Energy reversible traction substation, method and system

[0050] Generally, the urban rail transit traction power supply system includes an AC power grid, a DC contact network, and multiple traction substations, and each traction substation includes a diode rectifier unit. Such as figure 1 As shown, for ease of description, a traction substation is taken as an example to describe this embodiment in detail.

[0051] Generally, in the existing urban rail transit traction track system, regenerative braking energy will be generated when the train is braked at the station, and this energy will be consumed by the resistor, which will cause a waste of resources. In order to be able to reasonably and fully utilize the regenerative braking energy of the train, an energy reversible traction substation can be used in this embodiment, by controlling the DC set voltage of the four-quadrant converter unit in the energy reversible traction substation The value changes in real time, so that the regenerative braking energy of the train can be absorbed by the four-quadrant converters in multiple traction substations.

[0052] figure 2 It is a schematic diagram of the structure of the energy reversible traction substation provided by the present invention. Such as figure 2 As shown, the energy reversible traction substation of this embodiment includes: a four-quadrant converter unit, a controller, and a DC current sensor. The four-quadrant converter unit is connected to the AC power grid and the DC bus in the institute, the DC bus in the institute is connected to the DC catenary, the DC current sensor is connected to the DC side of the four-quadrant converter unit, and the DC current sensor is connected to the controller. Four-quadrant converter unit connection. The DC current sensor is used to measure the DC side current of the four-quadrant converter unit and transmit the DC side current to the controller. The controller is used to control the DC voltage setting value of the four-quadrant converter unit to change with the change of the DC side current.

[0053] Specifically, because the four-quadrant converter in the four-quadrant converter unit has the advantages of high fundamental power factor, lower harmonic current interference and excellent regenerative braking performance, and the four-quadrant converter can achieve The energy flows in both directions. Therefore, a four-quadrant converter unit can be used in this embodiment to realize energy conversion and flow. When the train enters the station for braking, the regenerative braking energy generated by the train under braking conditions can be changed by the four quadrants in this embodiment through the connection between the DC bus and the DC catenary and the connection between the train and the DC catenary. Flow unit absorption. Then, the four-quadrant converter unit can invert the regenerative braking energy of the train into alternating current and boost it to a certain alternating voltage (such as 35kV) to feed back to the alternating current grid for reuse, thereby realizing the reversibility of energy in the urban rail transit traction power supply system .

[0054] Furthermore, since the four-quadrant converter unit can realize the bidirectional flow of energy and the DC voltage setting value is adjustable, in order to make the four-quadrant converter unit of multiple energy reversible traction substations can absorb the train regeneration system together. Kinetic energy. In this embodiment, a virtual equivalent resistance can exist on the DC side of the four-quadrant converter unit through the control of the controller, which does not consume the regenerative braking energy of the train, but also allows the regenerative braking energy of the train to be shared by multiple energy sources. Reversible traction substation is absorbed. Among them, the model and type of the controller are not limited in this embodiment.

[0055] Further, in this embodiment, a DC current sensor can be provided on the DC side of the four-quadrant converter unit, and the DC current sensor can measure the DC side current of the four-quadrant converter unit. In this embodiment, the model and type of the DC current sensor are not limited.

[0056] Further, the primary input of the DC current sensor is connected to the DC side of the four-quadrant converter unit, and the measured DC side current can be transmitted to the controller through the secondary output of the DC current sensor. Then, the controller can control the DC voltage setting value of the four-quadrant converter unit according to the DC side current to change with the change of the DC side current, which is equivalent to a virtual equivalent that does not exist on the DC side of the four-quadrant converter unit. Resistance, the virtual equivalent resistance will not consume the regenerative braking energy of the train, but can also prevent a certain energy reversible traction substation from absorbing the regenerative braking energy of the train alone. When the value of the virtual equivalent resistance is large, the current when the train is braking can flow more evenly to each energy reversible traction substation. Therefore, the virtual equivalent resistance can be regarded as multiple energy reversible traction substations. The equilibrium index of the regenerative braking energy absorbed by the substation.

[0057] Specifically, in this embodiment, the regenerative braking energy absorption coefficient of the train can be artificially set according to the actual situation, so that there is a virtual equivalent resistance that does not actually exist on the DC side of the four-quadrant converter unit, thereby realizing the four-quadrant converter. The set value of DC voltage of the current unit changes with the change of the DC side current. In this embodiment, the specific form that the controller can control the DC voltage setting value of the four-quadrant converter unit to change with the change of the DC side current is not limited. Optionally, the controller is used to control the DC voltage setting value of the four-quadrant converter unit to change with the change of the DC side current through the following formula (1):

[0058] U * dc = U 1k -K·I dc Formula 1);

[0059] Where U * dc Is the given value of DC voltage of the four-quadrant converter unit, U 1k Is the no-load voltage of the four-quadrant converter unit, K is the energy absorption coefficient of train regenerative braking, I dc It is the DC side current of the four-quadrant converter unit.

[0060] Furthermore, in formula (1), the train regenerative braking energy absorption coefficient K can be regarded as the virtual equivalent internal resistance of the DC side of the four-quadrant converter unit. DC side current I of four-quadrant converter unit dc It can be measured by a DC current sensor, which can be regarded as a known value, and the no-load voltage U of the four-quadrant converter unit 1k Constant. When the train is braking, the measured I dc Is negative, the value of K remains constant, so when the DC side current I dc When it becomes larger, the DC voltage set value U * dc Will grow bigger. Among them, the regenerative braking energy absorption coefficient K value of the train can be manually set, and the specific size of the K value is not limited in this embodiment. Optionally, the value of the regenerative braking energy absorption coefficient K of the train is set according to the line resistance between the train and the energy reversible traction substation.

[0061] Specifically, the K value can be set to be much larger than the resistance value of the line resistance, so that the influence of the line resistance becomes smaller, and the energy reversible traction substation with a longer distance can absorb more regenerative braking energy of the train. And the larger the K value, the more balanced the current when the train is braking can flow to the energy reversible traction substations.

[0062] Furthermore, the existing multiple traction substations only include diode rectifier units. Therefore, it is impossible to recover and reuse train regenerative braking energy. In the multiple energy reversible traction substations of this embodiment, since there is a virtual equivalent resistance on the DC side of the four-quadrant converter unit, when the train is braking, the braking energy of the train is regenerated With the increase of braking power, the set value of DC voltage of the four-quadrant converter unit in the adjacent energy reversible traction substation will rise linearly within a certain range, thereby triggering the four in the adjacent energy reversible traction substation. Quadrant converter units are also put into operation, so that the train regenerative braking energy generated when the train enters the station can be absorbed by the four-quadrant converter units of multiple energy reversible traction substations. In addition, the larger the regenerative braking energy absorption coefficient of the train, the more balanced the regenerative braking energy absorbed by the energy reversible traction substations, thereby reducing the power attack on a certain energy reversible traction substation and facilitating the train regeneration system. Kinetic energy can be recycled and reused in the subway system, reducing the probability of train regenerative braking energy being sent back to the urban power grid.

[0063] The energy reversible traction substation provided in this embodiment is connected to the AC power grid and the DC bus in the substation through the four-quadrant converter unit, the DC bus in the substation is connected to the DC catenary, and the DC current sensor is connected to the DC side of the four-quadrant converter unit The DC current sensor is connected to the controller. The DC current sensor can transmit the measured DC side current of the four-quadrant converter unit to the controller, and the controller is connected to the four-quadrant converter unit. The controller can be based on the DC side current The DC voltage setting value of the control four-quadrant converter unit changes with the change of the DC side current, so that there is a virtual equivalent resistance on the DC side of the four-quadrant converter unit, so that when the train is braking, the generated train regeneration The braking energy is gradually increasing, so that multiple energy reversible traction substations can jointly absorb the regenerative braking energy of the train. And the larger the value of the virtual equivalent resistance, the more balanced the regenerative braking energy absorbed by the energy reversible traction substations. This embodiment realizes the process in which the train regenerative braking energy generated when the train enters the station can be absorbed by multiple adjacent energy reversible traction substations, and solves the problem that the existing urban rail transit traction power supply system cannot absorb the train regeneration system. The issue of kinetic energy can not only balance the power impact of each energy reversible traction substation, but also fully recycle the regenerative braking energy of the train in the urban rail transit traction power supply system.

[0064] On the basis of the above embodiment, the specific structure of the energy reversible traction substation in this embodiment will be described in detail.

[0065] First, continue to combine figure 2 In order to realize the function of supplying power to the train, the energy reversible traction substation in this embodiment also includes a diode rectifier unit. Among them, the diode rectifier unit is connected in parallel with the four-quadrant converter unit, and the DC side of the diode rectifier unit is connected with the DC bus in the station.

[0066] Specifically, during train traction, the diode rectifier unit in this embodiment can use the diode rectifier unit in the existing traction substation, which can step down the AC power grid (such as 35kV) and rectify the AC power into DC power (such as 750V). Or 1500V) and connected to the DC bus in the station, the DC bus in the station is connected to the DC catenary, and when the train is connected to the DC catenary, it can supply power to the train. When the train is braking, the diode rectifier unit does not work. In this embodiment, the specific implementation form of the diode rectifier unit is not limited, as long as the diode rectifier unit and the four-quadrant converter unit are connected in parallel.

[0067] Secondly, in order to be able to monitor the actual DC side voltage of the four-quadrant converter unit, a DC side voltage sensor can be used in this embodiment. Continue to combine figure 2 In this embodiment, the energy reversible traction substation further includes: a DC voltage sensor. Among them, the DC voltage sensor is connected to the DC side of the four-quadrant converter unit, and the DC voltage sensor is connected to the controller. The DC voltage sensor is used to measure the DC side voltage of the four-quadrant converter unit and transmit the DC side voltage to the controller. The controller is also used to control the DC side voltage to be equal to the given value of the DC voltage of the four-quadrant converter unit.

[0068] Specifically, in this embodiment, a DC voltage sensor can be provided on the DC side of the four-quadrant converter unit, and the DC voltage sensor can measure the DC side voltage of the four-quadrant converter unit. In this embodiment, the model and type of the DC voltage sensor are not limited.

[0069] Further, the primary input of the DC voltage sensor is connected to the DC side of the four-quadrant converter unit, and the measured DC side voltage can also be transmitted to the controller through the secondary output of the DC voltage sensor. Next, the controller can control the DC side voltage to be equal to the DC voltage set value of the four-quadrant converter unit, that is, through the feedback of the DC side voltage, act on the DC voltage set value of the four-quadrant converter unit, so that the DC side voltage is equal to The given value of DC voltage of the four-quadrant converter unit is equal, so as to correct the given value of DC voltage of the four-quadrant converter unit.

[0070] Further, the specific form in which the controller controls the DC side voltage to be equal to the given value of the DC voltage of the four-quadrant converter unit in this embodiment is not limited. Optionally, the controller is also used to control the DC side voltage to be equal to the given value of the DC voltage of the four-quadrant converter unit through the following formula (2):

[0071] U dc = U * dc Formula (2);

[0072] Where U * dc Is the given value of DC voltage of the four-quadrant converter unit, U dc Is the DC side voltage.

[0073] Furthermore, the diode sorting unit and the four-quadrant converter unit in the energy reversible traction substation work in different states of the train, so the energy reversible traction substation can not only feed back the regenerative braking energy of the train to the AC power grid for reprocessing. Utilization can also use the regenerative braking energy of the train to provide traction energy for the train, so as to realize the reversibility of energy in the urban rail transit traction power supply system. For ease of description, this embodiment uses the following image 3 Explain the specific implementation process.

[0074] image 3 The external characteristic curve diagram of the four-quadrant converter unit and diode rectifier unit provided by the present invention. Specifically, under normal conditions, when the train is traction, the diode rectifier unit in each traction substation in the urban rail transit traction power supply system works, and the AC power is stepped down and converted into DC power. The four-quadrant converter unit does not work. So only as image 3 The external characteristic curve of the diode rectifier unit in the middle rectifier zone ②, where U do Is the no-load voltage of the diode rectifier unit; U lim Is the inverter voltage limit value of the four-quadrant converter unit, the default is 1750V; A is the power limit point, AX is the power limit curve, the voltage rises along the AX direction, and the power remains unchanged, the default power limit value is 2MW; U ov It is the DC voltage protection value, and the default value is 2100V. When the train is braking, the four-quadrant converter unit in each traction substation works, and the regenerative braking energy of the train is converted into DC power through the DC contact network and transmitted to the AC power grid. The diode rectifier unit does not work. So only as image 3 The external characteristic curve of the four-quadrant converter unit in the middle inverter zone①, where U 1k It is the inverter turn-on voltage of the four-quadrant converter unit. What needs to be explained here is that for the convenience of explanation, image 3 The external characteristic curves of the four-quadrant converter unit and the diode rectifier unit are drawn on the left and right sides of the ordinate to facilitate the distinction between different working states. image 3 Middle, ordinate U dc Is the DC side voltage of the four-quadrant converter unit, the abscissa I dc It is the DC side current of the four-quadrant converter unit. In this way, the diode rectifier unit and the four-quadrant converter unit in each traction substation can work in coordination to achieve specific control goals.

[0075] In a specific embodiment, in order to be able to clearly describe the process in which multiple energy reversible traction substations can absorb the regenerative braking energy of the train at the same time when the train is braking, combined Figure 4 with Figure 5 , The specific structure of some components in the energy reversible traction substation is described in detail.

[0076] Figure 4 It is a schematic diagram of the structure of some components in the energy reversible traction substation provided by the present invention, Figure 5 The four-quadrant converter unit provided by the present invention adopts the external characteristic control schematic diagram of current decoupling control. Such as Figure 4 As shown, some components in an energy reversible traction substation include a four-quadrant converter, a controller, a DC current sensor, and a DC voltage sensor. Among them, the four-quadrant converter inverts the regenerative braking energy of the train into alternating current and boosts it to 35kV alternating current to feed it back to the alternating current grid for reuse.

[0077] Specifically, there are a DC current sensor and a DC voltage sensor on the DC side of the four-quadrant converter, and the DC side current measured by the DC current sensor and the DC side voltage measured by the DC voltage sensor can be output to the controller, thus controlling The converter can control the DC side of the four-quadrant converter according to the DC side current, so that the set value of the DC voltage of the four-quadrant converter changes, and can feedback according to the DC side voltage, which can be used to calibrate the four-quadrant converter The effect of the given value of DC voltage.

[0078] Further, as Figure 5 As shown, the controller can receive the DC side current measured by the DC current sensor and the DC side voltage measured by the DC voltage sensor. On the one hand, the DC side current is multiplied by the train's regenerative braking energy absorption coefficient K, and the product obtained is multiplied by the no-load voltage U of the four-quadrant converter 1k Through the function of the limiter, the DC voltage set value U of the four-quadrant converter can be obtained * dc , So that its amplitude is within the allowable range. On the other hand, through the measured DC side voltage U dc Feedback to get the DC side voltage U dc And DC voltage set value U * dc Error. Then, through a series of PI controller adjustments and limiters to get the current setpoint Among them, right The limiting amplitude can limit the AC input (or output) power of the four-quadrant converter, and the PI controller can ensure the DC side voltage U dc And DC voltage set value U * dc equal.

[0079] Further, there is an AC current sensor on the AC side of the four-quadrant converter, which can detect the three-phase AC current signal i a ,i b ,i c Input to the AC current closed-loop controller, and set the current value Input to the AC current closed-loop controller, which is used to control the AC side current of the four-quadrant converter. Finally, the output signal of the AC current closed-loop controller is driven by PWM pulse width modulation to control the four-quadrant converter.

[0080] Image 6 The process of the energy reversible traction transformation method provided for the present invention Figure one. The energy reversible traction substation method of this embodiment is applied to an energy reversible traction substation. The energy reversible traction substation includes a four-quadrant converter unit, a controller, and a DC current sensor. Such as Image 6 As shown, the energy reversible traction transformation method of this embodiment may include:

[0081] S101. Transmit the DC side current of the four-quadrant converter unit measured by the DC current sensor to the controller.

[0082] S102. The controller controls the DC voltage setting value of the four-quadrant converter unit to change with the change of the DC side current.

[0083] Specifically, in this embodiment, the DC side current of the four-quadrant converter unit is obtained through the primary input measurement of the DC current sensor, and the DC side current is input to the controller through the secondary output of the DC current sensor. Then, the controller controls the DC voltage setting value of the four-quadrant converter unit according to the DC side current to change with the change of the DC side current, so that the DC side of the four-quadrant converter unit has a virtual equivalent resistance that does not exist in itself. Therefore, when the train is braking, multiple energy reversible traction substations can simultaneously absorb the regenerative braking energy of the train.

[0084] Further, this embodiment may not limit the manner in which the given value of the DC voltage of the four-quadrant converter unit is controlled by the controller to change with the change of the DC side current. Optionally, the controller controls the DC voltage setting value of the four-quadrant converter unit to change with the DC side current through the following formula (1):

[0085] U * dc = U 1k -K·I dc Formula 1);

[0086] Where U * dc Is the given value of DC voltage of the four-quadrant converter unit, U 1k Is the no-load voltage of the four-quadrant converter unit, K is the energy absorption coefficient of train regenerative braking, I dc It is the DC side current of the four-quadrant converter unit.

[0087] Furthermore, in formula (1), the train regenerative braking energy absorption coefficient K can be regarded as the virtual equivalent internal resistance of the four-quadrant converter unit. DC side current I of four-quadrant converter unit dc It can be measured by a DC current sensor, which can be regarded as a known value, and the no-load voltage U of the four-quadrant converter unit 1k Constant. When the train is braking, the measured I dc Is negative, the value of K remains constant, so when the DC side current I dc When it becomes larger, the DC voltage set value U * dc Will grow bigger. Among them, the regenerative braking energy absorption coefficient K value of the train can be manually set, and the specific size of the K value is not limited in this embodiment. Optionally, the value of the regenerative braking energy absorption coefficient K of the train is set according to the line resistance between the train and the energy reversible traction substation.

[0088] Specifically, the K value can be set to be much larger than the resistance value of the line resistance, so that the influence of the line resistance becomes smaller, and the energy reversible traction substation with a longer distance can absorb more regenerative braking energy of the train. And the larger the K value, the more balanced the current when the train is braking can flow to the energy reversible traction substations.

[0089] Further, in the above Image 6 Based on the above, in order to be able to monitor the actual DC side voltage of the four-quadrant converter unit, the energy reversible traction substation also includes a DC voltage sensor, combined with Figure 7 The specific implementation of the energy reversible traction transformation method of this embodiment will be described in detail. Figure 7 The process of the energy reversible traction transformation method provided for the present invention Figure II ,Such as Figure 7 As shown, the energy reversible traction transformation method of this embodiment may further include:

[0090] S201: Transmit the DC side voltage of the four-quadrant converter unit measured by the DC voltage sensor to the controller.

[0091] S202: The controller controls the DC side voltage to be equal to the given value of the DC voltage of the four-quadrant converter unit.

[0092] Specifically, in this embodiment, the DC side voltage of the four-quadrant converter unit is obtained through the primary input measurement of the DC voltage sensor, and the DC side voltage is input to the controller through the secondary output of the DC voltage sensor. Next, the controller controls the DC voltage setting value of the four-quadrant converter unit to be equal to the DC side voltage according to the DC side voltage, and corrects and adjusts the DC voltage setting value of the four-quadrant converter unit.

[0093] Further, in this embodiment, the specific form in which the controller controls the DC side voltage to be equal to the given value of the DC voltage of the four-quadrant converter unit is not limited. Optionally, the controller controls the DC side voltage to be equal to the given value of the DC voltage of the four-quadrant converter unit through the following formula (2):

[0094] U dc = U * dc Formula (2);

[0095] Where U * dc Is the given value of DC voltage of the four-quadrant converter unit, U dc Is the DC side voltage.

[0096] The energy reversible traction substation method provided in this embodiment can transmit the measured DC side current of the four-quadrant converter unit to the controller through the DC current sensor, and the controller can control the four-quadrant converter unit according to the DC side current The given value of DC voltage changes with the change of the DC side current, so that there is a virtual equivalent resistance on the DC side of the four-quadrant converter unit, so that when the train is braking, the regenerative braking energy generated by the train gradually increases. This enables multiple energy reversible traction substations to jointly absorb train regenerative braking energy, and adjacent energy reversible traction substations can also simultaneously absorb train regenerative braking energy. And the larger the value of the virtual equivalent resistance, the more balanced the regenerative braking energy absorbed by the energy reversible traction substations. This embodiment realizes the process in which the train regenerative braking energy generated when the train enters the station can be absorbed by multiple adjacent energy reversible traction substations, and solves the problem that the existing urban rail transit traction power supply system cannot absorb the train regeneration system. The issue of kinetic energy can not only balance the power impact of each energy reversible traction substation, but also fully recycle the regenerative braking energy of the train in the urban rail transit traction power supply system.

[0097] Figure 8 It is a schematic diagram of the structure of the urban rail transit traction power supply system provided by the present invention. Such as Figure 8 As shown, the urban rail transit traction power supply system of this embodiment includes: an AC power grid, a DC contact network, and multiple energy reversible traction substations as described above.

[0098] Specifically, the number of energy reversible traction substations in this embodiment can be any number, which is usually determined by the line length of the train. Generally, an energy reversible traction substation is set at 2-3 kilometers. This embodiment does not limit this.

[0099] Optionally, the number of energy reversible traction substations is 3, which are the first energy reversible traction substation, the second energy reversible traction substation, and the third energy reversible traction substation.

[0100] Optionally, the DC side of the first energy reversible traction substation, the DC side of the second energy reversible traction substation, and the DC side of the third energy reversible traction substation are all connected to the DC bus in the substation;

[0101] When the train brakes, the train is connected to the DC catenary. The first energy reversible traction substation, the second energy reversible traction substation and the third energy reversible traction substation jointly absorb the train's regenerative braking energy .

[0102] Specifically, since the DC side of the four-quadrant converter unit in each energy reversible traction substation can be controlled by the controller to have a virtual equivalent resistance, so that the energy reversible traction substation can absorb together Train regenerative braking energy generated when the train is braking.

[0103] Further, this embodiment does not limit the number of energy reversible traction substations. When the number of energy reversible traction substations is 3, pass the DC side of the first energy reversible traction substation, the DC side of the second energy reversible traction substation, and the third energy reversible traction substation The DC side of the station is connected to the DC bus in the station, and the DC bus in the station is connected to the DC catenary. When the train is connected to the DC catenary, the first energy reversible traction substation and the second energy reversible traction substation can be realized. Therefore, together with the third energy reversible traction substation, the regenerative braking energy of the train generated under trains and other operating conditions is absorbed. Furthermore, the four-quadrant converter units in the first energy reversible traction substation, the second energy reversible traction substation, and the third energy reversible traction substation respectively convert it into alternating current and boost it to a certain An AC voltage (such as 35kV) is fed back to the AC grid for reuse.

[0104] The urban rail transit traction power supply system provided by this embodiment can be used in the technical solution of the energy reversible traction substation of this embodiment. The four-quadrant converter unit is connected to the AC power grid and the DC bus in the substation. The DC bus is connected to the DC contact net, the DC current sensor is connected to the DC side of the four-quadrant converter unit, and the DC current sensor is connected to the controller. The DC current sensor can transmit the measured DC side current of the four-quadrant converter unit to the control The controller is connected to the four-quadrant converter unit. The controller can control the DC voltage setting value of the four-quadrant converter unit to change with the change of the DC side current according to the DC side current, so that the DC side of the four-quadrant converter unit There is a virtual equivalent resistance, so that when the train is braking, the regenerative braking energy of the train gradually increases, so that multiple energy reversible traction substations can jointly absorb the regenerative braking energy of the train. And the larger the value of the virtual equivalent resistance, the more balanced the regenerative braking energy absorbed by the energy reversible traction substations. This embodiment realizes the process in which the train regenerative braking energy generated when the train enters the station can be absorbed by multiple adjacent energy reversible traction substations, and solves the problem that the existing urban rail transit traction power supply system cannot absorb the train regeneration system. The issue of kinetic energy can not only balance the power impact of each energy reversible traction substation, but also fully recycle the regenerative braking energy of the train in the urban rail transit traction power supply system.

[0105] A person of ordinary skill in the art can understand that all or part of the steps in the foregoing method embodiments can be implemented by a program instructing relevant hardware. The aforementioned program can be stored in a computer readable storage medium. When the program is executed, it executes the steps including the foregoing method embodiments; and the foregoing storage medium includes: ROM, RAM, magnetic disk, or optical disk and other media that can store program codes.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand: It is still possible to modify the technical solutions described in the foregoing embodiments, or equivalently replace some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. range.