Cogeneration systems achieve high energy savings by simultaneously producing both electricity and thermal energy from a single power supply plant to satisfy total energy demands of buildings or factories. The benefits of cogeneration systems have been realized through a steady growth in their distribution all over Japan, where energy conservation is an important social requirement.

It is usually essential to evaluate cogeneration system performance in terms of energy saving or economic efficiency prior to the installation of the plant. In order to evaluate a cogeneration-system’s performance, we need to know not only aggregated annual heat and electricity demands, but also hourly and monthly patterns as input data for the computer simulation. The set of demand data is an assumed premise of the simulation and is usually based on the result of actual measurements of the energy demand of the buildings that belong to the same category.

However, it is extremely expensive to survey actual hourly-demand data and store it over a long period. Here we face the question of whether it is really necessary to collect all such energy-consumption data, 24 h a day for 12 months. In some cases, knowing the total annual amount of electricity and heat demands may be sufficient to make a decision about introducing a cogeneration system. In other cases, hourly consumption patterns may be required.

For example, among the various energy-demand components such as “total demand”, “demand pattern”, “heat-to-electricity ratio” or “daily load factor”, we may need a very strict anticipation for one demand component, while rough estimates may be sufficient for the other demand components. Eventually we need a criterion to answer the question of what kind of demand components we should survey in the first place.

In this paper, we firstly construct a mathematical model to investigate the relationship between cogeneration systems and demand data based on information theory in order to answer the above question. Then we build quantitative criteria of relative importance for each energy-demand component using the actual energy-demand data.

We usually use “energy saving” or “financial merit” as an indicator of cogeneration system (CGS) efficiency. Of course it depends on both hardware factors, such as capacity or efficiency of the generator, and software factors, such as load variations or the control system.

Because our purpose here is to analyze the influence of the demand-prediction error upon the efficiency of the CGS, we assume the hardware factor does not change. Therefore, the evaluation function F(Y) depends only on Y.

The elements x₁,…,x₅ are considered to play important roles in estimating the CGS efficiency among all elements of Y. Each element is defined as follows:-

x₁: Annual energy demand.

x₂: Annual heat-to-electricity ratio (ratio of annual heat demand to annual electricity demand).

x₃: Annual cooling and heating-to-hot water ratio (ratio of annual cooling and heating demand to hot-water demand).

x₄: Yearly load factor (ratio of monthly average demand to monthly peak-demand).

x₅: Daily load factor (ratio of hourly average demand to hourly peak-demand).

We call these elements “demand components” in this paper. The other elements, x₆, x₇,…,x₁₁₅₂ are of course demand components. However it is expected that these components are less sensitive to CGS evaluation and so an explicit definition is not given to them in this paper. We assume, however, the transformation function X=T(Y) can be defined to be differentiable and have inverse functions at any point without loss of generality.

In order to evaluate the CGS performance, we have to estimate the building’s energy-demand first. However we cannot predict it precisely. In these cases, it is quite natural to use a probability-density function to describe these demand prediction errors.

Suppose we use a probability-density f₂(x) as a model to describe a certain phenomenon, while its true probability-density is f₁(x), we can use the Kullback–Leibler information defined below to estimate the difference between the model and the true density.

We can interpret this concept as the amount of information we can get when we know the true probability density function of a certain phenomenon is f₁(x), which was supposed to be f₂(x).

For mathematical brevity, we consider the building’s energy-demand vector to be a random variable vector with the normal distribution function.

Because F is a function of the independent variable X, F(X) can also be considered to be a random variable. Actual values of F() are calculated by computer simulation, with hourly energy balances of heat and electricity being taken into account. The electricity needed to move the auxiliary apparatus such as a heat-recovery pump or auxiliary boiler should also be considered. Therefore F() cannot be treated as an analytical function. However our purpose here is not to define F() in a strict way, so we assume linearity of F() in a predictable interval of X in order to avoid a mathematical difficulty.

In this paper, we analyze the amount of information for each demand component in apartment buildings, hotels and office buildings. We first assume the probability density of each building’s energy-demand vector. This is the probability density of prediction error for each demand component, when the prediction is based on the data that are available at the present time. This concept corresponds to the density as a model. Fig. 2 expresses an example of the data related to heating demand in apartment buildings available at present in Japan. We set the value of the variance using an unbiased variance of actually surveyed data. In the cases of yearly load-factor and daily load-factor, we determine a certain value a priori because there are not enough data to estimate the variance statistically.

As for the conditions of simulation, we assume an apartment building of 100 households each with 100 m² floor area, and a hotel and an office of 30,000 m² floor area. We also determined the standard value for the building’s energy vector Y for each type of building using published data.

Fig. 3 shows the hardware structure of the CGS considered in this simulation. In this system, the waste heat is used for heating, cooling and supplying hot water, but we also analyze the systems in which waste heat is used for only heating and supplying hot water, or supplying hot water only. In the simulation, we compare the performance of the CGS with that of the conventional system in order to evaluate the merit of cogeneration. In the conventional system, the hardware system consists of a gas absorption chiller-heater and a hot-water boiler, and the electricity is purchased from the grid to meet the demand.