CN104462837A - Method for determining power transmission line reinforcing scheme by comprehensive fault rate and economic efficiency evaluation - Google Patents

Abstract

The invention discloses a method for determining a power transmission line reinforcing scheme by comprehensive fault rate and economic efficiency evaluation. The method includes adopting the general extreme value theory to model historical ice coating data of an area to obtain probability of ice disasters of the area with specific ice coating thickness; establishing a circuit fault rate function based on physical stress analysis of power transmission lines according to the metal deformation theory, and establishing a fuzzy fault rate model of the lines by virtue of fuzzy offline rate; comprehensively considering the probability of the ice disasters in the area with the specific ice coating thickness and the fuzzy fault rate of the lines in the area to obtain comprehensive fault rate of the lines; calculating differential 'detraction' benefits by means of the comprehensive fault rate, establishing an economic efficiency evaluation index system of differential planning on this basis, and determining the sectional reinforcing scheme of the lines. The method for determining the power transmission line reinforcing scheme by the comprehensive fault rate plays an important role in guiding workout of the line-difference sectional reinforcing scheme in the differential planning and has great significance in improving anti-disaster ability of the power grid.

Description

By the method for resultant fault rate and economic evaluation determination transmission line of electricity strengthened scheme

Technical field

The invention belongs to the differentiation planning field of electric system, relate more specifically to the method by resultant fault rate and economic evaluation index determination transmission line of electricity segmentation strengthened scheme.

Background technology

The change of whole world meteorological condition, extreme weather events is caused frequently to occur in various places, the destructiveness wherein especially caused electrical network with ice disaster is maximum, within 1998, Quebec, Canada is attacked by snowstorm, southern china most area in 2008 meets with rare sleet and snow ice and attacks, the northwestward, Hubei in 2014 electrical network meets with rare freezing disaster, causes local power plant Transmission Corridor to interrupt.The safe and stable operation of the disaster accident serious threat electrical network that these take place frequently.How to reduce the destructive consequence that meteorological disaster brings to electrical network and cause numerous focus of attention.

Improve electrical network especially with the anti-disaster ability of the Large Copacity long-distance transmissions extra-high voltage grade power transmission network that is feature, need according to electrical network differentiation planning principles and thought, electrical network is being faced on the basis that possibility that Practical Meteorological Requirements geologic condition and element move back fortune fault analyzes, build core backbone frame, reasonable assessment and the strengthen construction grade selecting critical circuits simultaneously, but the further investigation of corresponding theory and technical method is lacked in the research of differentiation planning field.Li Canbing etc. in Automation of Electric Systems 2009,24 (33): 11-15 " the electrical network differentiation planning new methods " delivered; Ma Qinguo etc. at Shaanxi Power 2008,36 (8): 15-17 " the Shaanxi Power System differentiation planning researchs " delivered; Xu state newly waits in Automation of Electric Systems, 2010, the key concept planned electrical network differentiation in the papers such as 34 (03): 17-21 " disaster-resistant type Electric Power Network Planning pattern and the models " delivered and flow process are introduced, but for problem crucial in differentiation planning---how to realize differentiation planning, namely each element in bulk transmission grid is carried out to the differentiation reinforcement of which kind of rank, still do not propose concrete solution.

China 500kV above major network transmission path generally crosses over multiple meteorological condition region, carries out probability of malfunction calculating obviously do not meet reality with single meteorological condition; Secondly, when disaster occurs, the possibility that circuit and element break down is a complicated probability, needs comprehensively to take into account meteorological condition probability of happening and the probability of fortune appears moving back in element under this meteorological condition.Zou Xin etc. in Automation of Electric Systems 2011,35 (13): 7-11, " the cascading failure in power system probability assessment based on circuit operational reliability model " delivered on 71; . Yang Hongming etc. in electric power network technique 2012, " under ice storm disaster the transmission line malfunction probabilistic forecasting " delivered on 36 (4): 213-215; Duan Tao etc. are in protecting electrical power system and control; 2013; in papers such as " the taking into account the real-time assessment model of the transmission line malfunction probability of meteorologic factor " of delivering on 41 (15): 59-67; line failure rate calculating is carried out based on real-time operating condition; although relate to the impact of meteorologic factor; but for Electric Power Network Planning, meteorological condition does not all show to the interact relation of line fault probability is clear by these documents, is not therefore suitable in Electric Power Network Planning.

The segmentation of the transmission line of electricity crossing over many meteorological conditions is strengthened to the selection of rank, need on the basis considering meteorological condition, carry out economic index calculating and assessment.Liu Lu etc. are in Automation of Electric Systems 2012,36 (15): 45-50 " the power system economy appraisal procedures based on overall life cycle cost " delivered propose the power system economy appraisal procedure based on overall life cycle cost, but the method is only for the Electric Power Network Planning of routine, inapplicable to the Electric Power Network Planning economic evaluation after differentiation;

Song Chunli etc. are in electric power network technique 2013,37 (7): 1849-1855 " the Electric Power Network Planning economic evaluation methods based on differentiation overall life cycle cost " delivered propose the economic evaluation system and evaluation index that are applicable to the planning of electrical network differentiation, but the n mono-that the line failure rate related in these indexs adopts meets corresponding average annual failure rate, relatively simple, the result out of true of the economic index obtained with this.The present invention is based on generalized extreme value distribution theory and Metal Deformation theory, on the basis meeting circuit reinforcement standard reliability, maximum net proceeds indicatior according to circuit economy show that circuit strengthened scheme is more accurate with this line failure rate phase obtained method than before, and the circuit economic evaluation based on this is more concrete.

Summary of the invention

For background technology Problems existing, the invention provides a kind of method by resultant fault rate and economic evaluation determination transmission line of electricity strengthened scheme.The method adopts the theoretical history icing data modeling to region of generalized extreme value, obtain this region under specific ice covering thickness and the probability of ice damage occurs, theoretical according to Metal Deformation, set up the line failure rate function based on the physics force analysis of transmission line of electricity, the thought of the fuzzy outage rate of further reference, set up the fuzzy failure rate model of circuit, there is the fuzzy failure rate of circuit in the probability of ice damage and this region in the region considering specific ice covering thickness, obtain the resultant fault rate of circuit, utilize resultant fault rate calculated difference " impairment " benefit, set up through differentiation planning economic evaluation index system on this basis, and then determine the segmentation strengthened scheme of circuit.The formulation of the present invention to differentiation planning center line road differentiation segmentation strengthened scheme has important directive function, significant to raising electrical network anti-disaster ability.

In order to achieve the above object, the present invention adopts following technical scheme:

By the method for resultant fault rate and economic evaluation determination transmission line of electricity strengthened scheme, the method comprises the following step:

A, on only considering the transmission line of electricity that ice damage affects, circuit L passes through the weather region of m different icing degree, and these weather region are set to region 1,2,3 respectively ..., m, and the length l being positioned at region i _iroad total length L that the line is busy _Σratio be q _i.

B, adopt the theoretical history icing data modeling to region i of generalized extreme value, obtain the probability that ice damage occurs in this region under specific ice covering thickness.The standardization distribution function of generalized extreme value distribution is:

$\left\{\begin{array}{c}F\left(x\right)=\exp \{-{[1-k\frac{x-\mathrm{\β}}{\mathrm{\δ}}]}^{1/k}\},k\≠0,\\ F\left(x\right)=\exp \{-\exp [-\frac{x-\mathrm{\β}}{\mathrm{\δ}}\left]\right\},k=0.\end{array}\right.---\left(1\right)$

In formula (1), δ is scale parameter, and β is location parameter, and k is form parameter.

The method of L-moments estimation is adopted to realize the parameter estimation of generalized extreme value distribution.

Three rank weight squares of probability right square can be written as:

$\left\{\begin{array}{c}{b}_0=\stackrel{\‾}{x},\\ b_1=\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}\frac{(n-j)}{n(n-1)(n-2)}{x}_j,\\ b_2=\underset{j=1}{\overset{n-2}{\mathrm{\Σ}}}\frac{(n-j)(n-j-1)}{n(n-1)(n-2)}{x}_j.\end{array}\right.---\left(2\right)$

Calculate the linear combination of above-mentioned three formulas, i.e. L square, be respectively:

$\left\{\begin{array}{c}{\mathrm{\λ}}_1=b_0,\\ {\mathrm{\λ}}_2=2b_1-b_0,\\ {\mathrm{\λ}}_3=6b_2-6b_1+b_0.\end{array}\right.---\left(3\right)$

$\left\{\begin{array}{c}k=7.8590c+2.9554c^2,\\ c=\frac{2}{3+{\mathrm{\λ}}_3/{\mathrm{\λ}}_2}-\frac{\ln 2}{\ln 3},\\ \mathrm{\δ}=\frac{{\mathrm{\λ}}_{2}k}{(1-2^{-k})\mathrm{\Γ}(1+k)},\\ \mathrm{\β}={\mathrm{\λ}}_1-\frac{\mathrm{\δ}[1-\mathrm{\Γ}(1+k)]}{k}.\end{array}\right.---\left(4\right)$

By calculating coefficient R and square error S _sthe fitting effect of generalized extreme value distribution model is tested.Wherein:

$\left\{\begin{array}{c}R=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\sqrt{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2}},\\ S_S=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-y_i)}^2}{n}}.\end{array}\right.---\left(5\right)$

In formula, x _ifor theoretic frequency, y _ifor empirical Frequency, for the mean value of theoretic frequency, for the mean value of empirical Frequency.

Interval probability is adopted to calculate specific ice covering thickness x _pthere is the probability P (x of ice damage in this region lower _p| F) P (F), its computing method are:

P(x _P|F)P(F)

＝P(x+d≥x _P)-P(x-d≥x _P)

＝P(x≥x _P-d)-P(x≥x _P+d)

(6)

＝[1-F(x _p-d)]-[1-F(x _p+d)]

＝F(x _P+d)-F(x _P-d)

In formula (6), d is line design ice covering thickness.

C, theoretical according to Metal Deformation, after the ability to bear of shaft tower or circuit reaches and bears the limit, along with the increase of strain, ability to bear exponentially reduces rapidly, and the failure rate of circuit and ability to bear are inversely proportional to, its exponentially function rising.Line failure rate function following expression based on the physics force analysis of transmission line of electricity obtains:

${\mathrm{\&lambda;}}_F\left(x\right)=\left\{\begin{array}{c}0,x\&le;d\\ \exp \left[\frac{0.6931(x-d)}{4d}\right]-1,d<x<5d\\ 1,x\&GreaterEqual;5d\end{array}\right.---\left(7\right)$

In formula, x is ice thickness, and d is line design ice covering thickness.When d < x < 5d, failure rate exponentially increases, and from formula (7), this failure rate is the probability of line fault, has nothing to do with the working time before line fault.

Use for reference the thought of fuzzy outage rate, the data of association index failure rate, set up fuzzy failure rate model.

Definition logical variable Ex _pcharacterize the ice load of transmission line of electricity, domain is as follows:

The transmission line malfunction probabilistic logic variable R FR (E corresponding with ice load _xp), its domain is as follows:

Wherein d _iLfor Design ice thickness, 0.68 represents when ice covering thickness is 4 times of Design ice thickness, and this part of path has the possibility of 0.68 to break down.

Line fault probability under d, the probability considering specific ice covering thickness lower area generation ice damage and certain icing condition, obtaining circuit resultant fault rate is:

$\mathrm{\&lambda;}=P\left(x_P\right|F)P\left(F\right)\&CenterDot;P_{\mathrm{RFR}\left(E_{\mathrm{xP}}\right)}---\left(8\right)$

In formula (8), P (x _p| F) P (F) represents that ice covering thickness is x _pice damage probability of happening, represent that λ represents that ice covering thickness is x in failure rate corresponding to certain ice covering thickness line _pthe resultant fault rate of line.

Be n at Design ice thickness ₀d _iL, generation icing is nd _iL, and n ₀d _iL< n ₀d _iLtime, the failure rate being positioned at each section of circuit of zones of different is λ _i, the differentiation that may be adopted by circuit is strengthened standard a and is divided into 10amm (a=1,2,3); Arranging line sectionalizing reference numeral is 1,2,3 ..., m.And in i-th region, the circuit resultant fault rate determined by its meteorological condition is represent in i-th region, the resultant fault rate of circuit when corresponding reinforcement standard is.The resultant fault rate that circuit is strengthened in segmentation adopts following computing method:

1) first segmentation is carried out to the part of path crossing over different weather region, rely on the trans-regional meteorological condition of circuit and launch segmentation, obtain new part of path and divide: l (λ _i), i=1,2,3 ... m, the ratio that corresponding line section accounts for total line length is respectively: q _i, i=1,2,3 ... m, corresponding each section of reinforcement standard is 10a _i, corresponding each segment fault rate is λ _i;

2) the resultant fault rate of sectionalized line is taken as:

$\mathrm{\&lambda;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{q}_i*{\mathrm{\&lambda;}}_i---\left(9\right)$

E, utilize resultant fault rate calculated difference " impairment " benefit, and then set up through differentiation planning economic evaluation index system, determine the line sectionalizing strengthened scheme across different weather region.

Use for reference " have to have no contrast " principle in the economics of catastrophe, all only calculate in cost in differentiation planning due to differentiation design the cost that increase, namely only counted raising transmission line of electricity and combated a natural disaster standard and carry out transforming or newly-built increased cost.Decompose life cycle management differentiation cost, can obtain:

Q _LCC＝IC+OC+MC+DC (10)

In formula (10), IC is differentiation cost of investment, and OC is differentiation maintenance cost, and MC is differentiation operating cost, and DC is differentiation obsolescence cost.

Corresponding cost of investment is also different owing to strengthening rank difference for the circuit of segmentation reinforcement, therefore needs segmentation to calculate to its differentiation cost.If circuit L passes through the weather region of m different icing degree, the length l in zones of different _i,

The ratio accounting for total line length is q _i, in i-th region, corresponding reinforcement standard is a _i, cost is Ci _ai(ten thousand yuan/meter), thus the differentiation cost of investment that circuit is strengthened in segmentation is:

${\mathrm{IC}}_{\mathrm{\&alpha;}}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{l}_i{q}_i*{\mathrm{Ci}}_{\mathrm{ai}}---\left(11\right)$

Wherein, differentiation maintenance cost and operating cost can be estimated by differentiation cost of investment number percent:

OC+MC＝σIC _α(12)

In formula (12), σ is O&M cost scale-up factor.

The expression formula that differentiation scrap cost is converted into differentiation cost of investment is:

$\mathrm{DC}=\mathrm{\&omega;}{\mathrm{IC}}_{\mathrm{\&alpha;}}-\frac{{\mathrm{IC}}_{\mathrm{\&alpha;}}}{{(1+r)}^N}---\left(13\right)$

In formula (13), the right Section 1 represents circuit processing cost, and Section 2 represents the residual value of circuit at life cycle end, and ω is circuit processing cost coefficient, and r is average annual coefficient of depreciation, and N is plant life cycle.

To transmission line of electricity α, if its life cycle is N, in the kth year of life cycle management, its differentiation cumulative cost is:

$Q(\mathrm{\&alpha;},k)={\mathrm{IC}}_{\mathrm{\&alpha;}}{(1+i)}^k+{(\mathrm{OC}+\mathrm{MC})}_{\mathrm{\&alpha;}}\frac{{(1+i)}^k-1}{i}+\left\{\begin{array}{c}0,k=\mathrm{1,2},...,N-1\\ {\mathrm{DC}}_{\mathrm{\&alpha;}},k=N\end{array}\right.---\left(14\right)$

In formula (14), Q (α, k) the differentiation cumulative cost of circuit α in kth year is represented, when the right Section 1 represents consideration time value on assets, convert the track investment cost to kth year, the right Section 2 represents that circuit adds up operation expense to during kth year, and the right Section 3 represents the processing cost of circuit after N scraps and residual value.

Differentiation " impairment " benefit DB comprises direct benefit E ₁with indirect benefit E ₂:

DB(α)＝λ*(E ₁+E ₂) _α(15)

In formula (15), E ₁for circuit damages the direct circuit electricity price revenue losses brought, E ₂produce for damaging the workers and peasants business caused that has a power failure because of circuit the indirect loss brought, λ is the resultant fault rate considering icing Probability Condition line l.

In order to effectively weigh the economy of line sectionalizing strengthened scheme, in conjunction with differentiation cost, benefit, the differentiation planning economic evaluation index of proposition is as follows.

1) differentiation cumulative cost Q (α, k): during measurement kth year, circuit carries out the accumulative cost needing to drop into of differentiation planning, shown in (14).

2) differentiation accumulative benefit W (k, α): weigh circuit during kth year owing to carrying out the accumulative benefit obtained of differentiation planning, W (k, α)=k*DB (α).

3) differentiation accumulated net income H (α, k): weigh when arriving kth year and add up gained net proceeds, H (α after circuit removing differentiation cost, k)=W (α, k)-Q (α, k)=k*DB (α)-Q (α, k).

The differentiation planning economic evaluation index of the different segmentation strengthened scheme of alternative route, determines that line located accumulated net income H (α, k) is maximum, the segmentation strengthened scheme that economy is best.

The present invention has the following advantages:

1 electrical network differentiation planning is the important means improving electric system anti-disaster ability, and wherein ice damage is the key factor affecting power grid operation, therefore consider that meteorological condition probability carries out differentiation segmentation reinforcement to the different circuits that electrical network is positioned at zones of different, significant to raising electrical network anti-disaster ability.

2 consider the line fault probability under the ice damage probability of happening of specific ice covering thickness and certain icing condition that generalized extreme value distribution theory obtains, the circuit resultant fault rate obtained provides foundation for line sectionalizing strengthened scheme, and the investment that electrical network differentiation is planned to be increased can improve the anti-disaster ability of electrical network to greatest extent.

3 utilize resultant fault rate calculated difference " impairment " benefit, set up on this basis through differentiation planning economic evaluation index system, can be used for determining the line sectionalizing strengthened scheme across different weather region.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is Garver-6 system wiring figure in the present invention.

Fig. 3 is the ice covering thickness generalized extreme value distribution matched curve in region 1 (a) and region 2 (b) in the present invention.

Embodiment

The present invention adopts the theoretical history icing data modeling to region of generalized extreme value, obtains the probability that ice damage occurs in this region under specific ice covering thickness; Theoretical according to Metal Deformation, set up the line failure rate function of the physics force analysis based on transmission line of electricity, use for reference the thought of fuzzy outage rate further, set up the fuzzy failure rate model of circuit; There is the fuzzy failure rate of circuit in the probability of ice damage and this region in the region considering specific ice covering thickness, obtains the resultant fault rate of circuit; Utilize resultant fault rate calculated difference " impairment " benefit, set up on this basis through differentiation planning economic evaluation index system, and then determine the segmentation strengthened scheme of circuit.Below in conjunction with accompanying drawing, the present invention is further illustrated.

Embodiment 1

For the Garver-6 system shown in Fig. 2, as shown in Figure 1, the present invention comprises the following step:

Step 1, adopt the theoretical history icing data modeling to region i of generalized extreme value, obtain the probability that ice damage occurs in this region under specific ice covering thickness.

Two groups of icing data sequences are set respectively as shown in Table 1 and Table 2, for describing the icing degree of two zoness of different.

Table 1 region 1 icing standard ice thickness extreme value sequence

Time	1980	1981	1982	1983	1984	1985	1986	1987
									Standard ice thickness/mm	13.18	24.25	17.51	18.47	18.47	38.38	18.85	13.18
Time	1988	1989	1990	1991	1992	1993	1994	1995
									Standard ice thickness/mm	14.36	33.35	23.37	18.47	19.23	12.77	16.85	14.74
Time	1996	1997	1998	1999	2000	2001	2002	2003
									Standard ice thickness/mm	13.18	17.67	16.85	16.00	12.77	18.15	19.97	20.26

Table 2 region 2 icing standard ice thickness extreme value sequence

Time	1980	1981	1982	1983	1984	1985	1986	1987
									Standard ice thickness/mm	12.14	23.24	16.85	18.07	18.47	34.50	17.27	14.17
Time	1988	1989	1990	1991	1992	1993	1994	1995
									Standard ice thickness/mm	13.38	26.68	21.38	18.47	17.67	12.77	15.82	13.78
Time	1996	1997	1998	1999	2000	2001	2002	2003
									Standard ice thickness/mm	13.18	16.85	15.11	14.17	12.77	15.65	16.85	16.35

Adopt generalized extreme value distribution theory to carry out modeling to the icing data in two regions, adopt L moment estimation method to carry out parameter estimation to model, obtain the generalized extreme value distribution matched curve of the icing extreme value in two regions as shown in Figure 3.

Degree of fitting inspection is carried out to the generalized extreme value distribution matched curve of ice covering thickness, obtains assay as shown in table 3.As shown in Table 3, the degree of fitting coefficient R in region 1 and region 2 all controls about 0.996, and square error S _sthen control about 0.03, illustrate that fitting result is in the scope that error allows.

The icing probability generalized extreme value Scaling function degree of fitting inspection in table 3 region 1 and region 2

Index	Coefficient R	Square error Ss
			Region 1	0.9964	0.0308
Region 2	0.9963	0.0307

The standard ice covering thickness that can obtain two region different probability corresponding by the ice covering thickness generalized extreme value distribution curve in two regions in Fig. 3 is as shown in table 4.

Table 4 region 1 and standard ice thickness corresponding to region 2 different probability

Icing extreme value probability/%	1	2	3.3	5	10	20
							Ice covering thickness 1/mm	43.4	37.26	33.32	30.46	26.09	22.2
Ice covering thickness 2/mm	38.86	33.05	29.39	26.8	22.96	19.68

Step 2, theoretical according to Metal Deformation, set up the line failure rate function of the physics force analysis based on transmission line of electricity, use for reference the thought of fuzzy outage rate further, set up the fuzzy failure rate model of circuit;

Line fault probability under step 3, the probability considering specific ice covering thickness lower area generation ice damage and certain icing condition, obtains the resultant fault rate of circuit.

If be d according to the ice thickness value of original anti-ice standard design _iL=10mm, by the generalized extreme value distribution curve of icing extreme value, can obtain the probability that each group of icing extreme value is corresponding, and then to calculate in Design ice thickness value be d _iLthe result of the circuit resultant fault rate in=10mm time domain 1 and region 2 respectively as shown in table 5 and table 6.

The circuit resultant fault rate in table 5 region 1

Strengthen ice thickness extreme value/mm	20	30	40	50
					Icing probability	0.6928	0.2536	0.0391	0.0093
Line failure rate	0.2	0.41	0.68	1
					Resultant fault rate λ	0.1386	0.1040	0.0266	0.0093

The circuit resultant fault rate in table 6 region 2

Strengthen ice thickness extreme value/mm	20	30	40	50
					Icing probability	0.8137	0.1558	0.0216	0.0054
Line failure rate	0.2	0.41	0.68	1
					Resultant fault rate λ	0.1627	0.0639	0.0147	0.0054

Step 4, utilize resultant fault rate calculated difference " impairment " benefit, and then set up through differentiation planning economic evaluation index system, determine the line sectionalizing strengthened scheme across different weather region.

Because circuit cost numerical value arranges only in order to reflect that different ice thickness strengthens the difference of standard, in view of economic evaluation interpretation of result draws primarily of contrast, therefore to arrange line located unit price as shown in table 7 in the present invention, and the Design ice thickness setting non-differentiation planning circuit is 10mm.

The different ice thickness of table 7 strengthens standard line differentiation unit price

Region 1 and region 2 is crossed over for circuit 4-6, if circuit 4-6 and the ratio being positioned at region 1 part the line is busy road overall length are, strengthened scheme is as shown in table 8, and when circuit 4-6 adopts different segmentation strengthened scheme, differentiation cumulative cost, benefit and net proceeds result are as shown in table 9.

Table 8 circuit 4-6 segmentation strengthened scheme

Protocol Numbers	Be positioned at region 1 part and strengthen rank	Be positioned at region 2 part and strengthen rank
			1	20mm	20mm
2	30mm	20mm
			3	30mm	30mm
4	40mm	30mm
			5	40mm	40mm
6	50mm	40mm
			7	50mm	50mm

Differentiation cumulative cost, benefit and net proceeds when table 9 circuit 4-6 adopts different segmentation strengthened scheme

According to the economic evaluation result of calculation of table 9, the segmentation strengthened scheme of trans-regional circuit is analyzed as follows:

1) according to the order of scheme 1 to scheme 7, improve gradually owing to strengthening rank to line sectionalizing, line located cumulative cost constantly increases, and differentiation accumulative benefit also increases along with the raising of the standard of combating a natural disaster simultaneously.

2) when the length ratio that circuit is positioned at region 1 (region that icing is more serious) is different, if it is identical that line parts strengthens rank, now initial outlay is identical with O&M cost, anti-ice grade is also identical, and therefore differentiation cumulative cost, differentiation accumulative benefit and differentiation accumulated net income and value have nothing to do.

3) if line parts strengthens rank difference, namely compared with the part of path of critical regions, higher reinforcement rank is adopted to icing, then be positioned at icing more compared with the part of critical regions, differentiation cost is higher, differentiation benefit also can correspondingly increase thereupon, but differentiation accumulated net income is also relevant with differentiation benefit growth rate with differentiation cost, in different segmentation strengthened scheme, differentiation accumulated net income is not identical with the relation of value.In strengthened scheme 2, differentiation accumulated net income increases with the increase of value, and in strengthened scheme 4, differentiation accumulated net income reduces with the increase of value.This shows that differentiation accumulated net income and value do not have directly related relation.

Each strengthened scheme of Integrated comparative is known, when strengthening being 30mm for two sections that circuit adheres to zones of different separately simultaneously, differentiation accumulated net income is maximum, accumulated net income cost obtains maximal value than also simultaneously, under each segmentation strengthened scheme, obtainable largest cumulative net proceeds is also all strengthen obtaining maximal value for during 30mm at two sections, and the operation year number obtaining maximal value is 23 years, very close to cycle designed life, therefore comprehensive indices is known, under setting regions meteorological condition, circuit 4-6 adopts the economy of segmentation strengthened scheme 3 best.

Claims (1)

1., by the method for resultant fault rate and economic evaluation determination transmission line of electricity strengthened scheme, it is characterized in that, the method includes the steps of:

A, on only considering the transmission line of electricity that ice damage affects, circuit L passes through the weather region of m different icing degree, these weather region are set to respectively region 1,2,3 ..., m, be positioned at the length l of region i _iroad total length L that the line is busy _Σratio be q _i, i=1,2,3 ..., m;

B, adopt the theoretical history icing data modeling to region i of generalized extreme value, obtain the probability that ice damage occurs in this region under specific ice covering thickness, the standardization distribution function of generalized extreme value distribution is:

$\left\{\begin{array}{c}F\left(x\right)=\exp \{-{[1-k\frac{x-\mathrm{\&beta;}}{\mathrm{\&delta;}}]}^{1/k}\},k\&NotEqual;0,\\ F\left(x\right)=\exp \{-\exp [-\frac{x-\mathrm{\&beta;}}{\mathrm{\&delta;}]}\left]\right\},k=0.\end{array}\right.---\left(1\right)$

In formula (1), δ is scale parameter, and β is location parameter, and k is form parameter;

The method of L-moments estimation is adopted to realize the parameter estimation of generalized extreme value distribution.

Three rank weight squares of probability right square can be written as:

$\left\{\begin{array}{c}{b}_0=\stackrel{\&OverBar;}{x},\\ b_1=\underset{j=1}{\overset{n-1}{\mathrm{\&Sigma;}}}\frac{(n-j)}{n(n-1)(n-2)}{x}_j,\\ b_2=\underset{j=1}{\overset{n-2}{\mathrm{\&Sigma;}}}\frac{(n-j)(n-j-1)}{n(n-1)(n-2)}{x}_j.\end{array}\right.---\left(2\right)$

Calculate the linear combination of above-mentioned three formulas, i.e. L square, be respectively:

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_1=b_0,\\ {\mathrm{\&lambda;}}_2={2b}_1-b_0,\\ {\mathrm{\&lambda;}}_3={6b}_2-{6b}_1+b_0.\end{array}\right.---\left(3\right)$

The estimation formulas of generalized extreme value distribution parameter is:

$\left\{\begin{array}{c}k=7.8590c+2.9554c^2,\\ c=\frac{2}{3+{\mathrm{\&lambda;}}_3/{\mathrm{\&lambda;}}_2}-\frac{\ln 2}{\ln 3},\\ \mathrm{\&delta;}=\frac{{\mathrm{\&lambda;}}_{2}k}{(1-2^{-k})\mathrm{\&Gamma;}(1+k)},\\ \mathrm{\&beta;}={\mathrm{\&lambda;}}_1-\frac{\mathrm{\&delta;}[1-\mathrm{\&Gamma;}(1+k)]}{k}.\end{array}\right.---\left(4\right)$

By calculating coefficient R and square error S _sthe fitting effect of generalized extreme value distribution model is tested, wherein:

$\left\{\begin{array}{c}R=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(x_i-\stackrel{\&OverBar;}{x})(y_i-\stackrel{\&OverBar;}{y})}{\sqrt{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x_i-\stackrel{\&OverBar;}{x})}^2\&CenterDot;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-\stackrel{\&OverBar;}{y})}^2}},\\ S_S=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x_i-y_i)}^2}{n}}.\end{array}\right.---\left(5\right)$

In formula, x _ifor theoretic frequency, y _ifor empirical Frequency, for the mean value of theoretic frequency, for the mean value of empirical Frequency;

Interval probability is adopted to calculate specific ice covering thickness x _pthere is the probability P (x of ice damage in this region lower _p| F) P (F), its computing method are:

$\begin{array}{c}P\left(x_P\right|F)P\left(F\right)\\ =P(x+d\&GreaterEqual;x_P)-P(x-d\&GreaterEqual;x_P)\\ =P(x\&GreaterEqual;x_P-d)-P(x-d\&GreaterEqual;x_P)\\ =[1-F(x_p-d)]-[1-F(x_p+d)]\\ =F(x_P+d)-F(x_P-d)\end{array}---\left(6\right)$

Wherein, d is line design ice covering thickness;

C, theoretical according to Metal Deformation, the line failure rate function that the physics force analysis based on transmission line of electricity obtains is as follows:

${\mathrm{\&lambda;}}_F\left(x\right)=\left\{\begin{array}{cc}0,& x\&le;d\\ \exp \left[\frac{0.6931(x-d)}{4d}\right]-1,& d<x<5d\\ 1,& x\&GreaterEqual;5d\end{array}\right.---\left(7\right)$

In formula, x is ice thickness, and d is line design ice covering thickness;

Use the thought of fuzzy outage rate, the data of association index failure rate, set up fuzzy failure rate model:

Definition logical variable Ex _pcharacterize the ice load of transmission line of electricity, its domain is as follows:

The transmission line malfunction probabilistic logic variable R FR (E corresponding with ice load _xp), its domain is as follows:

Wherein d _iLfor Design ice thickness, 0.68 represents when ice covering thickness is 4 times of Design ice thickness, and this part of path has the possibility of 0.68 to break down;

Line fault probability under d, the probability considering specific ice covering thickness lower area generation ice damage and certain icing condition, obtaining circuit resultant fault rate is:

$\mathrm{\&lambda;}=P\left(x_P\right|F)P\left(F\right)\&CenterDot;P_{\mathrm{RFR}\left(E_{x_P}\right)}---\left(8\right)$

(8) in formula, P (x _p| F) P (F) represents that ice covering thickness is x _pice damage probability of happening, represent that λ represents that ice covering thickness is x in failure rate corresponding to certain ice covering thickness line _pthe resultant fault rate of line;

Be n at Design ice thickness ₀d _iL, generation icing is nd _iL, and n ₀d _iL< n ₀d _iLtime, the failure rate being positioned at each section of circuit of zones of different is λ _i, the differentiation that may be adopted by circuit is strengthened standard a and is divided into 10a mm (a=1,2,3); Arrange line sectionalizing reference numeral be 1,2,3 ..., m; And in i-th region, the circuit resultant fault rate determined by its meteorological condition is represent in i-th region, the resultant fault rate of circuit when corresponding reinforcement standard is; The resultant fault rate that circuit is strengthened in segmentation adopts following computing method:

1) first segmentation is carried out to the part of path crossing over different weather region, rely on the trans-regional meteorological condition of circuit and launch segmentation, obtain new part of path and divide: l (λ _i), i=1,2,3 ..., m, the ratio that corresponding line section accounts for total line length is respectively q _i, i=1,2,3 ..., m, corresponding each section of reinforcement standard is 10a _i, corresponding each segment fault rate is λ _i;

2) the resultant fault rate of sectionalized line is taken as:

$\mathrm{\&lambda;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{q}_i*{\mathrm{\&lambda;}}_i---\left(9\right)$

E, utilize resultant fault rate calculated difference " impairment " benefit, and then set up through differentiation planning economic evaluation index system, determine the line sectionalizing strengthened scheme across different weather region;

Use " have to have no contrast " principle in the economics of catastrophe, decompose life cycle management differentiation cost, can obtain:

Q _LCC＝IC+OC+MC+DC (10)

In formula (10), IC is differentiation cost of investment, and OC is differentiation maintenance cost, and MC is differentiation operating cost, and DC is differentiation obsolescence cost;

In i-th region, corresponding reinforcement standard is a _i, unit price is Ci _ai, thus the differentiation cost of investment that circuit is strengthened in segmentation is:

${\mathrm{IC}}_{\mathrm{\&alpha;}}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{l}_i{q}_i*{\mathrm{Ci}}_{\mathrm{ai}}---\left(11\right)$

Wherein, differentiation maintenance cost and operating cost can be estimated by differentiation cost of investment number percent:

OC+MC＝σIC _α(12)

In formula (12), σ is O&M cost scale-up factor;

The expression formula that differentiation scrap cost is converted into differentiation cost of investment is:

$\mathrm{DC}=\mathrm{\&omega;}{\mathrm{IC}}_{\mathrm{\&alpha;}}-\frac{{\mathrm{IC}}_{\mathrm{\&alpha;}}}{{(1+r)}^N}---\left(13\right)$

In formula (13), the right Section 1 represents circuit processing cost, and Section 2 represents the residual value of circuit at life cycle end, and ω is circuit processing cost coefficient, and r is average annual coefficient of depreciation, and N is plant life cycle;

To transmission line of electricity α, if its life cycle is N, in the kth year of life cycle management, its differentiation cumulative cost is:

$Q(\mathrm{\&alpha;},k)={\mathrm{IC}}_{\mathrm{\&alpha;}}{(1+i)}^k+{(\mathrm{OC}+\mathrm{MC})}_{\mathrm{\&alpha;}}\frac{{(1+i)}^k-1}{i}+\left\{\begin{array}{cc}0,k=1,2,\&CenterDot;\&CenterDot;\&CenterDot;,N-1& \\ {\mathrm{DC}}_{\mathrm{\&alpha;}},k=N& \end{array}\right.---\left(14\right)$

In formula (14), Q (α, k) the differentiation cumulative cost of circuit α in kth year is represented, when the right Section 1 represents consideration time value on assets, convert the track investment cost to kth year, the right Section 2 represents that circuit adds up operation expense to during kth year, and the right Section 3 represents the processing cost of circuit after N scraps and residual value;

Differentiation " impairment " benefit DB comprises direct benefit E ₁with indirect benefit E ₂:

DB(α)＝λ*(E ₁+E ₂) _α(15)

In formula (15), E ₁for circuit damages the direct circuit electricity price revenue losses brought, E ₂produce for damaging the workers and peasants business caused that has a power failure because of circuit the indirect loss brought, λ is the resultant fault rate considering icing Probability Condition line l;

Differentiation planning economic evaluation index is as follows:.

1) differentiation cumulative cost Q (α, k): during measurement kth year, circuit carries out the accumulative cost needing to drop into of differentiation planning;

2) differentiation accumulative benefit W (k, α): weigh circuit during kth year owing to carrying out the accumulative benefit obtained of differentiation planning, W (k, α)=k*DB (α);

3) differentiation accumulated net income H (α, k): weigh when arriving kth year and add up gained net proceeds, H (α after circuit removing differentiation cost, k)=W (α, k)-Q (α, k)=k*DB (α)-Q (α, k);

The differentiation planning economic evaluation index of the different segmentation strengthened scheme of alternative route, determines that line located accumulated net income H (α, k) is maximum, the segmentation strengthened scheme that economy is best.