Patent Description:
Wind power is considered one of the cleanest, most environmentally friendly energy sources presently available and wind turbines have gained increased attention in this regard. A modern wind turbine typically includes a tower, a generator, a gearbox, a nacelle, and one or more rotor blades. The rotor blades are the primary elements for converting wind energy into electrical energy. The blades typically have the cross-sectional profile of an airfoil such that, during operation, air flows over the blade producing a pressure difference between its sides. Consequently, a lift force, which is directed from the pressure side towards the suction side, acts on the blade. The lift force generates torque on the main rotor shaft, which is connected to a generator for producing electricity that is transferred to a power grid. The power grid transmits electrical energy from generating facilities to end users.

Wind power generation is typically provided by a wind farm, which contains a plurality of wind turbine generators (e.g. often <NUM> or more). Typical wind farms have a farm-level controller that regulates the voltage, reactive power, and/or power factor at the wind farm interconnection point (i.e. the point at which the local wind turbine generators are connected to the grid; may also be referred to as the point of common coupling). In such wind farms, the farm-level controller achieves its control objectives by sending reactive power or reactive current commands to the individual wind turbine generators within the wind farm. However, certain constraints of the local wind turbine generators within the wind farm can constrain the capability to supply reactive power. Such constraints, may include, for example, voltage limits, reactive power limits, and/or current limits. For example, document <CIT> a control method for dynamically controlling active and reactive power capability of a wind farm includes obtaining one or more real-time operating parameters of each of the wind turbines. The method includes obtaining one or more system limits of each of the wind turbines, and measuring at least one real-time wind condition at each of the wind turbines. Further, the method includes continuously calculating an overall maximum active power capability and an overall maximum reactive power capability for each of the wind turbines as a function of the real-time operating parameters, the system limits, and/or the real-time wind condition, and generating a generator capability curve for each of the wind turbines using the overall maximum active and reactive power capabilities and communicating the generator capability curves to a farm-level controller of the wind farm that can use the curves to maximize the instantaneous power output of the wind farm.

More specifically, when one or more of the wind turbine generators reaches one of the above constraints, the local turbine-level controllers may not be able to follow the requested reactive power command from the farm-level controller. Additionally, reaching one of the above constraints may cause a turbine-level controller to enter a different control mode, resulting in controller action that reduces priority of following the farm-level controller command. If the farm-level controller is not aware of these constraints, the farm-level controller may continue to increase or decrease its reactive power command without the expected change in its feedback, leading to windup of the farm-level controller.

Accordingly, the art is continuously seeking new and improved systems and methods for dynamically estimating wind turbine generator reactive power capability to improve farm-level volt/VAR control.

In accordance with an aspect of the present disclosure a method for controlling a power system according to claim <NUM> is presented. The method includes generating, via at least one inverter-based resource of the power system, one or more command signals via a regulator of at least one inverter-based resource. Further, the method includes dynamically estimating, via the at least one inverter-based resource, a reactive power capability of the at least one inverter-based resource based, at least in part, on a reactive power feedback signal and the one or more command signals. Further, the method includes sending, via the at least one inverter-based resource, the reactive power capability to a system-level controller of the power system. Thus, the method includes controlling the power system based on the reactive power capability.

The command signal(s) may include voltage command signals, reactive power command signals, and/or reactive current command signals.

The method includes dynamically estimating the reactive power capability of the at least one inverter-based resource based, at least in part, on the command signal(s) and upper and lower limits of the regulator.

The reactive power capability includes a reactive power capability upper value and a reactive power capability lower value.

Thus, dynamically estimating the reactive power capability of the at least one inverter-based resource includes if the one or more command signals equal the upper limit, then setting the reactive power capability upper value equal to the reactive power feedback signal and the reactive power capability lower value equal to a lower reactive power equipment rating for the at least one inverter-based resource.

Dynamically estimating the reactive power capability of the at least one inverter-based resource includes if the one or more command signals equal the lower limit, then setting the reactive power capability upper value equal to a upper reactive power equipment rating for the at least one inverter-based resource and the reactive power capability lower value equal to the reactive power feedback signal.

Dynamically estimating the reactive power capability of the at least one inverter-based resource includes if the one or more command signals do not equal the upper or lower limits, then setting the reactive power capability upper value equal to the upper reactive power equipment rating for the at least one inverter-based resource and the reactive power capability lower value equal to the lower reactive power equipment rating for the at least one inverter-based resource.

In certain embodiments, sending the reactive power capability to the system-level controller may include sending, via the at least one inverter-based resource, the reactive power capability upper value and the reactive power capability lower value to the system-level controller and setting upper and lower limits of a regulator of the system-level controller equal to the reactive power capability upper and lower values from the at least one inverter-based resource.

In particular embodiments, controlling the power system based on the reactive power capability may include generating a reactive power command for the at least one inverter-based resource using the regulator of the system-level controller with the reactive power capability upper and lower values from the at least one inverter-based resource set as the upper and lower limits of the regulator of the system-level controller.

In accordance with another aspect of the present disclosure a wind farm according claim <NUM> is presented. The wind farm includes a plurality of wind turbine generators, a plurality of turbine-level controllers for controlling the plurality of wind turbine generators, and a farm-level controller commutatively coupled to the plurality of turbine-level controllers. Each of the turbine-level controllers is configured to perform a plurality of operations, including but not limited to generating one or more command signals via a regulator of a respective wind turbine generator of the plurality of wind turbine generators of the wind farm, dynamically estimating a reactive power capability of the respective wind turbine generator based, at least in part, on a reactive power feedback signal and the one or more command signals, and sending the reactive power capability to the farm-level controller. Thus, the farm-level controller controls the wind farm based on the reactive power capability.

In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope of the invention, as defined in the appended claims.

Generally, the present disclosure is directed to a systems and methods for coordinating the inverter-based resource control and system-level control via sending dynamic estimations of reactive power capability from the inverter-based resources to the system-level control. Although the present technology described herein is explained with reference to a wind farm having a plurality of wind turbine generators, it should be understood that the present technology may also be implemented for any suitable application having the ability to rapidly control reactive power. As used herein, inverter-based resources generally refer to electrical devices that can generate or absorb electric power through switching of power-electronic devices. Accordingly, inverter-based resource may include wind turbine generators, solar inverters, energy-storage systems, STATCOMs, or hydro-power systems.

Referring now to the drawings, <FIG> illustrates a block diagram of a wind farm <NUM> having a plurality of wind turbine generators <NUM> coupled with a transmission grid <NUM>. <FIG> illustrates three wind generators <NUM>; however, any number of wind generators can be included in a wind farm <NUM>. Further, as shown, each of the wind turbine generators <NUM> includes a local controller <NUM> that is responsive to the conditions of the wind turbine generator <NUM> being controlled. In one embodiment, the controller for each wind turbine generator senses only the terminal voltage and current (via potential and current transformers). The sensed voltage and current are used by the local controller to provide an appropriate response to cause the wind turbine generator <NUM> to provide the desired reactive power.

Each wind turbine generator <NUM> is coupled to collector bus <NUM> through generator connection transformers <NUM> to provide real and reactive power (labeled Pwg and Qwg, respectively) to the collector bus <NUM>. Generator connection transformers and collector buses are known in the art.

The wind farm <NUM> provides real and reactive power output (labeled Pwf and Qwf, respectively) via wind farm main transformer <NUM>. The farm-level controller <NUM>, which is communicatively coupled to the turbine-level controllers <NUM>, senses the wind farm output, as well as the voltage at the point of common coupling (PCC) <NUM>, to provide a Q command signal <NUM> (QCMD) that indicates desired reactive power at the generator terminals to ensure a reasonable distribution of reactive power among the wind turbines. In alternate embodiments, the Q command signal (QCMD) <NUM> may be generated as the local or operator level (indicated by the "LOCAL" lines in <FIG>), for example in the event that the wind turbine generator(s) is in manual mode or otherwise not in communication with the wind farm-level controller <NUM>.

Referring now to <FIG>, a block diagram of one embodiment of suitable components that may be included within the turbine-level controllers <NUM> and/or the farm-level controller <NUM> in accordance with aspects of the present disclosure is illustrated. As shown, the controller <NUM>, <NUM> may include one or more processor(s) <NUM> and associated memory device(s) <NUM> configured to perform a variety of computer-implemented functions (e.g., performing the methods, steps, calculations and the like and storing relevant data as disclosed herein). Additionally, the controller <NUM>, <NUM> may also include a communications module <NUM> to facilitate communications between the controller <NUM>, <NUM> and the various components of the wind farm <NUM>. Further, the communications module <NUM> may include a sensor interface <NUM> (e.g., one or more analog-to-digital converters) to permit signals transmitted from one or more sensors <NUM>, <NUM>, <NUM> to be converted into signals that can be understood and processed by the processors <NUM>. It should be appreciated that the sensors <NUM>, <NUM>, <NUM> may be communicatively coupled to the communications module <NUM> using any suitable means. For example, as shown, the sensors <NUM>, <NUM>, <NUM> are coupled to the sensor interface <NUM> via a wired connection. However, in other embodiments, the sensors <NUM>, <NUM>, <NUM> may be coupled to the sensor interface <NUM> via a wireless connection, such as by using any suitable wireless communications protocol known in the art.

As used herein, the term "processor" refers not only to integrated circuits referred to in the art as being included in a computer, but also refers to a controller, a microcontroller, a microcomputer, a programmable logic controller (PLC), an application specific integrated circuit, and other programmable circuits. Additionally, the memory device(s) <NUM> may generally comprise memory element(s) including, but not limited to, computer readable medium (e.g., random access memory (RAM)), computer readable non-volatile medium (e.g., a flash memory), a floppy disk, a compact disc-read only memory (CD-ROM), a magneto-optical disk (MOD), a digital versatile disc (DVD) and/or other suitable memory elements. Such memory device(s) <NUM> may generally be configured to store suitable computer-readable instructions that, when implemented by the processor(s) <NUM>, configure the controller <NUM>, <NUM> to perform various functions as described herein.

The sensors <NUM>, <NUM>, <NUM> may include any suitable sensors configured to provide feedback measurements to the farm-level controller <NUM>. In various embodiments, for example, the sensors <NUM>, <NUM>, <NUM> may be any one of or combination of the following: voltage sensors, current sensors, and/or any other suitable sensors.

Referring now to <FIG>, embodiments of various systems and methods for controlling a wind farm by estimating reactive power capabilities at the turbine-level based on certain regulator commands reaching their limits according to the present disclosure are illustrated. In particular, <FIG> illustrates a functional diagram of one embodiment of farm-level and turbine-level regulators, which utilize reactive power capability estimations according to the present disclosure. <FIG> illustrates a flow diagram of one embodiment of a method <NUM> for controlling a wind farm according to the present disclosure. <FIG> illustrates a functional diagram of turbine-level control according to the present disclosure. <FIG> illustrates a schematic diagram of one embodiment of a reactive power capability module of a turbine-level controller according to the present disclosure.

Referring particularly to <FIG>, a practical implementation of the system <NUM> for controlling the wind farm <NUM> by coordinating the volt-var capability of the wind turbine generator(s) <NUM> with the farm-level controller <NUM> is illustrated. In particular, as shown, the farm-level controller <NUM> may be a voltage regulator <NUM> with dynamic upper and lower limits (e.g. QCapHi and QCapLo) that are determined by upper and lower reactive power capability estimations from the turbine-level controller(s) <NUM>. More specifically, in an embodiment, the turbine-level controller(s) <NUM> reactive power capability estimation is determined based on volt/var control signals generated by the regulator <NUM>. Thus, as shown, a QCap estimation module <NUM> for each wind turbine generator <NUM> is configured to estimate a reactive power capability <NUM>. As such, the system <NUM> of the present disclosure takes into account whether the wind turbine generator voltage regulator <NUM> is reaching or exceeding an upper or lower limit. If one of the voltage command limits is being reached or exceeded, either the upper or lower reactive power capability is changed from a fixed rated value to the present value of the reactive power feedback. If the command voltage is not reaching or exceeding limits, then the upper and lower reactive power capabilities are set to the reactive power ratings of the wind turbine generator(s) <NUM>.

Referring now to <FIG>, more detailed implementations of the system <NUM> of <FIG> are depicted and explained. In particular, in general, the method <NUM> described in <FIG> generally applies to operating the wind farm <NUM> described herein with respect to <FIG>. However, it should be appreciated that the disclosed method <NUM> may be implemented using any other power system that is configured to supply reactive power for application to a load, such as a power grid, such as a solar power system, a hydropower system, an energy storage power system, or combinations thereof. Further, <FIG> depicts steps performed in a particular order for purposes of illustration and discussion. Those of ordinary skill in the art, using the disclosures provided herein, will understand that various steps of any of the methods disclosed herein can be adapted, omitted, rearranged, or expanded in various ways without deviating from the scope of the present disclosure.

As shown at <NUM>, the method <NUM> includes generating, via at least one turbine-level controller <NUM>, one or more command signals via a regulator of at least one wind turbine generator <NUM> of the wind farm <NUM>. For example, as shown particularly in <FIG>, a control diagram of one embodiment of the regulator <NUM>, e.g. that may be implemented by the turbine-level controller <NUM>, is illustrated in accordance with aspects of the present subject matter. In several embodiments, the regulator <NUM> generally includes two loops: a voltage regulator loop and a Q regulator loop. The voltage regulator loop operates relatively fast (e.g., <NUM> rad/sec) as compared to the Q regulator loop (e.g., greater than <NUM> second closed loop time constant).

Conceptually, the control system of <FIG> provides for wind turbine generator terminal voltage control by regulating the voltage according to a reference set by a higher-than-generator-level (e.g., substation or wind farm) controller, such as the farm-level controller <NUM>. Reactive power is regulated over a longer term (e.g., several seconds) while wind turbine generator terminal voltage is regulated over a shorter term (e.g., less than several seconds) to mitigate the effects of fast grid transients.

An operator or farm level Q command <NUM> is a signal that indicates desired reactive power at the generator terminals. In farm-level operation, the wind turbine generator Q command <NUM> is set equal to the output of the farm level control (line <NUM> in <FIG>). In local control, the operator command is set manually, either at the wind generator location or at a remote location. The operator or farm level Q command <NUM> can be generated or transmitted by, for example, a computer system used to control the wind turbine generator. The operator or farm level Q command <NUM> can also come from a utility grid operator or substation.

In one embodiment, as shown, the operator or farm level Q command <NUM> is transmitted to a command limiter <NUM>, which operates to maintain reactive power commands within a predetermined range. Further, as shown in <FIG>, QMAX <NUM> and QMIN <NUM> may generally indicate the upper and lower bounds on the reactive power command range. Moreover, in an embodiment, the specific values used for QMAX <NUM> and QMIN <NUM> may be based on, for example, generator reactive capabilities. In one embodiment, as an example, the value for QMAX <NUM> may be <NUM> kVAR and the value for QMIN <NUM> may be -<NUM> kVAR for a <NUM> MW wind turbine generator. However, it should be readily appreciated that the specific values for QMAX <NUM> and QMIN <NUM> may generally depend upon the capability of the specific generators being used.

Still referring to <FIG>, the signal output by the command limiter <NUM> is a Q command <NUM>, which is a command indicating the target reactive power to be produced. The Q command <NUM> is in the range between QMAX <NUM> and QMIN <NUM>. Additionally, as shown, the Q command <NUM> may be compared to a signal indicating measured reactive power <NUM>. The resulting error signal, Q error <NUM>, indicates the difference between the measured reactive power and the commanded reactive power.

The Q error <NUM> is an input signal to a reactive power regulator <NUM> (hereinafter referred to as the VAR regulator <NUM>), which generates a voltage setpoint <NUM> (hereinafter referred to as the V command <NUM>) that indicates to a wind turbine generator <NUM> the reactive power to be provided by the generator. In one embodiment, the VAR regulator <NUM> may be a proportional integral (PI) controller that has a closed-loop time constant in the range of <NUM> to <NUM> seconds (e.g., <NUM> seconds, <NUM> seconds, <NUM> seconds). Other types of controllers may be also be used, for example, proportional derivative (PD) controllers, proportional integral derivative (PID) controllers, state space controllers, etc. Additionally, other time constants can be used for the VAR regulator <NUM> provided that the time constant for the VAR regulator <NUM> is numerically greater than the time constant for a voltage regulator <NUM> (described below).

In several embodiments, the V command <NUM> may be limited to a predetermined range between VMAX <NUM> and VMIN <NUM>. For example, in one embodiment, VMAX <NUM> and VMIN <NUM> may be defined in terms of a percentage of the rated generator output, such as by defining VMAX <NUM> as <NUM>% of the rated generator voltage while defining VMIN <NUM> can be <NUM>% of the rated generator voltage. However, it should be appreciated that alternate upper and lower limits may also be used.

Referring still to <FIG>, the V command <NUM> derived from the VAR regulator <NUM> may be compared to a signal indicating a measured terminal voltage <NUM> for the generator <NUM>. The difference between the V command <NUM> and the measured terminal voltage <NUM> is a voltage error signal <NUM>. Further, as shown, the voltage error signal <NUM> is then input into a voltage regulator <NUM> of the disclosed system <NUM>, which may be limited to a predetermined range between IirdMAX <NUM> and IirdMIN <NUM>. As such, the voltage regulator <NUM> generates a reactive current command <NUM>, which is used to control generator reactive current and, thus, generator reactive power (Qwg in <FIG>). In one embodiment, the voltage regulator <NUM> is a PI controller that has a closed-loop time constant of approximately <NUM> milliseconds. Other types of controllers can also be used, for example, PD controllers, PID controllers, etc. In addition, other time constants may also be used (e.g., <NUM> second, <NUM> milliseconds, <NUM> milliseconds, <NUM> milliseconds) for the voltage regulator <NUM> provided that the time constant for the regulator <NUM> is less than the time constant for the VAR regulator <NUM>.

Referring back to <FIG>, as shown at <NUM>, the method <NUM> includes dynamically estimating, via the turbine-level controller(s) <NUM>, a reactive power capability of the wind turbine generator(s) <NUM> based, at least in part, on the command signal(s) (e.g. such as the V command signal <NUM>). More specifically, as shown in <FIG>, in an embodiment, the QCap estimation module <NUM> is configured to dynamically estimate the reactive power capability <NUM> of the wind turbine generator(s) <NUM> based the V command signal <NUM>, upper and lower limits (e.g. VMAX <NUM> and VMIN <NUM>) of the regulator <NUM> and/or a reactive power feedback signal <NUM> (e.g. Qwtg_Fbk), or combinations thereof. The reactive power feedback signal <NUM>, as described herein, generally refers to a measured value, e.g. such as measured via one or more sensors. In particular embodiments, as shown in <FIG> and <FIG>, the reactive power capability <NUM> may include a reactive power capability upper value <NUM> and a reactive power capability lower value <NUM>.

Accordingly, in an embodiment, as shown in <FIG>, the QCap estimation module <NUM> may include various algorithms, look-up tables, and/or equations for dynamically estimating the reactive power capability <NUM> of the wind turbine generator(s) <NUM>. In one embodiment, as shown, if the one or more command signals (VCMD) equals the upper limit (VMAX), then the reactive power capability upper limit (QCapHi) may equal (i.e. may be set to) the reactive power feedback signal (Qwtg_Fbk) and the reactive power capability lower limit (QCapLo) may equal (i.e. may be set to) a lower reactive power equipment rating (-Qrat) for the wind turbine generator(s) <NUM>. Moreover, if the one or more command signals (VCMD) equals the lower limit (VMIN), then the reactive power capability upper limit (QCapHi) may equal (i.e. may be set to) a upper reactive power equipment rating (Qrat) for the wind turbine generator(s) <NUM> and the reactive power capability lower limit (QCapLo) may equal (i.e. may be set to) the reactive power feedback signal (Qwtg_Fbk). Still referring to <FIG>, if the one or more command signals do not equal the upper or lower limits (represented by ELSE), then the reactive power capability upper limit (QCapHi) may equal (i.e. may be set to) the upper reactive power equipment rating (Qrat) for the wind turbine generator(s) <NUM> and the reactive power capability lower limit (QCapLo) may equal (i.e. may be set to) the lower reactive power equipment rating (-Qrat) for the wind turbine generator(s) <NUM>.

Accordingly, referring back to <FIG>, as shown at <NUM>, the method <NUM> includes sending, via the turbine-level controller(s) <NUM>, the reactive power capability to the farm-level controller <NUM>. For example, in an embodiment, as shown in <FIG>, the turbine-level controller(s) <NUM> is configured to send the reactive power capability upper value <NUM> and the reactive power capability lower value <NUM> to the farm-level controller <NUM> and set upper and lower limits of the regulator <NUM> of the farm-level controller <NUM> equal to the reactive power capability upper and lower values <NUM>, <NUM>.

Referring back to <FIG>, as shown at <NUM>, the method <NUM> then includes controlling the wind farm <NUM> based on the reactive power capability. In certain embodiments, for example, controlling the wind farm <NUM> based on the reactive power capability <NUM> described herein may include generating a reactive power command (Q_Cmd) for the wind turbine generator(s) <NUM> using the regulator <NUM> of the farm-level controller <NUM> with the reactive power capability upper and lower values <NUM>, <NUM> set as the upper and lower limits of the regulator <NUM> of the farm-level controller <NUM>.

The concept for coordinating the reactive power capability of the wind turbine generator(s) <NUM> with the farm-level controller <NUM> can be extended to a multiple wind turbines, for example, by totaling farm upper and lower reactive power capabilities from each wind turbine, respectively. Further, in such embodiments, the total farm-level reactive power command (Q_Cmd) may be limited by the total farm upper capability and total farm lower capability. This total farm Q_Cmd can then distributed among the individual wind turbine generators <NUM> within the wind farm <NUM> in such a way to enforce the individual capability limits of each wind turbine generator <NUM> and meeting the total Q_Cmd requested by the farm control. In scenario's where portions of the wind turbine generators <NUM> are constrained on reactive power capability, these wind turbine generators <NUM> can receive a different reactive power command from the farm controller than the un-constrained wind turbine generators <NUM>.

In such embodiments, the method <NUM> may further include generating, via a plurality of turbine-level controllers <NUM>, a plurality of the one or more command signals via a plurality of regulator from the plurality of wind turbine generators <NUM>, dynamically estimating, via the plurality of turbine-level controllers <NUM>, a plurality of reactive power capabilities for the wind turbine generators <NUM> based, at least in part, on the plurality of the one or more command signals, sending, via the plurality of turbine-level controllers <NUM>, the plurality of reactive power capabilities for the wind turbine generators <NUM> to the farm-level controller <NUM>, and controlling the wind farm <NUM> based on the plurality of reactive power capabilities.

Claim 1:
A method for controlling a power system (<NUM>), the method comprising:
generating, via at least one inverter-based resource (<NUM>) of the power system (<NUM>), one or more command signals (<NUM>, VCMD) via a regulator (<NUM>) of at least one inverter-based resource;
dynamically estimating, via the at least one inverter-based resource (<NUM>), a reactive power capability (<NUM>) of the at least one inverter-based resource based, at least in part, on a reactive power feedback signal (<NUM>), the one or more command signals (<NUM>, VCMD), and upper and lower limits (<NUM>, VMAX, <NUM>, VMIN) of the regulator (<NUM>), characterised in that
the reactive power capability (<NUM>) comprises a reactive power capability upper value (<NUM>, QCapHi) and a reactive power capability lower value (<NUM>, QCapLo), wherein dynamically estimating the reactive power capability (<NUM>) of the at least one inverter-based resource comprises:
if the one or more command signals (<NUM>) equal the upper limit (<NUM>, VMAX), then setting the reactive power capability upper value (<NUM>, QCapHi) equal to the reactive power feedback signal (<NUM>) and the reactive power capability lower value (<NUM>, QCapLo) equal to a lower reactive power equipment rating (-Qrat) for the at least one inverter-based resource,
if the one or more command signals (<NUM>, VCMD) equal the lower limit (<NUM>, VMIN), then setting the reactive power capability upper value (<NUM>, QCapHi) equal to an upper reactive power equipment rating (Qrat) for the at least one inverter-based resource (<NUM>) and the reactive power capability lower value (<NUM>, QCapLo) equal to the reactive power feedback signal (<NUM>), and
if the one or more command signals (<NUM>, VCMD) do not equal the upper or lower limits (<NUM>, VMAX, <NUM>, VMIN), then setting the reactive power capability upper value (<NUM>, QCapHi) equal to the upper reactive power equipment rating (Qrat) for the at least one inverter-based resource (<NUM>) and the reactive power capability lower value (<NUM>, QCapLo) equal to the lower reactive power equipment rating (-Qrat) for the at least one inverter-based resource (<NUM>);
sending, via the at least one inverter-based resource (<NUM>), the reactive power capability (<NUM>) to a system-level controller (<NUM>) of the power system (<NUM>); and,
controlling the power system (<NUM>) based on the reactive power capability (<NUM>).