IPMVP report

This chapter explains IPMVP report building mechanics and reasoning.

1. Purpose

The main purpose of the IPMVP report in MyMaxwell is to prove that Maxwell additive has a positive effect on building’s HVAC system. This is achieved by showing that COP has increased.

2. Main Report Development Methodology

2.1 COP Curve Comparision

Methodology is best described going backwards from final desired figures to raw input data. Final report page consists of сomparison of the COP curve as a function of temperature and average COP increase, for example:

Averaged COP increase 13.1%

To compare COP curves from the baseline and reporting periods, it may be necessary to extrapolate the measured COP values over a wider temperature range. This is done under the assumption that COP varies linearly with outside air temperature (OAT). Linear extrapolation enables the comparison of COP curves that were originally obtained over different, non-overlapping temperature ranges.

The linear relationship can be expressed as:

\[ COP(OAT) = m \cdot OAT + q \] where:

• \(OAT\) is the outside air temperature in °C,
• \(m\) is the slope of the linear relationship,
• \(q\) is the intercept.

Note that comparision table uses data point from the model, not actual averaged COP data at specific OAT point.

2.2 COP Curve building

To build the COP curve, a statistical approach is required. First, the average COP values are calculated within discrete temperature bins, typically using 1°C intervals. These averaged data points \( (OAT_i,COP_i) \)are then used to construct a linear model that describes the relationship between COP and outside air temperature (OAT).

The linear regression model has the form: \[ \mathrm{COP}(OAT) = m \cdot OAT + q \]

\(m \) calculated as:

\[ m = \frac{ n \sum_{i=1}^n OAT_i COP_i - \sum_{i=1}^n OAT_i \sum_{i=1}^n COP_i }{ n \sum_{i=1}^n OAT_i^2 - \left(\sum_{i=1}^n OAT_i\right)^2 } \]

\( q \) calculated as:

\[ q = \frac{ \sum_{i=1}^n COP_i - m \sum_{i=1}^n OAT_i }{n} \] where \( n \) is the number of temperature bins.

The goodness of fit (linearity) of the model is assessed using the coefficient of determination \( R^2 \), defined as: \[ R^{2} = 1 - \frac{\sum_{i=1}^{n}(COP_{i} - \hat{COP_{i}})^2}{ \sum_{i=1}^{n} (COP_{i} - \bar{COP})^{2}} \] where:

• \( \hat{COP_{i}} = m \cdot OAT_i + q \) is the predicted value from the model,
• \( \bar{COP} \) is the mean of the observed COP values.

In the context of HVAC chiller COP curves, an \( R^2 \) value above 0.95 is considered acceptable, indicating a strong linear relationship between COP and outside air temperature. However, due to inherent variability in operational and environmental conditions, slightly lower values (e.g., around 0.9) may still be valid for practical analysis.

2.3 COP calculation

Coefficient of Performance (COP) represents the instantaneous efficiency of a chiller over a given time period.

\[ COP = \frac{|H|}{W} \]

where:

• \( H \) is the useful heat transferred by the chiller during the period,
• \( W > 0 \) is the net work input to the chiller.

In practical calculations, a correction factor of 0.8 is applied to account for system inefficiencies or measurement uncertainties. Needs explanation from Marco

To compute the chiller’s performance, the following measurements are required (averaged over 1 minute):

• \( Q\ (m^3/h)\) — fluid flow rate,
• \( t_{in}\ (°C) \) — fluid temperature at chiller inlet,
• \( t_{out}\ (°C) \) — fluid temperature at chiller outlet,
• \( P\ (\text{kW}) \) — power consumption,
• \( C_p\ (kJ/kg·K) \) — fluid specific heat capacity (constant, depends on fluid mixture),
• \( \rho\ (kg/m^3) \) — fluid density (constant, depends on fluid mixture).

The COP is calculated as:

\[ COP = \frac{ \frac{Q}{3600} \cdot \rho \cdot C_p \cdot (t_{in} - t_{out}) }{ P } \cdot 0.8 \]

COP should be computed for each time point after proper data sanitation.

2.4 Data sanitation

Since measurement data is taken continously regardless of currecnt chiller operation mode, it is required to do data sanitation to exclude irrelevant data points when chille ris not in steady operation mode. This includes any of the following conditions:

• Flow rate \( Q < 60\ m^3/h \)
• Flow rate \( Q > 75\ m^3/h \)
• Electrical power \( P < 20\ \text{kW} \)
• Electrical power \( P > 155\ \text{kW} \)

Marco: I assume these sanitation limits are chiller specific? maybe they should be specified in percentage of nominal power/flow rate?

3 Comparative analysis

IPMVP report should have comparative analysis of operation during baseline and reporting periods. This includes partload distribution and flow rate distribution analisis.

3.1 Partload distribution

Partload shows the chiller load percentage, calculated as:

\[ L = \frac{P_i}{P_{nominal}}\]

Where

• \( P_i\ (\text{kW})\) - power consumption measured,
• \( P_{nominal}\ (\text{kW})\) - nominal power consumption, from chiller datasheet.

Partload distribution is effectively a histogram showing how much time chiller spent in diffent operating conditions, for example:

Average Partload 35%

For comparative analisis it is important to plot both baseline and reporting period histograms on the same shart.

3.2 Flow rate distribution

Flow rate distribution is a histogram showing how much time chiller pump spent in different operating conditions. For example:

This histogram as well should be draw for both baseline and reporting periods on the same chart for comparision.

3.3 Data sanitation

Comparative analysis also exclude data points that are far from normal steady chiller operation. This includes any of the following:

• \( Q < 40\ m^3/h\)
• \(P_i < 50\ \text{kW}> \)