 Amortizing PV Costs • • More detailed analysis uses the capital recovery factor using an assumed discount rate Redo the previous example using a discount rate of 5% per year d (1 d )n 0.05 1.0520 A P 25, 000 n (1 d ) 1 1.0520 1 0.1327 A 25, 000 2006.6 These values vary 1.6533 linearly with the $2006.6/yr assumed PV =$0.2545/ kWh installed cost 7884 kWh/yr 3 Complications • • • "It's tough to make predictions, especially about the future", Yogi Berra (a baseball player/coach appearing as a player or coach in 21 world series) There is uncertainly about the rate of electric rate inflation, and the decreasing costs of solar panels Also, how long will you own the house, how is PV included in home's value https://qzprod.files.wordpress.com/2014/11/us-consumer-price-indexes-year-on-year-change-core-cpi-headline-cpi_chartbuilder.png?w=1280 4 Residential Solar Power Purchase Agreements • Solar PPAs are set so a customer has a developer design, • • • permit, finance and install a PV system on the customer's property Customer then buys the solar power from the developer at a fixed price (perhaps slowing inflating), typically below the utility rate for a fixed time period (say 20 years) The PPA requires little up front cost from the customer, and the developer maintains the system Can be transferred to a new owner if house is sold 5 Utility Scale Solar Prices Solar PV is usually purchased on longterm power purchase agreements (PPAs) Image Source: Steven Chu talk at NRC Next Generation Electric Grid Workshop, Irvine, CA, Feb 11, 2015 6 In the News: Minnesota and Renewable Energy • This month Minnesota is considering changing a requirement that the state get 1.5% of energy from solar by 2020 – – – • Proposed bill would allow utilities to meet requirements by wind, hydro or biomass if cheaper than solar It would also create rebates for geothermal heat pumps, wind, solar thermal or storage; would also allow new nuclear Also impacts net metering Bill is getting a negative reception from some, " "Never have I seen some people so upset over a bill that reduces energy pollution and lowers energy costs." Minnesota State Rep. Pat Garofalo 7 Stand-Alone Configurations 8 Key Issue is Intermittency of Renewable Sources • Unlike hydro, nuclear, and fossil, renewable energy from • • • wind or solar PV cannot be stored in fuel form In designing systems powered exclusively by such systems some storage is usually needed Image on right shows that wind stopped in BPA area for 11 days In Dec 2014 Chicago had ten days with only 30 minutes of total sun, and only got 16% of available sun up to Dec 22 Image Source: Steven Chu talk at NRC Next Generation Electric Grid Workshop, Irvine, CA, Feb 11, 2015 9 Battery I-V Curves • • Energy is stored in batteries for most off-grid applications An ideal battery is a voltage source VB • A real battery has internal resistance Ri V VB Ri I 10 Battery I-V Curves • • • Charging– I-V line tilts right with a slope of 1/Ri, applied voltage must be greater than VB Discharging battery- I-V line tilts to the left with slope 1/Ri, terminal voltage is less than VB A blocking diode can be used to prevent the battery from discharging into the PV at night. 11 Hourly I-V Curves • • • Current at any voltage is proportional to insolation VOC drops as insolation decreases Can just adjust the 1-sun I-V curve by shifting it up or down 12 Batteries and PV Systems • • Batteries in PV systems provide storage, help meet surge current requirements, and provide a constant output voltage. Lots of interest in battery research, primarily driven by the potential of pluggable hybrid electric vehicles – • $2.4 billion awarded in August 2009 There are many different types of batteries, and which one is best is very much dependent on the situation – Cost, weight, number and depth of discharges, efficiency, temperature performance, discharge rate, recharging rates 13 Lead Acid Batteries • • • Most common battery for larger-scale storage applications Invented in 1859 There are three main types: 1) SLI (Starting, Lighting and Ignition) : optimized for starting cars in which they are practically always close to fully charged, 2) golf cart : used for running golf carts with fuller discharge, and 3) deep-cycle, allow much more repeated charge/discharge such as in a solar application 14 Basics of Lead-Acid Batteries Positive Plate: PbO2 + 4H + + SO42 + 2e PbSO4 2H 2O (9.21) Negative Plate: PbO2 + SO42 PbSO4 2e (9.22) 15 Basics of Lead-Acid Batteries • • During discharge, voltage and specific gravity drops Sulfate adheres to the plates during discharge and comes back off when charging, but some of it becomes permanently attached 16 17 Battery Storage • Battery capacity has tended to be specified in amphours (Ah) as opposed to an energy value; multiply by average voltage to get watt-hours – – Value tells how many amps battery can deliver over a specified period of time. Amount of Ah a battery can delivery depends on its discharge rate; slower is better Figure shows how capacity degrades with temperature and rate Battery Costs have Been Decreasing Image Source: Steven Chu talk at NRC Next Generation Electric Grid Workshop, Irvine, CA, Feb 11, 2015 18 Battery Technologies Type Density, Wh/kG Cost $/kWh Cycles Charge time, hours Power W/kg Lead-acid, deep cycle 35 50-100 1000 12 180 Nickel-metal hydride 50 350 800 3 625 Lithium Ion 170 500-100 2000 2 2500 The above values are just approximate; battery technology is rapidly changing, and there are many different types within each category. For stationary applications lead-acid is hard to beat because of its low cost. It has about a 75% efficiency. For electric cars lithium ion batteries appear to be the current front runner 19 Number of Cycles Depends on Depth of Discharge • The below graph shows results for a lead acid battery Image Source: http://www.mpoweruk.com/life.htm Ballpark would be 1000 cycles at 50% discharge; if cost is $100 per kWh, or $200 per useable kWh, then the capital cost is $0.20/kWh This does not include energy cost; ballpark roundtrip efficiency is 80% 20 Stand-Alone System Energy Needs • • In many locations clouds can greatly reduce the available peak sun hours, sometimes for days at a time As a minimum the average peak sun hours must at least meet the average load – • • • Peak sun hours and perhaps the load have a seasonal dependence Sufficient storage is needed to supply full load at times when the sun isn’t available Probabilistic depending on location – how likely is a string of low sun days Inverter and battery efficiencies need to be considered 21 Estimating Storage Needs 22 Common PV System Usage: Pumping Water PV systems are widely used for pumping water, particularly in developing countries; if water is stored, when it is pumped does not much matter 23 PV Powered Water Pumping http://www.rajkuntwar.com/html/Solar.html http://www.oksolar.com/pumps/ http://solar-investment.us/solar-pv-surface-and-bore-waterpumping/ 24 DC Motors • • • DC motors have a magnetic field produced in the stator, and then some mechanism to change the current flow in the rotor (armature) (either brushes or electronic) Advantages include high starting torque and speed control over a wide of values Disadvantages include higher initial cost and the need for a dc source – A luxury car may have more than 100 dc motors 25 DC Motors • Main types are based on how the stator is powered: – – – – Separately excited (separate windings) Permanent magnet Shunt connection (field winding is in parallel with the armature); these motors have near constant speed regardless of load Series connection (field winding is in series with armature); these motors have high torque at low speed, but can have high speed with low torque 26 Separately Excited DC Motor • The equations are: v f if Rf Lf di f dt dia va ia Ra La Gmi f dt In steady-state (our concern) the derivatives are zero; if a permanent magnet then Gif is a replaced by a constant k With a shunt configuration, vf = va Image Source: M.A. Pai, Power Circuits and Electromechanics, Stipes Publishing, 2007 27 Torque, Speed and Voltage Relationships • For a permanent magnetic dc machine in steadystate we get va ia Ra km • • If Ra were zero then speed only depends on voltage Power to motor is va km Pmotor km ia a km Ra • Motor torque is Tmotor Pmotor m va km k k ia Ra Motor will not start until solar PV has enough current so torque is high enough to overcome static friction 28 Permanent Magnet DC Motor 29 DC Motor I-V Curve Linear Current Booster (LCB) helps the motor be able to start in low sunlight 30 Hydraulic Pumping Curves • • For pumping, the two key values are head, H (height water is pumped), and flow rate, Q (rate at which water is pumped) Mechanical power is then Pmech HQ Pmech (W ) 0.1885 H ( ft ) Q ( gal / min) Pmech (W ) 9.81 H (m) Q( L / s ) • Required electrical power depends on the efficiency 0.1885 H ( ft ) Q ( gal / min) Pelec (W ) Efficiency 31 Example: Energy to Pump Water from Shallow Well • How many kWh/day are required to pump 250 gallons/day with a 66 ft head, assuming 35% efficiency? With efficiency given, the below equation works for any rate, so calculate power required if the 250 gallons is pumped in one hour 0.1885 H ( ft ) Q( gal / min) Cost is Pelec (W ) Efficiency higher when 250gal / day pumping Q( gal / min) 4.167 gal / min into a 60 min/ day pressure 0.1885 66 4.167 Pelec (W ) 148 W (for one hour) tank (1 psi 0.35 = 2.31 ft) Cost is about $0.02 or Answer 0.148 kWh $0.08 per 1000 gallons 32