Output rating, temperature and efficiency
OUTPUT RATING, OPERATING TEMPERATURE AND EFFICIENCY
1. Inverters: continuous output rating as function of temperature
In our datasheets inverters, and the inverter function of Multis and Quattros, are rated at 25ºC (75ºF). On average, derating at higher temperatures is as shown below (see paragraph 4 for the theoretical background).
Temperature 
Cont. output 

ºC 
ºF 
% 
Low temp. 
100 

25 
77 
100 
30 
86 
96 
35 
95 
93 
40 
104 
90 
50 
122 
82 
60 
140 
75 
65 
149 
69 
High temp. 
0 
2. Battery chargers: continuous output rating as a function of temperature
In our datasheets battery chargers are rated at 40ºC (104ºF). The battery charger function of our Multis and Quattros is rated at 25ºC (77ºF). As explained in paragraph 4, derating for higher temperatures is approximately as follows:
Blue curve: products rated at 25ºC (77ºF) 

Red curve: products rated at 40ºC (104ºF) 

Temperature 
Cont. output 
Temperature 
Cont. output 

ºC 
ºF 
% 

ºC 
ºF 
% 
25 
77 
100 




30 
86 
95 




35 
95 
88 




40 
104 
80 

40 
104 
100 
50 
122 
62 

50 
122 
77 
60 
140 
36 

60 
140 
45 
65 
149 
0 

65 
149 
0 
3. Power loss and efficiency as a function of load
As an example let us look at the Phoenix Inverter 24/3000 or MultiPlus 24/3000/70 (both products have the same inverter). These products use high frequency switching to generate a sinewave, which is then transformed to the required output voltage by two toroidal transformers. Toroidal transformers have a higher efficiency and less no load losses than the more common Ecore transformers.
The measured efficiency curve is shown below:
Output power (W) 
Dissipation (W) 
Efficiency (%) 
0 
20 
0 
10 
20 
33,3 
20 
20 
50,0 
30 
20 
59,9 
50 
20 
71,3 
100 
21 
83,0 
200 
22 
90,1 
400 
28 
93,5 
800 
52 
93,9 
1600 
148 
91,5 
2500 
333 
88,3 
3000 
470 
86,5 
4000 
820 
83,0 
5000 
1270 
79,7 
Recently a new product has been introduced: the MultiPlusII 48/3000/3532 (this is exactly the same product as the MultiGridII 48/3000/3532)
The MultiPlusII has only one toroidal transformer, and several other improvements to reduce no load power consumption. As can be seen from the table and graph below, this product is more efficient, especially at low load.
Output power (W) 
Dissipation (W) 
Efficiency (%) 
0 
11 
0 
10 
11 
47,6 
20 
11 
64,5 
30 
11 
73,1 
50 
11 
81,8 
100 
12 
89,7 
200 
13 
93,9 
400 
19 
95,5 
800 
43 
94,9 
1600 
139 
92,0 
2500 
324 
88,5 
3000 
461 
86,7 
4000 
811 
83,1 
5000 
1261 
79,9 
4. The theory behind the graphs of paragraph 1 – 3
4.1. Operating temperature range
The operating temperature range may vary from one product to another.
The upper temperature is limited by the maximum operating temperature of certain components (for ex. semiconductors, electrolytic capacitors, relays).
The low temperature limit is mainly limited by the minimum operating temperature of semiconductors and electrolytic capacitors.
As has been shown in section 1 and 2, this does not mean that the full output rating is available over the whole temperature range.
Derating is needed at high ambient temperatures to prevent overheating of a.o. power semiconductors and transformers.
In general, output power cannot be increased at low temperatures due the maximum current rating of certain components (terminals, core saturation of filter chokes).
4.2. Power loss and efficiency
Electric current generates heat in the conductor through which it flows. The basic formula to calculate the rate of heat generation, or power dissipation, is:
P = R x I² (1)
where P stands for power (measured in Watts), R (Ohm) is the resistance of the conductor and I (Ampère, or Amps) the current.
What is interesting about this formula is that it shows that power dissipation increases with the square of the current. A resistance of for example 2 Ohm and a current of 10 Amps results in a dissipation of 2 x 10 x 10 = 200 W. Twice that current results in 4 times more heat generated: 2 x 20 x 20 = 800 W!
In power electronic circuits the situation is much more complicated: one has to do with DC losses and switching losses, losses in semiconductors and in high frequency transformers, etc. Very often, however, formula (1) appears to be a fairly good approximation of the overall losses in the circuit. The power dissipation P of the circuit can then be calculated by defining R as the overall resistance between input and output of the circuit and I as the output current.
An even better approximation is obtained if a factor is added to (1) to account for the noload power consumption or noload power dissipation. The noload power consumption is the power dissipated by the circuit when it is switched on without any load connected. It is an important specification especially of inverters since in the long run it can drain a battery.
Taking into account the noload power consumption results in the following formula:
Ploss = Po + R x I²out (2)
Ploss is the total power dissipation in the product; Po is the noload power dissipation (and by definition also the noload power consumption); R is the “resistance” between input and output; and Iout the output current.
With formula (2) efficiency, an important specification of inverters, can be calculated:
η = 100 x Pout / (Pout + Ploss) (3)
where η is the efficiency in % and Pout the output power (Pout = Vout x Iout).
At noload conditions the output current Iout = 0 and the output power Pout = 0, so that:
Ploss = Po (4)
and:
η = 0 / (0 + Po) = 0 % (5)
In other words: the efficiency is 0 at noload.
If there would be no power dissipation in the circuit (Ploss = 0), then:
η = 100 x Pout / (Pout + 0) = 100 % (6)
In words: if an ideal circuit without any losses could be made, efficiency would be 100 %.
Formula (2) shows that with increasing load the losses at first do not increase very quickly because Po will still be very much larger than R x I²out as long as Iout is small. Efficiency will start at 0 and increase when the load increases.
But with the load increasing further, R x I²out will increase even faster and become larger than Po, so that Ploss will start increasing approximately with the square of the load or output current. After reaching a maximum, efficiency will therefore start decreasing as the load increases further.
4.3. High temperature and derating
All power conversion products of Victron Energy are protected against damage due to overheating by temperature sensors placed on transformers and on the heatsink of the hottest semiconductors.
Inverters: When the power semiconductors and / or transformers reach a preset temperature, inverters will first show a temperature prewarning, and if temperature increases further, the inverter will shut down. After cooling down, it will restart.
Battery chargers: When the power semiconductors and / or transformers reach a preset temperature, the output current will automatically be reduced to prevent a further increase in temperature.
The power semiconductors are the most critical, with a preset maximum heatsink temperature of approximately 80ºC (167ºF).
High frequency magnetics are in general limited to 100ºC, and toroidal transformers to 110ºC.
The derating curve resulting from maximum heatsink temperature will therefore show a steeper downward slope than the derating curve resulting from high frequency magnetics or a toroidal transformer.
In general the toroidal transformer is the limiting factor in our inverters and inverter/chargers, while semiconductors are the limiting factor in our battery chargers. This explains the difference between the curves shown in paragraph 1 and paragraph 2.
Knowing that, in case of forced cooling, the cooling capacity of a heatsink or transformer is proportional to the temperature difference between the heatsink/transformer and the cooling air flow, formula (2) can be restated as follows:
Iout = K x √(Tmax  ΔTo  Tamb) (7)
where Iout is the output current; K is a constant; Tmax is the maximum heatsink or transformer temperature; ΔTo is the temperature rise of the heatsink or transformer due to the noload power dissipation; and Tamb is the temperature of the cooling air flow.
Formula (7) shows that when ΔTo + Tamb = Tmax, Iout = 0.
In words: when the ambient temperature is so high that the no load power dissipation alone will cause the heatsink or transformer to reach the maximum temperature limit, the output current of the circuit is 0. Any output current would increase temperature beyond the maximum and result in shut down of the circuit due to overheating.
The derating formula (7) is applicable when the ambient temperature increases beyond the temperature at which the full output power is specified, in general 25ºC (77ºF) for inverters and 40ºC (104ºF) for battery chargers.
Why 25°C (77°F) for inverters? Inverters are very often used with intermittent loads. Short term power and peak power are therefore more important than the continuous rated power. Battery chargers on the contrary will regularly operate at maximum output current for several hours and are therefore rated for continuous operation at 40°C (104°F).