Analysis of the Residential, Commercial and Industrial Electricity Consumption


 Oswald Malone
 2 years ago
 Views:
Transcription
1 1 Analysis of the Residential, Commercial and Industrial Electricity Consumption John D. Hobby and Gabriel H. Tucci Abstract This work explains how to analyze the aggregate electricity consumption of many consumers, and extract key components such as heating, ventilation and air conditioning (HVAC), residential lighting, and street lighting consumption from the total consumption. To avoid explicit modeling of dependencies on time of day and on working versus nonworking days, leastsquares fitting for outside temperature and natural illumination dependency proceeds independently for each hour of the day. Cubic polynomials model dependencies on Steadman apparent temperature and on logscale illumination, but spline surfaces are best when considering these variables jointly. The primary focus is on residential consumption, but the same techniques can be used for studying street lighting, commercial and industrial consumption. Index Terms Smart Grid; Electricity Consumption; Smart Metering; RECS Survey; Time of Use Survey I. INTRODUCTION AND OVERVIEW An important property of the electricity grid is that production must be carefully matched to consumption in order to keep voltage and frequency stable and avoid damaging expensive infrastructure. On the other hand, customer activities, needs, and desires, as well as weather, shape the patterns of electricity use, which vary seasonally and hourly. These patterns typically result in high concentrations of electricity use in peak periods. The larger the peak demand, the greater the amount of electrical resources (distribution, transmission, and generation assets) that are needed to meet it. Hence, it is of fundamental importance to have an accurate model of the demand of electricity consumption. The unpredictable variations in consumption force suppliers to operate some power plants inefficiently at less than full capacity, e.g., as spinning reserve. The more accurately demand can be predicted, the more efficiently the plant can be operated. Furthermore, it helps to predict demand a day or more in advance because some power plants take that long to start up, and there are other aspects of power production and distribution that can benefit from such advance notice. For instance, coal plants require significantly more start up time than natural gas plants. Upcoming smart grid technology should allow producers to shape demand, but they will still need to know in advance what changes are desirable. Smart grid technology uses computers and advanced telecommunications for twoway communication between power consuming appliances and the electrical John D. Hobby and Gabriel H. Tucci are with Bell Labs, Alcatel Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, and grid. Devices can respond intelligently to price variations and alter their consumption accordingly. It may be difficult to get consumers (particularly residential consumers) to accept realtime electricity pricing. One alternative is dayahead pricing whereby suppliers announce prices about 24 hours in advance, so human consumers and smart grid devices have time to react. Producers clearly need to be able to predict future demand in order to make effective use of such a system. The 24 hour time frame (or perhaps a few days) is convenient because electricity consumption is known to be weather dependent, and future demand predictions require weather forecasts. Suppose we have historical consumption data for a mediumsized city or a suitable metropolitan area, and we want to analyze this in conjunction with historical weather data in order to understand total consumption and use weather forecasts to make future predictions. The historical consumption data presumably has separate categories for residential, commercial and industrial consumers, so their weather dependencies can be analyzed separately. The U.S. government s Residential Energy Consumption Survey [21] shows that heating and cooling are the largest components of residential electricity consumption and that large parts of the country have substantial consumption for electric heat. Hence, Section II begins by extracting the weatherrelated component from the total residential consumption. More specifically, given the hourly electricity consumption in a mediumsized American city, we obtain the hourly temperature and relative humidity of this city for each hour of the day. With these data, we compute the hourly electricity consumption due to HVAC (Heating, Ventilation and Air Conditioning). Since residential consumption for lighting depends on natural illumination, we also extract the outside illumination and compute the hourly electricity consumption due lighting. It is often useful to extract these components jointly via least squares surface fitting. In Section III we apply these techniques to analyze the street lighting consumption, and Section IV considers commercial and industrial consumption. Remaining components of consumption can be understood in terms of a collection of electrical appliances, but we reserve that subject for a longer version of this paper. Finally, Section V presents prediction results. The numerical results we show are based on a single case. We have the residential electricity consumption data for a US city with a population of approximately 100,000 people for 2007, 2008 and We use the consumption of 2007 as past consumption data, take the weather data for
2 as it is (we assume perfect weather data here), and predict the hourly consumption for the entire year of We do the same with 2008 to predict II. WEATHER RELATED AND ILLUMINATION ELECTRICITY CONSUMPTION COMPONENTS A. Weather Related Component In this Section, we present a method for separating the weather related electricity consumption from the total electricity consumption. More specifically, and as mentioned in the introduction, we have the hourly residential, commercial and industrial consumption data from a mediumsized American city for the years 2007, 2008 and We also have the hourly temperature and relative humidity for the same city. We would like to extract from this information, a function of time that tells how much of this electricity is going to cooling and heating. We shall refer to this function as the weatherrelated electricity consumption. The difference between it and the total consumption is the nonweatherrelated electricity consumption. Our analysis depends on apparent temperature, i.e., how hot or cold it feels to the human body. The apparent temperature combines the air temperature and the relative humidity in an attempt to determine the humanperceived equivalent temperature. The human body uses evaporative cooling, which is less effective when the relative humidity is high. After studying this and other issues, Steadman [1] developed a formula for apparent temperature that depends on the partial pressure of water vapor. For this partial pressure, it is convenient to use an approximation due to [2]: e = ( T T T 3) ( 5450 ) exp H, T where T is the temperature in Celsius and H the relative humidity (as a fraction 1). Then Steadman s formula for apparent temperature in degrees Celsius [1] can be defined as at := T e. (1) This formula generalizes the popular heat index which we do not use because it is only properly defined when the actual temperature is above 27 Celsius. Here is how we extract the weather related component: First localize the data for each hour of the day (also separating working from non working days), and consider the electricity consumption versus apparent temperature, using the Steadman equation as we described above. In other words, for each hour of the day, we can plot of the electricity consumption as a function of the apparent temperature. We interpolate these data with a cubic polynomial and shift it down so the minimum is zero. The shifted curve is our model for the weatherrelated electricity consumption for this particular hour. Figure 1 gives this plot for 20h. A few remarks are in order here. First, the appendix explains why shifting this curve down is a reasonable thing to do. Fig. 1. The weather related model for 20 hrs (8 p.m.) Fig. 2. The nonweather related electricity consumption versus hour of the day in the month of January (blue) and July (red). Heuristically, this is based on the assumption that there exists a comfortable temperature where no air conditioning or heating is necessary. Second, the reason for using a cubic polynomial is to make the model as simple as possible while capturing the essence of the problem. We feel that higher degree polynomials, splines, or more complicated curves are unnecessary. Thus, for each hour of the day, we have a cubic polynomial that gives the weatherrelated electricity consumption as a function of the apparent temperature. Figure 2 illustrates how this model works for the months of January and and July. For each hour of the day, the Figure gives the electricity consumption for every day of the month so that there are 31 points for each hour. As this Figure suggests, we have now found the weatherrelated (apparent temperature) component, and we can remove it if desired. B. Lighting Electricity Consumption Component In this Section, we extract the electricity consumption due to residential lighting. The idea is to do a similar analysis as for the extraction of the weather related component, and obtain a function of time that gives the electricity consumption due to lighting. The lighting component is all the electricity that goes to illumination, including inside illumination, backyards, front yards, garages and any other type of light. For each hour of the day, we plot electricity consumption versus the outside illumination due to natural causes. For example, Figure 3 shows this data for 7am. (Each dot represents a day in the year 2008). Again, we interpolate this data with a cubic polynomial, and we shift it down do zero. The reasoning here is as before
3 3 and is heuristically based on the assumption that there is an outside illumination where almost no lighting is necessary. How do we determine outside illumination due to natural causes? The local weather station reports cloud cover once an hour, and the number of cloud layers and their coverage 3 fractions (e.g., 8 to 1 2 for scattered ) give attenuation estimates for sunlight an moonlight. Nielsen s study of twilight effects [3] models the effect of sun (and moon) elevation angle. Estimates for maximum illumination levels for full sunlight, for a full moon, for starlight and air glow are widely available. Moonlight reduction versus the fraction of moon illuminated is available from [4], and sun and moon altitudes and lunar illumination fractions can be computed by Moshier s astronomical ephemeris calculator program [5]. Some of these effects are probably insignificant, but this is hard to know a priori. Once we have the outside illumination, we can get polynomials for each hour of the day. These polynomials model the electricity consumption due to lighting as a function of the outside illumination. This illumination consumption can also be plotted versus time; e.g., results for January and July appear in Figure 4, and in the same Figure we see the electricity consumption due to lighting for the whole year. The red curve shows the typical average, but it is clear that we can also extract the variance for each hour or even higher moments if necessary. This gives us a good model for the energy spent at each hour of the day due to lighting. The use of log(lux) in Figure 3 reflects the widespread belief that human perception of brightness grows less than linearly with actual illumination. Rudd and Popa [6] explain that a subjective measure of perceived brightness is roughly Lux 1/3 but hypothetical neural response is more like log(lux) and exponentiation to give Lux 1/3 may be due to the manner in which observers read out the signal. There is a term directly proportional to Lux, namely the greenhouse effect that reduces heating requirements and increases the need for cooling. Our analysis so far requires this to be captured implicitly via the fact that typical illumination levels are correlated with the hour of the day. After we remove the illuminationrelated electricity consumption from the nonweatherrelated one, we obtain the nonweather and nonillumination related electricity consumption as a function of time. Figure 6 shows that the minimum is between 1am and 4am. This value corresponds to the electricity consumption for timeinvariant processes (all day running processes) such as Freezers and Refrigerators Water Heaters Standby appliances and devices (devices which are not being used but are plugged in) C. Joint extraction of the weather and illumination related components Many applications require nonweather and nonillumination related electricity consumption with no need to distinguish Fig. 3. The nonweather related electricity consumption versus outside illumination for 7am. Fig. 4. The illumination electricity consumption as a function of time localized for January (blue) and July (red). Fig. 5. The illumination electricity consumption as a function of time for the whole year. Fig. 6. The nonweather related and nonillumination related electricity consumption as a function of time.
4 4 between the two. Joint treatment of weather and illumination is conceptually more accurate since these components could possibly be positively correlated. Both the weather and illumination components are very much dependent on the hour of the day. For this reason it is better to do different fittings for each hour separately as we explained in Section II and IIB. More specifically, we fix the hour of the day, and for each data point, we plot in three dimensional space the vectors with coordinates apparent temperature, illumination and consumption. Using the Matlab procedure gridfit.m we find the surface that best fits these data points. See Figure 7 to see the data set and the fitted surface for 18h. We see that the fitted surface behaves convexly in the temperature for a fixed illumination, and it is increasing in the illumination component (as it gets darker) for a fixed temperature. Except for possible greenhouse effect at high illumination levels, this is the expected behavior of the consumption as a function of these two variables. We shift this surface down so that its minimum is zero as we did before. The shifted surface will be our function model for the weatherrelated and illumination electricity consumption as a function of the apparent temperature and illumination. Subtracting this function from the total consumption gives us the nonweather related and nonillumination related electricity consumption for 18h. We repeat this procedure for each hour of the day to get a complete model. Note that, as before, for each hour of the day we have a slightly different model. Fig. 7. Data points and fitted surface for 18h. The coordinates are illumination, apparent temperature and electricity consumption. D. Different Surface Fitting Algorithms It can be awkward to use Matlab for a large application, particularly if other languages like C or C++ are heavily used. Furthermore, gridfit.m is not documented in a manner that facilitates modification or reimplementation. Hence we implemented a rectangular array of bicubic surface patches, using a Bspline representation that guarantees C 2 continuity and uses (m + 3)(n + 3) degrees of freedom for m n patches. Since m = 3 and n = 6 prove to be sufficient for the illumination and temperature (respectively), a vector v R 54 determines the surface, where each point on the surface is a weighted average of 16 entries of v. The least squares problem is to choose v so as to minimize Av b 2, where each temperature, illumination, consumption data point (x i, y i, z i ) generates one row of matrix A. It has 16 nonzeros for the weighted average of v entries that gives the surface height at (x i, y i ), with z i as the corresponding entry in vector b. There are also rows of A for regularization terms that penalize for high second derivatives 2 z and 2 z 2 y. For each patch corner 2 i, j, there are row vectors ξ i,j and η i,j in R 54 (each with 9 nonzeros) such that the values of 2 z and 2 z 2 y at i, j are ξ 2 i,j v and η i,j v. Regularization terms for second derivatives at the edges of the surface involve A rows σ x ξ i,0 and σ x ξ i,n σ y η 0,j and σ y η m,j for 0 i m for 0 j n where σ x and σ y are scale factors and the 2m + 2n + 4 corresponding b entries are zeros. The regularization terms for 2 z on patch i, j generate four 2 rows of A: σ x 16 (ξ i,j + ξ i+1,j + ξ i,j+1 + ξ i+1,j+1 ), σ x 48 (ξ i,j ± (ξ i+1,j ξ i,j+1 ) ξ i+1,j+1 ), σ x 144 (ξ i,j ξ i+1,j ξ i,j+1 + ξ i+1,j+1 ), (2) where σ x is a scale factor and the corresponding b entries are all zero. Replacing ξ i,j... ξ i+1,j+1 by η i,j... η i+1,j+1 and σ x by another scale factor σ y gives terms for 2 z z 2. The motivation for (2) is that we treat 2 z and 2 z 2 y as approximately bilinear, and then integrate this bilinear approximation 2 over the surface patch. We tried this method on 24 surfaces with σ x = σ y = 364/18 and σx = σ y = /(18 28), where 364 is the number of (x i, y i, z i ) data points. This gave slightly better fits than gridfit.m (RMS error ranging from 82.1% to 99.3% as much), even though gridfit.m used about 800 degrees of freedom per surface. This large dimensionality slows down the least squares solver it is a parameter that can easily be reduced, but at the cost of surface roughness. The C 2 bicubic splines remain smooth regardless of how many patches are used. III. STREET LIGHTING Electricity consumption that goes into street lighting is a different category that considers energy spent by a city to illuminate its streets. Repeating an analysis similar to that in Section IIB produces a model for each hour of the day that gives energy for street illumination as a function of the outside illumination. Figure 8 gives this for 6am. Putting all the pieces together as we did in Section IIB, we can see in Figure 9 also the typical energy spent on street illumination for each hour of the day. The red curve shows the typical average energy consumption.
5 5 Fig. 8. In this Figure we see the street lighting electricity consumption versus outside illumination for 6am. Fig. 10. Data taken from the U.S. Energy Information Administration  Official Energy Statistics from the U.S. Government. Fig. 9. In this Figure we see the street lighting consumption as a function of time for the whole year. We expect the variations due to weather to be less strong for the industrial and commercial sectors. To test this, we repeated the analysis done before for the commercial and industrial electricity consumption. Again, for each hour of the day we obtain a surface that gives the consumption as a function of the natural illumination and apparent temperature. Figure 11 shows this dependence for the industrial sector. A similar behavior is presented in the commercial sector. IV. COMMERCIAL AND INDUSTRIAL ELECTRICITY CONSUMPTION As we saw, the residential electricity consumption varies significantly with the weather. For example, it has been shown by the U.S. Energy Information Administration that an average home in the Pacific region (consisting of California, Oregon, and Washington) consumes 35% less energy than a home in the South Central region. Most of the regional differences can be explained by climate. The heavily populated coastal areas of the Pacific states experience generally mild winters and summers, reducing the need for both home heating and air conditioning. The warm, humid climates of the South Central and South Atlantic regions lead to higher electricity usage, while the cold winters experienced in the Northeast and North Central regions result in much higher consumption of natural gas and heating oil. Another reason for regional differences is the variety of building codes and environmental regulations found at the local and state level. California has some of the strictest environmental laws and building codes in the country, which may contribute to the fact that its perhousehold energy consumption is lower than all other states except Hawaii. Major U.S. cities also show significant variation in per capita energy consumption. In addition to differences in regional climates and variations in building code standards, factors affecting energy use in cities include population density and building design. Townhouses are more energy efficient than singlefamily homes because less heat, for example, is wasted per person. Fig. 11. Data points and shifted down fitted surface for 7h for the industrial sector. The coordinates are illumination, apparent temperature and industrial electricity consumption. It is also instructive to examine this city s total industrial and commercial KWh per month as shown in Figure 12. The market sectors that are less temperature dependent also show less seasonal variation. Note that industrial electricity consumption refers to the aggregation of the consumption of all industrial buildings in the city, and commercial consumption is defined analogously. V. REAL CASE PERFORMANCE TEST In this Section we test the performance of our weather and illumination algorithm. Given the hourly consumption
6 6 Fig. 12. Monthly consumption for the residential, commercial and industrial (units 10 7 W) and the apparent temperature in yellow (units C). cons (2007), apparent temperature and natural illumination from 2007 we obtain a model for the weather and illumination related consumption cwir (2007) as explained in Section IIC. Now using the hourly apparent temperature and natural illumination from 2008 we predict the weather and illumination related consumption for the year We denote this function by pcwir (2008). The difference between the total consumption and the weather and illumination related consumption is the residual for 2007 res (2007) = cons (2007) cwir (2007). We estimate the hourly total consumption for 2008 denoted by pcons (2008) as pcons (2008) = res (2007) + pcwir (2008) taking care to use corresponding days of the week from res (2007). We can repeat the same experiment to predict the hourly consumption of 2009 from the 2008 data. The 2008 real hourly consumption figures range from 68,343Kw to 679,134Kw with a median of 261,505Kw, and the 2009 figures are very similar with ranges going from 68,477Kw to 677,887Kw with a median of 256,860Kw. Taking the RMS mean of the prediction errors for each hour of the year gives values between of 44,003Kw for the 2008 prediction and 44,080Kw for the one of We can see in Figure 13 the real and predicted consumption for some period of time in 2008 (others periods are similar). In order to put the prediction errors into context, we would like to highlight that one needs to consider both the time granularity of the predictions and the prediction horizon, and the size of the population responsible for the electricity consumption. In the analysis we have shared with you, we predict the hourly consumption for an entire year. If one looks at more aggregate consumption levels like daily or weekly consumption, as we demonstrate below, the error terms improve significantly. The standard deviation of percentage prediction error 1 for hourly, daily and weekly consumption is 14.9%, 6.5%, and 4.1%, respectively. Another dimension is the population size. As the size of the population increases, we expect to have significantly lower prediction errors. The error statistics we have shown you are for a city of 100,000 people. If you consider predicting electricity consumption at an hourly basis for an entire country which has a population of 50 million, the errors one can expect with our method would be much lower. Suppose the population is divided into 500 regions with 100,000 people in each region, and consider using the numerical methods from this paper to predict hourly consumption for each region. If each region has errors like that for the US city, and if these errors are independent, then the standard deviation of percentage prediction error for hourly consumption would be 0.7%. Moreover, almost 89% of all hourly predictions would be at most 1% off the actual consumption. Finally, we would also like to mention that the RECS survey [21] shows that air conditioning and heating contributes to 31.5% of the total electricity consumption (for the geographical region where our middle sized city is located). Our model predicts that for the 2008 data the weather related electricity consumption is % of the total consumption which is incredible close to the real case. VI. CONCLUSIONS We have presented a new method for computing weatherrelated electricity consumption and illuminationrelated electricity consumption. More precisely, given the hourly total consumption, we obtain the hourly weatherrelated and illuminationrelated electricity consumption. Analysis of the residual consumption is reserved for future work. It has daily, weekly and seasonal variations, and it could also be analyzed in terms of electrical appliances. The twostage data processing model and algorithms presented in this work can be used to construct a tool for predicting shortterm residential electricity consumption. APPENDIX A JUSTIFICATION FOR SHIFTING FITTED CURVES Fig. 13. Real Consumption of 2008 (blue) versus the predicted one from 2007 (red). We have a more elaborate treatment for the predicted residual using spectral analysis techniques but is out of the scope of this paper and we will leave for a future work. Consider consumption as a random function of the hour h = 1,..., 24 and the temperature T so consumption is F (h, T ). Represent F (h, T ) as a sum F (h, T ) = C wr (h, T ) + C nwr (h, T ), 1 Percentage prediction error is defined as prediction  actual consumption actual consumption 100
7 7 where C wr (h, T ) is the portion of consumption due to HVAC, and C nwr (h, T ) is the rest of the consumption. Now choose an hour h 0. For any T, consider the expectation E(C nwr (h 0, T )) = c nwr (h 0, T ) of the random variable C nwr (h 0, T ). It is reasonable to assume that it does not depend on T. In other words, c nwr (h 0, T ) = c nwr (h 0 ). Then for each hour h 0 and temperature T, the expectation E(F (h 0, T )) of the random variable F (h 0, T ) is equal to E(F (h 0, T )) = c wr (h 0, T ) + c nwr (h 0 ). Our main assumption for the shifting down procedure is that for every hour h 0, there exists a comfort temperature T min (h 0 ) such that c wr (h 0, T min (h 0 )) = 0, and thus no electricity is consumed for heating and/or air conditioning. Approximating E(F (h 0, T )) by a polynomial P (h 0, T ) in T with coefficients depending on h 0 gives [15] Tae Young Jung, Ordered Logit model for residential electricity demand in Korea, Energy Economics, pp , [16] Tsuji K., Sano F., Ueno T., and Saeki O., Bottomup Simulation Model for Estimating EndUse Energy Demand profiles in Residential Houses, Proc. of ACEEE Summer Study on Energy Efficiency in Buildings, California, ISBN , [17] Jessen Page, Darren Robinson and JeanLouis Scartezzini, Stochastic Simulations of Occupant Presence and Behaviour in Buildings, Proceedings: Building Simulation, [18] Yoshiyuki Shimoda, Takahiro Asahi, Ayako Taniguchi, Minoru Mizuno, Evaluation of cityscale impact of residential energy conservation measures using the detailed enduse simulation model, Energy, 32:9, pp , [19] American Time Use Survey, [20] Minkowski addition, addition [21] Residential Energy Consumption Survey, (2005 data), BIOGRAPHIES c wr (h 0, T ) = P (h 0, T ) min(p (h 0, T )) = P (h 0, T ) P (h 0, T c (h 0 )). ACKNOWLEDGMENT We would like to thank Yuliy Baryshnikov and Mustafa Dogru for many valuable discussions and comments. This work was partially funded by the Gachon Energy Research Institute in South Korea. REFERENCES [1] Robert G. Steadman, A Universal Scale of Apparent Temperature, J. of Applied Meteorology, vol. 23 no. 12, pp , [2] Kennneth G. Libbrecht, Properties of Ice, atomic/snowcrystals/ice/ice.htm. [3] Eric Tetens Nielsen, Illumination at Twilight, Oikos, vol. 14, no. 1, pp. 9 21, [4] C. D. Courter, How Bright is Moonlight?, kitathome/lunarlight/moonlight/gallery/technique/moonbright.htm, [5] Stephen L. Moshier, Selfcontained Ephemeris Calculator, [6] Michael E Rudd, Dorin Popa, Steven s Brightness Law, Contrast Gain Control and Edge Integration in Achromatic Color Perception: A Unified Model, J. Opt Soc. Am, Vol 23, No 9, pp , [7] A. Capasso, W. Grattieri, A. Prudenzi, A bottomup approach to residential load modeling, IEEE Transactions on Power Systems, 9:2, pp , May [8] Jukka V. Paatero and Peter D. Lund, A model for generating household electricity load profiles, International Journal of Energy Research, vol. 30, no. 5, pp , [9] Jeffrey A. Dubin and Daniel L. McFadden, An Econometric Analysis of Residential Electric Appliance Holdings and Consumption, Econometrica, vol. 52, no. 2, pp , [10] Anssi Seppälä, Load research and load estimation in electricity distribution, VTT Energy, [11] Peter C. Reiss, Matthew W. White, Household Electricity Demand Revisited, Working Paper 8687, [12] Michael Parti, Cyntia Parti, The total and appliancespecific conditional demand for electricity in the household sector, Bell Journal of Economics, 11:1, pp , [13] Bodil Merethe Larsen, Runa Nesbakken, Household electricity consumption for different end uses, [14] Bodil Merethe Larsen, Runa Nesbakken, Household electricity enduse consumption: results from econometric and engineering models, Energy Economics, 26:2, pp , John D. Hobby received his B.S. in Mathematics and Computer Science from the University of Washington in 1980, and his Ph.D. in Computer Science from Stanford University in Since then, he has been at Bell Labs (now part of Alcatel Lucent) in Murray Hill, New Jersey, and he is now a Distinguished Member of Technical Staff. His interests include graphics algorithms, computational geometry, document image analysis, scientific computing, and modeling and optimization, especially optmizing wireless systems. Gabriel H. Tucci was born in Montevideo, Uruguay. He received a B.Sc. in Mathematics and an Electrical Engineering Degree (M.Sc. equivalent) from the Universidad de la República in Uruguay in 2002 and 2003 respectively. He also received a Ph.D. in Mathematics from Texas A&M University in He later joined Bell Laboratories, AlcatelLucent in Murray Hill, where he is a member of Technical Staff in the Industrial Mathematics and Operations Research department. His interests are in analysis, probability, free probability, random matrices, hyperbolic geometry and their applications to wireless communications, coding theory, information theory, compress sensing and network optimization.
Optimum Solar Orientation: Miami, Florida
Optimum Solar Orientation: Miami, Florida The orientation of architecture in relation to the sun is likely the most significant connection that we can make to place in regards to energy efficiency. In
More informationClimate and Weather. This document explains where we obtain weather and climate data and how we incorporate it into metrics:
OVERVIEW Climate and Weather The climate of the area where your property is located and the annual fluctuations you experience in weather conditions can affect how much energy you need to operate your
More informationVOLATILITY AND DEVIATION OF DISTRIBUTED SOLAR
VOLATILITY AND DEVIATION OF DISTRIBUTED SOLAR Andrew Goldstein Yale University 68 High Street New Haven, CT 06511 andrew.goldstein@yale.edu Alexander Thornton Shawn Kerrigan Locus Energy 657 Mission St.
More informationShortTerm Energy Outlook Supplement: Summer 2013 Outlook for Residential Electric Bills
ShortTerm Energy Outlook Supplement: Summer 2013 Outlook for Residential Electric Bills June 2013 Independent Statistics & Analysis www.eia.gov U.S. Department of Energy Washington, DC 20585 This report
More informationMethodology For Illinois Electric Customers and Sales Forecasts: 20162025
Methodology For Illinois Electric Customers and Sales Forecasts: 20162025 In December 2014, an electric rate case was finalized in MEC s Illinois service territory. As a result of the implementation of
More information8. Time Series and Prediction
8. Time Series and Prediction Definition: A time series is given by a sequence of the values of a variable observed at sequential points in time. e.g. daily maximum temperature, end of day share prices,
More informationFACOGAZ Association of European Gas Meter Manufacturers
Page 1 of 13 GAS SMART METERING SYSTEM DRAFT MARCOGAZ/FACOGAZ POSITION PAPER FINAL 1. Introduction Marcogaz Members representing more than 100 million installed domestic gas meter in Europe owned by Distribution
More information2016 ERCOT System Planning LongTerm Hourly Peak Demand and Energy Forecast December 31, 2015
2016 ERCOT System Planning LongTerm Hourly Peak Demand and Energy Forecast December 31, 2015 2015 Electric Reliability Council of Texas, Inc. All rights reserved. LongTerm Hourly Peak Demand and Energy
More informationSoftware Development for Cooling Load Estimation by CLTD Method
IOSR Journal of Mechanical and Civil Engineering (IOSRJMCE) ISSN: 22781684Volume 3, Issue 6 (Nov.  Dec. 2012), PP 0106 Software Development for Cooling Load Estimation by CLTD Method Tousif Ahmed Department
More informationINTELLIGENT ENERGY MANAGEMENT OF ELECTRICAL POWER SYSTEMS WITH DISTRIBUTED FEEDING ON THE BASIS OF FORECASTS OF DEMAND AND GENERATION Chr.
INTELLIGENT ENERGY MANAGEMENT OF ELECTRICAL POWER SYSTEMS WITH DISTRIBUTED FEEDING ON THE BASIS OF FORECASTS OF DEMAND AND GENERATION Chr. Meisenbach M. Hable G. Winkler P. Meier Technology, Laboratory
More informationApplications to Data Smoothing and Image Processing I
Applications to Data Smoothing and Image Processing I MA 348 Kurt Bryan Signals and Images Let t denote time and consider a signal a(t) on some time interval, say t. We ll assume that the signal a(t) is
More informationA Comparative Study of the Pickup Method and its Variations Using a Simulated Hotel Reservation Data
A Comparative Study of the Pickup Method and its Variations Using a Simulated Hotel Reservation Data Athanasius Zakhary, Neamat El Gayar Faculty of Computers and Information Cairo University, Giza, Egypt
More informationA Model for Estimation of Derating in Diesel Engines used for Power Generation
International Journal of Energy Engineering 2016, 6(2): 3642 DOI: 10.5923/j.ijee.20160602.03 A Model for Estimation of Derating in Diesel Engines used for Power Generation U. G. Kithsiri 1,2,3, N. S.
More informationJoint models for classification and comparison of mortality in different countries.
Joint models for classification and comparison of mortality in different countries. Viani D. Biatat 1 and Iain D. Currie 1 1 Department of Actuarial Mathematics and Statistics, and the Maxwell Institute
More informationTime of use (TOU) electricity pricing study
Time of use (TOU) electricity pricing study Colin Smithies, Rob Lawson, Paul Thorsnes Motivation is a technological innovation: Smart meters Standard residential meters Don t have a clock Have to be read
More informationExample G Cost of construction of nuclear power plants
1 Example G Cost of construction of nuclear power plants Description of data Table G.1 gives data, reproduced by permission of the Rand Corporation, from a report (Mooz, 1978) on 32 light water reactor
More informationENERGY SAVING BY COOPERATIVE OPERATION BETWEEN DISTRICT HEATING AND COOLING PLANT AND BUILDING HVAC SYSTEM
Proceedings of Building Simulation 211: ENERGY SAVING BY COOPERATIVE OPERATION BETWEEN DISTRICT HEATING AND COOLING PLANT AND BUILDING HVAC SYSTEM Yoshitaka Uno 1, Shinya Nagae 1, Yoshiyuki Shimoda 1 1
More informationIntroduction to time series analysis
Introduction to time series analysis Margherita Gerolimetto November 3, 2010 1 What is a time series? A time series is a collection of observations ordered following a parameter that for us is time. Examples
More informationTrend and Seasonal Components
Chapter 2 Trend and Seasonal Components If the plot of a TS reveals an increase of the seasonal and noise fluctuations with the level of the process then some transformation may be necessary before doing
More information2014 ERCOT Planning LongTerm Hourly Peak Demand and Energy Forecast March 31, 2014
2014 ERCOT Planning LongTerm Hourly Peak Demand and Energy Forecast March 31, 2014 2014 Electric Reliability Council of Texas, Inc. All rights reserved. LongTerm Hourly Peak Demand and Energy Forecast
More informationDegree Reduction of Interval SB Curves
International Journal of Video&Image Processing and Network Security IJVIPNSIJENS Vol:13 No:04 1 Degree Reduction of Interval SB Curves O. Ismail, Senior Member, IEEE Abstract Ball basis was introduced
More informationShortTerm Forecasting in Retail Energy Markets
Itron White Paper Energy Forecasting ShortTerm Forecasting in Retail Energy Markets Frank A. Monforte, Ph.D Director, Itron Forecasting 2006, Itron Inc. All rights reserved. 1 Introduction 4 Forecasting
More informationEnergy savings in commercial refrigeration. Low pressure control
Energy savings in commercial refrigeration equipment : Low pressure control August 2011/White paper by Christophe Borlein AFF and l IIFIIR member Make the most of your energy Summary Executive summary
More informationAdaptive model for thermal demand forecast in residential buildings
Adaptive model for thermal demand forecast in residential buildings Harb, Hassan 1 ; Schütz, Thomas 2 ; Streblow, Rita 3 ; Müller, Dirk 4 1 RWTH Aachen University, E.ON Energy Research Center, Institute
More informationBuilding Energy Management: Using Data as a Tool
Building Energy Management: Using Data as a Tool Issue Brief Melissa Donnelly Program Analyst, Institute for Building Efficiency, Johnson Controls October 2012 1 http://www.energystar. gov/index.cfm?c=comm_
More informationGeography affects climate.
KEY CONCEPT Climate is a longterm weather pattern. BEFORE, you learned The Sun s energy heats Earth s surface unevenly The atmosphere s temperature changes with altitude Oceans affect wind flow NOW, you
More information2 Absorbing Solar Energy
2 Absorbing Solar Energy 2.1 Air Mass and the Solar Spectrum Now that we have introduced the solar cell, it is time to introduce the source of the energy the sun. The sun has many properties that could
More informationApproach to Energy Management for Companies
Approach to Energy Management for Companies Tomiyasu Ichimura Masahiro Maeeda Kunio Fukumoto Ken Kuroda Ryuzou Fukunaga Most companies in Japan are taking energysaving actions in an effort to cope with
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More informationBenchmarking Residential Energy Use
Benchmarking Residential Energy Use Michael MacDonald, Oak Ridge National Laboratory Sherry Livengood, Oak Ridge National Laboratory ABSTRACT Interest in rating the reallife energy performance of buildings
More informationTrace Gas Exchange Measurements with Standard Infrared Analyzers
Practical Environmental Measurement Methods Trace Gas Exchange Measurements with Standard Infrared Analyzers Last change of document: February 23, 2007 Supervisor: Charles Robert Room no: S 4381 ph: 4352
More informationApplication of Building Energy Simulation to Airconditioning Design
Hui, S. C. M. and K. P. Cheung, 1998. Application of building energy simulation to airconditioning design, In Proc. of the MainlandHong Kong HVAC Seminar '98, 2325 March 1998, Beijing, pp. 1220. (in
More informationExplanation of Blower Door Terms and Results. Information taken from TECTITE BUILDING AIRTIGHTNESS TEST by The Energy Conservatory
Explanation of Blower Door Terms and Results Information taken from TECTITE BUILDING AIRTIGHTNESS TEST by The Energy Conservatory AIRFLOW AT 50 PASCALS CFM50: This is the airflow (in Cubic Feet per Minute)
More informationTHE APPLICATION OF A DATA MINING FRAMEWORK TO ENERGY USAGE PROFILING IN DOMESTIC RESIDENCES USING UK DATA
Proceedings of the Research Students Conference on Buildings Don t Use Energy, People Do? Domestic Energy Use and CO 2 Emissions in Existing Dwellings 28 June 2011, Bath, UK THE APPLICATION OF A DATA MINING
More informationThe Effect of Schedules on HVAC Runtime for Nest Learning Thermostat Users
WHITE PAPER SUMMARY The Effect of Schedules on HVAC Runtime for Nest Learning Thermostat Users Nest Labs, Inc. September 2013! 1 1. Introduction Since the launch of the Nest Learning Thermostat in October
More informationFLORIDA SOLAR ENERGY CENTER
FLORIDA SOLAR ENERGY CENTER Creating Energy Independence Since 1975 Impact of EnergyEfficiency Parameters on Home Humidity Rob Vieira Florida Solar Energy Center A Research Institute of the University
More informationMarket Potential Study for Water Heater Demand Management
Market Potential Study for Water Heater Demand Management Rebecca Farrell Troutfetter, Frontier Associates LLC, Austin, TX INTRODUCTION Water heating represents between 13 and 17 percent of residential
More informationEnergy Storage for Renewable Integration
ESMAPSAREAP Renewable Energy Training Program 2014 Energy Storage for Renewable Integration 24 th Apr 2014 Jerry Randall DNV GL Renewables Advisory, Bangkok 1 DNV GL 2013 SAFER, SMARTER, GREENER DNV
More informationTime series analysis as a framework for the characterization of waterborne disease outbreaks
Interdisciplinary Perspectives on Drinking Water Risk Assessment and Management (Proceedings of the Santiago (Chile) Symposium, September 1998). IAHS Publ. no. 260, 2000. 127 Time series analysis as a
More informationPreparatory Paper on Focal Areas to Support a Sustainable Energy System in the Electricity Sector
Preparatory Paper on Focal Areas to Support a Sustainable Energy System in the Electricity Sector C. Agert, Th. Vogt EWE Research Centre NEXT ENERGY, Oldenburg, Germany corresponding author: Carsten.Agert@nextenergy.de
More informationMario Guarracino. Regression
Regression Introduction In the last lesson, we saw how to aggregate data from different sources, identify measures and dimensions, to build data marts for business analysis. Some techniques were introduced
More informationMCQ  ENERGY and CLIMATE
1 MCQ  ENERGY and CLIMATE 1. The volume of a given mass of water at a temperature of T 1 is V 1. The volume increases to V 2 at temperature T 2. The coefficient of volume expansion of water may be calculated
More informationMehtap Ergüven Abstract of Ph.D. Dissertation for the degree of PhD of Engineering in Informatics
INTERNATIONAL BLACK SEA UNIVERSITY COMPUTER TECHNOLOGIES AND ENGINEERING FACULTY ELABORATION OF AN ALGORITHM OF DETECTING TESTS DIMENSIONALITY Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree
More informationSubspace Analysis and Optimization for AAM Based Face Alignment
Subspace Analysis and Optimization for AAM Based Face Alignment Ming Zhao Chun Chen College of Computer Science Zhejiang University Hangzhou, 310027, P.R.China zhaoming1999@zju.edu.cn Stan Z. Li Microsoft
More information15.062 Data Mining: Algorithms and Applications Matrix Math Review
.6 Data Mining: Algorithms and Applications Matrix Math Review The purpose of this document is to give a brief review of selected linear algebra concepts that will be useful for the course and to develop
More informationCHAPTER 3. The sun and the seasons. Locating the position of the sun
zenith 90 summer solstice 75 equinox 52 winter solstice 29 altitude angles observer Figure 3.1: Solar noon altitude angles for Melbourne SOUTH winter midday shadow WEST summer midday shadow summer EAST
More informationGUIDE TO NET ENERGY METERING. www.heco.com
GUIDE TO NET ENERGY METERING www.heco.com Welcome to Net Energy Metering As a Net Energy Metering (NEM) customer, you are helping Hawaii reach its clean energy goals. Your photovoltaic (PV) system should
More informationFundamentals of Climate Change (PCC 587): Water Vapor
Fundamentals of Climate Change (PCC 587): Water Vapor DARGAN M. W. FRIERSON UNIVERSITY OF WASHINGTON, DEPARTMENT OF ATMOSPHERIC SCIENCES DAY 2: 9/30/13 Water Water is a remarkable molecule Water vapor
More informationPower (kw) vs Time (hours)
Solar Panels, Energy and Area Under the Curve Victor J. Donnay, Bryn Mawr College Power (kw) vs Time (hours) 3.0 2.5 Power (kw) 2.0 1.5 1.0 0.5 0.0 5 7 9 11 13 15 17 19 Time (hours) Figure 1. The power
More informationSolar Decathlon Load Profiling. Project Report
Solar Decathlon Load Profiling Project Report Prepared by Alexander Kon Alexander Hobby Janice Pang Mahan Soltanzadeh Prepared for TTP 289: A Path to Zero Net Energy 6/10/14 Executive Summary The U.S.
More informationBig Data and Energy Systems Integration
Big Data and Energy Systems Integration Henrik Madsen, DTU Compute http://www.henrikmadsen.org http://www.smartcitiescentre.org Quote by B. Obama: (U.N. Climate Change Summit, New York, Sept. 2014) We
More informationSoftComputing Models for Building Applications  A Feasibility Study (EPSRC Ref: GR/L84513)
SoftComputing Models for Building Applications  A Feasibility Study (EPSRC Ref: GR/L84513) G S Virk, D Azzi, K I Alkadhimi and B P Haynes Department of Electrical and Electronic Engineering, University
More informationNTC Project: S01PH10 (formerly I01P10) 1 Forecasting Women s Apparel Sales Using Mathematical Modeling
1 Forecasting Women s Apparel Sales Using Mathematical Modeling Celia Frank* 1, Balaji Vemulapalli 1, Les M. Sztandera 2, Amar Raheja 3 1 School of Textiles and Materials Technology 2 Computer Information
More informationDaniel C. Harris, Association for Energy Affordability Michael Bobker, CUNY Institute for Urban Systems
Peak Demand Limiting in New York Residential Housing: Automatic Air Conditioner Load Curtailment and Demand Limiting Using Wireless Mesh Communications Daniel C. Harris, Association for Energy Affordability
More informationEvaluation of Window Energy Rating Models for Different Houses and European Climates
Evaluation of Window Energy Rating Models for Different Houses and European Climates J. and A. Roos Department of Materials Science, The Ångström Laboratory Uppsala University P.O. Box 534, S751 21 Uppsala
More informationSolar and Wind Energy for Greenhouses. A.J. Both 1 and Tom Manning 2
Solar and Wind Energy for Greenhouses A.J. Both 1 and Tom Manning 2 1 Associate Extension Specialist 2 Project Engineer NJ Agricultural Experiment Station Rutgers University 20 Ag Extension Way New Brunswick,
More informationChapter 10: Peak Demand and TimeDifferentiated Energy Savings CrossCutting Protocols
Chapter 10: Peak Demand and TimeDifferentiated Energy Savings CrossCutting Protocols Frank Stern, Navigant Consulting Subcontract Report NREL/SR7A3053827 April 2013 Chapter 10 Table of Contents 1 Introduction...2
More informationResidential Energy Services Demand: Lisbon case study towards Net Zero Energy House
Residential Energy Services Demand: Lisbon case study towards Net Zero Energy House Abstract Technically, reaching Net Zero Energy House (NZEH) is no longer a too ambitious goal as most of the technologies
More informationComputer Graphics CS 543 Lecture 12 (Part 1) Curves. Prof Emmanuel Agu. Computer Science Dept. Worcester Polytechnic Institute (WPI)
Computer Graphics CS 54 Lecture 1 (Part 1) Curves Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) So Far Dealt with straight lines and flat surfaces Real world objects include
More informationChapter 4: Vector Autoregressive Models
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...
More informationResidential loads management by considering households satisfactory levels for smart meter applications
Residential loads management by considering households satisfactory levels for smart meter applications Kamon Thinsurat *, Suratsavadee Koonlaboon Korkua School of Engineering and resources, Walailak University,
More informationWeather stations: Providing business critical information
Weather stations: Providing business critical information As a nation, the U.S. consumes seven percent of the globe s energy, making it the largest energy user in the world by a considerable margin. Weather
More informationEnergy Analysis for Internal and External Window Film Applications for Existing Homes in Florida
Energy & Environmental Solutions Energy Analysis for Internal and External Window Film Applications for Existing Homes in Florida PREPARED FOR: INTERNATIONAL WINDOW FILM ASSOCIATION P.O. BOX 3871 MARTINSVILLE,
More information2014 Forecasting Benchmark Survey. Itron, Inc. 12348 High Bluff Drive, Suite 210 San Diego, CA 921302650 8587242620
Itron, Inc. 12348 High Bluff Drive, Suite 210 San Diego, CA 921302650 8587242620 September 16, 2014 For the third year, Itron surveyed energy forecasters across North America with the goal of obtaining
More informationTime Series Analysis. 1) smoothing/trend assessment
Time Series Analysis This (not surprisingly) concerns the analysis of data collected over time... weekly values, monthly values, quarterly values, yearly values, etc. Usually the intent is to discern whether
More informationBig Data Collection and Utilization for Operational Support of Smarter Social Infrastructure
Hitachi Review Vol. 63 (2014), No. 1 18 Big Data Collection and Utilization for Operational Support of Smarter Social Infrastructure Kazuaki Iwamura Hideki Tonooka Yoshihiro Mizuno Yuichi Mashita OVERVIEW:
More informationOBJECTIVE ASSESSMENT OF FORECASTING ASSIGNMENTS USING SOME FUNCTION OF PREDICTION ERRORS
OBJECTIVE ASSESSMENT OF FORECASTING ASSIGNMENTS USING SOME FUNCTION OF PREDICTION ERRORS CLARKE, Stephen R. Swinburne University of Technology Australia One way of examining forecasting methods via assignments
More informationMultivariate Normal Distribution
Multivariate Normal Distribution Lecture 4 July 21, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #47/21/2011 Slide 1 of 41 Last Time Matrices and vectors Eigenvalues
More informationSIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS. J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID
SIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID Renewable Energy Laboratory Department of Mechanical and Industrial Engineering University of
More informationNTC Project: S01PH10 (formerly I01P10) 1 Forecasting Women s Apparel Sales Using Mathematical Modeling
1 Forecasting Women s Apparel Sales Using Mathematical Modeling Celia Frank* 1, Balaji Vemulapalli 1, Les M. Sztandera 2, Amar Raheja 3 1 School of Textiles and Materials Technology 2 Computer Information
More informationUsing simulation to calculate the NPV of a project
Using simulation to calculate the NPV of a project Marius Holtan Onward Inc. 5/31/2002 Monte Carlo simulation is fast becoming the technology of choice for evaluating and analyzing assets, be it pure financial
More informationEECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines
EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation
More informationLeast Squares Estimation
Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN13: 9780470860809 ISBN10: 0470860804 Editors Brian S Everitt & David
More informationGlobal Seasonal Phase Lag between Solar Heating and Surface Temperature
Global Seasonal Phase Lag between Solar Heating and Surface Temperature Summer REU Program Professor Tom Witten By Abstract There is a seasonal phase lag between solar heating from the sun and the surface
More informationRosevilleProject. LoE _ 2 Glass Products. You can reduce your cooling energy usage by 25% or more. Here is the proof.
RosevilleProject Glass Products You can reduce your cooling energy usage by 25% or more. Here is the proof. HotButton Issues Residents of California, Arizona, and Nevada don t need a weather forecast
More informationELECTRICITY DEMAND DARWIN ( 19901994 )
ELECTRICITY DEMAND IN DARWIN ( 19901994 ) A dissertation submitted to the Graduate School of Business Northern Territory University by THANHTANG In partial fulfilment of the requirements for the Graduate
More informationgasnetworks.ie Methodology for forecasting gas demand
gasnetworks.ie Methodology for forecasting gas demand 1 Contents 1 Introduction 2 1.1 Scope of the report 3 1.2 Use and publication of the forecasts 4 1.3 Structure of the document 5 2 Conceptual background
More informationUsing Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data
Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable
More informationSmall Business Services. Custom Measure Impact Evaluation
National Grid USA Small Business Services Custom Measure Impact Evaluation March 23, 2007 Prepared for: National Grid USA Service Company, Inc. 55 Bearfoot Road Northborough, MA 01532 Prepared by: RLW
More informationEnergy Demand Forecasting Industry Practices and Challenges
Industry Practices and Challenges Mathieu Sinn (IBM Research) 12 June 2014 ACM eenergy Cambridge, UK 2010 2014 IBM IBM Corporation Corporation Outline Overview: Smarter Energy Research at IBM Industry
More informationData Center Industry Leaders Reach Agreement on Guiding Principles for Energy Efficiency Metrics
On January 13, 2010, 7x24 Exchange Chairman Robert Cassiliano and Vice President David Schirmacher met in Washington, DC with representatives from the EPA, the DOE and 7 leading industry organizations
More informationIntegrating Energy Efficiency into Utility Load Forecasts. Introduction: A LEED Gold Building s Effect on Utility Load
Integrating Energy Efficiency into Utility Load Forecasts Shawn Enterline, Vermont Energy Investment Corporation Eric Fox, Itron Inc. ABSTRACT Efficiency Vermont s efficiency programs are being integrated
More informationUNDERSTANDING AND MOTIVATING ENERGY CONSERVATION VIA SOCIAL NORMS. Project Report: 2004 FINAL REPORT
UNDERSTANDING AND MOTIVATING ENERGY CONSERVATION VIA SOCIAL NORMS Project Report: 2004 FINAL REPORT Robert Cialdini, Ph.D. Arizona State University Wesley Schultz, Ph.D. California State University, San
More informationSolution of Linear Systems
Chapter 3 Solution of Linear Systems In this chapter we study algorithms for possibly the most commonly occurring problem in scientific computing, the solution of linear systems of equations. We start
More informationEmpirical study of the temporal variation of a tropical surface temperature on hourly time integration
Global Advanced Research Journal of Physical and Applied Sciences Vol. 4 (1) pp. 051056, September, 2015 Available online http://www.garj.org/garjpas/index.htm Copyright 2015 Global Advanced Research
More informationReview of Transpower s. electricity demand. forecasting methods. Professor Rob J Hyndman. B.Sc. (Hons), Ph.D., A.Stat. Contact details: Report for
Review of Transpower s electricity demand forecasting methods Professor Rob J Hyndman B.Sc. (Hons), Ph.D., A.Stat. Contact details: Telephone: 0458 903 204 Email: robjhyndman@gmail.com Web: robjhyndman.com
More informationthe points are called control points approximating curve
Chapter 4 Spline Curves A spline curve is a mathematical representation for which it is easy to build an interface that will allow a user to design and control the shape of complex curves and surfaces.
More informationAbsolute and relative humidity Precise and comfort airconditioning
Absolute and relative humidity Precise and comfort airconditioning Trends and best practices in data centers Compiled by: CONTEG Date: 30. 3. 2010 Version: 1.11 EN 2013 CONTEG. All rights reserved. No
More informationAppendix J Demand Response Pilot
Appendix J Demand Response Pilot City Light s power resources are unusual for an electric utility serving a major urban area. About 90% of the energy served to Seattle originates from water, or hydropower.
More informationThe Quest for Energy Efficiency. A White Paper from the experts in BusinessCritical Continuity
The Quest for Energy Efficiency A White Paper from the experts in BusinessCritical Continuity Abstract One of the most widely discussed issues throughout the world today is the rapidly increasing price
More informationCGC1D1: Interactions in the Physical Environment Factors that Affect Climate
Name: Date: Day/Period: CGC1D1: Interactions in the Physical Environment Factors that Affect Climate Chapter 12 in the Making Connections textbook deals with Climate Connections. Use pages 127144 to fill
More informationPrinciple Component Analysis and Partial Least Squares: Two Dimension Reduction Techniques for Regression
Principle Component Analysis and Partial Least Squares: Two Dimension Reduction Techniques for Regression Saikat Maitra and Jun Yan Abstract: Dimension reduction is one of the major tasks for multivariate
More informationVISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University
VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS
More informationCrawl space heat and moisture behaviour
Crawl space heat and moisture behaviour Miimu Airaksinen, Dr., Technical Research Centre of Finland, VTT miimu.airaksinen@vtt.fi, www.vtt.fi KEYWORDS: crawl space, moisture, evaporation from ground, ground
More informationAlgebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 201213 school year.
This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra
More informationNew ball swing. Copyright Vaughan Roberts, 2007 Page 13
New ball swing New ball swing effect due to seam Experimental results for the amount of swing of a new ball at various angles of the seam and at different Reynolds numbers The new ball swings more at a
More informationArizona State University. Understanding the Impact of Urban Heat Island in Phoenix
Understanding the Impact of Urban Heat Island in Phoenix ( ) Summer Nighttime 'minlow' temperatures and its impact on the energy consumption of various building typologies Presented By: Sandeep Doddaballapur
More informationElectricity and Natural Gas Consumption Trends in the Australian Capital Territory 20092013. Environment and Planning Directorate
Electricity and Natural Gas Consumption Trends in the Australian Capital Territory 20092013 Environment and Planning Directorate January 2015 Contents Executive Summary... 3 Introduction... 4 Energy costs
More informationDhiren Bhatia Carnegie Mellon University
Dhiren Bhatia Carnegie Mellon University University Course Evaluations available online Please Fill! December 4 : Inclass final exam Held during class time All students expected to give final this date
More informationExperiment 7: Familiarization with the Network Analyzer
Experiment 7: Familiarization with the Network Analyzer Measurements to characterize networks at high frequencies (RF and microwave frequencies) are usually done in terms of scattering parameters (S parameters).
More information