The power output in any electrical system is the product of output voltage, output current, and power factor (pf) as given in the equation Electrical Power in Watts=Voltage*Current*pf.
The maximum power transfer theorem states that maximum power is transferred from source to load when the load impedance is equal to the source impedance.
When the circuit is designed for maximum power output, only 50% of the input power is utilized for useful work, making the power efficiency of the circuit equal to 50%.
Figure 1: High power efficiency is a requirement of any engineering system.
When analyzing machine or circuit characteristics, it’s a general trend to plot the power efficiency curve. The power efficiency of a system is the ratio of output power to input power, expressed in percentage, and the efficiency curve is the graph plotted between power output and percentage efficiency as abscissa and ordinate, respectively. The efficiency curve hits the maximum value at some output power, which may not be the maximum power output. The maximum power efficiency and maximum power output are not the same. You cannot map maximum efficiency conditions to maximum power output conditions in a system. In this article, we clear this misconception and examine how maximum power output and maximum efficiency are interrelated.
Maximum Power Output and Heat Loss
In any system design, whether it's a transformer or a complete rectifier-inverter set in a renewable power system, the engineer designs for maximum efficiency. Maximum power output is not a major concern in these circuits, but we design for a rated output power which is not necessarily the maximum. The methodology followed in electrical system design is to fix the input voltage, output voltage, and output current, and design the components of the system so that it works at maximum efficiency.
Maximum efficiency can be ensured by reducing loss. When the objective is loss reduction, heat loss is a major concern in almost all electrical and electronic systems. Heat loss, also called I2R loss, is due to the circuit resistance offered to the current flow in the circuit. The heat loss and output current in the circuit are directly proportional, and the output current also influences the power output of the system. The power output in any electrical system is the product of output voltage, output current, and power factor (pf) as shown in equation 1 (below).
Where pf=cos, is the angle between the voltage and current waveforms
Let's use a DC circuit as an example: the maximum power output in a DC circuit corresponds to maximum voltage and maximum current, as pf is equal to unity. As the current is maximum, the I2R losses and total losses in the circuit are at max, leading to poor efficiency. Here, the circuit is working at maximum power output, but the efficiency is low. In the case of the AC circuit, pf also matters, along with output voltage and output current. The maximum value of the power factor is unity, and this occurs when the circuit is resistive, making it similar to the DC circuit in the example above. When the circuit is reactive, the power factor is less than unity and this further reduces the power output.
Now let’s correlate the maximum power output and thermal management in circuits. When the circuit is designed to give maximum power output, the circuit will turn out to be a ‘hot box’. It takes a considerable amount of investment and footprints of thermal management solutions to cool down the heated circuit. As we move towards compact electrical and electronic systems, maximum power output will ruin the concept of miniaturization.
Figure 2: DC circuits supply maximum power output when RL=Rs❳
Maximum Power Output versus Maximum Efficiency
The conflict between maximum power output and maximum efficiency can be easily understood from the ‘maximum power transfer theorem’. The maximum power transfer theorem states that maximum power is transferred from source to load when the load impedance is equal to the source impedance.
Let’s see what the efficiency of the circuit is when it supplies maximum power to load. Consider a simple DC circuit, shown in Figure 2, with input voltage V and source resistance Rs. The load resistance RL is selected in such a way that the circuit is working at maximum output power condition. According to the maximum power transfer theorem, the circuit gives maximum power output when RL=Rs. Let ‘I’ be the current in the circuit.
When the circuit is designed for maximum power output, only 50% of the input power is utilized for useful work, making the power efficiency of the circuit equal to 50%. The other half of the input power is lost as heat in the circuit. We design circuits for maximum efficiency for the given input and output conditions. If all the circuits in use today are designed for maximum power output, then global power consumption and thermal management of electrical and electronic devices will collapse.
Maximum Power Output Requirements in Communication Systems
When a circuit transfers maximum power, heat is the main byproduct, affecting the efficiency and challenging the thermal solutions. However, in certain systems, we require maximum output rather than maximum efficiency. In communication systems, the signal strength is the main focus, rather than overall efficiency. Impedance matching in communication circuits is mainly focused on achieving maximum amplitude at the receiving or output end. Take the example of a public addressing system—we employ amplifiers and loudspeakers to make the public address loud enough so that everyone in a large crowd can hear it. The point of this is to maximize output, so the impedance of the speaker (load) is matched with that of the amplifier (source).
Now let’s consider a multi-stage amplifier circuit. In multi-stage amplifiers, the output of one amplifier is given as the input of the next immediate amplifier, and this chain continues until we get the desired amplification. In n-stage amplifiers, the impedance of each stage is matched with the previous stage for achieving maximum power output.
The circuit designer should study the application before going for maximum power output or maximum efficiency. If you are designing an audio amplifier system, your concern should be maximum output. For transformer design, the maximum power transfer operation will be like slowly setting a fire. Next time you design a circuit, check the efficiency and losses for maximum output power so that you have a practical understanding of their ill-effects.