ABSTRACT If daily heat load variations could be eliminated in district heating-systems, it would make the operation of the district heating system less costly and more competitive . There would be several advantages in the operation such as: 

H Gadd

S Werner

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The 12th International Symposium on District Heating and Cooling, 
September 5
th
  to September 7
th
 , 2010, Tallinn, Estonia 
  
199 
 
DAILY HEAT LOAD VARIATION IN SWEDISH DISTRICT HEATING SYSTEMS 
H. Gadd and S. Werner
 
School of Business and Engineering, Halmstad University 
SE-301 18  Halmstad, Phone: +46 35 167757 
henrik.gadd@hh.se, sven.werner@hh.se, www.hh.se 
 
ABSTRACT 
If daily heat load variations could be eliminated in 
district heating-systems, it would make the operation of 
the district heating system less costly and more 
competitive . There would be several advantages in the 
operation such as: 
· Less use of expensive peak load power where 
often expensive fuels are used. 
· Less need for peak load power capacity. 
· Easier to optimize the operation that leads to 
higher conversion efficiencies. 
· Less need for maintenance because of more 
smooth operation of the plants 
There are a number of ways to handle the daily 
variations of the heat load. Two often used are large 
heat storages or using the district heating network as 
temporary storage. If it would be possible to centrally 
control the customer substations, it would also be 
possible to use heavy buildings connected to the 
district heating system as heat storages. 
To be able to find the best way to reduce or even 
eliminate the daily heat load variations, you need to 
understand the characteristics of the daily variations. 
This paper will describe a way of characterizing daily 
heat load variations in some Swedish district heating-
systems. 
INTRODUCTION 
For all heat generation/distribution systems, heat load 
variations leads to inefficiencies. You need to design 
your system for the peak load even though you only 
need the top capacity for a very short period of time of 
the year. This is of cause expensive. The solution to 
this problem is heat storage. There are a number of 
possibilities to store heat in DH systems: 
· Large heat storages at the heat generation plants 
· Heat storage in district heating networks 
· Heat storage in heavy buildings in by allowing 
small variation in indoor temperatures[1]. 
If it would be possible to extinguish daily variations it 
would lead to several profitable advantages such as: 
· Less use of expensive peak load power where 
often expensive fuels are used. 
· Less need for peak load power capacity. 
· Easier to optimize the operation that leads to 
higher conversion efficiencies. 
· Less need for maintenance because of more 
smooth operation of the plants 
To do this some questions need to be answered: 
· What input and output capacity to/from the heat 
storage is needed? 
· What size of the heat storage is needed? 
· Are the daily heat variations in the specific system 
large or small during a year? 
METHOD 
Nomenclature 
Ph= Present hour value [MWh/h] 
Pd= Mean hour value for the present day [MWh/h] 
Pa= Mean hour value for the whole year [MWh/h] 
Sh = Energy transfer capacity [MWh/h] 
Sd = Size of heat storage [MWh/day] 
Sa = Total annual daily heat load variation 
h
t = Momentary daily variation [h/h] 
d
t = Total daily variation [h/day] 
a
t = Total annual relative daily variation [h/year] 
Variables 
Measured data has been collected from some district 
heating systems in Sweden. The collected data is the 
heat power that is generated and fed into the district 
heating network. It is hour mean power that is used, i.e. 
8 760 data points per year. Only whole years is used 
from 1 of January to 31 of December. To describe the 
daily variation three variables is defined. 
1. Momentary daily variation (
h
t ) 
2. Total daily variation. (
d
t ) 
3. Total annual relative daily variation. (
a
t ) 
Three system examples are presented in this paper to 
exemplify the method to characterize district heating 
daily heat load variation: 
System A: From a city in South of Sweden with an 
annual heat generation of 200 GWh. 
The 12th International Symposium on District Heating and Cooling, 
September 5
th
  to September 7
th
 , 2010, Tallinn, Estonia 
  
200 
 
System B: From a city in Southwest of Sweden with an 
annual heat generation of 64 GWh. 
System C: From a city in the middle of Sweden with an 
annual heat generation of 1550 GWh. 
Momentary daily variation (
h
t ) 
The momentary daily variation is proportional to the 
amount of heat that needs to be fed in or out to the DH 
network to extinguish the daily variation. This variable 
describe the heat power capacity needed for in and out 
put from and to the heat storage. For each district 
heating systems you will get 8 760 (8 784 during leap 
years) values per system and year. 
The momentary daily variation is defined as the 
difference of each hourly measured value and the 
mean value of heat per hour of the same day divided 
by the mean heat per hour of the year. 
a
dh
h
P
PP -
=t  
The momentary daily variation is presented in Fig. 1 for 
the three example systems. The figure shows that the 
variations are more pronounced in the two smaller 
systems compared to the larger system. 
Momentary daily variation
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0 1000 2000 3000 4000 5000 6000 7000 8000
Hour of the year
M
o
m
e
n
ta
ry
 d
a
il
y
 v
a
ri
a
ti
o
n
, 
τ h
[h
/h
]
Systen A
System B
System C
Fig. 1 Momentary daily variation sorted by size hour by 
hour for the three different district heating systems. 
Total daily variation ( dt ) 
Total daily variation is defined for each day and is a 
variable that is proportional to the amount of heat that 
divert from the daily mean heat load. If you want to 
extinguish the daily variation in a system this variable 
describe the size of the heat storage. For each DH 
systems you will get 365 (366 during leap years) values 
per system and year. 
The total daily variation is defined as the sum over the 
day of the difference of each hourly measuring value 
and the mean value of energy per hour of the same 
day divided by two times the mean energy per hour of 
the year. 
a
d
h
h
d
P
PP -
=
å
=
24
12
1
t  
The total daily variation is presented in Fig. 2 for the 
three example systems. The figure verifies that the 
variations are more pronounced in the two smaller 
systems compared to the larger system. Another 
implication is that the highest day values are very few, 
giving an incentive to construct heat storages 
somewhat smaller than the peaks in the figure. Hence, 
the investment costs will be reduced more the lost 
benefits from the storage, giving a more optimised heat 
storage. 
Total daily variation
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
-  50 100 150 200 250 300 350 
Days of the year
T
o
ta
l 
d
a
il
y
 v
a
ri
a
ti
o
n
, 
τ d
[h
/d
a
y
]
Systen A
System B
System C
 
Fig. 2 Total daily variation sorted by size day by day for 
the three different district heating systems. 
Total annual relative daily variation (
a
t ) 
Total annual daily variation is a variable that is 
proportional to the total amount of energy that at daily 
basis divert from the mean value accumulated for a 
period of one year. It is used to compare different 
systems between themselves. For each DH systems 
you will get 1 value per system and year. 
Total annual daily variation is defined as the sum over 
the year of the difference between each hourly 
measuring value and the mean value of energy per 
hour of the same day divided by two times the mean 
energy per hour of the year. 
a
d
dh
h
a
P
PP -
=
å
==
365,8760
1,12
1
t  
 
The annual daily variation is presented in Fig. 3 for 10 
different Swedish district heating systems. Since the 
annual daily load variation has a magnitude of  
250–500 h, only 3–6% of the annual heat load is 
generated above the daily average heat loads. Hence, 
it is the seasonal variations that dominate the heat load 
variations in the Swedish district heating systems. 
The 12th International Symposium on District Heating and Cooling, 
September 5
th
  to September 7
th
 , 2010, Tallinn, Estonia 
  
201 
 
Total annual daily variation
0
50
100
150
200
250
300
350
400
450
500
1 10 100 1 000 10 000 
Annual heat supply [GWh]
T
o
ta
l 
a
n
n
u
a
l 
d
a
il
y
 v
a
ri
a
ti
o
n
, 
τ
a
[h
/y
e
a
r]
SYSTEM C
SYSTEM B
SYSTEM A
 
Fig.  3 Total annual daily variation for 10 different district 
heating systems in Sweden. 
RESULTS 
To characterize daily heat load variations in district 
heating systems three variables have been defined. 
h
t = Momentary daily variation 
d
t = Total daily variation 
a
t = Total annual daily variation 
Together with the mean annual heat per hour (Pa) and 
the energy transfer capacity in and out of the heat 
storage, size of storage to extinguish the systems daily 
variation and the total daily variation and can be 
determined according to the expressions below. 
Energy transfer capacity: 
Sh= ht ·Pa [MWh/h] 
Size of heat storage: 
Sd = dt ·Pa [MWh/day] 
Total annual daily heat load variation: 
Sa = at ·Pa  [MWh/year] 
CONCLUSIONS 
An expected conclusion would be that large district 
heating systems have smaller relative daily variations 
(
a
t ) than small district heating systems. There are two 
reasons for that: 
1. In a large district heating system, the use of heat 
power is spread on different distances from the heat 
plant, i e the chilled water in the return pipe return back 
to the heat generation at different time compared to 
when the return water left ach substation (geographical 
diversity) 
2. In large district heating networks, you would expect 
that the operators have more active operation of the 
heat distribution network with respect to temporary heat 
storage. 
But as can be observed in the Fig. 3 there does not 
seem to be such a trend. One explanation could be that 
the heat users differ in different systems. e.g. in the 
system in Fig 3 with an annual heat supply of 9 GWh, 
mostly single and multi family houses are connected 
and very few industry or office buildings are connected. 
Since there is a large diversity among the annual daily 
variation more data need to be collected to be able to 
make any further conclusions.  
REFERENCES 
[1] Olsson L, Werner S: “Building mass used as short 
term heat storage”, The 11th International 
Symposium on District Heating and Cooling 
Reykjavik 2008. 


Daily heat load variations in Swedish district heating systems

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Daily heat load variations in Swedish district heating systems

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