he current method of DC/AC analysis does not properly compute the DC input power to the inverter required to support electrical loads. The current methodology requires the DC power source be a battery or a fuel cell that can provide enough real power to the inverter to meet the load on the motor and this approach does not consider the reactive power component. What the theory is the DC power source must provide enough power to meet the motor apparent power needs and not just the real power needs. If the power calculations are inaccurate, then this will impact the battery powering the inverter and lead to improperly sized components and possible thermal issues.

A new power flow analysis is required to determine how much power needs to be provided to the inverter and motor, and a new approach is needed to compute component efficiency. A new method would provide a better understanding of losses and heat generation, which would also lead to a more robust electromechanical system.

One of the fundamental rules of mathematics is that we can only add numbers of the same units; we can add mass to mass to get a combined mass. But, in the world of alternating current, we are adding real power, P(W), to reactive power, Q(VAR), to compute apparent power, S(VA), as shown in Figure 1.

The product of voltage and current will yield Watts, but reactive power and apparent power have different units; how can we complete this operation? Even when adding force vectors, they are all the same units, so they do add up, as shown in Figure 2.

Why does reactive power have different units? Is it power that is not used? And what if the reactive power is in units of Watts? Would it make the power triangle work? A new approach is needed to analyze the power and energy flow of an electrical system with the use of thermodynamics; the conservation of energy cannot be violated.

The conservation of energy applied to DC/AC systems, like the ones used in battery electric vehicles, can provide insight into mapping the power flow and heat losses in these systems.

Typically, a battery or a fuel cell will provide power to the inverter, which transforms the DC into AC, and the AC power is fed to the motor, as shown in Figure 3.

The function of the inverter is to convert DC power to AC, and the current energy balance is shown in Equation 1.

Where P_DC is the electrical power into the inverter and P_{AC, out} is the real component of the AC power out, and P_{losses, inv} are the internal losses of the inverter. With the current process, the efficiency of the inverter is defined as the ratio of the real power out divided by the real power in, as shown in Equation 2.

On the other hand, we have a reactive power component Q, which is also provided at the outlet of the inverter. The real component of the power does the real work, and the reactive power is required to produce the electromagnetic field which allows the motor to generate torque. Without the reactive power, the AC motor will not produce any electrical work.

Once the inverter converts the DC to AC, the AC motor will take the electrical power and convert the electricity into torque and angular speed.

The AC motor will convert the AC power into mechanical power. The energy balance of the motor is shown in Equation 3.

The efficiency of the AC motor is currently defined as real power out divided by real power in, as shown in Equation 4.

Note that these equations do not take into consideration the reactive component of power, nor do they consider the apparent power. An examination of the reactive component and apparent component is required to see how they will impact electrical systems. We do know the reactive power is required to obtain real work.

The first assumption is that reactive power has units of Watts like the real component, so the power triangle can be completed. If the reactive power and apparent power have the same units, then we add them in the power triangle without violating the math and engineering fundamentals, as shown in Figure 4.

The change to the power triangle does allow us to add units without violating any fundamentals.

In the case of the inverter, it is taking the real power from the battery and producing both DC power and apparent power, as shown in Figure 5.

The output power of the inverter can be expressed in terms of the apparent power S. If we apply the conservation of energy, the DC power in should equal the apparent power, as shown in Equation 5.

But we are going to have losses in the inverter; thus, Equation 6 is obtained.

If we look at the efficiency as the ratio of energy of interest to energy of cost, we get Equation 7.

This efficiency will compute the real efficiency of the inverter, and the efficiency can also be used to compute the heat generation of the inverter by using Equation 8.

The new process factors in the real and reactive components of the power based on using the apparent power. The apparent power can always be broken down into its real and reactive components.

The next step in the power mapping is the AC motor; at this point, the inverter has already converted the DC power to AC for the motor. The AC motor is taking in apparent power and converting the power into mechanical power through torque and angular speed.

If the apparent power is used for the input power, the reactive component is used to create the electric/magnetic field. The reactive component is required to generate the real torque.

The other electrical assumption is that the reactive power is used to generate the magnetic/electric field. Without the electric field, the real work could not be accomplished.

The conservation of energy would show the AC power in is equal to mechanical power out, as shown in Equation 9.

There are losses in the motor, and these losses need to be considered. Equation 9 is modified and thus we obtain Equation 10.

The proposed efficiency of the motor is the apparent power in and mechanical power out, as shown in Equation 11.

If both the motor efficiency from Equation 11 and Equation 7 are combined, the power transmission efficiency is then calculated, as shown in Equation 12.

This would be the same as the current method of analysis by taking Equation 2 and Equation 4, as shown in Equation 13.

As shown in both Equation 12 and Equation 13 cases, the output of the inverter AC power drops out and relates the output power of the motor to the DC power in. But, in both cases, the interaction between the inverter and the motor is not fully examined or understood.

The proposed changes will impact the heat generation of the motor and inverter, and it will impact efficiency.

The other item that needs to be addressed between the mechanical and electrical systems is the mechanical power-to-electrical power relationship at the motor.

The required output power from the motor comes from the mechanical domain. The question now becomes: does the real power from the mechanical domain need to be real power into the motor, or is it a combination of both the real and the reactive powers?

Without reactive power, the motor would not have the magnetic fields required to produce the mechanical work needed.

The main difference between Equation 4 and Equation 11 is the motor efficiency and how it is defined. The apparent power can never be zero, as there will always be either a reactive or real component.

One unusual anomaly found in constant power testing is that the input current to the inverter is dependent on the input voltage; as the input voltage decreases, current increases.

The increase in current will lead to Joule heating and a loss of efficiency. We must understand voltage and current to see how this impacts power transfer.

In previous testing, an electrical system under constant load at different input voltages was provided to the inverter, and the inverter could only control current to meet the power demands. It was found that as the input voltage decreased, the current required increased, as shown in Figure 6.

Under a constant power load, the DC current into the inverter depends on the input voltage. As the input voltage decreases, the current increases; the higher current would produce higher generation due to Joule heating.

The AC output of the inverter has the real component, a reactive component; the AC power component is shown in Figure 7.

The real and reactive powers are out of phase with one another, and the reactive power is required. The distinction between real and reactive power needs to be better understood.

Losses in any system will be seen as light, heat, or sound; in this case, the losses would show up as heat. The next step is to compare the efficiency of the inverter and motor. The comparison of the motor efficiency is shown in Figure 8. The comparison shows the current method of computing efficiency, and the second method is a new efficiency calculation using apparent power.

The current efficiency was giving values greater than one, which cannot be achieved. On the other hand, the proposed efficiency has values between 0.1 and 1, which does not violate thermodynamics and means the output energy is less than the input energy. The lower efficiency will also mean that heat generation in the motor will be higher. If the heat generation is estimated more accurately, then the cooling for the motor can be performed more effectively, and the motor temperature can be maintained.

The question that comes up is what component of the apparent power generates the real work being done by the motor. Is it real power from Equation 4 or the apparent power from Equation 11?

If we use only Equation 4, then we neglect the impact of the reactive component. But if we consider Equation 11, we know it is the apparent power. But how much real power do we need and how much reactive power do we need?

This needs to be further analyzed because the mechanical power output is real. So how does this real power transmit to the input power required to the motor? And then we have to ask, how does this power transmit to the output of the inverter?

Our future research will involve the power transfer in the inverter, and the real and reactive power will have to be further examined along with the phase angle. The goal of the inverter research is to obtain an efficiency less than 1 and to better estimate the heat generated from the inverter.