CN109950983B - A multi-transmission single-reception wireless power transmission system parameter configuration method - Google Patents

Abstract

The embodiment of the present invention discloses a parameter configuration method of a multi-transmission single-reception wireless power transmission system, including: building a multi-transmission single-reception wireless power transmission system, including more than two high-frequency voltage sources, more than two transmitting coils and A single receiving coil; establish the corresponding equivalent circuit to obtain the expression of the power obtained by the load and the expression of the transmission efficiency of the system; according to the expression of the power obtained by the load and the expression of the transmission efficiency of the system, the high-frequency voltage source voltage and load resistance are used as the optimized self- Variables, the optimal load parameter configuration conditions under the maximum load obtained power, and the optimal feed voltage parameter configuration conditions and the optimal load parameter configuration conditions under the maximum system transmission efficiency are obtained. By adopting the foregoing method, high system transmission efficiency and high load-acquired power transmission of a multi-transmission single-reception wireless power transmission system in a two-dimensional plane can be realized.

Description

A multi-transmission single-reception wireless power transmission system parameter configuration method

technical field

The invention relates to the field of wireless power transmission, in particular to a parameter configuration method of a multi-transmission single-reception wireless power transmission system.

Background technique

As human beings enter the era of electrification, the number of electrical equipment is increasing day by day, and there are various types. The traditional way to feed these electrical equipment is to supply power through wires. However, because the wire power supply has the disadvantage of inconvenient movement and easy to generate electric sparks in the process of wire contact, it causes a lot of inconvenience in the process of power supply. For example, intense electrical sparks can shorten the life of electrical equipment and wires. In addition, when conducting wire power supply in special occasions such as coal mines or underwater, electric sparks generated by wire contact may cause major accidents and dangers of electric leakage. The wireless power transmission technology based on magnetic coupling can effectively avoid the above problems. Since 2007, scholars have made a major breakthrough in the research of single-transmission and single-reception magnetic resonance wireless power transmission systems, and magnetic resonance wireless power transmission systems have been extensively studied.

There are mainly two structures of the wireless power transmission system: a two-coil structure and a four-coil coupling structure. Among them, the two-coil structure uses the principle of magnetic induction to realize the short-distance transmission of electric energy, and the four-coil coupling structure is often used for medium-distance transmission of electric energy. Specifically, the first coil and the fourth coil of the four-coil coupling structure are used for wireless power transmission system input and The output impedance is matched to obtain the maximum load power. In order to increase the effective power transmission distance, a wireless power transmission system loaded with relay coils has also been proposed by many scholars.

However, the research on the wireless power transfer system mentioned above is all about how to effectively improve the transmission efficiency of the system or the power obtained by the load on a one-dimensional straight line. There is still a lack of a set of clear and theoretically mature design solutions for how to achieve high transmission efficiency in a wider range or high load power on a two-dimensional plane.

Contents of the invention

The present invention provides a parameter configuration method of a multi-transmission single-reception wireless power transmission system, mainly related to the configuration method of feed voltage parameters and load parameters, for the wireless power transmission system to achieve high transmission efficiency or high load acquisition in a two-dimensional plane Power provides clear guidance.

The present invention provides a parameter configuration method of a multi-transmission single-reception wireless power transmission system, including:

Step 1, building a multi-transmission single-reception wireless power transmission system, the multi-transmission single-reception wireless power transmission system includes more than two high-frequency voltage sources, more than two transmitting coils and a single receiving coil;

Step 2, according to the multi-transmission-single-reception wireless power transfer system, establish a corresponding equivalent circuit, and obtain the load gain power expression and system transmission efficiency expression of the multi-transmission-single-reception wireless power transfer system;

Step 3, according to the load obtained power expression and the system transmission efficiency expression, using the high-frequency voltage source voltage and load resistance as optimized independent variables, calculate the optimal load parameter configuration conditions under the maximum load obtained power, and the maximum Optimal feed voltage parameter configuration conditions and optimal load parameter configuration conditions under system transmission efficiency.

Further, in an implementation manner, the step 1 includes:

The two or more transmitting coils and the single receiving coil are arranged in a two-dimensional plane, and the arrangement is as follows: the two or more transmitting coils are evenly distributed around the charging area, and the single receiving coil is located in the charging area At any position, under the condition that the distance between any two transmitting coils is the same, the range of the charging area expands as the number of transmitting coils increases.

Further, in an implementation manner, the step 2 includes:

According to the multi-transmit single-receive wireless power transfer system, the transmission quality factor Q _TiR between the i-th transmit coil and the receive coil in the multi-transmit single-receive wireless power transfer system is obtained:

Among them, ω ₀ is the resonant frequency of the multi-transmitting single-receiving wireless power transfer system, M _TiR is the mutual inductance between the i-th transmitting coil and the receiving coil, 1≤i≤n, n represents the multi-transmitting single-receiving wireless power transfer system The total number of transmitting coils, and n is a positive integer greater than or equal to 2, r _Ti is the total parasitic resistance of the i-th transmitting coil and its upper resonant capacitor, r _R is the total parasitic resistance of the receiving coil and its upper resonant capacitor;

According to the transmission quality factor Q _TiR between the i-th transmitting coil and receiving coil in the multi-transmitting single-receiving wireless power transfer system, the comprehensive expression between all transmitting coils and receiving coils in the multi-transmitting single-receiving wireless power transfer system is obtained Factor A _n :

Further, in an implementation manner, the step 2 includes:

According to the following formula, the load obtained power PDL expression of the multi-transmission single-reception wireless power transfer system is calculated:

Among them, V _Ti is the voltage value of the voltage source loaded on the i-th transmitting coil, and _RL is the load resistance value;

According to the following formula, the system transmission efficiency PTE expression of the multi-transmission single-reception wireless power transfer system is calculated:

Among them, M _TtR is the mutual inductance between the t-th transmitting coil and the receiving coil, r _Tt is the total parasitic resistance of the t-th transmitting coil and its upper resonant capacitor, V _Tt is the voltage value of the voltage source loaded on the t-th transmitting coil , 1≤t≤n, and t≠i.

Further, in an implementation manner, the step 3 includes:

According to formula (1), to obtain the optimal load resistance R _{L under the maximum load power, the configuration conditions of OPT/PDL} parameters are:

When the load resistance value R _L is determined, the optimal feed voltage parameter configuration conditions under the maximum system transmission efficiency can be obtained from formula (2) when M _TtR V _Ti -M _TiR V _Tt = 0 is established:

V _Ti : V _Tt = M _TiR : M _TtR ,

Under the condition of the optimal feed voltage parameter configuration, the system optimal efficiency PTE′ _OPT is obtained:

According to formula (3), the optimal load resistance R _{L under the maximum system transmission efficiency is obtained, and the configuration conditions of OPT/PTE} parameters are:

_{RL, OPT/PTE} = r _R A _n .

It can be known from the above technical solution that the embodiment of the present invention provides a parameter configuration method of a multi-transmission single-reception wireless power transmission system. The method includes: step 1, building a multi-transmission single-reception wireless power transmission system, the multi-transmission single-reception wireless power transmission system includes more than two high-frequency voltage sources, more than two transmitting coils and a single receiving coil; step 2. According to the multi-transmit single-receive wireless power transfer system, establish a corresponding equivalent circuit to obtain the load obtained power expression and system transmission efficiency expression of the multi-transmit single-receive wireless power transfer system; step 3, according to the The expression of the obtained power of the load and the expression of the system transmission efficiency are described, and the optimal load parameter configuration conditions under the maximum load obtained power and the maximum system transmission efficiency are obtained by taking the high-frequency voltage source voltage and the load resistance as the optimized independent variables. Optimal feed voltage parameter configuration conditions and optimal load parameter configuration conditions.

The present invention starts from the two aspects of obtaining the maximum transmission efficiency of the system or the power obtained by the maximum load, and proposes the configuration conditions of optimal feed voltage parameters and optimal load resistance parameters. In addition, the area of the charging area can be effectively enlarged when the number of evenly distributed transmitting coils is appropriately increased. The present invention solves the key problem of high-energy-efficiency transmission in a two-dimensional plane of a wireless power transmission system with a multi-transmission and single-reception mode, and provides a clear solution for the large-scale transmission of a multi-transmission and single-reception wireless power transmission system in a two-dimensional plane guide.

Description of drawings

In order to illustrate the technical solution of the present invention more clearly, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, on the premise of not paying creative labor, Additional drawings can also be derived from these drawings.

Fig. 1 is a schematic workflow diagram of a parameter configuration method of a multi-transmission single-reception wireless power transmission system provided in the embodiment part of the present invention;

Fig. 2 is a schematic diagram of an equivalent circuit of a multi-transmission single-reception wireless power transmission system provided in the embodiment part of the present invention;

Fig. 3 is a schematic diagram of a wireless power transmission system model provided in the embodiment part of the present invention;

Fig. 4a is a schematic diagram of a model of a multi-transmission single-reception wireless power transmission system with two transmitting coils provided in the embodiment of the present invention;

Fig. 4b is a schematic diagram of a multi-transmission single-reception wireless power transfer system model with three transmitting coils provided in the embodiment of the present invention;

Fig. 4c is a schematic diagram of a model of a multi-transmitting single-receiving wireless power transmission system with four transmitting coils provided in the embodiment of the present invention.

Fig. 5a is a schematic diagram of power obtained by loads in various places in the charging area when no load parameters are configured in a wireless power transmission system with 4 transmitting coils and single reception provided in the embodiment of the present invention.

Fig. 5b is a schematic diagram of power obtained by loads in various places in the charging area after optimal configuration of load parameters in a multi-transmitting single-receiving wireless power transmission system with 4 transmitting coils provided in the embodiment of the present invention.

Fig. 5c is a schematic diagram of the transmission efficiency of a multi-transmitting single-receiving wireless power transmission system with 4 transmitting coils provided in the embodiment of the present invention when no load parameters and feed voltage parameters are configured, at various places in the charging area.

Fig. 5d is a schematic diagram of the transmission efficiency of a multi-transmission single-reception wireless power transmission system with four transmitting coils provided in the embodiment of the present invention after optimizing the configuration of load parameters and feed voltage parameters in various places in the charging area.

Detailed ways

In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, it is a schematic workflow diagram of the parameter optimization configuration method of the multi-transmit single-receive wireless power transfer system based on two-dimensional transmission provided by the present invention, including the following steps:

Step 1, building a multi-transmission single-reception wireless power transmission system, the multi-transmission single-reception wireless power transmission system includes more than two high-frequency voltage sources, more than two transmitting coils and a single receiving coil;

Step 2, according to the multi-transmission-single-reception wireless power transfer system, establish a corresponding equivalent circuit, and obtain the load gain power expression and system transmission efficiency expression of the multi-transmission-single-reception wireless power transfer system;

Step 3, according to the load obtained power expression and the system transmission efficiency expression, using the high-frequency voltage source voltage and load resistance as optimized independent variables, calculate the optimal load parameter configuration conditions under the maximum load obtained power, and the maximum Optimal feed voltage parameter configuration conditions and optimal load parameter configuration conditions under system transmission efficiency;

Further, in this step, the maximum load obtained power and the maximum system transmission efficiency can be obtained by combining the load obtained power expression and the system transmission efficiency expression.

As shown in Figure 2, a schematic diagram of an equivalent circuit of a multi-transmitting single-receiving wireless power transmission system includes more than two high-frequency voltage sources, more than two transmitting coils, a single receiving coil, a high-frequency compensation capacitor and a load. Among them, C _Ti is the compensation capacitor connected in series on the i-th transmitting coil to generate resonance, L _Ti is the self-inductance of the i-th transmitting coil, I _Ti is the current flowing through the i-th transmitting coil, 1≤i ≤n, n represents the total number of transmitting coils in the multi-transmitting single-receiving wireless power transfer system, and n is a positive integer greater than or equal to 2, C _R is the compensation capacitor connected in series on the receiving coil to generate resonance, L _R It is the self-inductance of the receiving coil, and I _R is the current flowing through the receiving coil. The voltage of the high-frequency voltage source can be adjusted according to the coupling distance between a single receiving coil and each transmitting coil; the high-frequency compensation capacitor is connected in series with the corresponding coil; the multi-transmitting single-receiving wireless power transmission system works in resonance state, configure the load as a resistive load.

Said step 1 includes:

The two or more transmitting coils and the single receiving coil are arranged in a two-dimensional plane, and the arrangement is as follows: the two or more transmitting coils are evenly distributed around the charging area, and the single receiving coil is located in the charging area At any position, under the condition that the distance between any two transmitting coils is the same, the range of the charging area expands as the number of transmitting coils increases.

Said step 2 includes:

According to the multi-transmit single-receive wireless power transfer system, the transmission quality factor Q _TiR between the i-th transmit coil and the receive coil in the multi-transmit single-receive wireless power transfer system is obtained:

Among them, ω ₀ is the resonant frequency of the multi-transmitting single-receiving wireless power transfer system, M _TiR is the mutual inductance between the i-th transmitting coil and the receiving coil, 1≤i≤n, n represents the multi-transmitting single-receiving wireless power transfer system The total number of transmitting coils, and n is a positive integer greater than or equal to 2, r _Ti is the total parasitic resistance of the i-th coil and its upper resonant capacitor, r _R is the total parasitic resistance of the receiving coil and its upper resonant capacitor;

According to the transmission quality factor Q _TiR between the i-th transmitting coil and receiving coil in the multi-transmitting single-receiving wireless power transfer system, the comprehensive expression between all transmitting coils and receiving coils in the multi-transmitting single-receiving wireless power transfer system is obtained Factor A _n :

Said step 2 includes:

According to the equivalent circuit and Kirchhoff's voltage law, the load obtained power PDL expression of the multi-transmission single-reception wireless power transmission system is obtained:

Among them, V _Ti is the voltage value of the voltage source loaded on the i-th transmitting coil, and _RL is the load resistance value;

According to the equivalent circuit and Kirchhoff's voltage law, the system transmission efficiency PTE expression of the multi-transmission single-reception wireless power transmission system is obtained:

Among them, M _TtR is the mutual inductance between the t-th transmitting coil and the receiving coil, r _Tt is the total parasitic resistance of the t-th transmitting coil and its upper resonant capacitor, V _Tt is the voltage value of the voltage source loaded on the t-th transmitting coil , 1≤t≤n, and t≠i.

Said step 3 includes:

Find the partial derivative about the load resistance _RL according to the formula (1), and make the partial derivative expression equal to zero, solve the equation to obtain the optimal load resistance RL under the maximum load power _{, OPT/PDL} parameter configuration The conditions are:

Further, in this step, under the condition of _RL,OPT/PDL , combined with the comprehensive expression factor A _n between the i-th transmitting coil and receiving coil, the maximum load power PDL _OPT is obtained according to the formula (1):

When _RL is determined, M _TtR V _Ti -M _TiR V _Tt = 0 can be obtained from the above formula (2) to effectively improve the value of the transmission efficiency, so that the high-frequency voltage source under the maximum system transmission efficiency can be obtained from this equation The optimal feed voltage parameter configuration conditions are:

V _Ti : V _Tt = M _TiR : M _TtR ,

Under the configuration conditions of the optimal feed voltage parameters, the formula (2) is simplified to formula (3)

Among them, PTE′ _OPT is the optimal efficiency of the system obtained after the optimal configuration of the feed voltage parameters.

Find the partial derivative about the load resistance _RL for the formula (3), and make the partial derivative expression equal to zero, solve the equation to obtain the optimal load resistance RL under the maximum system transmission efficiency _{, OPT/PTE} parameter configuration The conditions are:

_{RL, OPT/PTE} = r _R A _n .

Further, in this step, under the optimal load resistance R _L,OPT/PTE parameter configuration condition, combined with the comprehensive expression factor A _n between the i-th transmitting coil and receiving coil, the optimal feeder The voltage parameter configuration conditions and the configuration conditions of the optimal load resistance _{RL, OPT/PTE} parameters are brought into the formula (3) to obtain the maximum transmission efficiency PTE _OPT :

PTE _OPT = (A _n -1)/(A _n +1),

As shown in Figure 3, the receiving coil is in the position of the charging area, and the charging area is set as a circular surface in the present invention, and the circular radius R _SA of the charging area expands with the increase of the number of transmitting coils, and the receiving coil The center O' of RX does not exceed the circular boundary of the charging area.

As shown in Figure 4a, Figure 4b and Figure 4c, the multi-transmitting single-receiving wireless power transfer system models with 2, 3 and 4 transmitting coils on a two-dimensional plane are built respectively. Taking the 2, 3 and 4 transmitting coils in the figure as examples, the corresponding charging area radii are R _SA1 =D/2-(R _TX +R _RX ), and

Among them, R _TX and R _RX are the radii of the transmitting coil and the receiving coil respectively, obviously R _SA1 <R _SA2 <R _SA3 . Therefore, when the distance between any two transmitting coils is the same, the range of the charging area expands as the number of transmitting coils increases.

In this embodiment, the transmitting coil radius R _TX =5.5cm, the multi-strand Litz wire tightly wound coil height is 3.4cm, and the number of coils is 25; the receiving coil radius R _RX =15.75cm, the coil height is 1.5cm, The number is 11; the distance between each transmitting coil is D=1m. The charging area radii of the 2, 3 and 4 transmitting coil systems are respectively: R _SA1 =28.75 cm, R _SA2 =36.49 cm, R _SA3 =49.47 cm. At the set resonant frequency of the system at 1.073MHz, the actual measured total parasitic resistances of the transmitting coil and the receiving coil plus their respective series capacitors are 5Ω and 5.1Ω, respectively.

This embodiment provides 4 transmitting coils with a single receiving coil, the feeding voltage V ₁ =1V, V ₂ =2V, V ₃ =3V, V ₄ =4V and the load R _L =10Ω applied to the transmitting coils TX ₁ ,..., TX ₄ The load obtains the power PDL value, and the comparison also gives the maximum load obtained power PDL _OPT value of V ₁ =1V, V ₂ =2V, V ₃ =3V, V ₄ =4V and load R _L = _{RL, OPT/PDL} . In terms of efficiency, this embodiment gives the system transmission efficiency PTE value of V ₁ :V ₂ :V ₃ :V ₄ =1:2:3:4 and the load R _L =10Ω, and also gives V ₁ :V ₂ :V ₃ :V ₄ =1:2:3:4 and load _RL =RL, the maximum system transmission efficiency PTE _OPT value _{of OPT/PTE} . The distributions of load obtained power PDL, maximum load obtained power PDL _OPT , system transmission efficiency PTE and maximum system transmission efficiency PTE _OPT are shown in Figures 5a, 5b, 5c and 5d, respectively.

The multi-transmission single-reception wireless power transmission system parameter optimization configuration method of the present invention mainly includes: Step 1, building a multi-transmission single-reception wireless power transmission system, the multi-transmission single-reception wireless power transmission system includes more than two high-frequency voltage sources , more than two transmitting coils and a single receiving coil; step 2, according to the multi-transmission single-reception wireless power transfer system, establish a corresponding equivalent circuit, and obtain the load obtained power expression of the multi-transmission single-reception wireless power transfer system formula and system transmission efficiency expression; Step 3, according to the load obtained power expression and system transmission efficiency expression, with the high-frequency voltage source voltage and load resistance as optimized independent variables, calculate the maximum load obtained power Optimal load parameter configuration conditions, optimal feed voltage parameter configuration conditions and optimal load parameter configuration conditions under maximum system transmission efficiency.

The present invention starts from the two aspects of obtaining the maximum transmission efficiency of the system or the power obtained by the maximum load, and proposes the configuration conditions of optimal feed voltage parameters and optimal load resistance parameters. In addition, the area of the charging area can be effectively enlarged when the number of evenly distributed transmitting coils is appropriately increased. The invention has detailed steps, sufficient theory, and strong practicability, and solves the key problem of high energy-efficiency transmission in a two-dimensional plane for a wireless power transmission system with multiple transmission and single reception modes. In-plane large-scale transmission provides clear guidance.

The purpose of the above-mentioned embodiments is to illustrate the substantive content of the present invention, but not to limit the protection scope of the present invention. Those skilled in the art should understand that the technical solution of the present invention can be modified or equivalently replaced without departing from the essence and protection scope of the technical solution of the present invention.

In a specific implementation, the present invention also provides a computer storage medium, wherein the computer storage medium can store a program, and when the program is executed, it can include the parameter configuration method of a multi-transmission single-reception wireless power transmission system provided by the present invention. Part or all of the steps in each embodiment. The storage medium may be a magnetic disk, an optical disk, a read-only memory (English: read-only memory, ROM for short), or a random access memory (English: random access memory, RAM for short), and the like.

Those skilled in the art can clearly understand that the technologies in the embodiments of the present invention can be implemented by means of software plus a necessary general-purpose hardware platform. Based on this understanding, the essence of the technical solutions in the embodiments of the present invention or the part that contributes to the prior art can be embodied in the form of software products, and the computer software products can be stored in storage media, such as ROM/RAM , magnetic disk, optical disk, etc., including several instructions to enable a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

The embodiments of the present invention described above are not intended to limit the protection scope of the present invention.

Claims (3)

1. the method for parameter configuration that a kind of multi-emitting list receives radio energy transmission system, it is characterised in that:

Step 1, it builds multi-emitting list and receives radio energy transmission system, the multi-emitting list receives radio energy transmission system packet Include more than two high frequency voltage sources, more than two transmitting coils and single receiving coil；

Step 2, radio energy transmission system is received according to the multi-emitting list, establishes corresponding equivalent circuit, obtains described more The single load for receiving radio energy transmission system of transmitting obtains power expression and system efficiency of transmission expression formula；

The step 2, comprising: radio energy transmission system is received according to the multi-emitting list, the multi-emitting list is obtained and receives Transmission quality factor Q in radio energy transmission system between i-th of transmitting coil and receiving coil_TiR:

Wherein, ω₀The resonance frequency of radio energy transmission system, M are received for multi-emitting list_TiRFor i-th of transmitting coil and receive Mutual induction amount between coil, 1≤i≤n, n indicate that multi-emitting list receives the total number of transmitting coil in radio energy transmission system, and N is the positive integer more than or equal to 2, r_TiTotal dead resistance of resonant capacitance for i-th of transmitting coil and thereon, r_RTo receive line Circle and the thereon total dead resistance of resonant capacitance；

The transmission quality in radio energy transmission system between i-th of transmitting coil and receiving coil is received according to the multi-emitting list Factor Q_TiR, obtain the synthesis in the multi-emitting list reception radio energy transmission system between whole transmitting coils and receiving coil Express factors A_n:

According to the following formula, the load acquisition power P DL expression formula that the multi-emitting list receives radio energy transmission system is calculated:

Wherein, V_TiFor on-load voltage source voltage value, R on i-th of transmitting coil_LFor load resistor value；

According to the following formula, the system efficiency of transmission PTE expression formula that the multi-emitting list receives radio energy transmission system is calculated:

Wherein, M_TtRFor the mutual induction amount between t-th of transmitting coil and receiving coil, r_TtResonance electricity for t-th of transmitting coil and thereon The total dead resistance held, V_TtFor on-load voltage source voltage value, 1≤t≤n, and t ≠ i on t-th of transmitting coil；

Step 3, power expression and system efficiency of transmission expression formula are obtained according to the load, with high frequency voltage source voltage and born The independent variable that resistance is optimization is carried, the optimal load parameter configuration condition under maximum load acquisition power is calculated, and most Optimal feed voltage parameter configuration condition and optimal load parameter configuration condition under big system efficiency of transmission.

2. the method according to claim 1, wherein the step 1 includes:

Described two above transmitting coils and the single receiving coil are arranged in two-dimensional surface, arrangement mode are as follows: described two A above transmitting coil is uniformly distributed around charged area, and the single receiving coil is in any position in charged area It sets, in the identical situation of spacing of any two transmitting coil, the range of the charged area is with transmitting coil quantity Increase and expands.

3. the method according to claim 1, wherein the step 3 includes:

According to formula (1), the optimal load resistance R under maximum load acquisition power is obtained_L,OPT/PDLThe configuration condition of parameter:

In load resistor value R_LWhen determining, M is obtained by formula (2)_TtRV_Ti-M_TiRV_TtWhen=0 establishment, under maximum system efficiency of transmission Optimal feed voltage parameter configuration condition:

V_Ti:V_Tt=M_TiR:M_TtR,

Under the conditions of the optimal feed voltage parameter configuration, system optimization efficiency PTE ' is obtained_OPT:

According to formula (3), the optimal load resistance R under maximum system efficiency of transmission is obtained_L,OPT/PTEThe configuration condition of parameter are as follows:

R_L,OPT/PTE=r_RA_n。