CN103886182A - Parameter equating method for aggregation model of doubly-fed generator set wind power station - Google Patents

Abstract

The invention discloses a parameter equating method for a aggregation model of a doubly-fed generator set wind power station. The parameter equating method mainly includes: subjecting the doubly-fed generator set in a wind power station to generator model parameter equating, shaft system parameter equating, transformer parameter equating and wind speed equating; subjecting an inner current collection circuit of the wind power station to equivalence processing according to a connection mode, and integrating the aggregation equating parameters of above links to obtain the aggregation model of the doubly-fed generator set wind power station. By the parameter equating method, defections like poor stability, low reliability and small application range in an existing aggregation modeling technology of the wind power station can be overcome, and the parameter equating method has the advantages of good stability, high stability and wide application range.

Description

A kind of double-fed unit wind energy turbine set polymerization model parameter equivalence method

Technical field

The present invention relates to the wind energy turbine set equivalent modeling technical field of wind-power electricity generation and grid-connected control thereof, particularly, relate to a kind of double-fed unit wind energy turbine set polymerization model parameter equivalence method.

Background technology

The large-scale wind electricity base majority that China's wind-powered electricity generation produces after entering the large-scale development stage is positioned at " three northern areas of China " (northwest, northeast, North China); large-scale wind electricity base is generally away from load center, and its electric power need to be transported to load center and dissolve through long-distance, high voltage.Due to intermittence, randomness and the undulatory property of wind-resources, cause the wind-powered electricity generation in large-scale wind power base to be exerted oneself fluctuation in a big way can occur thereupon, further cause the fluctuation of power transmission network charge power, bring series of problems to safe operation of electric network.

By in November, 2013, the installed capacity of Gansu Power Grid grid connected wind power has reached 6,680,000 kilowatts, accounts for 21% of Gansu Power Grid total installation of generating capacity, becomes the second largest main force power supply that is only second to thermoelectricity.Along with improving constantly of wind-electricity integration scale, the uncertainty of wind-power electricity generation and uncontrollability are brought problems to the safety and stability economical operation of electrical network.Therefore need the relevant issues of large-scale wind generating to analyse in depth research, especially need to study large-scale wind power and concentrate the wind energy turbine set polymerization model problem in grid-connected situation, calculate for the Power System Analysis containing large-scale wind power.

Realizing in process of the present invention, inventor finds that in prior art, at least existence and stability is poor, reliability is low and the defect such as the scope of application is little.

Summary of the invention

The object of the invention is to, for the problems referred to above, propose a kind of double-fed unit wind energy turbine set polymerization model parameter equivalence method, to realize good stability, reliability is high and the scope of application is large advantage.

For achieving the above object, the technical solution used in the present invention is: a kind of double-fed unit wind energy turbine set polymerization model parameter equivalence method, mainly comprise: respectively double-fed unit is carried out to equivalence and process, wind energy turbine set inside current collection circuit is carried out to equivalence and process, integrate the polymerization model that obtains this double-fed unit wind energy turbine set.

Further, the described operation of double-fed unit being carried out to equivalent processing, at least comprises:

A, to the generator model parameter of double-fed unit carry out equivalence process;

B, to the axle of double-fed unit be parameter carry out equivalence process;

C, to the transformer parameter of double-fed unit carry out equivalence process;

D, to the wind speed of double-fed unit carry out equivalence process.

Further, described step a, specifically comprises:

Suppose in the aerogenerator of n platform same model and have m platform equivalence to become 1 unit, equivalent calculation formula is as follows:

$\left\{\begin{array}{c}{S}_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i=\mathrm{mS},\\ P_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{P}_i=\mathrm{mP},Q_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{Q}_i=\mathrm{mQ}\\ X_{m-\mathrm{eq}}=\frac{x_m}{m}\\ X_{s-\mathrm{eq}}=\frac{x_s}{m},X_{r-\mathrm{eq}}=\frac{x_r}{m},\\ r_{s-\mathrm{eq}}=\frac{r_s}{m},r_{r-\mathrm{eq}}=\frac{r_s}{m}\end{array}\right.---\left(1\right);$

In formula (1), S _eqrepresent equivalent generator capacity, S _irepresent i platform generator capacity; M is the wind turbine number of organizing a performance; P _eqrepresent the active power after equivalence; P _irepresent the active power of i platform unit; P represents the average active power of each unit; Q _eqrepresent the reactive power after equivalence; Q _irepresent the reactive power of i platform unit; Q represents the average reactive power of each unit; X _m-eqfor the generator excitation reactance after equivalence; x _mfor generator excitation reactance; X _s-eqfor the generator unit stator reactance after equivalence; x _sfor generator unit stator reactance; X _r-eqfor the generator amature reactance after equivalence; x _rfor generator amature reactance; r _s-eqfor the generator unit stator resistance after equivalence; r _sfor generator unit stator resistance; r _r-eqfor the generator amature resistance after equivalence; r _rfor generator amature resistance.

Further, in step b, described is that parameter is carried out equivalent formula and is to axle:

$\left\{\begin{array}{c}{H}_{g\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{gi}}=m{H}_g\\ H_{t\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{ti}}=m{H}_t\\ H_{s\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{si}}=m{H}_s\end{array}\right.---\left(2\right);$

In formula (2), H _{g_eq}for the generator amature inertia time constant after equivalence; H _gfor generator amature inertia time constant; H _{t_eq}for the wind mill rotor inertia time constant after equivalence; H _tfor wind mill rotor inertia time constant; K _{s_eq}for the axis rigidity coefficient after equivalence; K _sfor axis rigidity coefficient; M is the wind turbine number of organizing a performance.

Further, in step c, describedly transformer parameter is carried out to equivalent formula be.

$\left\{\begin{array}{c}{S}_{T\_\mathrm{eq}}={\mathrm{mS}}_T\\ Z_{T\_\mathrm{eq}}=\frac{Z_T}{m}\end{array}\right.---\left(3\right);$

In formula (3), S _{t_eq}for the transformer capacity after equivalence; S _tfor transformer capacity; Z _{t_eq}for the transformer impedance after equivalence; Z _tfor transformer impedance; M is the wind turbine number of organizing a performance.

Further, in steps d, described wind speed is carried out to equivalent operation, specifically comprises:

While adopting the grouping method based on propeller pitch angle action situation, equivalent wind speed is:

$v_{\mathrm{eq}}=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i---\left(4\right);$

In formula (4), v _iit is the wind speed that i platform unit is captured; The mechanical output that polymerization model is caught is:

$P_m=m\left(\frac{1}{2}\mathrm{\ρ}{\mathrm{AC}}_{p\max }{V}_{\mathrm{eq}}^3\right)---\left(5\right);$

In formula (5), m is unit number of units, and ρ is wind power concentration, and A is unit wind sweeping area, C _pmaxfor maximal wind-energy usage factor, v _eqfor equivalent wind speed.

Further, wind energy turbine set inside current collection circuit is being carried out to equivalent operation, need to adopt different disposal routes according to the mode of connection of wind energy turbine set inside current collection circuit, specifically comprising:

1) in the time that the mode of connection of the inner current collection circuit of wind energy turbine set is the trunk line type mode of connection, equivalent impedance is:

$Z_{\mathrm{eq}\_n}=\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{i}^2{Z}_i\right]/n^2---\left(6\right);$

In formula (6), Z _{eq_n}for the equiva lent impedance of cable, n is unit number of units on circuit, Z _iit is the impedance of i bar of cable.

2) when the mode of connection of the inner current collection circuit of wind energy turbine set is many branched lines while being connected to the mode of connection of same node, equiva lent impedance is:

$Z_{\mathrm{eq}\_n}=\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i^2{Z}_i\right]/{\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i\right]}^2---\left(7\right);$

In formula (7), Z _{eq_n}for the equiva lent impedance of cable, n _mfor the number of units of unit on every circuit, n is total blower fan number of units.

Further, for the branch road of admittance over the ground of cable line, ignore the voltage differences in wind energy turbine set, equivalence is admittance Y over the ground _eqequal equivalent front all admittance Y _ibranch road and, that is:

$Y_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{Y}_i---\left(8\right);$

Wherein, i, m are natural number.

The double-fed unit wind energy turbine set polymerization model parameter equivalence method of various embodiments of the present invention, owing to mainly comprising: be that parameter, transformer parameter, wind speed are carried out equivalence and processed to generator model parameter, the axle of double-fed unit respectively, wind energy turbine set inside current collection circuit is carried out to equivalence and process, integrate each link parameter and obtain the polymerization model of this double-fed unit wind energy turbine set; The error of this model emulation result of calculation and practical operation situation is within the scope of acceptable, can reliably reflect wind energy turbine set actual motion characteristic, can be for the relevant issues of large-scale wind generating be analysed in depth, concentrate in grid-connected situation at large-scale wind power, the Power System Analysis containing large-scale wind power is calculated; This model can overcome poor stability in prior art, reliability is low and the scope of application is little defect, to realize good stability, reliability is high and the scope of application is large advantage.

Other features and advantages of the present invention will be set forth in the following description, and, partly from instructions, become apparent, or understand by implementing the present invention.

Below by drawings and Examples, technical scheme of the present invention is described in further detail.

Accompanying drawing explanation

Accompanying drawing is used to provide a further understanding of the present invention, and forms a part for instructions, for explaining the present invention, is not construed as limiting the invention together with embodiments of the present invention.In the accompanying drawings:

Fig. 1 is the structural representation of double-fed unit wind energy turbine set polymerization model parameter equivalence method apoplexy group of motors trunk line type wiring part of the present invention;

Fig. 2 is the structural representation of multiple wind-powered electricity generation unit parallel joins in double-fed unit wind energy turbine set polymerization model parameter equivalence method of the present invention;

Fig. 3 is the schematic flow sheet of double-fed unit wind energy turbine set polymerization model parameter equivalence method of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described, should be appreciated that preferred embodiment described herein, only for description and interpretation the present invention, is not intended to limit the present invention.

According to the embodiment of the present invention, as shown in Figure 1, Figure 2 and Figure 3, provide a kind of double-fed unit wind energy turbine set polymerization model parameter equivalence method.

The double-fed unit wind energy turbine set polymerization model parameter equivalence method of the present embodiment, mainly comprises the following steps:

Step 1: double-fed unit generator model parameter is carried out to equivalence.

Suppose in the aerogenerator of n platform same model and have m platform equivalence to become 1 unit, equivalent calculation formula is as follows:

$\left\{\begin{array}{c}{S}_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i=\mathrm{mS},\\ P_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{P}_i=\mathrm{mP},Q_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{Q}_i=\mathrm{mQ}\\ X_{m-\mathrm{eq}}=\frac{x_m}{m}\\ X_{s-\mathrm{eq}}=\frac{x_s}{m},X_{r-\mathrm{eq}}=\frac{x_r}{m},\\ r_{s-\mathrm{eq}}=\frac{r_s}{m},r_{r-\mathrm{eq}}=\frac{r_s}{m}\end{array}\right.---\left(1\right);$

In formula (1), S _eqrepresent equivalent generator capacity, S _irepresent i platform generator capacity; M is the wind turbine number of organizing a performance; P _eqrepresent the active power after equivalence; P _irepresent the active power of i platform unit; P represents the average active power of each unit; Q _eqrepresent the reactive power after equivalence; Q _irepresent the reactive power of i platform unit; Q represents the average reactive power of each unit; X _m-eqfor the generator excitation reactance after equivalence; x _mfor generator excitation reactance; X _s-eqfor the generator unit stator reactance after equivalence; x _sfor generator unit stator reactance; X _r-eqfor the generator amature reactance after equivalence; x _rfor generator amature reactance; r _s-eqfor the generator unit stator resistance after equivalence; r _sfor generator unit stator resistance; r _r-eqfor the generator amature resistance after equivalence; r _rfor generator amature resistance.

Step 2: double-fed shaft system of unit parameter is carried out to equivalence.

$\left\{\begin{array}{c}{H}_{g\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{gi}}=m{H}_g\\ H_{t\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{ti}}=m{H}_t\\ H_{s\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{si}}=m{H}_s\end{array}\right.---\left(2\right);$

In formula (2), H _{g_eq}for the generator amature inertia time constant after equivalence; H _gfor generator amature inertia time constant; H _{t_eq}for the wind mill rotor inertia time constant after equivalence; H _tfor wind mill rotor inertia time constant; K _{s_eq}for the axis rigidity coefficient after equivalence; K _sfor axis rigidity coefficient; M is the wind turbine number of organizing a performance.

Step 3: double-fed unit transformer parameter is carried out to equivalence.

$\left\{\begin{array}{c}{S}_{T\_\mathrm{eq}}={\mathrm{mS}}_T\\ Z_{T\_\mathrm{eq}}=\frac{Z_T}{m}\end{array}\right.---\left(3\right);$

In formula (3), S _{t_eq}for the transformer capacity after equivalence; ST is transformer capacity; Z _{t_eq}for the transformer impedance after equivalence; ZT is transformer impedance; M is the wind turbine number of organizing a performance.

Step 4: wind speed is carried out to equivalence.

As adopted the grouping method based on propeller pitch angle action situation time, equivalent wind speed is:

$v_{\mathrm{eq}}=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i---\left(4\right);$

In formula (4), v _iit is the wind speed that i platform unit is captured; The mechanical output that polymerization model is caught is:

$P_m=m\left(\frac{1}{2}\mathrm{\ρ}{\mathrm{AC}}_{p\max }{V}_{\mathrm{eq}}^3\right)---\left(5\right);$

In formula (5), m is unit number of units, and ρ is wind power concentration, and A is unit wind sweeping area, C _pmaxfor maximal wind-energy usage factor, v _eqfor equivalent wind speed.

Step 5: wind energy turbine set inside current collection circuit is carried out to equivalence.

Due to wind field mode of connection difference, need to divide situation discussion:

1) trunk line type wiring construction, as shown in Figure 1.

Equivalent impedance is:

$Z_{\mathrm{eq}\_n}=\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{i}^2{Z}_i\right]/n^2---\left(6\right);$

In formula (6), Z _{eq_n}for the equiva lent impedance of cable, n is unit number of units on circuit, Z _iit is the impedance of i bar of cable.

2) many branched lines are connected on same node, as shown in Figure 2.

Equivalent impedance is:

$Z_{\mathrm{eq}\_n}=\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i^2{Z}_i\right]/{\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i\right]}^2---\left(7\right);$

In formula (7), Z _{eq_n}for the equivalent impedance of cable, n _mfor the number of units of unit on every circuit, n is total blower fan number of units.

The inner current collection circuit of wind energy turbine set is divided into 2 kinds of cable and overhead transmission lines, and the charging capacitor of cable is very large, is generally 20～25 times of overhead transmission line, has been equivalent to reactive-load compensation equipment in parallel in the line, and overhead transmission line charging capacitor generally can be ignored.For the branch road of admittance over the ground of cable line, can ignore the voltage differences in wind energy turbine set, equivalence is admittance Y over the ground _eqequal equivalent front all admittance Y _ibranch road and, that is:

$Y_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{Y}_i---\left(8\right);$

Wherein, i, m are natural number.

Finally it should be noted that: the foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, although the present invention is had been described in detail with reference to previous embodiment, for a person skilled in the art, its technical scheme that still can record aforementioned each embodiment is modified, or part technical characterictic is wherein equal to replacement.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (8)

1. a double-fed unit wind energy turbine set polymerization model parameter equivalence method, it is characterized in that, mainly comprise: respectively double-fed unit carried out equivalence processing and wind energy turbine set inside current collection circuit carried out to equivalence and process, then integrating each link polymerization parameter, obtaining the polymerization model of this double-fed unit wind energy turbine set.

2. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 1, is characterized in that, the described operation of double-fed unit being carried out to equivalent processing, at least comprises:

A, to the generator model parameter of double-fed unit carry out equivalence process;

B, to the axle of double-fed unit be parameter carry out equivalence process;

C, to the transformer parameter of double-fed unit carry out equivalence process;

D, to the wind speed of double-fed unit carry out equivalence process.

3. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 2, is characterized in that, described step a, specifically comprises:

Suppose in the aerogenerator of n platform same model and have m platform equivalence to become 1 unit, equivalent calculation formula is as follows:

$\left\{\begin{array}{c}{S}_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{S}_i=\mathrm{mS},\\ P_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{P}_i=\mathrm{mP},Q_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{Q}_i=\mathrm{mQ}\\ X_{m-\mathrm{eq}}=\frac{x_m}{m}\\ X_{s-\mathrm{eq}}=\frac{x_s}{m},X_{r-\mathrm{eq}}=\frac{x_r}{m},\\ r_{s-\mathrm{eq}}=\frac{r_s}{m},r_{r-\mathrm{eq}}=\frac{r_s}{m}\end{array}\right.---\left(1\right);$

In formula (1), S _eqrepresent equivalent generator capacity, S _irepresent i platform generator capacity; M is the wind turbine number of organizing a performance; P _eqrepresent the active power after equivalence; P _irepresent the active power of i platform unit; P represents the average active power of each unit; Q _eqrepresent the reactive power after equivalence; Q _irepresent the reactive power of i platform unit; Q represents the average reactive power of each unit; X _m-eqfor the generator excitation reactance after equivalence; x _mfor generator excitation reactance; X _s-eqfor the generator unit stator reactance after equivalence; x _sfor generator unit stator reactance; X _r-eqfor the generator amature reactance after equivalence; x _rfor generator amature reactance; r _s-eqfor the generator unit stator resistance after equivalence; r _sfor generator unit stator resistance; r _r-eqfor the generator amature resistance after equivalence; r _rfor generator amature resistance.

4. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 2, is characterized in that, in step b, described is that parameter is carried out equivalent formula and is to axle:

$\left\{\begin{array}{c}{H}_{g\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{gi}}=m{H}_g\\ H_{t\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{ti}}=m{H}_t\\ H_{s\_\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{H}_{\mathrm{si}}=m{H}_s\end{array}\right.---\left(2\right);$

In formula (2), H _{g_eq}for the generator amature inertia time constant after equivalence; H _gfor generator amature inertia time constant; H _{t_eq}for the wind mill rotor inertia time constant after equivalence; H _tfor wind mill rotor inertia time constant; K _{s_eq}for the axis rigidity coefficient after equivalence; K _sfor axis rigidity coefficient; M is the wind turbine number of organizing a performance.

5. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 2, is characterized in that, in step c, describedly transformer parameter is carried out to equivalent formula is.

$\left\{\begin{array}{c}{S}_{T\_\mathrm{eq}}={\mathrm{mS}}_T\\ Z_{T\_\mathrm{eq}}=\frac{Z_T}{m}\end{array}\right.---\left(3\right);$

In formula (3), S _{t_eq}for the transformer capacity after equivalence; S _tfor transformer capacity; Z _{t_eq}for the transformer impedance after equivalence; Z _tfor transformer impedance; M is the wind turbine number of organizing a performance.

6. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 2, is characterized in that, in steps d, described wind speed is carried out to equivalent operation, specifically comprises:

While adopting the grouping method based on propeller pitch angle action situation, equivalent wind speed is:

$v_{\mathrm{eq}}=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{v}_i---\left(4\right);$

In formula (4), v _iit is the wind speed that i platform unit is captured; The mechanical output that polymerization model is caught is:

$P_m=m\left(\frac{1}{2}\mathrm{\ρ}{\mathrm{AC}}_{p\max }{V}_{\mathrm{eq}}^3\right)---\left(5\right);$

In formula (5), m is unit number of units, and ρ is wind power concentration, and A is unit wind sweeping area, C _pmaxfor maximal wind-energy usage factor, v _eqfor equivalent wind speed.

7. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 1, is characterized in that, the described operation of wind energy turbine set inside current collection circuit being carried out to equivalent processing, specifically comprises:

According to the mode of connection of wind energy turbine set inside current collection circuit, wind energy turbine set inside current collection circuit is waited to Value Operations, specifically comprise:

1) in the time that the mode of connection of the inner current collection circuit of wind energy turbine set is the trunk line type mode of connection, equivalent impedance is:

$Z_{\mathrm{eq}\_n}=\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{i}^2{Z}_i\right]/n^2---\left(6\right);$

In formula (6), Z _{eq_n}for the equiva lent impedance of cable, n is unit number of units on circuit, Z _iit is the impedance of i bar of cable;

2) when the mode of connection of the inner current collection circuit of wind energy turbine set is many branched lines while being connected to the mode of connection of same node, equiva lent impedance is:

$Z_{\mathrm{eq}\_n}=\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i^2{Z}_i\right]/{\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_i\right]}^2---\left(7\right);$

In formula (7), Z _{eq_n}for the equiva lent impedance of cable, n _mfor the number of units of unit on every circuit, n is total blower fan number of units.

8. double-fed unit wind energy turbine set polymerization model parameter equivalence method according to claim 7, is characterized in that, for the branch road of admittance over the ground of cable line, ignore the voltage differences in wind energy turbine set, equivalence is admittance Y over the ground _eqequal equivalent front all admittance Y _ibranch road and, that is:

$Y_{\mathrm{eq}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{Y}_i---\left(8\right);$

Wherein, i, m are natural number.

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