Reprint of Paper for INTELEC´99, Kopenhagen, Juni 1999 revised edition, nomenclature and abbreviations where slightly changed according to international standards
State of charge - What do we really speak about ? Dirk Uwe Sauer1, Georg Bopp1, Andreas Jossen2, Jürgen Garche2, Martin Rothert3, Michael Wollny3 1
2 3
Fraunhofer Institute for Solar Energy Systems ISE, Oltmannsstr. 5, D-79100 Freiburg, Germany Fax. ++49 761 45 88 2 17, phone ++49 761 45 88 219, email:
[email protected] Centre for Solar Energy and Hydrogen Research (ZSW Ulm), Helmholtzstr. 8, 89081 Ulm, Germany Institut für Solare Energieversorgungstechnik (ISET), Königstor 59, 34119 Kassel, Germany
1. INTRODUCTION For the energy management in autonomous energy supply systems state of charge of the battery storage is a most important input parameter. Therefore algorithms determining the state of charge are of high evidence and under investigation since years. State of charge determination is difficult in autonomous energy supply systems with renewable energies because full charging of the battery as it is done frequently with conventional battery chargers is very seldom. If state of charge is calculated, the question occurs, what is the meaning of the specific values. Figure 1 shows different definitions of the battery capacity and the corresponding definitions of state of charge. The measured capacity of a battery might be smaller or even higher than the rated capacity given by the manufacturer. During the lifetime the measured capacity decreases more and more due to ageing effects. The practical capacity is even smaller as the measured capacity, due to the special conditions with renewable energy sources batteries are almost never completly recharged (number of charging hours is limited). Further on the system defines an end-ofcharge criteria which usually differs from the end-ofcharge criteria used for capacity tests. Therefore the practical battery capacity is lower than the measured capacity. Until now different authors and manufacturers use different definitions but calling them state of charge in all cases. This makes comparison of results from state of charge meters and algorithms difficult. This paper aims at describing the various different state-of-charge definition in order to define a standard for an easy use and better understanding.
2. DEFINITIONS What is the state of charge of a battery ? In general one understands the still available amount of charge in relation to the capacity of the battery. But the capacity
of the battery is not at all constant. Different parameters as temperature, discharge current, end-of-discharge voltage and state of health of the battery influence the capacity markedly. This is true especially for lead-acid batteries. Therefore the state of charge can be defined in different ways. Only precise and universal definitions of all items can lead to a clear understanding. Figure 1 shows different definitions for the capacity. Differences are due to the definition of full state of charge and the available battery res. the end-ofdischarge criteria of the battery. This results directly in different state-of-charge definitions. full state of charge
end-of-discharge criteria in system operation rated capacity measured capacity practical capacity
100 % 100 % 1
SOCo - practical state of charge SOCr - relative state of charge SOC - state of charge
0% 0% 0
Figure 1: Comparison of different definitions of battery capacity and the corresponding definitions of state of charge Table 1 summarises the different definitions for the capacity, state of charge and full state of charge. Further on definitions on open circuit voltage and state of health are included, because some state-of-charge meters and algorithms are using these definitions as well.
Reprint of Paper for INTELEC´99, Kopenhagen, Juni 1999 revised edition, nomenclature and abbreviations where slightly changed according to international standards
. name rated capacity or
symbol CN
nominal capacity
definition The rated or nominal capacity is the value for the capacity given by the manufacturer at nominal operating conditions (defined by temperature, current and end-of-discharge voltage). As a standard the 10 h capacity (N = 10) should be used. A transformation between any temperature between 10 to 30°C and the nominal temperature is possible with the given equation. If the manufacturers delivers only values for the 100 h, the 20 h or the 5 h capacity, a rough approximation of the CN capacity can be gained from the rules of thumb : CN = C100h / 1.2; CN = C20h / 1.1; CN = C5h / 0.9
CT 1 + z ⋅ (T − 20°C )
CN =
with
unit
range
Ah
>0
z =0,006K −1
initial capacity
C0
The initial capacity is the capacity available at a capacity test with I10 down to 1.8 V/cell (according to DIN 43539) starting at full state of charge FULL (DIN 43539) after taking the battery into operation according to the manufacturers recommendations.
Ah
>0
measured capacity
Cm
The measured capacity is the capacity available at a capacity test with I10 down to 1.8 V/cell (according to DIN 43539) starting at full state of charge FULL (DIN 43539) at any time after taking the battery into operation.
Ah
×0
practical capacity
Cp
The practical capacity is the capacity between the practical state of charge FULLp and the end-of-discharge threshold defined in the system.
Ah
×0
remaining capacity Qr
The remaining capacity is the amount of charge available at a certain time without any previous charging with an I10 discharge down to 1.8 V/cell.
Ah
×0
charge balance
net discharged charge from a battery since the last full state of charge FULL
Ah
×0
Qb
∫
Qb = I MR ⋅ dt ,
I MR ≡ main reaction current
t
depth of discharge
DOD
The depth of discharge is the ratio of the charge balance and the rated -capacity. The depth of discharge is 0 when reaching the full state of charge and 1 after a net discharge of the rated capacity.
Q DOD = b CN state of charge
SOC
The state of charge is the ratio between the difference of the rated capacity and -the charge balance on the one hand and the rated capacity on the other hand. State of charge is 1 when full state of charge FULL is reached and 0 after a net discharge of the rated capacity.
SOC = 1 − DOD = relative state of charge
SOCr
practical state of charge
SOCp
or 0 to
× 100%
1 to
Ø0
or 100 to
Ø0%
--
1 to 0 or 100 to 0 %
C m − Qb Cm
The practical state of charge is the ratio between the difference of the practical capacity and the charge balance on the one hand and the practical capacity on the other hand. The practical state of charge is 1 when the practical full state of charge is reached and 0 after a net discharge of the practical capacity
SOCo =
×1
C N − Qb CN
The relative state of charge is the ratio between the difference of the measured capacity and the charge balance on the one hand and the measured capacity on the other hand. The relative state of charge is 1 when full state of charge FULL is reached and 0 after a net discharge of the measured capacity
SOC r =
0 to
C p − Qb Cp
--
1 to 0 or 100 to 0 %
dynamic relative state of charge
SOCrd
only of relevance at currents > I10 , dynamic correction of the measured capacity with the available battery current and the battery temperature
SOC rd =
C m ⋅ F − Qb ; Cm ⋅ F
--
1 to
Ø0
or
F = f (T , I battery )
100 to
Ø0%
F ∈ [0, 1] dynamic practical state of charge
SOCpd
only of relevance at currents > I10 , dynamic correction of the practical capacity with the available battery current and the battery temperature
SOC pd =
C p ⋅ F − Qb Cp ⋅ F
;
--
1 to
Ø0
or 100 to
F = f (T , I battery )
Ø0%
F ∈ [0, 1] full state of charge
FULL
Full state of charge is reached (according to DIN 43539), if the battery current is not changing within 2 hours at a constant charge voltage and constant temperature.
practical full state of charge
FULLp
The practical full state of charge is the state of charge, which can be reached in a system under normal operating conditions (depending of the charge voltage, the maximum charge current and the short-time history of the battery).
open circuit voltage
OCV
The open circuit voltage is the voltage measured at a battery at open circuit (Ibatt = 0) while the voltage changes less than 0.5 mV/cell within 2 h.
V
2,2 – 1.9
approximate open circuit voltage
OCVx
The approximate open circuit voltage is the voltage of a battery at open circuit (Ibatt = 0) while the voltage changes less than x mV/cell/hour. the approximate open circuit voltage with x=0.25 mV/cell/hour is equivalent with the open circuit voltage (OCV0.25 = OCV).
V
2,2 – 1.9
state of health
SOH
The state of health is the ration between the measured capacity and the rated capacity. State of health is 1, when the measured capacity equals the rated capacity. A state of health greater than 1 means more measured capacity than promised by the rated capacity. Per definition a battery is at its end of lifetime at a state of health of 0.8 .
SOH =
× 1 to 0
Cm CN
Table 1 : List of definition for state of charge calculation including different capacity definitions The rated or nominal capacity is defined as the 10 hour discharge capacity defined by the manufacturer. This is related to the state of charge (SOC). The rated or nominal capacity is not changing during the life of a battery where as the measured capacity is changing by time. The measured capacity might be even bigger than the rated capacity at the beginning of the lifetime or after several initial cycles and decreases with increasing lifetime. State of charge with respect to the measured capacity is called relative state of charge (SOCr). The practical capacity Cp is always less than the measured capacity. This definition takes into account, that especially in PV-hybrid-systems a full charging according to the recommendations of the norms and the manufacturers occurs very seldom. Further more the endof-discharge criteria is set to avoid any deep discharge of the battery, e.g. at 70% DOD. This reduce the practical capacity significantly. The relative state of charge definition is the practical state of charge (SOCp).
3. REFERENCE TEST DATA To allow fast and effective testing and comparison of new or already available state-of-charge algorithms it is necessary to examine them in a comparable manner. Testing in real systems is cost effective and takes a lot of time. Therefore usually most tests are done offline with test data. Therefore we are currently defining six reference data sets with data of current, voltage and temperature with a time resolution of at least 10 minutes from real PV systems. These sets of data should represent the different classes of operating conditions of batteries in PV systems as defined in [1,2]. The criteria for the reference data are : •
representing the different classes of operating conditions
•
one year of data with out any vacancies
•
high resolution (at least 10 minute mean values)
•
full states of charge close to the beginning and the end of the data sets
Figures 2 and 3 show timeseries of state of charge from two reference data sets calaculated with a reference algorithms for calculating state of charge on the basis of an Ah-balancing with automatic detection of practical full states of charge and backwards calculation [3]. The state of charge is calculated with respect to the rated capacity.
4 CONCLUSION As shown by figure 1 and table 1 the definition of state of charge is not a simple task at all. To avoid misleading expression it is necessary to define carefully what is really calculated res. shown by state-of-charge meters. Reference data will help to compare different state-ofcharge algorithms easy. Data sets from different classes assure, that the algorithms are tested under different operating conditions, which is necessary to see advantages and disadvantages of the different algorithms.
state of charge [%]
100
80
60
Eight reference data sets and a reference SOC calculation algorithm are available from the end of June on a CD for scientific purposes for a protective charge of 50,- DM.
40
For further information or order please contact the authors.
20
0 0
50
100
150
200 days
250
300
350
Figure 2: State of charge within a period of 365 days from a PV-battery-system without back-up generator (class 1)
state of charge [%]
100
80
60
40
20
0 0
50
100
150
200 days
250
300
350
Figure 3: State of charge within a period of 365 days from a PV-hybrid system with diesel generator and lead acid battery (class 4)
REFERENCES
[1] Sauer, D.U., Bächler, M., Bopp, G., Höhe, W., Mittermeier, J., Sprau, P., Willer, B., Wollny, M. : “Analysis of the performance parameters of lead/acid batteries in photovoltaic systems”, J. Power Sources, 64 (1997) 197-201 [2] Sauer, D.U., Bopp, G., Bächler, M., Höhe, W., Jossen ,A., Sprau, P., Willer, B., Wollny, M. : “What happens to batteries in PV systems or Do we need one special battery for solar applications ?”, 14th European Photovoltaic Solar Energy Conference, Barcelona 1997, Vol. II, pp. 1692-1695 [3] Bopp, G., Gabler, H., Sauer, D.U., Jossen, A., Höhe, W., Mittermeier, J., Bächler, M., Sprau, P., Willer, B., Wollny, M. : “A systematic effort to define evaluation and performance parameters and criteria for lead-acid batteries in PV systems”, 13th European Photovoltaic Solar Energy Conference, Nice, Vol. II, pp. 1763-1769
This work is supported by BMBF and BMWi.
State of Charge - What do we really speak about ? Georg Bopp1 , Jürgen Garche2 , Andreas Jossen2 , Sabine Piller2 , Martin Rothert3 , Dirk Uwe Sauer1 , Michael Wollny3 for Solar Energy and Hydrogen Research Ulm (ZSW) für Solare Energieversorgungstechnik Kassel (ISET)
Definitions
Reference Data (examples)
State of charge can be defined in different ways. Only precise and universal definitions of all items can lead to comparability. Most important definitions are given below. rated capacity or nominal capacity
CN
- a list of definitions was compiled (see centre column and proceedings)
inital capacity
C0
measured capacity
Cm
see figure 1
- reference data from PV systems based on measured data were selected
practical capacity
Cp
see figure 1
Therefore
Reference data for comparable offline evaluation of SOC algorithms (examples in the right column) contain :
data of one year without data gaps
data measured on various types of lead-acid batteries
20
50
100
150
200
250
300
350
Qb
250
300
350
Solar street lamp (PV system) 100
R
= t IMR
dt
main reaction current
practical full state of charge
end-of-discharge criteria in system operation
rated capacity measured capacity
80
60
40
20
0 0
50
100
practical capacity
150
200
time [days]
Self-sufficient solar house (PV-fuel cell-system) SOCp - practical state of charge 100% 0%
description of the systems
different battery operating conditions
40
time [days]
a calcuated reference SOC
averaging periods between one and ten minutes
60
0
Qb
IMR
measured values of voltage, current and temperature
80
0
charge balance
full state of charge
see figure 1
100
100
SOCr - relative state of charge 100%
0% SOC - state of charge
1
0
Figure 1 : Relation between different capacity and state of charge defintions
state of charge
SOC
relative SOC
SOCr
practical SOC
SOCp
= CQNb = CNC;NQb = CmC;mQb = CpC;pQb
full state of charge
FULL
def. in norms
practical full
FULLp
see figure 1
state of health
SOH
Eight reference data sets and a reference SOC calculation algorithm are available from the end of June on a CD for scientific purposes only for a protective charge of 50,- DM.
depth of discharge
For further information or order please contact Dr. Andreas Jossen ZSW Ulm Helmholtzstr. 8 D-89081 Ulm / Germany email :
[email protected]
DOD
= CCmN
state of charge SOC [%]
State of charge (SOC) is the most important parameter for energy management systems and battery operation systems. Algorithms for SOC determination are of high relevance. Comparability is difficult because of various definitions and missing test data.
3 Institut
80
60
40
20
0 0
50
100
150
200
250
300
350
250
300
350
time [days]
Farm house (PV-diesel-system) 100
state of charge SOC [%]
State of Charge Algorithm
2 Centre
state of charge SOC [%]
Institute for Solar Energy Systems ISE Oltmannsstraße 5, D-79100 Freiburg Fax: +49 (0) 7 61 45 88-2 17, email:
[email protected]
state of charge SOC [%]
1 Fraunhofer
80 60 40 20 0 -20 -40 0
50
100
150
200
time [days]
This work is supported by BMBF and BMWi.
Marine school (PV-wind-diesel-system)
