CN101436222A - Accidental production analogy method based on equivalent electric quantity function method - Google Patents

Abstract

The invention relates to the field of power system planning and operation scheduling, and discloses a random production simulation method based on an equivalent electric quantity function method. The random production simulation method comprises the following steps: firstly, determining expected energy not supplied EENS and the loss of load probability LOLP in the operation of a power system; secondly, acquiring a load curve of the power system and capabilities and forced outage rates of all generating sets so as to determine the load priority of the generating sets; and finally, according to the load priority of the generating sets, supposing that the generating sets are put into operation sequentially, and working out the expected energy not supplied EENS and the loss of load probability LOLP of the power system sequentially by the equivalent electric quantity function method, and searching the best combination of the generating sets which meet the expected energy not supplied EENS and the loss of load probability LOLP at the same time, namely meeting the expected energy not supplied EENS and the loss of load probability LOLP at the same time under the condition that the number of generating sets is smallest.

Description

A kind of production analogy method at random based on the equivalent electric quantity function method

Technical field

The present invention relates to electrical production plan or power source planning field, particularly a kind of production analogy method at random based on the equivalent electric quantity function method.

Background technology

In order to formulate a rational electrical production plan or to select a rational power source planning scheme, often need up to a hundred times production analog computation.Producing the initial period that Power System Analysis is introduced in simulation at random, equivalent sustained load curve is to describe with the functional value of discrete point.For the electric system of general scale,, often need hundreds of discrete point to describe its sustained load curve for the degree of accuracy that guarantees to calculate.Because the functional value that all must recomputate these discrete points is calculated in each convolution and deconvolution, calculated amount is quite big.Along with the expansion of electric system scale and the consideration of Hydropower Unit and segmentation unit, the method that this employing recursive calculation is handled discrete point sharply rises calculated amount, brings very big difficulty for the practical application of producing simulation at random.

Stoppage in transit at random with sustained load curve and each genset of the numerical characteristic cumulant descriptive system of stochastic distribution, this method is producing the convolution algorithm of operand maximum in the simulation and the plus and minus calculation that de-convolution operation is reduced to several cumulant at random, whole counting yield is significantly improved, promoted the widespread use of production analogue technique at random in electric system.But, the cumulant method intrinsic error problem but hindered its further popularization.When less and system loading curve was more smooth when the electric system scale, the cumulant method may cause bigger error, calculated power shortage probability LOLP in the simulation and also happened occasionally for negative situation producing at random.And China's electric system exactly has this characteristics, adopts said method to have defective.

In fact, the cumulant method is a practical calculation method.Theoretically, the convergence of Gram-Charlier expansion and Edgeworth expansion can not be guaranteed, the error range of practical application can not be provided definitely.Therefore in practical power systems at random during the production analog computation, its error often is difficult to estimate and control, causes Power System Reliability and economic evaluation error very big.Error problem at the cumulant method, cause Power System Reliability and economic evaluation error problem to propose some innovative approachs in succession, but these measures are cost to sacrifice the high efficiency advantage of cumulant method all, also make algorithm complicated simultaneously, thereby remain further perfect.

Summary of the invention

Defective or deficiency at above-mentioned prior art existence, the object of the present invention is to provide a kind of production analogy method at random based on the equivalent electric quantity function method, it can carry out electric weight calculating rapidly and accurately, accurately assesses Power System Reliability and economy, optimizes Operation of Electric Systems.

In order to achieve the above object, the present invention by the following technical solutions: a kind of production analogy method at random based on the equivalent electric quantity function method, it is characterized in that, may further comprise the steps:

At first, determine the best expected loss of energy EENS and the best power shortage probability LOLP of Operation of Electric Systems;

Secondly, gather the capacity and the forced outage rate of power system load curve and all genset, determine the priority of genset on-load;

At last, priority according to the genset on-load, suppose to drop into successively genset, utilize the equivalent electric quantity function method to calculate electric system expected loss of energy EENS and power shortage probability LOLP one by one, the best genset combination of best expected loss of energy EENS and best power shortage probability LOLP is satisfied in search simultaneously, promptly satisfy best not enough expectation value EENS and best power shortage probability LOLP simultaneously, and genset quantity minimum.

At present the reliability index of generating system that adopts mainly contains: power shortage probability LOLP is meant that electricity generation system nargin is less than 0 probability; Expected loss of energy EENS is meant that in research cycle it can be converted into the loss of outage expense, thereby carries out technical economical analysis because electricity shortage causes the have a power failure expectation value of the electric weight that loses of user.The present invention is by calculating power shortage probability LOLP fast and accurately, the expectation value of expected loss of energy EENS and each genset generated energy, compare according to the best not enough expectation value EENS of Operation of Electric Systems and best power shortage probability LOLP and practical power systems ruuning situation, can be optimized scheduling to practical power systems on the one hand, adjust putting into operation and withdrawing from of genset; On the other hand, can be used for the electric system power source planning, generating set capacity that the designing and calculating electric system need increase and quantity.

Description of drawings

Fig. 1 is general electric system sustained load curve map;

Fig. 2 is the geometric interpretation figure of equivalent electric quantity function method;

Fig. 3 is equivalent sustained load curve f ⁽ⁿ⁾(x) find the solution the LOLP synoptic diagram;

Fig. 4 is a multimode genset running status synoptic diagram;

Fig. 5 is the calculation flow chart of equivalent electric quantity function method;

Fig. 6 is the daily load curve figure in the manual example;

Fig. 7 is load curve and equivalent electric quantity function E in the manual example ⁽⁰⁾(J) synoptic diagram.

Embodiment

The present invention is based on the equivalent electric quantity function method that the inventor proposes.In theory, the equivalent electric quantity function method is electric weight computing method accurately.Because this method directly utilizes electric weight to carry out convolution and de-convolution operation, and calculated amount is significantly descended, and very flexible when handling the genset (as Hydropower Unit, water-storage unit) of given electric weight.Results of calculation shows, this method not only precision height, speed is fast, and program is very simple.

1. the ultimate principle of equivalent electric quantity function method

At first provide the definition of electric quantity function.If the interior system of known T research cycle sustained load curve (see figure 1)

t＝F(x)

Wherein t represents the time, and x represents load;

The probability distribution of then knowing the sustained load curve is

p＝f(x)＝F(x)/T

The x axle is pressed x/ Δ x segmentation, so can define a discrete electric quantity function

$E\left(J\right)=\underset{x}{\overset{x+\mathrm{\Δx}}{\∫}}F\left(x\right)\mathrm{dx}=T\underset{x}{\overset{x+\mathrm{\Δx}}{\∫}}f\left(x\right)\mathrm{dx}---\left(1\right)$

J=in the formula＜x/ Δ x 〉+1

The integer that is not more than x/ Δ x represented to get in the point parantheses.E (J) is corresponding to the area under from x to this section of x+ Δ x load curve, i.e. the corresponding electric weight of this section load.If system's peak load is x _Max, then Dui Ying discrete variable value is

N _R＝<x _max/Δx>+1

Total electric weight of power system load is

$E_D=\underset{0}{\overset{x_{\max }}{\&Integral;}}F\left(x\right)\mathrm{dx}=\underset{J=1}{\overset{N_E}{\mathrm{\&Sigma;}}}E\left(J\right)---\left(2\right)$

Equivalent electric quantity function is genset to be stopped transport at random influence the electric quantity function of taking into account.In conventional recursive algorithm, the stoppage in transit factor of genset is to consider with the method for revising equivalent sustained load curve ELDC.In the equivalent electric quantity function method, revise electric quantity function with the influence that genset is stopped transport at random.

If the probability distribution of original sustained load curve is f ⁽⁰⁾(x), Dui Ying electric quantity function is E ⁽⁰⁾(J).Arranging to obtain equivalent sustained load curve f after the operation of i-1 platform genset ^(i-1)(x), Dui Ying equivalent electric quantity function is E ^(J-1)(J).Arrange the operation of i platform genset now, establishing its capacity is C _i, forced outage rate is q _i, then equivalent sustained load curve f ⁽ⁱ⁾(x) can be expressed as

f ⁽ⁱ⁾(x)＝p _if ^(i-1)(x)+q _if ^(i-1)(x-C _i) (3)

P in the formula _i=1-q _iCan be converted to corresponding equivalent electric quantity function to following formula according to formula (1)

$E^{\left(i\right)}\left(J\right)=T\underset{x}{\overset{x+\mathrm{\&Delta;x}}{\&Integral;}}{f}^{\left(i\right)}\left(x\right)\mathrm{dx}$

With formula (3) substitution following formula, as can be known

E ⁽ⁱ⁾(J)＝p _iE ^(i-1)(J)+q _iE ^(i-1)(J-K _i) (4)

K in the formula _i=C _i/ Δ x (5)

Because Δ x will select according to the greatest common factor of all generating set capacities, so K _iBe integer.

The form of formula (4) is similar to formula (3), and it is the convolutional calculation formula of equivalent electric quantity function method.The geometric interpretation of this formula as shown in Figure 2.E in the formula ^(i-1)(J), E ⁽ⁱ⁾(J) corresponding with area abcd and abef among the figure respectively, and area abgh and E ^(i-1)(J-K _i) corresponding.

The generated energy E of i platform genset _GiFor

$E_{\mathrm{gi}}={\mathrm{Tp}}_i\underset{x_{i-1}}{\overset{x_{i-1}+{\mathrm{\&sigma;}}_i}{\&Integral;}}{f}^{(i-1)}\left(x\right)\mathrm{dx}$

(6)

$=p_i\underset{J=J_{i-1}+1}{\overset{J_I}{\mathrm{\&Sigma;}}}{E}^{(i-1)}\left(J\right)$

In the formula, J _I-1=x _I-1/ Δ x

J _i＝(x _i-1+C _i)/Δx＝J _i-1+K _i (7)

By formula (7) as can be known, in order to ask the generated energy of genset i, as long as with discrete point J _I-1+ 1 to J _iBetween equivalent electric quantity function value sum multiply by Probability p _iGet final product.

After arranging the operation of i platform genset, preceding i platform genset band interval (1, J _i) load, at this moment the still unsatisfied load electric weight of system should be

$E_{\mathrm{Di}}=\underset{J>J_I}{\mathrm{\&Sigma;}}{E}^{\left(i\right)}\left(J\right)---\left(8\right)$

E in the formula _DiBe the electric weight that system behind the preceding i platform unit on-load still lacks, establish electric system total n platform genset, then E _DnBe the expected loss of energy of this system

$\mathrm{EENS}=E_{\mathrm{Dn}}=\underset{J>J_n}{\mathrm{\&Sigma;}}{E}^{\left(n\right)}\left(J\right)---\left(9\right)$

The computing method of the not enough probability LOLP of systematic electricity need by means of equivalent sustained load curve f ⁽ⁿ⁾(x) illustrate.Fig. 3 has represented f ⁽ⁿ⁾The situation of right-hand member afterbody (x).Set up departments the system genset total working capacity C _i, then the LOLP value is corresponding with figure middle conductor AB.Because f ⁽ⁿ⁾(x) be a dull continuous curve that descends, so LOLP should be greater than the functional value of any arbitrarily in the Δ x neighborhood of its right side, thereby also greater than this interval inner function f ⁽ⁿ⁾(x) mean value

2. the processing of multimode unit and segmentation unit

As previously mentioned, consider genset because when utility appliance fault and derate operation, unit should be regarded the multimode unit as when needs.

Multimode unit i has N in Fig. 4 _sThe situation of individual state is used C _s, p _s(s=1,2 ... N _s) represent the working capacity and the corresponding probability of each state respectively, corresponding to working capacity C _sThe stoppage in transit capacity use

Expression.

Definition K _sWith

For

K _s=C _s/ Δ x reaches $\stackrel{\&OverBar;}{K_s}=\stackrel{\&OverBar;}{C_s}/\mathrm{\&Delta;x}$

By formula $C_s+\stackrel{\&OverBar;}{C_s}=C_{\mathrm{Ns}}$ As can be known

$\stackrel{\&OverBar;}{K_s}=K_{\mathrm{Ns}}-K_s---\left(11\right)$

K wherein _NsBe the discrete value of genset rated capacity correspondence, K _Ns=C _Ns/ Δ x

Formed equivalent electric quantity function E after being located at the convolution algorithm of finishing preceding i-1 platform genset ^(i-1)(J), then

$E^{\left(i\right)}\left(J\right)=\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\left[E^{(i-1)}(J-\stackrel{\&OverBar;}{K_s})p_s\right]---\left(12\right)$

This formula is the popularization of formula (4).

Ask the generated energy formula of multimode unit i now.After i platform genset on-load, the still unsatisfied load electric weight of system is

$E_{\mathrm{Di}}=\underset{J>J_I}{\mathrm{\&Sigma;}}{E}^{\left(i\right)}\left(J\right)$

$E_{\mathrm{Di}}=\underset{J>J_{I-1}}{\mathrm{\&Sigma;}}{E}^{(i-1)}\left(J\right)-\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\left[p_s\underset{J=J_{i-1}+1}{\overset{J_{i-1}+K_s}{\mathrm{\&Sigma;}}}{E}^{(i-1)}\left(J\right)\right]$

$E_{\mathrm{Di}}=E_{D,i-1}-\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\left[p_s\underset{J=J_{i-1}+1}{\overset{J_{i-1}+K_s}{\mathrm{\&Sigma;}}}{E}^{(i-1)}\left(J\right)\right]$

The generated energy of multimode genset i is as can be known

$E_{\mathrm{gi}}=\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\left[p_s\underset{J=J_{i-1}+1}{\overset{J_{i-1}+K_s}{\mathrm{\&Sigma;}}}{E}^{(i-1)}\left(J\right)\right]---\left(13\right)$

Utilize simple algebraic transformation, can obtain E _GiDeformation formula

$E_{\mathrm{gi}}=\underset{s=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\left[{p_s}^{*}\underset{J=J_{i-1}+1}{\overset{J_s}{\mathrm{\&Sigma;}}}{E}^{(i-1)}\left(J\right)\right]---\left(14\right)$

In the formula $p_s^{*}=1-\underset{l=1}{\overset{s}{\mathrm{\&Sigma;}}}{p}_l---\left(15\right)$

J _s＝J _i-1+K _s (16)

More than the formula of Tui Daoing (14), (15) and formula (16) are to handle the fundamental formular of multimode genset in the equivalent electric quantity function method.

Processing and deconvolution computing formula for the segmentation unit are as follows.If it is the different segmentations of same unit that i+1 platform genset has been arranged the genset b that moves with the front.When arranging i+1 platform unit, should form equivalent electric quantity function E ⁽ⁱ⁾(J), can be expressed as following convolution algorithm to it

$E^{\left(i\right)}\left(J\right)=\stackrel{*}{E^{(i-1)}}\&CirclePlus;G_b---\left(17\right)$

In the formula Be original electric quantity function E ⁽⁰⁾(J) with except unit b (be G _b) result of i platform unit convolution algorithms before all in addition.Obviously, in order to get rid of the stoppage in transit influence of unit b, the generated energy of genset i should be according to equivalent electric quantity function

Calculate.Must utilize formula (16) to obtain by de-convolution operation for this reason

If the capacity of unit b is C _b, its forced outage rate is identical with unit i+1, equals q _I+1Formula (17) is launched

$E^{\left(i\right)}\left(J\right)=p_{i+1}\stackrel{*}{E^{(i-1)}}\left(J\right)+q_{i+1}\stackrel{*}{E^{(i-1)}}(J-K_s)---\left(18\right)$

P in the formula _I+1=1-q _I+1

K _b＝C _b/Δx

Can derive following deconvolution formula by formula (18)

$\stackrel{*}{E^{(i-1)}}\left(J\right)=[E^{\left(i\right)}\left(J\right)-{\stackrel{*}{E^{i-1}(J-K_b)}q}_{i+1}]/p_{i+1}---\left(19\right)$

For the multimode unit, its deconvolution formula is

$\stackrel{*}{E^{(i-1)}}\left(J\right)=[E^{\left(i\right)}\left(J\right)-\underset{s=2}{\overset{N_s}{\mathrm{\&Sigma;}}}{p}_s{E}^{(i-1)}(J-\stackrel{\&OverBar;}{K_s})]/p_i---\left(20\right)$

With

$\stackrel{*}{E^{i-1}(J-\stackrel{\&OverBar;}{K_{N_s}})}=[E^{\left(i\right)}\left(J\right)-\underset{s=1}{\overset{N_s-1}{\mathrm{\&Sigma;}}}{p}_s\stackrel{*}{E^{(i-1)}(J-\stackrel{\&OverBar;}{K_s})}]/p_{N_s}---\left(21\right)$

Ask when utilizing formula (19)

The time, need known E ⁽ⁱ⁾(J) reach

The system minimum load of setting up departments is p _MinCorresponding discrete value is

N _F＝<P _min/Δx> (22)

Obviously, work as J-K _b≤ K _F

Can derive:

$\stackrel{*}{E^{(i-1)}(J-K_b)}=\mathrm{T\&Delta;x}---\left(23\right)$

Therefore, should from interval J ∈ [0, N _F+ N _b] interior beginning, recursively the direction that increases to J is carried out deconvolution calculating.

From producing on the viewpoint of simulation at random, the numerical evaluation stability of formula (19) is fine, and its round-off error is with q _I+1/ p _I+1Ratio descend, if can make full use of this point, can obtain the very high approximate data of efficient.

Here adopt the example of 36 genset to be illustrated.Certain electric system has 36 genset, and its parameter is as shown in table 1, supposes that the order in the table is the priority of genset on-load.The peak load of system is 7652MW, and is as shown in table 2 at the load curve of certain month (730h).First perunit value of classifying load level as in this table, second classifies the corresponding definite probability that meets as, and the 3rd classifies the cumulative probability of load as, that is load is at the sustained load curve of this month.The total load electric weight is 4319.8GWh.Following process has provided the detailed process that the equivalent electric quantity function method is produced simulation at random.Correctness and advantage for explanation equivalent electric quantity function method have adopted the comparison with conventional recursive convolution method, cumulant method.

The analog result of three kinds of algorithms is shown in table 3 and table 4.In table 3, listed the expectation value of each genset generated energy that three kinds of algorithms try to achieve.By table as can be seen, the equivalent electric quantity function method is almost completely consistent with conventional recursive convolution method result of calculation.Though cumulant method precision of calculation results is roughly satisfactory, the error of some genset reaches 5.68% as the error of genset 13.

In table 4, list the overall comparable situation of these three kinds of methods, therefrom can obviously find out the superiority of equivalent electric quantity function method.

Table 1 genset data

Table 2 load data

The comparison of table 3 genset generated energy

The machine group number	With conventional recursive convolution algorithm computation	Calculate with the cumulant method	Calculate with the equivalent electric quantity function method	The machine group number	With conventional recursive convolution algorithm computation	Calculate with the cumulant method	Calculate with the equivalent electric quantity function method
								1	760.37	760.37	760.37	19	8.72	8.37	8.73
2	760.37	760.37	760.37	20	8.60	8.08	8.41
								3	370.99	370.99	370.99	21	8.07	7.80	8.08
4	370.99	370.99	370.99	22	7.75	7.53	7.77
								5	256.59	262.17	256362	23	7.44	7.25	7.45
6	249.49	251.76	249.56	24	7.13	6.99	7.14
								7	235.56	237.55	235.70	25	6.83	6.73	6.85
8	115.39	117.49	115.51	26	6.53	6.47	6.55
								9	110.50	112.50	110.69	27	6.25	6.21	6.26
10	104.75	107.18	104.83	28	5.97	5.98	5.97
								11	99.21	101.58	99.49	29	5.69	5.73	5.69
12	304.09	310.09	304.41	30	5.42	5.48	5.43
								13	243.39	229.56	243.77	31	5.16	5.25	5.17
14	55.97	51.57	56.11	32	4.91	5.02	4.92
								15	48.86	48.08	48.85	33	4.66	4.80	4.67
16	42.57	40.52	42.66	34	4.61	4.59	4.43
								17	9.38	8.96	9.41	35	4.18	4.38	4.19
18	9.05	8.66	9.07	36	3.95	4.18	3.96

The comparison of three kinds of algorithms of table 4

	The equivalent electric quantity function method	Conventional recursive convolution algorithm	The cumulant method
				Total electric weight (GWh)	4317.88	4315.83	4324.34
Expected loss of energy	59.98	56.98	65.14
				The electric weight amount of unbalance	1.71	3.67	-4.74
LOLP	0.1203	0.1214	0.1172

For expected loss of energy EENS among the present invention and the acquisition methods of power shortage probability LOLP more clearly are described,, provide a manual example flow process with reference to Fig. 5.

(1) the genset data see Table 5.

Table 5-genset data

Sequence number	Capacity (MW)	Forced outage rate
			1	40	0.1
2	40	0.1
			3	20	0.2

(2) the daily load curve data see Table 6, and daily load curve is seen Fig. 6.

Table 6-daily load curve data

Time (time)	Load (MW)	Time (time)	Load (MW)	Time (time)	Load (MW)	Time (time)	Load (MW)
								1	32	7	62	13	68	19	72
2	34	8	65	14	72	20	68
								3	34	9	65	15	72	21	68
4	42	10	74	16	72	22	62
								5	50	11	72	17	72	23	58
6	65	12	68	18	82	24	46

(3) the load electric weight of computing system:

The capacity of three genset is respectively 40,40,20MW, so choose step delta x=20MW, then electric quantity function $E\left(J\right)=\underset{x}{\overset{x+\mathrm{\&Delta;x}}{\&Integral;}}F\left(x\right)\mathrm{dx}=T\underset{x}{\overset{x+\mathrm{\&Delta;x}}{\&Integral;}}f\left(x\right)\mathrm{dx}$ J=＜x/ Δ x wherein 〉+1, (institute asks, and E (J) is the corresponding electric weight of load section (x, x+ Δ x))

The peak load x of system _Max=82MW, then the total load electric weight of system is

$4+2\&times;2+1\&times;8=1465\left(\mathrm{MWh}\right)$

According to equivalent electric quantity function $E^{\left(0\right)}\left(J\right)=T\underset{x}{\overset{x+\mathrm{\&Delta;x}}{\&Integral;}}{f}^{\left(0\right)}\left(x\right)\mathrm{dx}$ Can calculate the numerical value of equivalent electric quantity function, as shown in Figure 7.(4) arrange first unit (unit 1) operation:

Capacity C by first unit ₁, forced outage rate q ₁,

The generated energy of genset 1:

${\mathrm{<figure-callout\; id="1"\; label="E\; g"\; filenames="A200810232625E00162.png,A200810232625E00181.png"\; state="\{\{state\}\}">E</figure-callout>}}_g={\mathrm{<figure-callout\; id="1"\; label="Tp"\; filenames="A200810232625E00162.png,A200810232625E00181.png"\; state="\{\{state\}\}">Tp</figure-callout>}}_1{\&Integral;}_{x_0}^{x_0+C_1}{f}^{\left(0\right)}\left(x\right)\mathrm{dx}$

$={\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="A200810232625E00162.png,A200810232625E00181.png"\; state="\{\{state\}\}">p</figure-callout>}}_1\underset{k=1}{\overset{k1}{\mathrm{\&Sigma;}}}\left[{\&Integral;}_{x_0+(k-1)\mathrm{\&Delta;x}}^{x_0+\mathrm{k\&Delta;x}}{f}^{\left(0\right)}\left(x\right)\mathrm{dx}\right]$

$={\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="A200810232625E00162.png,A200810232625E00181.png"\; state="\{\{state\}\}">p</figure-callout>}}_1\underset{J={\mathrm{<figure-callout\; id="0"\; label="J"\; filenames="A200810232625E00172.png,A200810232625E00191.png"\; state="\{\{state\}\}">J</figure-callout>}}_0+1}{\overset{J_1}{\mathrm{\&Sigma;}}}{E}^{\left(0\right)}\left(J\right)$

$=p_1[E^{\left(0\right)}\left(1\right)+E^{\left(0\right)}\left(2\right)]$

$=0.9\&times;(480+460)$

$=846\left(\mathrm{MWh}\right)$

Then arrange the expected loss of energy of system behind first unit

E _D1＝E _D-E _g1＝1465-846＝619(MWh)

(5) arrange second unit (unit 2) operation

Capacity C by unit 1 ₁, forced outage rate q ₁And original sustained load curve f ⁽⁰⁾(x) can get, arrange unit 1 postrun equivalent sustained load curve

f ⁽¹⁾(x)＝p ₁f ⁽⁰⁾(x)+q ₁f ⁽⁰⁾(x-C ₁)

Arrange unit 1 postrun equivalent electric quantity function

E ⁽¹⁾(J)=p ₁E ⁽⁰⁾(x)+q ₁E ⁽⁰⁾(J-k ₁), k wherein ₁=C ₁/ Δ x

The generated energy of unit 2:

${\mathrm{<figure-callout\; id="2"\; label="E\; g"\; filenames="A200810232625E00191.png,A200810232625E00192.png"\; state="\{\{state\}\}">E</figure-callout>}}_g={\mathrm{<figure-callout\; id="2"\; label="Tp"\; filenames="A200810232625E00191.png,A200810232625E00192.png"\; state="\{\{state\}\}">Tp</figure-callout>}}_2{\&Integral;}_{x_1}^{x_1+C_2}{f}^{\left(1\right)}\left(x\right)\mathrm{dx}$

$={\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A200810232625E00191.png,A200810232625E00192.png"\; state="\{\{state\}\}">p</figure-callout>}}_2\underset{k=1}{\overset{k2}{\mathrm{\&Sigma;}}}\left[{\&Integral;}_{x_1+(k-1)\mathrm{\&Delta;x}}^{x_1+\mathrm{k\&Delta;x}}{f}^{\left(1\right)}\left(x\right)\mathrm{dx}\right]$

$={\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A200810232625E00191.png,A200810232625E00192.png"\; state="\{\{state\}\}">p</figure-callout>}}_2\underset{J={\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="A200810232625E00162.png,A200810232625E00181.png"\; state="\{\{state\}\}">J</figure-callout>}}_1+1}{\overset{J_2}{\mathrm{\&Sigma;}}}{E}^{\left(1\right)}\left(J\right)$

$=p_2[E^{\left(1\right)}\left(2\right)+E^{\left(1\right)}\left(3\right)]$

$=0.9\&times;(381.9+182.8)$

$=508.23\left(\mathrm{MWh}\right)$

Then arrange second system's expected loss of energy behind the unit operation

E _D2＝E _D1-E _g2＝619-508.23＝110.77(MWh)

(6) peace ranked third platform unit (unit 3) operation

Capacity C by unit 2 ₂, forced outage rate q ₂And the equivalent sustained load curve f behind the arrangement unit 1 ⁽¹⁾(x) can get: arrange unit 2 postrun equivalent sustained load curves

f ⁽²⁾(x)＝p ₂f ⁽¹⁾(x)+q ₂f ⁽¹⁾(x-C ₂)

Arrange unit 2 postrun equivalent electric quantity functions

E ⁽²⁾(J)=p ₂E ⁽¹⁾(x)+q ₂E ⁽¹⁾(J-k ₂), k wherein ₂=C ₂/ Δ x

The generated energy of unit 3:

$E_{g3}={\mathrm{Tp}}_3{\&Integral;}_{x_2}^{x_2+C_3}{f}^{\left(2\right)}\left(x\right)\mathrm{dx}$

$=p_3\underset{k=1}{\overset{k3}{\mathrm{\&Sigma;}}}\left[{\&Integral;}_{x_2+(k-1)\mathrm{\&Delta;x}}^{x_2+\mathrm{k\&Delta;x}}{f}^{\left(2\right)}\left(x\right)\mathrm{dx}\right]$

$={\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A200810232625E00191.png,A200810232625E00192.png"\; state="\{\{state\}\}">p</figure-callout>}}_2\underset{J={\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="A200810232625E00191.png,A200810232625E00192.png"\; state="\{\{state\}\}">J</figure-callout>}}_2+1}{\overset{J_3}{\mathrm{\&Sigma;}}}{E}^{\left(2\right)}\left(J\right)$

$=0.8\&times;73.2$

$=58.56\left(\mathrm{MWh}\right)$

Then peace ranked third the expected loss of energy of system behind the platform unit operation

E _D3＝E _D2-E _g3＝110.77-58.56＝52.51 (MWh)

Promptly obtain the expected loss of energy EENS=E of system behind all unit operations this moment _D3=52.51 (MWh)

(7) ask power shortage probability LOLP

By equivalent electric quantity function E ⁽⁰⁾(J) can get:

Arrange unit 1 postrun equivalent electric quantity function E ⁽¹⁾(J)=p ₁E ⁽⁰⁾(x)+q ₁E ⁽⁰⁾(J-k ₁), k wherein ₁=C ₁/ Δ x

Arrange unit 2 postrun equivalent electric quantity function E ⁽²⁾(J)=p ₂E ⁽¹⁾(x)+q ₂E ⁽¹⁾(J-k ₂), k wherein ₂=C ₂/ Δ x

Arrange unit 2 postrun equivalent electric quantity function E ⁽³⁾(J)=p ₃E ⁽²⁾(x)+q ₃E ⁽²⁾(J-k ₃), k wherein ₃=C ₃/ Δ x

So, be limited on the LOLP: $\frac{E^{\left(3\right)}(J_3+1)}{T\&CenterDot;\mathrm{\&Delta;x}}=\frac{E^{\left(3\right)}\left(6\right)}{T\&CenterDot;\mathrm{\&Delta;x}}$

Under be limited to: $\frac{E^{\left(3\right)}\left(J_3\right)}{T\&CenterDot;\mathrm{\&Delta;x}}=\frac{E^{\left(3\right)}\left(5\right)}{T\&CenterDot;\mathrm{\&Delta;x}}$

Then the value of LOLP can be got by the estimation of bound mean value:

$\mathrm{LOLP}=\frac{E^{\left(3\right)}\left(6\right)+E^{\left(3\right)}\left(5\right)}{T\&CenterDot;\mathrm{\&Delta;x}}=0.14678$

Above computation process available equivalents electric quantity function method reckoner is listed, and is as shown in table 3

Table 3-equivalent electric quantity function method reckoner

Production analogy method at random based on the equivalent electric quantity function method of the present invention mainly may further comprise the steps:

At first, determine the best expected loss of energy EENS and the best power shortage probability LOLP of Operation of Electric Systems.Best expected loss of energy EENS and best power shortage probability LOLP can determine according to national standard, also can determine according to the reliability cost and benefit optimization of electric system reality on the basis of reference national standard.

Secondly, gather the capacity and the forced outage rate of power system load curve and all genset, determine the priority of genset on-load.For example: the priority of genset on-load is arranged successively according to wind-powered electricity generation, water power, thermoelectricity.Wherein, for wind energy turbine set, preferentially all put into operation; For Hydropower Unit, utilize the descending arrangement load order of hourage according to it; For fired power generating unit, according to the ascending arrangement load order of fuel cost.

At last, priority according to the genset on-load, suppose to drop into successively genset, utilize the equivalent electric quantity function method to calculate electric system expected loss of energy EENS and power shortage probability LOLP one by one, the best genset combination of best expected loss of energy EENS and best power shortage probability LOLP is satisfied in search simultaneously, promptly satisfy best expected loss of energy EENS and best power shortage probability LOLP simultaneously, and the combination of genset quantity minimum.

Thought of the present invention can be used for electric power system dispatching, genset and best genset combination comparison according to the electric system actual motion, adjust putting into operation and withdrawing from of genset,, realize reliability cost and benefit optimization finally according to best genset combined running.

Thought of the present invention can also be used for the electric system power source planning, as the best not enough expectation value EENS and the best power shortage probability LOLP that determine Operation of Electric Systems, can be according to electric load curve, designing and calculating goes out generating set capacity and the quantity that electric system need increase.

Claims (1)

1, a kind of production analogy method at random based on the equivalent electric quantity function method is characterized in that, may further comprise the steps:

At first, determine the best expected loss of energy EENS and the best power shortage probability LOLP of Operation of Electric Systems;

Secondly, gather the capacity and the forced outage rate of power system load curve and all genset, determine the priority of genset on-load;

At last, priority according to the genset on-load, suppose to drop into successively genset, utilize the equivalent electric quantity function method to calculate electric system expected loss of energy EENS and power shortage probability LOLP one by one, the best genset combination of best expected loss of energy EENS and best power shortage probability LOLP is satisfied in search simultaneously, promptly satisfy best expected loss of energy EENS and best power shortage probability LOLP simultaneously, and the combination of genset quantity minimum.

Images