Power-voltage curve

Last updated
Normalized P-V curve PV curve.png
Normalized P-V curve

Power-voltage curve (also P-V curve) describes the relationship between the active power delivered to the electrical load and the voltage at the load terminals in an electric power system under a constant power factor. [1] When plotted with power as a horizontal axis, the curve resembles a human nose, thus it is sometimes called a nose curve. [2] The overall shape of the curve (similar to a parabola placed on its side) is defined by the basic electrical equations and does not change much when the characteristics of the system vary: leading power factor lead stretches the "nose" further to the right and upwards, while the lagging one shrinks the curve. [3] The curve is important for voltage stability analysis, as the coordinate of the tip of the nose defines the maximum power that can be delivered by the system.

As the load increases from zero, the power-voltage point travels from the top left part of the curve to the tip of the "nose" (power increases, but the voltage drops). The tip corresponds to the maximum power that can be delivered to the load (as long as sufficient reactive power reserves are available). Past this "collapse" point additional loads cause drop in both voltage and power, as the power-voltage point travels to the bottom left corner of the plot. [2] Intuitively this result can be explained when a load that consists entirely of resistors is considered: as the load increases (its resistance thus lowers), more and more of the generator power dissipates inside the generator itself (that has it own fixed resistance connected sequentially with the load). [4] Operation on the bottom part of the curve (where the same power is delivered with lower voltage – and thus higher current and losses) is not practical, as it corresponds to the "uncontrollability" region. [2]

If sufficient reactive power is not available, the limit of the load power will be reached prior to the power-voltage point getting to the tip of the "nose". The operator shall maintain a sufficient margin between the operating point on the P-V curve and this maximum loading condition, otherwise, a voltage collapse can occur. [5]

A similar curve for the reactive power is called Q-V curve. [1]

Related Research Articles

In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of RMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average product of the two. A negative power factor occurs when the device generates real power, which then flows back towards the source.

<span class="mw-page-title-main">Voltage regulator</span> System designed to maintain a constant voltage

A voltage regulator is a system designed to automatically maintain a constant voltage. It may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism, or electronic components. Depending on the design, it may be used to regulate one or more AC or DC voltages.

<span class="mw-page-title-main">Single-line diagram</span> Simplest symbolic representation of an electric power system

In power engineering, a single-line diagram (SLD), also sometimes called one-line diagram, is a simplest symbolic representation of an electric power system. A single line in the diagram typically corresponds to more than one physical conductor: in a direct current system the line includes the supply and return paths, in a three-phase system the line represents all three phases.

In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation.

Electric power quality is the degree to which the voltage, frequency, and waveform of a power supply system conform to established specifications. Good power quality can be defined as a steady supply voltage that stays within the prescribed range, steady AC frequency close to the rated value, and smooth voltage curve waveform. In general, it is useful to consider power quality as the compatibility between what comes out of an electric outlet and the load that is plugged into it. The term is used to describe electric power that drives an electrical load and the load's ability to function properly. Without the proper power, an electrical device may malfunction, fail prematurely or not operate at all. There are many ways in which electric power can be of poor quality, and many more causes of such poor quality power.

<span class="mw-page-title-main">AC power</span> Power in alternating current systems

In an electric circuit, instantaneous power is the time rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of the direction of energy flow. Its SI unit is the watt.

<span class="mw-page-title-main">Volt-ampere</span> SI unit of apparent power in an electrical circuit

The volt-ampere is the unit of measurement for apparent power in an electrical circuit. It is the product of the root mean square voltage and the root mean square current. Volt-amperes are usually used for analyzing alternating current (AC) circuits. In direct current (DC) circuits, this product is equal to the real power, measured in watts. The volt-ampere is dimensionally equivalent to the watt: in SI units, 1 V⋅A = 1 W. VA rating is most used for generators and transformers, and other power handling equipment, where loads may be reactive.

<span class="mw-page-title-main">Synchronous condenser</span> Machinery used to adjust conditions on the electric power transmission grid

In electrical engineering, a synchronous condenser is a DC-excited synchronous motor, whose shaft is not connected to anything but spins freely. Its purpose is not to convert electric power to mechanical power or vice versa, but to adjust conditions on the electric power transmission grid. Its field is controlled by a voltage regulator to either generate or absorb reactive power as needed to adjust the grid's voltage, or to improve power factor. The condenser’s installation and operation are identical to large electric motors and generators.

<span class="mw-page-title-main">Maximum power point tracking</span> Solar cell power extraction method

Maximum power point tracking (MPPT), or sometimes just power point tracking (PPT), is a technique used with variable power sources to maximize energy extraction as conditions vary. The technique is most commonly used with photovoltaic (PV) solar systems, but can also be used with wind turbines, optical power transmission and thermophotovoltaics.

An induction generator or asynchronous generator is a type of alternating current (AC) electrical generator that uses the principles of induction motors to produce electric power. Induction generators operate by mechanically turning their rotors faster than synchronous speed. A regular AC induction motor usually can be used as a generator, without any internal modifications. Because they can recover energy with relatively simple controls, induction generators are useful in applications such as mini hydro power plants, wind turbines, or in reducing high-pressure gas streams to lower pressure.

Electrical power system simulation involves power system modeling and network simulation in order to analyze electrical power systems using design/offline or real-time data. Power system simulation software's are a class of computer simulation programs that focus on the operation of electrical power systems. These types of computer programs are used in a wide range of planning and operational situations for electric power systems.

<span class="mw-page-title-main">Electric power system</span> Network of electrical component deployed to generate, transmit & distribute electricity

An electric power system is a network of electrical components deployed to supply, transfer, and use electric power. An example of a power system is the electrical grid that provides power to homes and industries within an extended area. The electrical grid can be broadly divided into the generators that supply the power, the transmission system that carries the power from the generating centers to the load centers, and the distribution system that feeds the power to nearby homes and industries.

Ancillary services are the services necessary to support the transmission of electric power from generators to consumers given the obligations of control areas and transmission utilities within those control areas to maintain reliable operations of the interconnected transmission system.

A magnetically-controlled shunt reactor represents electrotechnical equipment purposed for compensation of reactive power and stabilization of voltage level in high voltage (HV) electric networks rated for voltage classes 36 – 750 kV. MCSR is shunt-type static device with smooth regulation by means of inductive reactance.

Wide-area damping control (WADC) is a class of automatic control systems used to provide stability augmentation to modern electrical power systems known as smart grids. Actuation for the controller is provided via modulation of capable active or reactive power devices throughout the grid. Such actuators are most commonly previously-existing power system devices, such as high-voltage direct current (HVDC) transmission lines and static VAR compensators (SVCs) which serve primary purposes not directly related to the WADC application. However, damping may be achieved with the utilization of other devices installed with the express purpose of stability augmentation, including energy storage technologies. Wide-area instability of a large electrical grid unequipped with a WADC is the result of the loss of generator rotor synchronicity, and is typically envisioned as a generator oscillating with an undamped exponential trajectory as the result of insufficient damping torque.

Power system operations is a term used in electricity generation to describe the process of decision-making on the timescale from one day to minutes prior to the power delivery. The term power system control describes actions taken in response to unplanned disturbances in order to provide reliable electric supply of acceptable quality. The corresponding engineering branch is called Power System Operations and Control. Electricity is hard to store, so at any moment the supply (generation) shall be balanced with demand. In an electrical grid the task of real-time balancing is performed by a regional-based control center, run by an electric utility in the traditional electricity market. In the restructured North American power transmission grid, these centers belong to balancing authorities numbered 74 in 2016, the entities responsible for operations are also called independent system operators, transmission system operators. The other form of balancing resources of multiple power plants is a power pool. The balancing authorities are overseen by reliability coordinators.

<span class="mw-page-title-main">Capability curve</span>

Capability curve of an electrical generator describes the limits of the active (MW) and reactive power (MVAr) that the generator can provide. The curve represents a boundary of all operating points in the MW/MVAr plane; it is typically drawn with the real power on the horizontal axis, and, for the synchronous generator, resembles a letter D in shape, thus another name for the same curve, D-curve. In some sources the axes are switched, and the curve gets a dome-shaped appearance.

Voltage control and reactive power management are two facets of an ancillary service that enables reliability of the transmission networks and facilitates the electricity market on these networks. Both aspects of this activity are intertwined, so within this article the term voltage control will be primarily used to designate this essentially single activity, as suggested by Kirby & Hirst (1997). Voltage control does not include reactive power injections within one AC cycle; these are a part of a separate ancillary service, so-called system stability service. The transmission of reactive power is limited by its nature, so the voltage control is provided through pieces of equipment distributed throughout the power grid, unlike the frequency control that is based on maintaining the overall active power balance in the system.

In an electrical grid, the short circuit ratio is the ratio of the short circuit apparent power (SCMVA) in the case of a line-line-line-ground (3LG) fault at the location in the grid where some generator is connected to the power rating of the generator itself (GMW). Since the power that can be delivered by the grid varies by location, frequently a location is indicated, for example, at the point of interconnection (POI):

The reactances of synchronous machines comprise a set of characteristic constants used in the theory of synchronous machines. Technically, these constants are specified in units of the electrical reactance (ohms), although they are typically expressed in the per-unit system and thus dimensionless. Since for practically all machines the resistance of the coils is negligibly small in comparison to the reactance, the latter can be used instead of (complex) electrical impedance, simplifying the calculations.

References

Sources