JP6397613B2 - Control circuit for controlling inverter circuit, inverter device provided with the control circuit, power system provided with the inverter device, and control method - Google Patents

Description

  The present invention relates to a control circuit that controls an inverter circuit, an inverter device that includes the control circuit, a power system that includes the inverter device, and a control method.

  2. Description of the Related Art Conventionally, an inverter device has been developed that converts DC power generated by a solar cell or the like into AC power and supplies it to an electric power system. In addition, in a photovoltaic power plant such as a mega solar power generator, a large amount of power is supplied to the power system by connecting a large number of inverter devices in parallel. SVC (Static Var Compensator: Static Reactive Power Compensator) is also connected in parallel to alleviate the voltage rise of the transmission line that sends power from the photovoltaic power plant to the power system. Mainly, SVC compensates reactive power, thereby controlling the voltage at the interconnection point where each inverter device is connected in parallel to suppress the voltage rise of the transmission line.

  FIG. 13 is a diagram showing a photovoltaic power plant in which a plurality of conventional general inverter devices are connected in parallel.

  Each inverter device A 'converts the DC power generated by the DC power source 1 including the solar battery into AC power and outputs the AC power. A large number of inverter devices A 'are connected in parallel, and the electric power output from each inverter device A' is combined and supplied to the power system B. Each inverter device A 'includes an inverter circuit 2 and a control circuit 3'. The inverter circuit 2 converts a DC voltage input from the DC power source 1 into an AC voltage by switching a switching element (not shown) based on the PWM signal input from the control circuit 3 ′. The control circuit 3 ′ generates and outputs a PWM signal for controlling the inverter circuit 2. The control circuit 3 'includes a reactive power control unit 32'. The reactive power control unit 32 'performs control so that the output reactive power of the inverter device A' becomes a target value. The inverter device A ″ constitutes the SVC and has the same configuration as the inverter device A ′.

  The monitoring device C is for centrally monitoring each inverter device A ′ and the inverter device A ″, and sets a target value of output reactive power of each inverter device A ′, A ″ (for example, see Patent Document 1). ). The monitoring device C causes the inverter device A ″ to compensate the reactive power as much as possible, and causes the inverter devices A ′ to evenly compensate for the amount that the inverter device A ″ cannot compensate. In addition, when the temperature of a certain inverter device A ′ rises or is severe in capacity, the monitoring device C reduces the reactive power to be compensated by the inverter device A ′ and burdens the other inverter device A ′. Let

JP2013-99132A

Reza Olfati-Saber, J. Alex Fax, and Richard M. Murray, "Consensus and Cooperation in Networked Multi-Agent Systems", Proceedings of the IEEE, Vol. 95, No. 1, (2007) Mehran Mesbahi and Magnus Egerstedt, "Graph Theoretic Methods in Multiagent Networks", Princeton (2010)

  However, when the monitoring device C sets the target value of the output reactive power of each inverter device A ′, A ″, the system becomes a large scale, and it is difficult to flexibly cope with the increase / decrease in the inverter devices A ′, A ″. Are vulnerable. That is, it is necessary to provide a monitoring device C and communicate with each inverter device A ′, A ″. In the case of wired communication, the monitoring device C and each inverter device A ′, A ″ are connected by a communication line. There is a need. In the case of wireless communication, it is necessary to prevent radio waves from being blocked by obstacles. Further, when the inverter devices A ′ and A ″ are increased or decreased, it is necessary to change the control program of the monitoring device C. Further, when the monitoring device C fails, there is a problem that the target value cannot be set. Even when one inverter device A ′ (master) having the function of the monitoring device C outputs a target value to the other inverter devices A ′ and A ″ (slave), the same problem occurs.

  The present invention has been conceived under the circumstances described above, and can solve the above-described problems and control reactive power compensated by each inverter device A ′, A ″. The purpose is to provide.

  In order to solve the above problems, the present invention takes the following technical means.

  A control circuit provided by a first aspect of the present invention is a control circuit that controls an inverter circuit included in each inverter device in a power system in which a plurality of inverter devices that are not in a master-slave relationship are connected in parallel. Interconnection point voltage control means for generating a compensation value for controlling the system point voltage to a target value, cooperative correction value generation means for generating a correction value for cooperation with each of the inverter devices, and the compensation value PWM signal generating means for generating a PWM signal based on a correction compensation value obtained by adding the correction value, weighting means for weighting the correction compensation value, and communication means for communicating with at least one other inverter device. The communication unit transmits the weighted correction compensation value to the other inverter device, and the cooperative correction value generation unit transmits the weighted correction value. And 償値, said communication means using a calculation result based on the received compensation value received from the other inverter, and generates the correction value. Note that “not in the master-slave relationship” means that one of the inverter devices (master: master) does not monitor or control the other (slave: slave), but all have equal relationships. Means. The “electric power system” means, for example, a power plant (for example, a mega solar) in which a large number of inverter devices are connected in parallel to perform solar power generation, a wind farm that performs wind power generation, or the like.

  In a preferred embodiment of the present invention, the cooperative correction value generation means includes a calculation means for performing a calculation based on the weighted correction compensation value and the reception compensation value, and a calculation result output by the calculation means. Integrating means for integrating to calculate the correction value.

  In a preferred embodiment of the present invention, the calculation means calculates the calculation result by subtracting the weighted correction compensation value from the reception compensation value and adding all the subtraction results.

  In a preferred embodiment of the present invention, the calculating means subtracts the weighted correction compensation values from the reception compensation values, adds all the subtraction results, and the communication means performs communication. The operation result is calculated by dividing by the number of inverter devices.

  In a preferred embodiment of the present invention, the computing means subtracts the weighted correction compensation value from the reception compensation value, adds all the subtraction results, and multiplies the weighted correction compensation value. Thus, the calculation result is calculated.

  In a preferred embodiment of the present invention, the calculation means subtracts the reception compensation value from the weighted correction compensation value, adds all the subtraction results, and squares the weighted correction compensation value. The result of the operation is calculated by multiplying.

  In a preferred embodiment of the present invention, the weighting means performs weighting by dividing the correction compensation value by a preset weighting value.

  In a preferred embodiment of the present invention, the apparatus further comprises temperature detecting means for detecting the temperature of the inverter circuit, and weighting value setting means for setting a weighting value corresponding to the temperature, wherein the weighting means includes the weighting value. Weighting is performed by dividing the correction compensation value by the weighting value set by the setting means.

  In a preferred embodiment of the present invention, the clock means for outputting the date or time, and the weight value are stored in association with the date or time, and the date or time corresponding to the date or time output by the clock means is stored. Weighting value setting means for setting a weighting value, and the weighting means performs weighting by dividing the correction compensation value by the weighting value set by the weighting value setting means.

  In a preferred embodiment of the present invention, the weighting unit further includes an active power calculating unit that calculates an output active power of the inverter circuit, and a weighting value setting unit that sets a weighting value corresponding to the output active power. Performs weighting by dividing the correction compensation value by the weighting value set by the weighting value setting means.

  The inverter device provided by the second aspect of the present invention includes the control circuit provided by the first aspect of the present invention and an inverter circuit.

  The power system provided by the third aspect of the present invention is characterized in that a plurality of inverter devices provided by the second aspect of the present invention are connected in parallel.

  A control method provided by the fourth aspect of the present invention is a control method for controlling an inverter circuit included in each inverter device in a power system in which a plurality of inverter devices that are not in a master-slave relationship are connected in parallel. A first step of generating a compensation value for controlling the point voltage to a target value; a second step of generating a correction value for cooperating with each of the inverter devices; and adding the correction value to the compensation value A third step of generating a PWM signal based on the corrected compensation value, a fourth step of weighting the correction compensation value, and transmitting the weighted correction compensation value to at least one other inverter device A fifth step and a sixth step of receiving the value transmitted by the other inverter device as a reception compensation value are performed by each inverter device, and the second step is Using the a weighted modified compensation value, said sixth calculation result based on the received compensation value received in the step, and generating the correction value.

  According to the present invention, the cooperative correction value generation means generates a correction value using a calculation result based on the weighted correction compensation value and the reception compensation value. When the cooperative correction value generating means of each inverter device performs this, the weighted correction compensation values of all the inverter devices converge to the same value. Therefore, the correction compensation value of each inverter device is a value corresponding to each weight. Since the output reactive power of each inverter device is controlled based on the correction compensation value, the reactive power corresponding to the weighting can be compensated by each inverter device. Each inverter device only needs to perform mutual communication with at least one inverter device (for example, a device located in the vicinity or a device with which communication has been established). There is no need to communicate with the inverter device. Therefore, the system does not become a big deal. Even when a certain inverter device breaks down, it is only necessary that all other inverter devices can communicate with any one of the inverter devices. Moreover, it can respond flexibly to the increase / decrease of the inverter device.

  Other features and advantages of the present invention will become more apparent from the detailed description given below with reference to the accompanying drawings.

It is a figure for demonstrating the inverter apparatus which concerns on 1st Embodiment. It is a figure which shows the solar power plant which concerns on 1st Embodiment. It is a figure for demonstrating the reactive power control system (interconnection point voltage control system) of an inverter apparatus. It is a figure for demonstrating the connection point voltage control system of the whole electric power system. 3 is a graph representing the power system shown in FIG. It is a figure showing the control system of the connection point voltage of the whole electric power system which concerns on 1st Embodiment. It is a figure for demonstrating the internal structure of a current control part. It is a figure which shows the simulation result which confirmed the fluctuation | variation suppression of the connection point voltage in an electric power system. It is a figure which shows the simulation result which confirmed the fluctuation | variation suppression of the connection point voltage in an electric power system. It is a figure for demonstrating the inverter apparatus which concerns on 2nd Embodiment. It is a figure for demonstrating the inverter apparatus which concerns on 3rd Embodiment. It is a figure for demonstrating the inverter apparatus which concerns on 4th Embodiment. It is a figure which shows the solar power plant in which the conventional general inverter apparatus was connected in multiple numbers.

  Hereinafter, embodiments of the present invention will be specifically described with reference to the drawings, taking as an example a case where a control circuit according to the present invention is used in an inverter device of a solar power plant.

  FIG. 1 is a diagram for explaining the inverter device according to the first embodiment. FIG. 2 is a diagram illustrating a photovoltaic power plant (power system) in which a plurality of inverter devices according to the first embodiment are connected in parallel.

  The inverter device A is a so-called power conditioner, and includes an inverter circuit 2, a control circuit 3, a current sensor 4, a voltage sensor 5, and a DC voltage sensor 6, as shown in FIG. The inverter device A converts the DC power output from the DC power source 1 into AC power by the inverter circuit 2 and outputs the AC power. Although not shown, a transformer for boosting (or stepping down) the AC voltage is provided on the output side of the inverter circuit 2.

  Further, as shown in FIG. 2, the inverter device A is connected in parallel with the other inverter device A. FIG. 2 shows a state where five inverter devices A (A1 to A5) are connected. In the actual power system, more inverter devices A are connected, but for the sake of simplicity of explanation, extremely few cases are shown. In the present embodiment, the inverter device A5 constitutes the SVC. The DC power source 1 is not connected to the inverter device A5, and the capacitor at the input end has a large capacity.

  The arrows shown in FIG. 2 indicate that communication is being performed. That is, the inverter device A1 performs mutual communication only with the inverter device A2, and the inverter device A2 performs mutual communication only with the inverter device A1 and the inverter device A3. The inverter device A3 communicates only with the inverter device A2 and the inverter device A4, the inverter device A4 communicates only with the inverter device A3 and the inverter device A5, and the inverter device A5 communicates with the inverter device A4. Only doing mutual communication.

  Returning to FIG. 1, the DC power source 1 outputs DC power and includes a solar cell. A solar cell generates direct-current power by converting solar energy into electrical energy. The DC power source 1 outputs the generated DC power to the inverter circuit 2. Note that the DC power source 1 is not limited to one that generates DC power from a solar cell. For example, the DC power source 1 may be a fuel cell, a storage battery, an electric double layer capacitor, a lithium ion battery, or AC power generated by a diesel engine generator, a micro gas turbine generator, a wind turbine generator, or the like. It may be a device that converts to DC power and outputs it.

  The inverter circuit 2 converts DC power input from the DC power source 1 into AC power and outputs the AC power. The inverter circuit 2 includes a PWM control inverter and a filter (not shown). The PWM control inverter is a three-phase inverter provided with three sets of six switching elements (not shown). Based on the PWM signal input from the control circuit 3, each switching element is switched on and off to generate DC power. Convert to AC power. The filter removes high frequency components due to switching. The inverter circuit 2 is not limited to this. For example, the PWM control inverter may be a single-phase inverter or a multi-level inverter. Further, the present invention is not limited to PWM control, and other methods such as phase shift control may be used.

  The current sensor 4 detects an instantaneous value of the three-phase output current of the inverter circuit 2. The current sensor 4 digitally converts the detected instantaneous value and outputs it to the control circuit 3 as current signals Iu, Iv, Iw (the three current signals may be collectively described as “current signal I”). . The voltage sensor 5 detects an instantaneous value of the three-phase interconnection point voltage of the inverter device A. The voltage sensor 5 digitally converts the detected instantaneous value, calculates an effective value, and outputs it to the control circuit 3 as a voltage signal V. The DC voltage sensor 6 detects the input voltage of the inverter circuit 2. The DC voltage sensor 6 digitally converts the detected voltage and outputs it to the control circuit 3 as a voltage signal Vdc.

  The control circuit 3 controls the inverter circuit 2 and is realized by, for example, a microcomputer. The control circuit 3 according to the present embodiment controls the input voltage of the inverter circuit 2, the connection point voltage, and the output current of the inverter circuit 2. Among these, about the connection point voltage, all the inverter apparatuses A (A1-A5) (refer FIG. 2) connected to the electric power system control in cooperation.

  Below, the control system of the connection point voltage which concerns on this invention is demonstrated with reference to FIGS.

  FIG. 3 is a diagram for explaining a reactive power control system (interconnection point voltage control system) of the inverter device A.

FIG. 3A shows a model of the inverter device A. The change amount of the active power output from the inverter device A is ΔP, the change amount of the reactive power is ΔQ, the change amounts of the d-axis component and the q-axis component of the output current of the inverter device A are ΔId and ΔIq (each target value is ΔId ^* And ΔIq ^* ), the input voltage is Vdc (target value is Vdc ^* ), and the interconnection point voltage is V (target value is V ^* ). The d-axis component and the q-axis component are two-phase components of the rotating coordinate system after being converted by a three-phase / two-phase converting process and a rotating coordinate converting process described later. Assuming that the internal phase of the inverter device A completely follows the phase of the interconnection point voltage, the q-axis component of the output voltage is Vq = 0 and the d-axis component is Vd = V.
ΔP = Vd · ΔId + Vq · ΔIq = V · ΔId
ΔQ = Vd · ΔIq−Vq · ΔId = V · ΔIq
It has become.

  The dynamics of the current control system, the PWM and the inverter main circuit can be ignored because they are faster than the dynamics of the power control system. FIG. 3B is a model approximated by ignoring these. FIG. 3C shows a model in which the active power control system is ignored from the model shown in FIG. 3B and only the reactive power control system is focused.

FIG. 4 is a diagram for explaining an interconnection point voltage control system of the entire power system. The reactive power output from each of the inverter devices A1 to A5 is changed by ΔQ ₁ to ΔQ ₅ respectively, and the reactive power supplied to the interconnection point is changed by a change amount ΔQ obtained by adding these. The interconnection point voltage V fluctuates due to fluctuations in the reactive power Q supplied and fluctuations in the active power P. These are shown in FIG. 4 (a). R and X are the resistance component and reactance component of the line impedance of the transmission line. Further, the fluctuation (disturbance) ΔP of the active power includes a fluctuation due to a load fluctuation or a change in the output of the solar cell.

  If the multiplication of V performed in each inverter device A is modified so as to multiply after the addition, FIG. 4A to FIG. 4B can be obtained. FIG. 4B shows a system that suppresses fluctuations in the interconnection point voltage by adjusting the reactive power of each inverter device A. However, in this case, since each inverter device A does not output reactive power in cooperation, the reactive power output by each inverter device A is determined by an internally set gain, an arrangement location, and the like. . For example, it is impossible to make the inverter device A5 compensate the reactive power as much as possible and to make the inverter devices A1 to A4 evenly compensate for the amount that the inverter device A5 cannot compensate, or to compensate according to the capacity of each inverter device A.

  Next, a method for the inverter devices A to output reactive power in cooperation with each other will be described.

  There is known a consensus algorithm for converging a plurality of control target state values to the same value (see Non-Patent Documents 1 and 2). When each control target is a vertex and the communication state between each control target is expressed as a graph, if the graph is connected by an undirected graph in the graph theory, the state of each control target is determined using a consensus algorithm. The values can converge to the same value to achieve consensus. For example, when the power system shown in FIG. 2 is expressed in a graph, it is as shown in FIG. The vertices A1 to A5 represent the inverter devices A1 to A5, respectively, and the sides with arrows represent the communication states between the inverter devices. Each side indicates that mutual communication is performed, and the graph is an undirected graph. Since a communication path exists for any two vertices of the graph, the graph is connected. Therefore, in the case of the power system shown in FIG. 2, consensus can be achieved. In addition, since the graphs shown in FIGS. 5B and 5C are also connected by undirected graphs, the communication states of the inverter devices A1 to A5 in the power system of FIG. Consensus can be achieved. In this way, the inverter device A performs mutual communication with at least one inverter device A among the inverter devices A connected to the power system, and any two inverter devices A connected to the power system. As long as a communication path exists (hereinafter, this state is referred to as a “connected state”), it is necessary to communicate with all inverter devices A connected to the power system. Absent.

In the present embodiment, the value of the state of each control target is not converged to the same value, but weighting is performed to converge the weighted value to the same value. That is, the weighting value W _i of each inverter device A is set in advance, weighting is performed by dividing the state value by the weighting value W _i , and the weighted value is converged to the same value. Thus, the value of each state converges to a value corresponding to the weighting value W _i. For example, if W ₁ = W ₂ = W ₃ = W ₄ = 1 and W ₅ = 10, the value of the state of the inverter device A ₅ converges to 10 times the value of the state of the other inverter device A. To do.

  FIG. 6 is a system in which a consensus algorithm and weighting are added to the system shown in FIG. 4B, and each inverter apparatus A cooperates to compensate for reactive power that is a share of the system, thereby connecting the connection point voltage. The control system which suppresses the fluctuation | variation of is represented.

By the consensus algorithm, the compensation value ΔIq _i ′ (= ΔIq _i / W _i ) obtained by dividing the compensation value ΔIq _i by the weighting value W _i converges to the same value. When the convergence value is ΔIqα ′, each inverter device A _i compensates reactive power according to the compensation value ΔIq _i = W _i · ΔIqα ′. That is, the reactive power corresponding to the weight value W _i is compensated. Therefore, for example, if W ₁ = W ₂ = W ₃ = W ₄ = 1 and W ₅ = 10, the inverter device A ₅ can compensate for 10 times the reactive power of the other inverter devices A.

  Returning to FIG. 1, the control circuit 3 performs PWM based on the current signal I input from the current sensor 4, the voltage signal V input from the voltage sensor 5, and the voltage signal Vdc input from the DC voltage sensor 6. A signal is generated and output to the inverter circuit 2. The control circuit 3 includes an input voltage control unit 31, an interconnection point voltage control unit 32, a cooperative correction value generation unit 33, an adder 34, a current control unit 35, a command signal generation unit 36, a PWM signal generation unit 37, and a weighting unit 38. , And a communication unit 39.

The input voltage control unit 31 is for controlling the input voltage of the inverter circuit 2. The input voltage control unit 31 controls the input power by controlling the input voltage, thereby controlling the output active power of the inverter circuit 2. The input voltage control unit 31 receives a deviation ΔVdc between the voltage signal Vdc input from the DC voltage sensor 6 and the input voltage target value Vdc ^{* that} is the target value, performs PI control (proportional integration control), and active power Output the compensation value. The active power compensation value is input to the current control unit 35 as the target value Id ^* . The control of the input voltage control unit 31 is not limited to PI control, and other control such as I control (integration control) may be performed.

The connection point voltage control unit 32 is for controlling the connection point voltage. The interconnection point voltage control unit 32 controls the interconnection point voltage by controlling the reactive power output from the inverter circuit 2. The interconnection point voltage control unit 32 receives a deviation ΔV between the voltage signal V input from the voltage sensor 5 and the interconnection point voltage target value V ^{* that} is the target value, performs PI control, and reacts to the reactive power compensation value. Is output. The reactive power compensation value is input to the adder 34. The control of the interconnection point voltage control unit 32 is not limited to PI control, and other control such as I control (integration control) may be performed.

  The cooperation correction value generation unit 33 generates a cooperation correction value for cooperation with each inverter device A. Details of the cooperative correction value generation unit 33 will be described later.

The adder 34 adds the cooperative correction value input from the cooperative correction value generation unit 33 to the reactive power compensation value input from the interconnection point voltage control unit 32 to calculate the correction compensation value ΔIq _i . The correction compensation value ΔIq _i is input to the current control unit 35 as the target value Iq ^* . The adder 34 also outputs the calculated correction compensation value ΔIq _i to the weighting unit 38.

  The current control unit 35 is for controlling the output current of the inverter circuit 2. The current control unit 35 generates a current compensation value based on the current signal I input from the current sensor 4 and outputs the current compensation value to the command signal generation unit 36.

  FIG. 7 is a functional block diagram for explaining the internal configuration of the current control unit 35.

  The current control unit 35 includes a three-phase / two-phase conversion unit 351, a rotation coordinate conversion unit 352, an LPF 353, an LPF 354, a PI control unit 355, a PI control unit 356, a stationary coordinate conversion unit 357, and a two-phase / three-phase conversion unit. 358.

  The three-phase / two-phase conversion unit 351 performs a so-called three-phase / two-phase conversion process (αβ conversion process). The three-phase / two-phase conversion process is a process that converts a three-phase AC signal into an equivalent two-phase AC signal. The three-phase AC signal is a stationary orthogonal coordinate system (hereinafter referred to as “static coordinate system”). In this case, the signals are decomposed into orthogonal α-axis and β-axis components and the components of the respective axes are added to each other, thereby converting into an AC signal of the α-axis component and an AC signal of the β-axis component. The three-phase / two-phase converter 351 converts the three-phase current signals Iu, Iv, and Iw input from the current sensor 4 into an α-axis current signal Iα and a β-axis current signal Iβ, and a rotational coordinate converter 352. Output to.

The conversion process performed by the three-phase / two-phase conversion unit 351 is represented by a determinant represented by the following equation (1).

  The rotation coordinate conversion unit 352 performs a so-called rotation coordinate conversion process (dq conversion process). The rotation coordinate conversion process is a process of converting a two-phase signal in the stationary coordinate system into a two-phase signal in the rotation coordinate system. The rotating coordinate system is an orthogonal coordinate system having orthogonal d-axis and q-axis and rotating in the same rotational direction at the same angular velocity as the fundamental wave of the interconnection point voltage. The rotating coordinate conversion unit 352 converts the α-axis current signal Iα and β-axis current signal Iβ of the stationary coordinate system input from the three-phase / two-phase conversion unit 351 based on the phase θ of the fundamental wave of the interconnection point voltage. It is converted into a d-axis current signal Id and a q-axis current signal Iq in the rotating coordinate system and output.

The conversion process performed by the rotation coordinate conversion unit 352 is expressed by a determinant represented by the following expression (2).

  LPF 353 and LPF 354 are low-pass filters and pass only the DC components of d-axis current signal Id and q-axis current signal Iq, respectively. Through the rotation coordinate conversion process, the fundamental wave components of the α-axis current signal Iα and the β-axis current signal Iβ are converted into DC components of the d-axis current signal Id and the q-axis current signal Iq, respectively. That is, the LPF 353 and the LPF 354 remove unbalanced components and harmonic components and pass only the fundamental wave components.

The PI control unit 355 performs PI control based on the deviation between the DC component of the d-axis current signal Id and the target value, and outputs a current compensation value Xd. The active power compensation value input from the input voltage control unit 31 is used as the target value Id ^* of the d-axis current signal Id. The PI control unit 356 performs PI control based on the deviation between the DC component of the q-axis current signal Iq and the target value Iq ^*, and outputs a current compensation value Xq. The correction compensation value ΔIq _i input from the adder 34 is used as the target value Iq ^* of the q-axis current signal Iq.

  The stationary coordinate conversion unit 357 converts the current compensation values Xd and Xq respectively input from the PI control unit 355 and the PI control unit 356 into the current compensation values Xα and Xβ of the stationary coordinate system. In contrast to 352, the conversion processing is performed. The static coordinate conversion unit 357 performs a so-called static coordinate conversion process (inverse dq conversion process), and calculates the current compensation values Xd and Xq of the rotating coordinate system based on the phase θ and the current compensation value Xα of the static coordinate system. , Xβ.

The conversion process performed by the stationary coordinate conversion unit 357 is represented by a determinant represented by the following expression (3).

  The two-phase / three-phase conversion unit 358 converts the current compensation values Xα and Xβ input from the stationary coordinate conversion unit 357 into three-phase current compensation values Xu, Xv, and Xw. The two-phase / three-phase conversion unit 358 performs a so-called two-phase / three-phase conversion process (reverse αβ conversion process), and performs a conversion process opposite to the three-phase / two-phase conversion unit 351.

The conversion process performed by the two-phase / three-phase conversion unit 358 is represented by a determinant represented by the following equation (4).

  In addition, although this embodiment demonstrated the case where the inverter apparatus A was a three-phase system, a single phase system may be sufficient. In the case of a single-phase system, the current control unit 35 may control the single-phase current signal that detects the output current of the inverter circuit 2.

  The command signal generator 36 generates a command signal based on the current compensation values Xu, Xv, Xw input from the current controller 35 and outputs the command signal to the PWM signal generator 37.

  The PWM signal generation unit 37 generates a PWM signal. The PWM signal generation unit 37 generates a PWM signal by a triangular wave comparison method based on the carrier signal and the command signal input from the command signal generation unit 36. For example, a pulse signal that is high when the command signal is larger than the carrier signal and low when the command signal is equal to or less than the carrier signal is generated as a PWM signal. The generated PWM signal is output to the inverter circuit 2. The PWM signal generation unit 37 is not limited to the case where the PWM signal is generated by the triangular wave comparison method. For example, the PWM signal generation unit 37 may generate the PWM signal by a hysteresis method.

The weighting unit 38 weights the correction compensation value ΔIq _i input from the adder 34. A weighting value W _i is set in the weighting unit 38 in advance. The weighting unit 38 outputs the weighted correction compensation value ΔIq _i ′ obtained by dividing the correction compensation value ΔIq _i by the weighting value W _i to the communication unit 39 and the cooperative correction value generation unit 33.

The weight value W _i is set in advance according to the amount of reactive power to be compensated by the inverter device A. For example, in order to compensate as much as possible reactive power to the SVC of the inverter device A5 (see FIG. 2), the weighting value W ₅ of the inverter device A5, the weighting value of the other inverter apparatuses Al to A4 W ₁ to _W-4 Set a larger value than. Further, the weight values W _{1 to} W ₄ may be the same value if the reactive power is evenly compensated by the inverter devices A1 to A4, and the capacities if the capacity of the inverter devices A1 to A4 are different from each other. The value may be set according to. It is also possible to set the weighting value W _i in accordance with the size of the solar cell panel is connected to the inverter A. That is, when the connected solar cell panels are small, the generated power is small and there is room for the capacity of the inverter device A. Therefore, the weighting value _Wi is increased in order to compensate for a large amount of reactive power. Conversely, when the connected solar cell panel is large, the weighting value _Wi is decreased.

The communication unit 39 communicates with the control circuit 3 of the other inverter device A. The communication unit 39 receives the weighted correction compensation value ΔIq _i ′ from the weighting unit 38 and transmits it to the communication unit 39 of another inverter device A. In addition, the communication unit 39 outputs the compensation value ΔIq _j ′ received from the communication unit 39 of the other inverter device A to the cooperative correction value generation unit 33. Note that the communication method is not limited, and may be wired communication or wireless communication.

For example, when the inverter device A is the inverter device A2 shown in FIG. 2, the communication unit 39 transmits the weighted correction compensation value ΔIq ₂ ′ to the communication units 39 of the inverter devices A1 and A3, and the communication unit of the inverter device A1. 39 receives the compensation value ΔIq ₁ ′, and receives the compensation value ΔIq ₃ ′ from the communication unit 39 of the inverter device A3.

  Next, details of the cooperative correction value generation unit 33 will be described.

The cooperative correction value generation unit 33 receives the weighted correction compensation value ΔIq _i ′ (hereinafter abbreviated as “compensation value ΔIq _i ′”) input from the weighting unit 38 and the communication unit 39. Using the compensation value ΔIq _j ′ of the other inverter device A, a cooperative correction value for cooperating with each inverter device A is generated. Even if the compensation value ΔIq _i ′ and the compensation value ΔIq _j ′ are different, the calculation value in the cooperative correction value generation unit 33 is repeated so that the compensation value ΔIq _i ′ and the compensation value ΔIq _j ′ are a common value. Converge to. As shown in FIG. 1, the cooperative correction value generation unit 33 includes a calculation unit 331, a multiplier 332, and an integrator 333.

The computing unit 331 performs computation based on the following equation (5). That is, the calculation unit 331 subtracts the compensation value ΔIq _i ′ input from the weighting unit 38 from each compensation value ΔIq _j ′ input from the communication unit 39, and adds the calculation result u _i obtained by adding all the subtraction results. The result is output to the multiplier 332.

For example, if the inverter apparatus A of the inverter device A2 (see FIG. 2), computation unit 331 performs calculation of the following equation (6), and outputs the operation result u _2.

The multiplier 332 multiplies the calculation result u _i input from the calculation unit 331 by a predetermined coefficient ε and outputs the result to the integrator 333. The coefficient ε is a value that satisfies 0 <ε <1 / d _max and is set in advance. d _max is the _maximum of all the inverter devices A connected to the power system among d _i that is the number of other inverter devices A with which the communication unit 39 communicates. That is, among the inverter devices A connected to the power system, the number of internal phases θ _j input to the communication unit 39 of those communicating with the largest number of other inverter devices A. Incidentally, the coefficient epsilon, operation result u _i becomes too large (small), in order to suppress the fluctuation of the cooperative correction value becomes too large, it is intended to be multiplied to the calculation result u _i. Therefore, when the process in the cooperative correction value generation unit 33 is a continuous time process, it is not necessary to provide the multiplier 332.

  The integrator 333 generates and outputs a cooperative correction value by integrating the value input from the multiplier 332. The integrator 333 generates a cooperative correction value by adding the value input from the multiplier 332 to the previously generated cooperative correction value. The cooperative correction value is output to the adder 34.

  In the present embodiment, the case where the control circuit 3 is realized as a digital circuit has been described, but it may be realized as an analog circuit. Further, the processing performed by each unit may be designed by a program, and the computer may function as the control circuit 3 by executing the program. The program may be recorded on a recording medium and read by a computer.

In the present embodiment, the cooperative correction value generation unit 33 uses the compensation value ΔIq _i ′ input from the weighting unit 38 and the compensation value ΔIq _j ′ of the other inverter device A input from the communication unit 39. Then, a cooperative correction value is generated. When the compensation value ΔIq _i ′ is larger than the arithmetic mean value of each compensation value ΔIq _j ′, the computation result u _i output from the computation unit 331 becomes a negative value. Then, the cooperative correction value becomes small, and the compensation value ΔIq _i ′ also becomes small. On the other hand, when the compensation value ΔIq _i ′ is smaller than the arithmetic mean value of each compensation value ΔIq _j ′, the computation result u _i output from the computation unit 331 becomes a positive value. As a result, the cooperative correction value increases and the compensation value ΔIq _i ′ also increases. That is, the compensation value ΔIq _i ′ approaches the arithmetic average value of each compensation value ΔIq _j ′. By performing this process in each inverter device A, the compensation value ΔIq _i ′ of each inverter device A converges to the same value. It has been mathematically proved that the value of the state to be controlled converges to the same value by using the consensus algorithm (see Non-Patent Documents 1 and 2). In the case of the present embodiment, the compensation value ΔIq _i ′ is the value of the state to be controlled.

  Hereinafter, in the power system shown in FIG. 2, a description will be given of a simulation in which each inverter apparatus A confirms that the fluctuation of the interconnection point voltage is suppressed by cooperatively compensating reactive power.

The proportional gain Kp ₁ of the connection point voltage control unit 32 of the inverter device A1 is “0.5”, the integral gain Ki ₁ is “5”, and the proportional gain Kp ₂ of the connection point voltage control unit 32 of the inverter device A2 is “ 1 ”, integral gain Ki ₂ is“ 8 ”, proportional gain Kp ₃ of interconnection point voltage control unit 32 of inverter device A3 is“ 1 ”, integral gain Ki ₃ is“ 4 ”, and interconnection point voltage of inverter device A4 The proportional gain Kp ₄ of the control unit 32 is “0.2”, the integral gain Ki ₄ is “2”, the proportional gain Kp ₅ of the interconnection point voltage control unit 32 of the inverter device A5 is “0.3”, and the integral gain Ki ₅ is “3”, and the weighting values W _{1 to} W ₅ set in the weighting unit 38 of the inverter devices A1 to A5 are set to W ₁ = W ₂ = W ₃ = W ₄ = 1 and W ₅ = 10. . FIGS. 8 and 9 show the results of the simulation, and FIG. 8 shows a configuration in which the cooperation is not performed (that is, the configuration without the cooperation correction value generation unit 33, the weighting unit 38, and the communication unit 39 shown in FIG. 1). FIG. 9 shows a case where cooperation is performed (that is, the configuration shown in FIG. 1).

In both cases, after 1 second from the start of the simulation, the fluctuation of the interconnection point voltage 0.05 [p. u. ] Was injected. In the case of FIG. 9, the weighting value W ₁ of the inverter device A1 is changed from “1” to “0.2” 50 seconds after the simulation is started. FIG. 8A and FIG. 9A show the time change of the interconnection point voltage deviation ΔV (= V ^* −V). FIGS. 8B and 9B show temporal changes in the correction compensation values ΔIq _{1 to} ΔIq ₅ output from the adders 34 of the inverter devices A1 to A5, respectively.

In the case of FIG. 8, fluctuations in the interconnection point voltage can be immediately suppressed, but the values of the correction compensation values ΔIq _{1 to} ΔIq ₅ are fixed to values corresponding to the respective gains. Therefore, the reactive power compensated by each inverter device A1 to A5 cannot be controlled. In the case of FIG. 8B, the inverter device A2 compensates for the most reactive power, and the inverter device A5 that should compensate for the most reactive power compensates for the reactive power only slightly.

In the case of FIG. 9 as well, as in the case of FIG. 8, the fluctuation of the interconnection point voltage can be immediately suppressed. Further, in the case of FIG. 9, each inverter A1~A5 compensates the reactive power according to the respective weighting value W ₁ to _W-5. That is, as shown in FIG. 9B, the correction compensation values ΔIq _{1 to} ΔIq ₄ converge to the same value in about 30 seconds from the start of the simulation, and the correction compensation value ΔIq ₅ is corrected to the correction compensation values ΔIq _{1 to} ΔIq. _It converges to a value about 10 times the convergence value of ₄ . Therefore, the inverter device A5 compensates about 10 times the reactive power of the inverter devices A1 to A4. Further, after changing the weighting value W ₁ after 50 seconds from the start of the simulation, the correction compensation value ΔIq ₁ becomes large (ie, the reactive power to be compensated is small), and the correction compensation values ΔIq _{2 to} ΔIq _{5 become} small (ie, Many reactive power to compensate). That is, the inverter devices A2 to A5 bear a part of the reactive power compensated by the inverter device A1.

A simulation was also performed for each of the cases where the communication state of the power system of FIG. 2 is the graphs shown in FIGS. In these cases, as in the case of FIG. 9, the variation of the interconnection point voltage can be immediately suppressed, the inverter device A1~A5 compensation reactive power in accordance with the weighting value W ₁ to _W-5, respectively I was able to confirm. Further, in the case of the graph of FIG. 5B, the time until the correction compensation values ΔIq _{1 to} ΔIq ₅ converge is shorter than in the case of FIG. 9 (in the case of the graph of FIG. 5A). In the case of the graph (c), the time until convergence is further shortened. The simulation results are not shown.

According to the present embodiment, the cooperative correction value generation unit 33 generates a cooperative correction value using a calculation result based on the compensation value ΔIq _i ′ and the compensation value ΔIq _j ′. When the cooperative correction value generation unit 33 of each inverter device A1 to A5 performs this, the compensation value ΔIq _i ′ of all the inverter devices A1 to A5 converges to the same value. Therefore, the correction compensation values ΔIq _i of the inverter devices A1 to A5 are values corresponding to the respective weighting values W _{1 to} W ₅ . Since the output reactive power of each inverter device A1 to A5 is controlled based on the correction compensation value ΔIq _i , the reactive power corresponding to the weighted values W _{1 to} W ₅ can be compensated for each inverter device A1 to A5.

  In addition, each inverter device A connected to the power system performs mutual communication only with at least one inverter device A (for example, a device that is located in the vicinity or that has established communication), and the power system It is only necessary that the connection state is established, and it is not necessary for one inverter device A or the monitoring device to communicate with all the other inverter devices A. Therefore, the system does not become a big deal. Moreover, even when a certain inverter device A fails or when a certain inverter device A is reduced, all the other inverter devices A can communicate with any one of the inverter devices A, and the power system is in a connected state. Good. Further, when the number of inverter devices A is increased, it is only necessary that the inverter device A performs mutual communication with at least one inverter device A. Therefore, the increase / decrease in the inverter device A can be flexibly dealt with.

In the first embodiment, the case where the arithmetic expression set in the arithmetic unit 331 is the above expression (5) has been described, but the present invention is not limited to this. Another equation for converging the compensation value ΔIq _i ′ of the inverter devices A1 to A5 to the same value may be used.

For example, even when the calculation formula set in the calculation unit 331 is the following formula (7), the compensation value ΔIq _i ′ can be converged to the same value. d _i is the number of other inverter devices A with which the communication unit 39 communicates, that is, the number of compensation values ΔIq _j ′ input to the communication unit 39.

Further, even when the calculation formulas set in the calculation unit 331 are the following formulas (8) to (10), the compensation value ΔIq _i ′ can be converged to the same value.

  In the said 1st Embodiment, although the case where the fixed value was preset as a weighting value of each inverter apparatus A was demonstrated, it is not restricted to this. The weighting value of each inverter device A may be changeable.

FIG. 10 is a diagram for explaining an inverter device A according to the second embodiment. In FIG. 10, only the control circuit 3 is illustrated, and the description of the control circuit 3 that is common to the control circuit 3 according to the first embodiment (see FIG. 1) is omitted. The inverter device A according to the second embodiment differs from the inverter device A according to the first embodiment in that the weighting value _Wi is changed according to the temperature of the inverter circuit 2. As shown in FIG. 10, the inverter device A according to the second embodiment further includes a temperature detection unit 40 and a weight value setting unit 41 in the control circuit 3.

Although not shown, a temperature sensor is attached to the heat sink of the inverter circuit 2. The temperature detection unit 40 detects the temperature detected by the temperature sensor, and outputs the detected temperature to the weight value setting unit 41. The weight value setting unit 41 sets the weight value W _i corresponding to the temperature input from the temperature detection unit 40 in the weight unit 38. When the temperature of the inverter circuit 2 is high, it is considered that the inverter circuit 2 is burdened, so it is better to reduce the burden for reactive power compensation. Therefore, the weight value setting unit 41 sets the weight value W _i to be set to a smaller value as the temperature input from the temperature detection unit 40 increases. In the present embodiment, compared to a threshold value that sets the temperature input from the temperature detecting section 40 in advance, the temperature is changed to a smaller value the weighting value W _i if the threshold is greater than. Incidentally, may be set a plurality of threshold values, the weighting value W _i may be stepwise changed. Further, a calculation formula for linearly calculating the weighted value W _i from the temperature input from the temperature detection unit 40 may be set, and the calculation result of the calculation formula may be set.

According to the second embodiment, when an excessive load is applied to the inverter circuit 2 of the inverter device A and the temperature of the inverter circuit 2 becomes high, the weighting value _Wi is changed to a small value. Thereby, the reactive power which the said inverter apparatus A compensates is reduced, and the other inverter apparatus A bears the compensation of the reactive power by that amount. Accordingly, the burden on the inverter circuit 2 of the inverter device A is reduced. Also in the second embodiment, the same effects as in the first embodiment can be obtained.

FIG. 11 is a diagram for explaining an inverter device A according to the third embodiment. FIG. 11A shows only the control circuit 3 of the inverter device A according to the third embodiment, and the common part of the control circuit 3 with the control circuit 3 according to the first embodiment (see FIG. 1). Is omitted. The inverter device A according to the third embodiment is different from the inverter device A according to the first embodiment in that the weighting value _Wi is changed according to the date and time. As shown in FIG. 11A, the inverter device A according to the third embodiment further includes a clock unit 42 and a weight value setting unit 41 ′ in the control circuit 3.

  The clock unit 42 outputs the date and time (hereinafter collectively referred to as “date and time”) to the weight value setting unit 41 ′.

The weighting value setting unit 41 ′ sets the weighting value W _i corresponding to the date and time input from the clock unit 42 in the weighting unit 38. Since the position of the sun changes with time, the shadowed area such as a building changes with time. In addition, since the sun's orbit changes depending on the date (for example, the sun's orbit differs greatly between the summer solstice and the winter solstice), the shadowed area such as a building also changes depending on the date. When the solar cell panel connected to the inverter device A is shaded, the electric power generated by the solar cell panel is reduced. In this case, since there is room for the capacity of the inverter device A, a large amount of reactive power may be compensated. In this embodiment, by investigating the solar panel shadows such advance, the weighting value W _i of the inverter device A shadow takes solar panel is connected, to switch to a larger value in the shadow takes time ing. In addition, the weighting value _Wi is increased as the shadowed area increases. Specifically, the weight value setting unit 41 ′ stores a table of weight values W _i shown in FIG. 11B in the memory, and sets the weight value W _i corresponding to the date and time input from the clock unit 42. Read and set. In FIG.11 (b), since a shadow is applied to a solar cell panel from 9:00 to 12:00 in January, a larger value than usual is set at this date and time. The weight value W _i may be changed only by time regardless of the date, or may be changed only by date regardless of the time.

According to the third embodiment, on the date and time when the solar cell panel connected to the inverter device A is shaded, the weighting value _Wi is changed to a larger value, and more reactive power than usual can be compensated. In the third embodiment, the same effects as in the first embodiment can be obtained.

FIG. 12 is a diagram for explaining an inverter device A according to the fourth embodiment. In FIG. 12, the description of the control circuit 3 common to the control circuit 3 according to the first embodiment (see FIG. 1) is omitted. The inverter device A according to the fourth embodiment is different from the inverter device A according to the first embodiment in that the weighting value _Wi is changed according to the output active power of the inverter circuit 2. As shown in FIG. 12, the inverter device A according to the fourth embodiment further includes an active power calculation unit 43 and a weight value setting unit 41 ″ in the control circuit 3.

  The active power calculation unit 43 calculates the output active power P of the inverter circuit 2, and the current signals Iu, Iv, Iw input from the current sensor 4 and the three-phase continuous signal input from the voltage sensor 5. The output active power P is calculated from the voltage signals Vu, Vv, Vw obtained by digitally converting the instantaneous value of the system point voltage. The active power calculation unit 43 outputs the calculated output active power P to the weighting value setting unit 41 ″.

Weighting value setting unit 41 "when setting the weighting value W _i corresponding to the output effective power P input from the effective power calculator 43 to the weighting section 38. Output active power P is large, the capacity of the inverter apparatus A In the present embodiment, the reactive power to be compensated is reduced. That is, the weight value setting unit 41 ″ uses the output active power P input from the active power calculation unit 43 in advance. compared to set to have a threshold, the output active power P is changed to a smaller value the weighting value W _i if the threshold is greater than. Incidentally, may be set a plurality of threshold values, the weighting value W _i may be stepwise changed. Alternatively, a calculation formula for linearly calculating the weighted received value W _i from the output active power P may be set, and a calculation result of the calculation formula may be set.

According to the fourth embodiment, when the output active power P of the inverter device A is large, the weighting value _Wi is changed to a small value. Thereby, the reactive power which the said inverter apparatus A compensates is reduced, and the other inverter apparatus A bears the compensation of the reactive power by that amount. Accordingly, the burden on the inverter circuit 2 of the inverter device A is reduced. Moreover, also in 4th Embodiment, there can exist an effect similar to 1st Embodiment.

In the fourth embodiment, the case where the weighting value _Wi is decreased when the output active power P of the inverter device A is large has been described, but the present invention is not limited to this. Conversely, as the output active power P increases, the weight value W _i may be increased to increase the output reactive power, and the power factor of each inverter device A may be matched.

  The control circuit, inverter device, power system, and control method according to the present invention are not limited to the above-described embodiments. The specific configuration of each part of the control circuit, the inverter device, the power system, and the control method according to the present invention can be varied in design in various ways.

A, A1-A4 Inverter device A5 Inverter device (SVC)
DESCRIPTION OF SYMBOLS 1 DC power supply 2 Inverter circuit 3 Control circuit 31 Input voltage control part 32 Linkage point voltage control part 33 Cooperation correction value generation part 331 Calculation part 332 Multiplier 333 Integrator 34 Adder 35 Current control part 351 Three-phase / two-phase conversion Unit 352 rotational coordinate conversion unit 353, 354 low pass filter 355, 356 PI control unit 357 stationary coordinate conversion unit 358 two-phase / three-phase conversion unit 36 command signal generation unit 37 PWM signal generation unit 38 weighting unit 39 communication unit 40 temperature detection unit 41, 41 ′, 41 ″ Weight value setting unit 42 Clock unit 43 Active power calculation unit 4 Current sensor 5 Voltage sensor 6 DC voltage sensor B Power system

Claims (13)

In a power system in which a plurality of inverter devices that are not in a master-slave relationship are connected in parallel, a control circuit that is provided in one of the plurality of inverter devices and controls the inverter circuit of the inverter device. ,
A connection point voltage control means for generating a compensation value for controlling the connection point voltage to a target value;
Cooperative correction value generation means for generating a correction value for cooperation with each of the inverter devices;
PWM signal generation means for generating a PWM signal based on a correction compensation value obtained by adding the correction value to the compensation value;
Weighting means for weighting the correction compensation value;
Communication means for communicating with at least one other inverter device;
With
The communication means transmits a weighted correction compensation value to the other inverter device,
The cooperative correction value generation means generates the correction value using a calculation result based on the weighted correction compensation value and the reception compensation value received by the communication means from the other inverter device.
A control circuit characterized by that. The cooperative correction value generating means
A calculation means for performing a calculation based on the weighted correction compensation value and the reception compensation value;
Integrating means for calculating the correction value by integrating the calculation result output by the calculating means;
The control circuit according to claim 1, comprising: The calculation means subtracts the weighted correction compensation value from the reception compensation value, and calculates the calculation result by adding all the subtraction results.
The control circuit according to claim 2. The arithmetic means subtracts the weighted correction compensation value from the reception compensation value, adds all the subtraction results, and divides the addition result by the number of other inverter devices with which the communication means is communicating. To calculate the calculation result,
The control circuit according to claim 2. The calculation means subtracts the weighted correction compensation value from the reception compensation value, adds all the subtraction results, and multiplies the weighted correction compensation value by the addition result to calculate the calculation result. To
The control circuit according to claim 2. The calculation means subtracts the reception compensation value from the weighted correction compensation value, adds all the subtraction results, and multiplies the addition result by the square of the weighted correction compensation value. Compute the result,
The control circuit according to claim 2. The weighting unit performs weighting by dividing the correction compensation value by a preset weighting value.
The control circuit according to claim 1. Temperature detecting means for detecting the temperature of the inverter circuit;
Weighting value setting means for setting a weighting value corresponding to the temperature;
Further comprising
The weighting unit performs weighting by dividing the correction compensation value by a weighting value set by the weighting value setting unit.
The control circuit according to claim 1. Clock means for outputting the date or time;
A weighting value setting means for storing a weighting value in association with the date or time, and for setting a weighting value corresponding to the date or time output by the clock means;
Further comprising
The weighting unit performs weighting by dividing the correction compensation value by a weighting value set by the weighting value setting unit.
The control circuit according to claim 1. Active power calculating means for calculating output active power of the inverter circuit;
Weighting value setting means for setting a weighting value corresponding to the output active power;
Further comprising
The weighting unit performs weighting by dividing the correction compensation value by a weighting value set by the weighting value setting unit.
The control circuit according to claim 1.   An inverter device comprising the control circuit according to claim 1 and an inverter circuit.   A power system, wherein a plurality of the inverter devices according to claim 11 are connected in parallel. In a power system in which a plurality of inverter devices not in a master-slave relationship are connected in parallel, a control method for controlling an inverter circuit included in one of the plurality of inverter devices,
A first step of generating a compensation value for controlling the interconnection point voltage to a target value;
A second step of generating a correction value for cooperating with each inverter device;
A third step of generating a PWM signal based on a correction compensation value obtained by adding the correction value to the compensation value;
A fourth step of weighting the correction compensation value;
A fifth step of transmitting the weighted correction compensation value to at least one other inverter device;
A sixth step of receiving a value transmitted by the other inverter device as a reception compensation value;
Equipped with a,
The second step generates the correction value using a calculation result based on the weighted correction compensation value and the reception compensation value received in the sixth step.
A control method characterized by that.