7.5
Conservation of AC Power
The principle of AC power conservation states that the complex, real, and reactive powers generated by the source are equivalent to the total complex, real, and reactive powers consumed by the loads.
This principle can be illustrated through a simplified circuit model.
The circuit's total impedance is calculated first, followed by determining the total source current.
The complex power of the source is then calculated using the complex conjugate of this current and the source voltage.
By separating the real and imaginary parts, the active and reactive power of the source can be derived.
Next, the voltage drop across each load is calculated.
The complex power is determined by taking the product of the conjugate current and the voltage drop across each section. From this, the real and reactive powers are deduced.
When comparing all the calculated powers, it becomes evident that the power of the source equals the sum of the power of individual sections, confirming the power conservation principle.
This principle holds true irrespective of the loads connected in series or parallel.
The principle of power preservation is applicable to both ac and dc circuits. This principle, when applied to AC power, asserts that the complex, real, and reactive powers produced by the source are equal to the total complex, real, and reactive powers absorbed by the loads. When two load impedances are connected in parallel to an ac source V, the complex power provided by the source can be calculated using the relation
where S1 and S2 represent the complex powers delivered to loads Z1 and Z2 respectively. If these loads are connected in series with the voltage source, the complex power supplied by the source remains unchanged. This suggests that regardless of whether the loads are connected in series or parallel (or in any other configuration), the total power provided by the source is equal to the total power received by the load. In general, for a source connected to N loads, the complex power is given by
This implies that the total complex power in a network is the sum of the complex powers of its individual components. This holds true for real power and reactive power, but not for apparent power. This articulates the principle of AC power conservation. From this, it can be deduced that the real (or reactive) power flow from sources in a network equals the real (or reactive) power flow into the other components of the network.
The principle of AC power conservation states that the complex, real, and reactive powers generated by the source are equivalent to the total complex, real, and reactive powers consumed by the loads.
This principle can be illustrated through a simplified circuit model.
The circuit's total impedance is calculated first, followed by determining the total source current.
The complex power of the source is then calculated using the complex conjugate of this current and the source voltage.
By separating the real and imaginary parts, the active and reactive power of the source can be derived.
Next, the voltage drop across each load is calculated.
The complex power is determined by taking the product of the conjugate current and the voltage drop across each section. From this, the real and reactive powers are deduced.
When comparing all the calculated powers, it becomes evident that the power of the source equals the sum of the power of individual sections, confirming the power conservation principle.
This principle holds true irrespective of the loads connected in series or parallel.
From Chapter 7:
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