The paper presents the way to determine the required heat power for heat source diagnostics for the existing residential building. For this purpose, it was proposed to designate the required thermal power of the building using the original method of multiple short heat consumption measurement in existing residential building with natural ventilation. The first part presents the main ideas of the method.

W artykule zaprezentowano określanie wymaganej mocy cieplnej dla diagnostyki źródła ciepła istniejącego budynku mieszkalnego. W celu zaproponowano wyznaczanie wymaganej mocy cieplnej budynku z wykorzystaniem oryginalnej metody kilkukrotnego krótkiego pomiaru zużycia ciepła w istniejącym budynku mieszkalnym z wentylacją naturalną. W części pier- wszej przedstawiono główne idee metody.

The thermal diagnostics of heating systems and heat source is connected with the verification of compatibility of the required and actual power of the heat source and heating systems [

In [_{T}_{V}_{b}_{Z,oc}+ ϕ_{Z,eq}). This method uses, among others, multiple short _{T}_{V}

The basic assumptions for determining the in-situ short-time measurements of the required heat source power for an existing building are as follows:

the temperatures in the heated rooms are similar to the design values of indoor air temperature,

the settlement of the building is similar to the design, and the individual internal heat gains from people and equipment correspond to the typical values of a residential building,

the current air tightness of the building determines the mass of air flowing into the building under average heating conditions close to the minimum flow resulting from hygienic needs,

measurements are made during the heating season in conditions close to average.

Determining the heat loss transmission and ventilation coefficients, and the number of ventilation air changes _{V}

To determine value of measurements’ group, it is necessary to:

make several short (daily) measurements of the heat consumption in the building for the purpose of central heating (using a heat meter, a heat flux meter or gas meter, fuel volume oil meter, mass or volume of solid fuel) and the temperature of the heating factor and, if it is possible, daily course of external air temperature and, if there is a need, internal air temperature, and also one-time measurement of the air temperature in the basement and if necessary in the selected area in the ceiling (eg. on the border of the plaster and the construction layer of the ceiling) or control temperature measurements of the inner surface of the outer wall (walls), as well as the ceiling above top floor.

daily heat consumption by central heating installation ϕ_{u}, kWh,

average daily outdoor air temperature

average air temperature in the building’s heated space on measured days,

average daily temperature in the basement.

These measurements should be supplemented with the results obtained from the nearest meteorological station, measured routinely:

hourly daily course of outdoor air temperature _{e}

hourly course of daily wind speed,

hourly daily passes of average direct and diffuse solar radiation streams,

The basis for the implementation of the method is also to determine the geometrical and structural features of the building and its functional characteristics, such as the number of inhabitants, the type and number of heated rooms, and also the type and parameters of central heating and possibly heat sources. These values are derived from the operational documentation of the building or are obtained by means of rapid thermal diagnostics of the building.

The days chosen for measurements should be these without rain and snow and with moderate wind. As measurement days also very cloudy days should be avoided as well as days with moderate outside temperatures (not above 5 (7)°C, as a midday temperature) and at the same time very sunny days, which would be accompanied by significant overheating of the rooms and / or opening of the windows by inhabitants.

On the basis of the determined measurement data, the daily thermal balances for the building under consideration can be calculated as follows:

_{i}

_{u}

_{trt}

_{sw}

_{z}

_{ehg}

_{Z,oc}

_{Z,eq}

_{Z,tr}

_{V}

_{B}^{3},

_{p}

_{p}^{3},

1....j......k – numbers of measurement days.

Several times (k-fold) daily measurement of heat consumption for purposes of central heating of a building _{u}

In the system of equations (

_{p}^{2},

_{p}^{2}K),

_{M}

_{M}

Accepting the record _{z}_{Z,oc}_{Z,eq}_{b}^{2}.

Numerous attempts to solve the system for the relevant measurement data (affected by some errors) by method of determinants or linear regression have led to results that are not physically correct.

Therefore, in relation to the system (_{v}_{b}

Another form of the system (

Further part presents procedures of designation _{b}_{z}

In order to implement it, the terms _{Z}

Subtracting the equations from one another should be done in such a way, that representing of all equations of the system (

The condition of equal representation of equations (_{b}.

The linear approximation

The condition for applying this procedure is as follows: in equation (

From the equations system (5c) are chosen equations with days (m … ..n), for which

The efficiency _{ehg}_{Z}_{Z}_{ehg}

After subtracting from the successive equations [(m … n) − (r..s)] the selected equations (r..s) of the system (

Subtracting the equations from one another should be done in such a way that representing all of the equations of the system (

The system (

^{T}^{T}^{−1} - inverse matrix of the matrix product ^{T}

If omitted in the system equations (_{b}_{jp}_{mm}

If the mean temperature difference is _{mm}_{mm}

After returning to the system (

The system can be presented as:

The system gives the solution:

After substituting to the system (_{b}

The system gives the solution:

Condition of use: system (3b, _{b}_{Z}

_{Z}_{b}

Using a transformed system (3b, _{b}_{Z}

Determination of

On this basis it is possible to estimate:

Specifying _{b}

The temperatures

_{i}

_{e}

_{e}

_{i}

Coefficients are equal to:

_{sha}^{2},

_{sha}^{2}K),

_{w}^{2},

_{i}^{2}K/W,

_{n}^{2},

_{n}^{2}K).

Determination of coefficients, _{1}, _{2}, _{3}, _{4}, _{5} requires the estimation of the heat loss coefficient for ventilation _{V}_{w}

It is recommended to take the time interval Δτ as =24 h ⋅ 5= 120 h.

Determining _{b}_{Z}_{b}_{Z}

Determination of coefficients _{3}_{4}_{5}_{w}

The determined heat loss transmission coefficient was defined in the presented analysis as:

_{sha}^{2},

_{sha}^{2}K),

_{t}

_{i}

_{n}

_{e}

_{n}^{2}K),

_{n}^{2}.

The average temperature of the inner surface of the envelope partitions surrounding the heated space of the building _{i}

_{k}

^{2},

^{2}K/W,

_{i}_{e}

The assumption of the predicted coefficient _{sha}

The next steps in assumption _{sha}

determining the windows area _{w}_{w}

determining the surface of the envelope surrounding the heated space of the building omitting the ceiling over the unheated basement _{sha}

determining of the ceiling surface over the unheated basement _{n}

estimation of the _{n}_{n}

_{tw}

_{tw}

_{ip}

assumption based on the thermal protection requirements in force during the construction of the building or thermal modernization of the external partition coefficient _{sp}

determining on the basis of assumed assumptions and findings (resulting from e.g the technical documentation of the building or the requirements of thermal protection in force during the building or thermal modernization) of the projected coefficient _{sha}

The value _{sha}

_{MT}_{MT}

When adopting a new value _{sha}_{sha}_{i}_{e}_{i}_{i}_{sp}

The new value _{i}

A similar correction can be made for layer _{i}_{i}_{i}_{i}_{sd}_{sd}_{n}_{sd}_{sd}_{sp}_{a}_{i}_{i}_{e}_{3}_{4}_{5}

_{zj}_{zj}_{zj}_{z}

_{v}

_{B}^{3},

_{p}

_{p}^{3}.

On the basis of the values obtained

The final verification of the days taken for the final analysis should also be made on the basis of the estimated pre-determined average gains _{Zj}

As the basis for expected returns the indicators given in [

in the Regulation of the Minister of Infrastructure of 6 November 2008 on the methodology for calculating the energy characteristic of a building constituting an independent technical and utility unit as well as the way of drawing up and specifying the certificates of their energy characteristic (Journal of Laws 2008 No. 201 item 1240) as 3.2 – 6.0 W/m^{2} for multi-family buildings and 2.5 – 3.5 W/m^{2} for single-family houses

in the Regulation of the Minister of Infrastructure of June 3, 2014 on the methodology for calculating the energy characteristic of a building and a dwelling or a part of a building constituting an independent technical and utility unit and the manner of drawing up and specifying energy characteristic certificates (Journal of Laws of 2014, item 888) as 7.1 W/m^{2} for residential and 1.0 W/m^{2} for staircases in multi-family buildings and 6.8 W/m^{2} for single-family houses.

After omitting in the generalized balance equation of the system (_{b}_{b}

By using the set value _{b}_{Zj}

The efficiency of using internal gains can be determined on the basis of the total heat gains of the building: _{u}_{Z}_{Z.tr}_{den}

The basic stages (steps) of the method of multiple daily measurements in order to determine the values allowing to determine the thermal characteristics of a building are as follows:

on the basis of analysis of

the system of equations characteristic of the multiple-measurement method should be created by at least 8-day balance equations. If during the days of measurements a significant constance of operating conditions of the building was maintained (constant number of people staying in the building, moderate weathering, constant room air temperature) and reliable information has been obtained on the partitions surrounding the heated space of the building, then the number of measurement days can be reduced to the specified lower limit. In case of significant incompatibility of balance equations, steps should be taken to obtain system with more equations greater than 8,

it is profitable for a proper determination of the coefficient _{b}

among the days of measurement should also be a few days with

in systems of differential equations, equations with significant temperature

equations of each pair of equations making up the differential equations should have approximate estimated values

for the determination of the sought values, it is advantageous to take into account the daily heat balances of heat accumulation from solar radiation through the windows in the form of the adoption of the average daily heat gains flux from solar radiation containing ¾ of gains resulting from the radiation transmitted by windows on the considered day and ¼ of the gains from the radiation of the previous day,

in the created differential equation system there should be a equilibrium representation of balance equations in the form of the minuends and subtrahends,

determined values _{Zj}_{Zj}_{Zj}

on the basis of the determined values _{Zj}_{Zj}_{Zj}

in the case of significantly different values _{Zj}_{Zj}_{Z max}_{Zj}_{Z}_{max}_{Z}_{max}

if the determined distribution of internal gains covers _{Zj}_{Z max}_{Zj}_{Z}

the results obtained with the solution of the overdetermined system of balance equations by means of the matrix method and the determinants, with the course of proceedings presented in the monograph, do not deviate significantly from the results obtained by the multiple regression method. Such a state of results is inter alia the result of the accepted measured uncertainties. The results obtained by the regression method, however, are also accompanied by the determination of their uncertainty,

using the meaningful temperature in place of the outside air temperature in a multiple-daily measuring method to determine the values allowing to determine the building’s thermal characteristics leads to a significant change in the results (improvement of their accuracy).

The determined values _{V}

The work was founded within: 08/010/BK_17/0024 (BK 227/RIE1/2017) and 08/10/BKM-16/0019 supported by Polish Ministry of Science and Higher Education