Abstract: The calculation of the variance of a correlation coefficient matrix for a photovoltaic fleet can be completed in linear space as a function of decreasing distance between pairs of photovoltaic plant locations. When obtaining irradiance data from a satellite imagery source, irradiance statistics must first be converted from irradiance statistics for an area into irradiance statistics for an average point within a pixel in the satellite imagery. The average point statistics are then averaged across all satellite pixels to determine the average across the whole photovoltaic fleet region. Where pairs of photovoltaic systems are located too far away from each other to be statistically correlated, the correlation coefficients in the matrix for that pair of photovoltaic systems are effectively zero. Consequently, the double summation portion of the calculation can be simplified to eliminate zero values based on distance between photovoltaic plant locations, substantially decreasing the size of the problem space.

Abstract: Long-term photovoltaic system degradation can be predicted through a simple, low-cost solution. The approach requires the configuration specification for a photovoltaic system, as well as measured photovoltaic production data and solar irradiance, such as measured by a reliable third party source using satellite imagery. Note the configuration specification can be derived. This information is used to simulate photovoltaic power production by the photovoltaic system, which is then evaluated against the measured photovoltaic production data to determine the degree of error between simulated and measured production. The simulated production is adjusted to account for the error and to infer degradation that can be projected over time to forecast long-term photovoltaic system degradation.

Abstract: A system and method to evaluate building heating fuel consumption with the aid of a digital computer is described. The evaluation can be used for quantifying personalized electric and fuel bill savings. Such savings may be associated with investment decisions relating to building envelope improvements; HVAC equipment improvements; delivery system efficiency improvements; and fuel switching. The results can also be used for assessing the cost/benefit of behavioral changes, such as changing thermostat temperature settings. Similarly, the results can be used for optimizing an HVAC control system algorithm based on current and forecasted outdoor temperature and on current and forecasted solar irradiance to satisfy consumer preferences in a least cost manner. Finally, the results can be used to correctly size a photovoltaic (PV) system to satisfy needs prior to investments by anticipating existing energy usage and the associated change in usage based on planned investments.

Abstract: A computer-implemented system and method to determine building thermal performance parameters through empirical testing is described. Three building-specific parameters, thermal conductivity, thermal mass, and effective window area, are empirically derived. Thermal conductivity is evaluated through an empirical test conducted in the absence of solar gain with constant indoor temperature and no HVAC. Thermal mass is evaluated through a second empirical test conducted in the absence of solar gain and no HVAC. Effective window area is evaluated through a third empirical test conducted in the presence of solar gain and no HVAC. Thermal HVAC system power rating and conversion and delivery efficiency are also parametrized. The parameters are estimated using short duration tests that last at most several days. The parameters and estimated HVAC system efficiency can be used to simulate a time series of indoor building temperature, annual fuel consumption, or maximum indoor temperature.

Abstract: Statistically representing point-to-point photovoltaic power estimation and area-to-point conversion of satellite pixel irradiance data are described. Accuracy on correlated overhead sky clearness is bounded by evaluating a mean and standard deviation between recorded irradiance measures and the forecast irradiance measures. Sky clearness over the two locations is related with a correlation coefficient by solving an empirically-derived exponential function of the temporal distance. Each forecast clearness index is weighted by the correlation coefficient to form an output set of forecast clearness indexes and the mean and standard deviation are proportioned. Additionally, accuracy on correlated satellite imagery is bounded by converting collective irradiance into point clearness indexes. A mean and standard deviation for the point clearness indexes is evaluated. The mean is set as an area clearness index for the bounded area.

Abstract: A computer-implemented system and method for tuning photovoltaic power generation plant forecasting is provided. Global horizontal irradiance (GHI), ambient temperature and wind speed for a photovoltaic power generation plant over a forecast period are obtained. Simulated plane-of-array (POA) irradiance is generated from the GHI and the plant's photovoltaic array configuration as a series of simulated observations. Inaccuracies in GHI conversion are identified and the simulated POA irradiance at each simulated observation is corrected as a function of the conversion inaccuracies. Simulated module temperature is generated based on the simulated POA irradiance, ambient temperature and wind speed. Simulated power generation over the forecast period is generated based on the simulated POA irradiance, simulated module temperature and the plant's specifications and status.

Abstract: A Thermal Performance Forecast approach is described that can be used to forecast heating and cooling fuel consumption based on changes to user preferences and building-specific parameters that include indoor temperature, building insulation, HVAC system efficiency, and internal gains. A simplified version of the Thermal Performance Forecast approach, called the Approximated Thermal Performance Forecast, provides a single equation that accepts two fundamental input parameters and four ratios that express the relationship between the existing and post-change variables for the building properties to estimate future fuel consumption. The Approximated Thermal Performance Forecast approach marginally sacrifices accuracy for a simplified forecast.

Abstract: A computer-implemented system and method to assist consumers with decisions affecting a change in fuel requirements is provided. Fuel consumption for heating can be considered by evaluating changes that would affect thermal conductivity, average indoor temperature, HVAC efficiency, and solar gain. In a further embodiment, a computer-implemented system and method to evaluate investment's in a building's shell is provided. Thermal conductivity and the surface area of a surface that is under consideration for improvement are obtained, after which revised thermal conductivity can be modeled based on the existing and proposed thermal performance of that building surface. In a still further embodiment, fuel consumption for heating modeling results can be comparatively evaluated, with one fuel consumption model operating over an annual (or periodic) scope and another fuel consumption model operating on an hourly (or interval) scope.

Abstract: A computer-implemented system and method to evaluate building heating fuel consumption is described. The evaluation can be used for quantifying personalized electric and fuel bill savings. Such savings may be associated with investment decisions relating to building envelope improvements; HVAC equipment improvements; delivery system efficiency improvements; and fuel switching. The results can also be used for assessing the cost/benefit of behavioral changes, such as changing thermostat temperature settings. Similarly, the results can be used for optimizing an HVAC control system algorithm based on current and forecasted outdoor temperature and on current and forecasted solar irradiance to satisfy consumer preferences in a least cost manner. Finally, the results can be used to correctly size a photovoltaic (PV) system to satisfy needs prior to investments by anticipating existing energy usage and the associated change in usage based on planned investments.

Abstract: A system and method to determine building thermal performance parameters through empirical testing is described. The parameters can be formulaically applied to determine fuel consumption and indoor temperatures. To generalize the approach, the term used to represent furnace rating is replaced with HVAC system rating. As total heat change is based on the building's thermal mass, heat change is relabeled as thermal mass gain (or loss). This change creates a heat balance equation that is composed of heat gain (loss) from six sources, three of which contribute to heat gain only. No modifications are required for apply the empirical tests to summer since an attic's thermal conductivity cancels out and the attic's effective window area is directly combined with the existing effective window area. Since these tests are empirically based, the tests already account for the additional heat gain associated with the elevated attic temperature and other surface temperatures.

Abstract: The accuracy of photovoltaic simulation modeling is predicated upon the selection of a type of solar resource data appropriate to the form of simulation desired. Photovoltaic power simulation requires irradiance data. Photovoltaic energy simulation requires normalized irradiation data. Normalized irradiation is not always available, such as in photovoltaic plant installations where only point measurements of irradiance are sporadically collected or even entirely absent. Normalized irradiation can be estimated through several methodologies, including assuming that normalized irradiation simply equals irradiance, directly estimating normalized irradiation, applying linear interpolation to irradiance, applying linear interpolation to clearness index values, and empirically deriving irradiance weights. The normalized irradiation can then be used to forecast photovoltaic fleet energy production.

Abstract: HVAC load can be shifted to change indoor temperature. A time series change in HVAC load data is used as input modified scenario values that represent an HVAC load shape. The HVAC load shape is selected to meet desired energy savings goals, such as reducing or flattening peak energy consumption load to reduce demand charges, moving HVAC consumption to take advantage of lower utility rates, or moving HVAC consumption to match PV production. Time series change in indoor temperature data can be calculated using only inputs of time series change in the time series HVAC load data combined with thermal mass, thermal conductivity, and HVAC efficiency. The approach is applicable for both winter and summer and can be applied when the building has an on-site PV system.

Abstract: The calculation of the variance of a correlation coefficient matrix for a photovoltaic fleet can be completed in linear space as a function of decreasing distance between pairs of photovoltaic plant locations. When obtaining irradiance data from a satellite imagery source, irradiance statistics must first be converted from irradiance statistics for an area into irradiance statistics for an average point within a pixel in the satellite imagery. The average point statistics are then averaged across all satellite pixels to determine the average across the whole photovoltaic fleet region. Where pairs of photovoltaic systems are located too far away from each other to be statistically correlated, the correlation coefficients in the matrix for that pair of photovoltaic systems are effectively zero. Consequently, the double summation portion of the calculation can be simplified to eliminate zero values based on distance between photovoltaic plant locations, substantially decreasing the size of the problem space.

Abstract: A building loses or gains heat through its envelope based on the differential between the indoor and outdoor temperatures. The losses or gains are due to conduction and infiltration. Conventionally, these effects are typically estimated by performing an on-site energy audit. However, total thermal conductivity, conduction, and infiltration can be determined empirically. The number of air changes per hour are empirically measured using a CO2 concentration monitoring device, which enables the infiltration component of total thermal conductivity to be measured directly. The conduction component of thermal conductivity can then be determined by subtracting the infiltration component from the building's total thermal conductivity.

Abstract: A photovoltaic system's configuration specification can be inferred by an evaluative process that searches through a space of candidate values for the variables in the specification. Each variable is selected in a specific ordering that narrows the field of candidate values. A constant horizon is assumed to account for diffuse irradiance insensitive to specific obstruction locations relative to the photovoltaic system's geographic location. Initial values for the azimuth angle, constant horizon obstruction elevation angle, and tilt angle are determined, followed by final values for these variables. The effects of direct obstructions that block direct irradiance in the areas where the actual horizon and the range of sun path values overlap relative to the geographic location are evaluated to find the exact obstruction elevation angle over a range of azimuth bins or directions. The photovoltaic temperature response coefficient and the inverter rating or power curve of the photovoltaic system are determined.

Abstract: The overall thermal performance of a building UATotal can be empirically estimated through a short-duration controlled test. Preferably, the controlled test is performed at night during the winter. A heating source, such as a furnace, is turned off after the indoor temperature has stabilized. After an extended period, such as 12 hours, the heating source is briefly turned back on, such as for an hour, then turned off. The indoor temperature is allowed to stabilize. The energy consumed within the building during the test period is assumed to equal internal heat gains. Overall thermal performance is estimated by balancing the heat gained with the heat lost during the test period.

Abstract: A computer-implemented system and method for inferring operational specifications of a photovoltaic power generation system using net load is provided. Photovoltaic plant configuration specifications can be accurately inferred with net load data and measured solar resource data. A time series of net load data is evaluated to identify, if possible, a time period with preferably minimum and consistent power consumption. Power generation data is simulated for a range of hypothetical photovoltaic system configurations based on a normalized solar power simulation model. Net load data is estimated based on a base load and, if applicable, any binary loads and any variable loads. The set of key parameters corresponding to the net load estimate that minimizes total squared error represents the inferred specifications of the photovoltaic plant configuration.

Abstract: Operational specifications of a photovoltaic plant configuration can be inferred through evaluation of historical measured system production data and measured solar resource data. Based upon the location of the photovoltaic plant, a time-series power generation data set is simulated based on a normalized and preferably substantially linearly-scalable solar power simulation model. The simulation is run for a range of hypothetical photovoltaic system configurations. The simulation can be done probabilistically. A power rating is derived for each system configuration by comparison of the measured versus simulated production data, which is applied to scale up the simulated time-series data. The simulated energy production is statistically compared to actual historical data, and the system configuration reflecting the lowest overall error is identified as the inferred (and optimal) system configuration.

Abstract: The accuracy of photovoltaic simulation modeling is predicated upon the selection of a type of solar resource data appropriate to the form of simulation desired. Photovoltaic power simulation requires irradiance data. Photovoltaic energy simulation requires normalized irradiation data. Normalized irradiation is not always available, such as in photovoltaic plant installations where only point measurements of irradiance are sporadically collected or even entirely absent. Normalized irradiation can be estimated through several methodologies, including assuming that normalized irradiation simply equals irradiance, directly estimating normalized irradiation, applying linear interpolation to irradiance, applying linear interpolation to clearness index values, and empirically deriving irradiance weights. The normalized irradiation can then be used to forecast photovoltaic fleet energy production.

Abstract: Probabilistic forecasts of the expected power production of renewable power sources, such as solar and wind, are generally provided with a degree of uncertainty. The expected power production for a fleet can be projected as a time series of power production estimates over a time period ahead of the current time. The uncertainty of each power production estimate can be combined with the costs and risks associated with power generation forecasting errors, and displayed or visually graphed as a single, deterministic result to assist power grid operators (or planners) in deciding whether to rely on the renewable power source.