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Principal component analysis for building combined cooling heating and power application potential.

BCHP system and Principal Component Analysis introduction

The Building cooling heating and power is similar to combined heat and power (CHP) system which is simultaneously producing thermal and electrical energy from a single thermal source(ASHRAE, 2008). BCHP is an integrated distributed generation (DG) represents an economic and environmental solution in fuel consumption, utility cost and carbon footprints. As a typical DG, BCHP system reduces the loss in electricity transmission and distribution from the grid. The investment in power plants is reduced as well. A major difference between separate heat and power (SHP) is that in a traditional building energy paradigm, roughly 33% of the energy is converted into electricity; most of the energy is discharged as waste heat in the power plant. As an on-site power solution, BCHP recovers most of the heat from the waste energy so the overall building efficiency is around 75% to 90%(EPA,US, 2013). The BCHP system is a sequential or simultaneous generation of heating, cooling energy and electricity. The waste heat is recovered for heating, or absorption chillers for cooling. The recovered heat also could be used to drive the prime mover to produce electricity(Petchers, 2002). A well designed BCHP system can deliver benefits in cost saving for consumers, lower carbon footprint, the reliance on fossil fuels, investment in power system infrastructure, power "peak shaving" (IEA, 2008). In 2008, International Energy Agency (IEA) reported CHP consists of 9% of power generation in US, while in Russia, Finland and Demark the percentage could be 30% to 50%. IEA predicts in the year 2030, around 20% of power generation is from the BCHP system in the US(IEA, 2008).

A traditional method to quantify the application potential is weighting factor analysis (United Technologies Research Center, 2006), the limitation of weighting factors are based on the personal opinions and its own knowledge. Generally, there are correlations between variables, the internal effect of each variable is hard to quantify. In this paper, the PCA is adapted to eliminate the correlated effect between relevant variables and discoved the latent effect to quantify the BCHP application potential.

Principal Component Analysis methodology

High correlation between predictors may reduce the reliability and stability of the model. The Principal Component Analysis is a statistical method that converts correlated predictors into orthogonal variables via linear combinations of original predictors. Those linear combinations are called principal components which have the same variance of all original predictors under the uncorrelated constraint. The PCA decompose the eigenvalue of a data covariance matrix. The principal component with largest variance is the first component. Principal components can keep as much variability and information as original predictors. Especially, under jointly normal distribution, principal components are mutually independent. To be precise, suppose X = ([X.sub.1], [X.sub.2] ... ., [X.sub.P]) is a random vector, which exitsts second moment. Denote [mu] = [epsilon](X), [SIGMA] = D(X) the mean and covariance of the random of vector X repectively. Considering a linear combination of X,


It is easy to see that Var([Y.sub.i]) = [l'.sub.i][SIGMA][l.sub.i], Cov([Y.sub.i], [Y.sub.j]) = [l'.sub.i][SIGMA][l.sub.j], i, j = l, ..., p

Set Sample matrix is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. After standardized every column of X, the sample correlation matrix is

R = [1/n][X.sup.T]X

By eigenvalue decomposition, we have

R = [p.summation over (i=1)] [[lambda].sub.i][Z.sub.i][Z.sup.T.sub.i]

Where [[lambda].sub.i] is the eigenvalue and [z.sub.i] are the corresponding eigenvector. We sort eigenvalues in decreasing orders as ([[lambda].sub.(1)], [[lambda].sub.(2)], ..., [[lambda].sub.(p)]) and eigenvectors ([Z.sub.(1)], [Z.sub.(2)], ..., [Z.sub.(p)]).

The principal components of n sample is


The contribution ratio of ith principal compost is [[lambda].sub.i]/[[summation].sup.p.sub.1][[lambda].sub.[kappa]]. The cumulative contribution of previous m th is [[summation].sup.m.sub.1][[lambda].sub.i]/[[summation].sup.p.sub.1][[lambda].sub.j].

Generally, when the cumulative contribution of principal components is higher than 75%, it is agreed that the m th components are sufficient to cover the enough information in the dataset. The detail explanation of PCA is in(Jolliffe, 2002)and (Jackson, 2005).

BCHP application potential analysis

The success of BCHP involves several important factors; different state has its particular environment to apply the BCHP. In this paper, the approach is to collect the related important parameter, identify the overall energy needs and other parameters in terms of economic, fuel availability, geographical information and weather conditions. It is believed that the state with highest application potential is an ideal candidate to promote BCHP; the related parameter information is discussed below.

Application potential parameters

The economic and environmental success in BCHP involves several parameters and the importance of each parameter is different. This paper chooses the most related parameters for the analysis and discussed below:

Building energy consumption (MMBTU): This factor is the total building energy consumption in the US for each state. The state with high energy consumption generally will have higher potential for energy conservation, emission and cost reductions. The energy consumption includes annual electricity (MMBTU), natural gas (MMBTU).

Energy expenditure: This factor collects the electricity and natural gas expenditure information. It is believed that the state with high expenditure in buildings will have more motivation for the building owners or designers to pay for additional expenditure in investing BCHP system.

Weather degree day data: Thermal load demand is a key factor to determine the success of BCHP system. The building load profile determines the chances and availability to effectively use the recovered heat. The degree day data includes annual heating degree days, annual cooling degree days. The high degree days means the region is favorable to BCHP in terms of thermal load.

Demographic information: The number of household and population are included in this factor. The population is generally closely related to a state's gross domestic product (GDP), governments tax income, energy consumption and carbon dioxide reduction.

Utility rate: An important factor influencing BCHP economic benefit is the utility rate for electricity and natural gas respectively. The price difference is an incentive to motivate people choosing BCHP system. The spark spread is a good index to spot the difference. Spark spread is the relative difference between the price of fuel and the price of power (Energy Protection Agency, 2010). In the calculation, it was assumed the average BCHP efficiency is 80%.

Economics: It is assumed that the region with better economy is more probable to adopt BCHP system because of the extra initial investment. The economics is considered as the average annual income per household.

Emission status: In US, coal is the major fuel source in the power plant(U.S. Energy Information Administration, 2011). BCHP system uses natural gas which it is considered as the cleanest fossil fuel (Energy Protection Agency, 2013), The state with high emission rate will benefits more from the natural gas for carbon footprint reduction.

Average electricity generation efficiency: The BCHP system could increase the overall building energy efficiency to around 75-90%. A typical mircoturbine electricity generation efficiency ranges from 35-38% (United Technologies Research Center, 2006) which is higher than traditional power plant efficiency.

Natural gas availability: Customers will accept natural gas easier if the gas pipeline or infrastructure is available. This factor is quantified by the natural gas heating percentage in the residential buildings.

Opportunity renewable fuel: Renewable fuels are naturally replenished which includes biomass, wind power, hydropower, solar energy and geothermal energy. Biomass is considered in this research; it may enhance the fuel diversity and reduce carbon emissions.

In the data collecting process, Hawaii State is excluded because it is very special in location, population, areas and natural resources. It deviates substantially from the average of other states.

PCA results

In the principal component analysis, each component describes one aspect of the problem which requires the explanation of the researcher. In most applications, statisticians and engineers agree that when the accumulative contribution up to 75% is enough is keep the accuracy of the research(Dunteman, 1989). The PCA result is shown in the table below:

From the results, four components covers accumulative 77% of information; therefore the analysis can be based on top four components and the rest is dropped. The detail of each component is shown below:


In first principal component (PC), the electricity/natural gas expenditure, population, total energy cost, natural gas/electricity consumption, housing units and population has large and relatively close coefficients. This means the importance for those variables in PC1 are close. The PC1 is considered as overall consumption and expenditure components which describe the information of energy consumption and expenditure in each state. A large number of population and housing units in a state require higher energy consumption in electricity, natural gas and corresponding expenditure. The state with high rank in PC1 will achieve higher absolute number of saving values from the fuel consumption and utility cost.

In PC2, natural gas price, spark spread, electricity retail price has larger but negative coefficients. PC2 demonstrates the effect of the fuel price on the application of BCHP system. It is desirable to have high electricity price and low natural gas to promote the application of BCHP system. However, the coefficients of those important factors are negative; PC2 is considered as inversely proportional to the application potential of BCHP system.


In PC3, it exhibits an internal effect of natural gas on the application of BCHP. The spark spared, natural gas heating percentage, average degree days, natural gas consumption and electricity price has prevailing coefficients. A region with high consumption of natural gas generally has a well-developed infrastructure. The high spark spread could further motivate people switch from electricity to natural gas. To summarize, PC 3 relates to the effect of natural gas on BCHP system and is directly proportional to the potential of application potential.


In PC4, electricity generation efficiency, total emission factor, NG heating percentage and coal percentage in electricity generation efficiency have higher coefficients. The electricity production efficiency has the largest positive and total emission factor has the largest negative coefficient. The negative sign means a low emission factor will have a score in PC4. High average electricity generation efficiency in power plant and low emission factors reduces the benefits of implementing BCHP systems. Therefore, PC4 is considered as negative environmental component and it is inversely proportional to the potential of BCHP.


The final score of each state is the sum of score at individual principal component multiplied by the component contribution percentage. The positive sign of the component means it is directly proportional to the application potential. The negative sign means an inverse relationship between the component and potential. The coefficient of each component is the contribution ratio for the individual principal component. The final potential score equation is given below.

Final Score = 36.67% x PC1 - 17.21% x PC2 + 13.21% x PC3 - 10.48% x PC4

The final total score of top ten states are in the table below
State           Score

California       3.5
New York         2.6
Texas            2.5
Florida         1.56
Illinois        1.19
New Jersey      1.18
Pennsylvania    1.17
Ohio            0.87
Michigan        0.75
Massachusetts   0.53

The top seven states are California, New York, Texas, Florida, Illinois, New Jersey and Pennsylvania. For regions, East North Central and Middle Atlantic region have higher potential. From the component analysis above, generally, the region or state has high overall energy consumption, favorable fuel prices; good natural gas availability is more favorable to promote BCHP systems.


An evaluation strategy to quantify the CHP application potential with comprehensive consideration of relevant factors was discussed and demonstrated. The method is based on the PCA model to systematically compare the influence of different parameters on the application potential and gives quantified scores to prioritize the state and regions that are more favorable for BCHP system. Depending on the coefficient of parameters on each principal component, the meaning of each component is addressed. Given the results from the PCA above, the state or region with high application potential should emphasis more on BCHP development plan or policies incentives in terms of primary energy saving, carbon footprints reduction and operation cost reduction.


ASHRAE. (2008). 2008 ASHRAE Handbook- Systems and Equipment (I-P). American Society of Heating, Refrigerating and Air-Conditioning Engineers.

Dunteman, G. H. (1989). Principal components analysis. Newbury Park, Calif.: Sage.

Energy Protection Agency. (2013). Natural Gas. Retrieved July 15, 2013, from

EPA, U. (2010). Definitions, Combined Heat and Power. Retrieved July 15, 2013, from

EPA,US. (2013). Combined Heat and Power Partnership | US EPA. Retrieved August 9, 2013, from

IEA. (2008). Combined Heat and Power Evaluating the benefits of greater global investment. International Energy Agency. Retrieved from Jackson, J. E. (2005). A User's Guide to Principal Components. Wiley.

Jolliffe, I. (2002). Principal component analysis (2nd Ed.). New York: Springer.

Petchers, N. (2002). Combined Heating, Cooling & Power Handbook: Technologies & Applications: An Integrated Approach to Energy Conservation. Fairmont Press.

U.S. Energy Information Administration. (2011). AnnualEnergyReview2011.

United Technologies Research Center. (2006, June). Micro-CHP Systems for Residential Applications Final Report. U.S. Department of Energy National Energy Technology Laboratory.

Bo Lin

Student Member ASHRAE

James Freihaut Ph.D.


Zhao Chen Ph.D.

Bo Lin is a Ph.D Candidate at The Pennsylvania State University
Table 1. Principal Component Analysis Results

Principal    Eigenvalue   Difference   Contribution Ratio
Component                                     (%)

PC1            6.234        3.308            36.67
PC2            2.926        0.679            17.21
PC3            2.247        0.464            17.21
PC4            1.783        0.756            10.49
PC5            1.027        0.164             6.04
PC6            0.864        0.122             5.08
PC7            0.742        0.322             4.37
PC8            0.421        0.122             2.48
PC9            0.299        0.108             1.76
PC10           0.191        0.028             1.12
PC11           0.162        0.098             0.96
PC12           0.061        0.038             0.38
PC13           0.026        0.019             0.16
PC14           0.008        0.003             0.05
PC15           0.005        0.005             0.03
PC16             0            0                0

Principal    CumContribution (%)

PC1                 36.67
PC2                 53.82
PC3                 67.09
PC4                 77.59
PC5                 83.63
PC6                 88.71
PC7                 93.08
PC8                 95.55
PC9                 97.31
PC10                98.44
PC11                99.40
PC12                99.78
PC13                99.93
PC14                99.97
PC15                 100
PC16                 100

Table 1 (a) Eigenvalue: Eigenvalue of the principal component. (b)
Difference: The difference between eigenvalue (c) Contribution Ratio:
The percentage of information covered in the data set. (d)
CumContribution: Cumulative contribution of covering information,
the sum of the previous contribution ratio.

Table 2. Description of Principal Component

Standardized Variable               PC1       PC2       PC3       PC4

Electricity Expenditure          0.3732    0.0178    -0.1291   -0.1151
Natural Gas Price                -0.0002   -0.4453   -0.1629   -0.2366
Population                       0.3919    0.0251    -0.0005   -0.0089
Total Fuel Cost                  0.3954    0.0283    -0.0293   -0.0450
Electricity Consumption          0.3529    0.0830    -0.2014   -0.1385
Natural Gas Consumption          0.3306    0.0856    0.2649    0.1565
Spark Spread                     0.0832    -0.3655   0.4520    0.0469
Electricity Price                0.0636    -0.5085   0.2625    -0.0856
Housing Units                    0.3925    0.0383    -0.0195   -0.0195
Average Household Income         -0.0269   -0.1956   0.2565    -0.0593
Degree Days                      -0.1632   0.1123    0.3397    0.2156
Coal Percentage                  -0.0698   0.2702    0.1342    -0.2536
Total Emission Factor            -0.0726   0.2642    0.2512    -0.5086
Efficiency in Power Plant        -0.0155   -0.0207   -0.3156   0.5970
Natural Gas Heating Percentage   0.0402    0.2574    0.3587    0.3460
Biomass Feedstock                0.0607    0.0023    -0.1623   -0.0642
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Author:Lin, Bo; Freihaut, James; Chen, Zhao
Publication:ASHRAE Transactions
Article Type:Report
Date:Jul 1, 2014
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