Passive sign convention


In electrical engineering, the passive sign convention is a sign convention or arbitrary standard rule adopted universally by the electrical engineering community for defining the sign of electric power in an electric circuit. The convention defines electric power flowing out of the circuit into an electrical component as positive, and power flowing into the circuit out of a component as negative. So a passive component which consumes power, such as an appliance or light bulb, will have positive power dissipation, while an active component, a source of power such as an electric generator or battery, will have negative power dissipation. This is the standard definition of power in electric circuits; it is used for example in computer circuit simulation programs such as SPICE.
To comply with the convention, the direction of the voltage and current variables used to calculate power and resistance in the component must have a certain relationship: the current variable must be defined so positive current enters the positive voltage terminal of the device. These directions may be different from the directions of the actual current flow and voltage.

The convention

The passive sign convention states that in components in which the conventional current variable i is defined as entering the device through the terminal which is positive as defined by the voltage variable v,
the power p and resistance r are given by
In components in which the current i is defined such that positive current enters the device through the negative voltage terminal, power and resistance are given by
With these definitions, passive components will have p > 0 and r > 0, and active components will have p < 0 and r < 0.

Explanation

Active and passive components

In electrical engineering, power represents the rate of electrical energy flowing into or out of a given component or control volume. Power is a signed quantity; negative power just represents power flowing in the opposite direction from positive power. From the standpoint of power flow, electrical components in a circuit can be divided into two types:
Some components can be either a source or a load, depending on the voltage or current through them. For example, a rechargeable battery acts as a source when it is used to produce power, but as a load when it is being recharged.
Since it can flow in either direction, there are two possible ways to define electric power; two possible reference directions: either power flowing into an electrical component, or power flowing out of the component, can be defined as positive. Whichever is defined as positive, the other will be negative. The passive sign convention arbitrarily defines power flowing out of the circuit as positive, so passive components have "positive" power flow.
In an AC circuit the current and voltage switch direction with each half-cycle of the current, but the definitions above still apply; at any given instant, in passive components the current flows from the positive terminal to the negative, while in active components it flows the other direction.

Sign conventions

The above discussion shows that choosing the relative direction of the voltage and current variables in a component determines the direction of power flow that is considered positive. The reference directions of the individual variables are not important, only their relation to each other. There are two choices:
In practice it is not necessary to assign the voltage and current variables in a circuit to comply with the PSC. Components in which the variables have a "backward" relationship, in which the current variable enters the negative terminal, can still be made to comply with the PSC by changing the sign of the constitutive relations and used with them. A current entering the negative terminal is equivalent to a negative current entering the positive terminal, so in such a component

Conservation of energy

One advantage of defining all the variables in a circuit to comply with the PSC is that it makes it easy to express conservation of energy. Since electric energy cannot be created or destroyed, at any given instant every watt of power consumed by a load component must be produced by some source component in the circuit. Therefore the sum of all the power consumed by loads equals the sum of all the power produced by sources. Since with the PSC the power dissipation in sources is negative and power dissipation in loads is positive, the algebraic sum of all the power dissipation in all the components in a circuit is always zero

AC circuits

Since the sign convention only deals with the directions of the variables and not with the direction of the actual current, it also applies to alternating current circuits, in which the direction of the voltage and current periodically reverses. In an AC circuit, even though the voltage and current reverse direction during the second half of the cycle, at any given instant it obeys the PSC: in passive components the instantaneous current flows through the device from the positive to the negative terminal, while in active components it flows through the component from the negative to positive terminal. Since power is the product of voltage and current, and both the voltage and current reverse direction, the two sign reversals cancel each other, and the sign of the power flow is unchanged in both halves of the cycle.

Alternative convention in power engineering

In practice, the power output of power sources such as batteries and generators is not given in negative numbers, as required by the passive sign convention. No manufacturer sells a "−5 kilowatt generator". The standard practice in electric power circuits is to use positive values for the power and resistance of power sources, as well as loads. This avoids confusion over the meaning of "negative power", and particularly "negative resistance". In order to make the power for both sources and loads come out positive, instead of the PSC, separate sign conventions must be used for sources and loads. These are called the "generator-load conventions" which are used in electric power engineering
Using this convention, positive power flow in source components is power produced, while positive power flow in load components is power consumed.
As with the PSC, if the variables in a given component do not conform to the applicable convention, the component can still be made to conform by using negative signs in the constitutive equations and
This convention may seem preferable to the PSC, since the power P and resistance R always have positive values. However it cannot be used in electronics, because it is not possible to classify some electronic components unambiguously as "sources" or "loads". Some electronic components may act as sources of power with negative resistance in some portions of their operating range, and as absorbers of power with positive resistance in other portions, or even in different portions of the AC cycle. The power consumption or production of a component depends on its current–voltage characteristic curve. Whether the component acts as a source or load may depend on the current i or voltage v in it, which is not known until the circuit is analyzed. For example, if the voltage across a rechargeable battery's terminals is less than its open-circuit voltage, it will act as a source, while if the voltage is greater it will act as a load and recharge. So it is necessary for power and resistance variables to be able to take on both positive and negative values.