CN105654245A - Static voltage stability risk evaluation method of power grid based on load uncertainty modeling - Google Patents

Abstract

The invention relates to a static voltage stability risk evaluation method of a power grid and particularly relates to a static voltage stability risk evaluation method of the power grid based on load uncertainty modeling, aiming at solving the problem of an existing static voltage stability risk evaluation method that an evaluation result is inaccurate. The static voltage stability risk evaluation method of the power grid based on the load uncertainty modeling is realized by the following steps: (1) establishing a load uncertainty model; (2) establishing a trend operation model; and (3) establishing a risk evaluation index, and recognizing a high-operation-risk region in the power grid by applying the risk evaluation index. The static voltage stability risk evaluation method of the power grid based on the load uncertainty modeling is applicable to static voltage stability risk evaluation of the power grid.

Description

Based on the electrical network static voltage stability methods of risk assessment of the uncertain modeling of load

Technical field

The present invention relates to the static electric voltage stability methods of risk assessment of electrical network, specifically a kind of uncertain based on loadThe electrical network static voltage stability methods of risk assessment of modeling.

Background technology

In the actual moving process of electrical network, quiescent voltage collapses the Voltage Instability accident causing can have a strong impact on electrical networkSteady stability operation, causes thus huge economic loss, thereby has a strong impact on national product. Therefore, in order to prevent that voltage from losingThe generation of steady accident, need to carry out risk assessment to the static electric voltage stability of electrical network. Existing static electric voltage stability riskAppraisal procedure mainly comprises following two kinds: the first is certainty appraisal procedure, and the problem of this kind of appraisal procedure existence is: due toCannot take into account the probability distribution of multiple uncertain factor, cause its assessment result to be difficult to objective, to reflect all sidedly electrical network realityBorder operation conditions, causes assessment result inaccurate thus. The second is the probability assessment method that can take into account uncertain factor, thisThe problem of planting appraisal procedure existence is: fail, taking historical load Changing Pattern as basis, to take into account accurately, all sidedly and be present in initiallyUncertainty in node serial number and load growth situation that increasing appears in load consumption, load, and lack and there is physics meaningJustice, can be from the risk indicator of reflection static voltage stability degree at all levels, therefore this kind of probability assessment method can cause equallyAssessment result is inaccurate. Given this, be necessary to invent a kind of brand-new static electric voltage stability methods of risk assessment, existing to solveThere is the inaccurate problem of static electric voltage stability methods of risk assessment assessment result.

Summary of the invention

The present invention, in order to solve the inaccurate problem of existing static electric voltage stability methods of risk assessment assessment result, providesA kind of based on load uncertain modeling electrical network static voltage stability methods of risk assessment.

The present invention adopts following technical scheme to realize: based on the electrical network static voltage stability of the uncertain modeling of loadMethods of risk assessment, the method is to adopt following steps to realize:

1) set up load uncertainty models; Described load uncertainty models comprises: first lotus fluctuation probability Distribution Model,There is the node cluster model of cognition, the load stochastic growth model that increase in load;

2) set up trend operational model: first determine in electrical network and occur according to the node cluster model of cognition of load appearance growthThe node serial number of load growth, afterwards based on monte carlo simulation methodology gather respectively in just lotus fluctuation probability Distribution Model at the beginning ofLoad increment sample in lotus consumption sample and load stochastic growth model, finally takes into account synthetic load spy based on sample valueThe continuous tide computing of property;

3) set up risk assessment index, and use the high operation risk region in risk indicator identification electrical network; Described riskEvaluation index comprises network limit load level risk indicator, the low compressive load risk indicator of node, circuit through-put power accounting windDanger index, line threshold transmission nargin risk indicator.

Described step 1) in,

The method of setting up just lotus fluctuation probability Distribution Model specifically comprises the steps:

1.1) getting clusters number is 2, generates at random one group of initial value that is subordinate to matrix element;

1.2) historical load data are carried out to fuzzy C-means clustering for the first time;

1.3) calculate the interior Classification Index BWP of class between the class of evaluating this cluster result; Specific formula for calculation is as follows:

$BWP(j,i)=\frac{b(j,i)-w(j,i)}{b(j,i)+w(j,i)}---\left(1\right);$

$b(j,i)=\underset{1\≤k\≤m,k\≠j}{\min }\left(\frac{1}{n_k}\underset{p=1}{\overset{n_k}{\Σ}}\right||x_p^k-x_i^j|{|}^2)---\left(2\right);$

$w(j,i)=\frac{1}{n_j-1}\underset{q=1,q\≠i}{\overset{n_j}{\Σ}}\left|\right|x_q^j-x_i^j|{|}^2---\left(3\right);$

In formula (1)-(3): BWP (j, i) is the interior Classification Index of class between class; B (j, i) is the infima species of i sample of j classSpacing; W (j, i) is the inter-object distance of i sample of j class; J and k are class mark; I, p and q are specimen number; M is cluster numbersOrder; n_kIt is the number of samples in k class; n_jIt is the number of samples of j class;Be p sample of k class;Be j class iIndividual sample;Be q sample of j class;

1.4) again produce at random one group and be subordinate to matrix element initial value, repeating step 1.2)-1.3), until cluster number of times reachesTill historical load data length 1/2;

1.5) make clusters number add 1, generate at random one group of initial value that is subordinate to matrix element, repeating step 1.2)-1.4), straightTill clusters number reaches the evolution value of historical load data length;

1.6) add up the interior Classification Index of class between whole classes; Select the interior Classification Index maximum of class between class to be BWP_optTime correspondenceCluster result, the period dividing mode as to load power consumption time graph:

${\mathrm{BWP}}_{opt}=max\left\{\frac{1}{n}\underset{j=1}{\overset{m}{\Σ}}\underset{i=1}{\overset{n_j}{\Σ}}BWP(j,i)\right\},2\≤m\≤Csize---\left(4\right);$

In formula (4): BWP_optFor Classification Index in class between the class of corresponding optimum cluster result; N is total sample number; Csize isThe evolution value of load sample total length;

1.7), to every type load power consumption period, calculate the coefficient correlation of all payload node power consumptions of the whole network and form phase relationMatrix number;

1.8) utilize Cholesky method decomposition step 1.7) in every correlation matrix corresponding to type load power consumption period,Obtain obeying the first lotus power consumption sample of multidimensional normal distribution; So far, the modeling of first lotus fluctuation probability Distribution Model is complete.

Load occurs that the node cluster model of cognition increasing is specifically expressed as follows:

${\mathrm{\ρ}}_{xy}=\frac{\mathrm{cov}(x,y)}{\sqrt{D\left(x\right)\·D\left(y\right)}}---\left(5\right);$

$I_{xy}={\∫}_x{\∫}_{y}p(x,y)\·ln\left(\frac{p(x,y)}{p\left(x\right)\·p\left(y\right)}\right)dxdy---\left(6\right);$

In formula (5)-(6): ρ_xyFor the coefficient correlation of x and y; I_xyFor the mutual information of x and y; Cov (x, y) is the association of x and yVariance; D (x) and D (y) are respectively the variance of x, y; P (x) and p (y) are respectively the marginal probability density of x, y; P (x, y) is x and yJoint probability density;

Load stochastic growth model is specifically expressed as follows:

$\mathrm{\θ}=ar\cos \left(\frac{D1\·D0}{\left|D1\right|\·\left|D0\right|}\right)---\left(9\right);$

In formula (7)-(9): the reference direction that D0 is load growth; D1 is the actual growing direction of load; (S₁,S₂,...,S_Nload) one-dimensional vector of the each payload node apparent energy of serving as reasons composition; Nload is payload node number;Being i carriesThe power factor (1≤i≤Nload) of lotus point; S_ΔbaseFor the power reference value of system; k_LiFor load growth coefficient, k_LiValueSet can be by step 1) described method determines, also can be determined by the approximating method of probability distribution.

Described step 2) in,

First, according to given threshold values ρ₁、ρ₂And I₁、I₂, determine the node serial number that occurs load growth in electrical network:

ρ₁≤ρ_xy≤ρ₂(10)；

I₁≤I_xy≤I₂(11)；

In formula (10)-(11): x and y are node serial number; ρ₁And ρ₂Be respectively lower limit and the upper limit of coefficient correlation; I₁And I₂Be respectively lower limit and the upper limit of mutual information;

Afterwards, utilize step 1) method introduced, try to achieve first lotus consumption sample in just lotus fluctuation probability Distribution Model andLoad increment sample in load stochastic growth model, determines k_LiValue set;

Trend operational model is specifically expressed as follows:

$\left\{\begin{array}{c}{P}_{Gi}(1+{\mathrm{\λk}}_{Gi})-P_{Li0}-P_{Li}-U_i\underset{j=1}{\overset{j=n}{\mathrm{\Σ}}}{U}_j(G_{ij}{\mathrm{cos\δ}}_{ij}+B_{ij}{\mathrm{sin\δ}}_{ij})=0\\ Q_{Gi}-Q_{Li0}-Q_{Li}-U_i\underset{j=1}{\overset{j=n}{\Σ}}{U}_j(G_{ij}{\mathrm{sin\δ}}_{ij}-B_{ij}{\mathrm{cos\δ}}_{ij})=0\end{array}\right.---\left(12\right);$

In formula (12)-(13): the sustainable growth factor that λ is load; P_Li0、Q_Li0Be respectively initial meritorious, the nothing of node iMerit power load amount;For the power factor of node i; δ_ijFor the phase angle difference of node i and j voltage; In the time of i=j, Y_ii＝G_ii+jB_iiFor node self-admittance; In the time of i ≠ j, Y_ij＝G_ij+jB_ijFor node transadmittance; S_ΔbaseFor the power reference value of system; k_LiFor load growth coefficient, k_GiFor the exert oneself growth factor relevant with power generation dispatching strategy; Integrated load model is commonly used constant current, perseveranceImpedance, permanent power-type are loaded and the static equivalent model of induction conductivity represents, while taking into account integrated load model, and node admittance squareThe building method of battle array is:

Y_ij＝Y_In+Y_Zn+Y_Mn(14)；

Y_In＝I_n0/V_n0(15)；

Y_Zn＝1/Z_n(16)；

Y_Mn＝1/(R+jX)(17)；

$R=\frac{r_m{(r_2/s)}^2+(r_m^2+x_m^2)(r_2/s)+r_m{x}_2^2}{Z_{2m}}---\left(18\right);$

$X=\frac{x_2(r_m^2+x_m^2)+x_m({(r_2/s)}^2+x_2^2)}{Z_{2m}}---\left(19\right);$

Z_2m＝(r_m+r₂/s)²+(x_m+x₂)²(20)；

T_m＝l·(α+(1-α)(1-s)^p)(21)；

$T_e=\frac{V_i^2\·r_2/s}{{(r_1+r_2/s)}^2+{(x_1+x_2)}^2}---\left(22\right);$

In formula (14)-(22): Y_In、Y_ZnAnd Y_MnBe respectively the equivalence of constant current type, constant-impedance type and induction motor loadAdmittance value; S, r_m+jx_mAnd r₂/s+jx₂Be respectively revolutional slip, excitation impedance and the secondary equiva lent impedance of induction conductivity; V_iFor jointThe voltage magnitude of point i; L, α and p are respectively induction motor load rate, repose resistance square and mechanical load performance index;

Based on step 1) set up load uncertainty models, utilize one group of load sample of the every collection of DSMC,Just the trend operational model that synthetic load is taken into account in application calculates, until gathered whole load samples.

Described step 3) in,

Network limit load level risk indicator is specifically expressed as follows:

$P_{collapse}=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{P}_{Ltotal}\left(M_i\right)p\left(M_i\right)---\left(23\right);$

$Q_{collapse}=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{Q}_{Ltotal}\left(M_i\right)p\left(M_i\right)---\left(24\right);$

In formula (23)-(24): m is total simulation number of times; P_Ltotal(M_i) and p (M_i) be respectively the system of i kind load scenariosThe probability of ultimate load amount and appearance thereof, the implication of idle parameter and meritorious situation are similar, repeat no more;

The low compressive load risk indicator of node is specifically expressed as follows:

${\left(busrisk\right)}_i=\underset{j=1}{\overset{ai}{\Σ}}p\left(collapse\right|A_{ij})\·res\left(A_{ij}\right)---\left(25\right);$

$res\left(A_{ij}\right)=\frac{1}{{\left(P_{collapse}\right)}_j/{\left(P_{collapse}\right)}_{mean}}---\left(26\right);$

In formula (25)-(26):For i node voltage is the event sets that the whole network is minimum; P (*) is event A_ijWhen generationThe probability of system crash; Event result res (*) is the system maximum load amount after ultimate load desired value normalized;

Circuit through-put power accounting risk indicator is specifically expressed as follows:

${\left(linerisk1\right)}_l=\underset{k=1}{\overset{Kl}{\Σ}}p\left(collapse\right|L_{lk})\·res1\left(L_{lk}\right)---\left(27\right);$

$res1\left(L_{lk}\right)=\frac{{(p\_transfer)}_{lk}}{{\left(pcollapse\right)}_k}\·100\%---\left(28\right);$

In formula (27)-(28):For the limit transmitted power of circuit l in the whole network thing the highest with the ratio of system load amountPart set; P (*) is event L_lkThe probability of system crash when generation; (p_transfer)_lk(pcollapse)_kBe respectively eventUpper active power and the system limits load capacity transmitting of circuit l when k occurs;

Line threshold transmission nargin risk indicator is specifically expressed as follows:

${\left(linerisk2\right)}_l=\underset{m=1}{\overset{LM}{\Σ}}p\left(collapse\right|L_{lM})\·res2\left(L_{lM}\right)---\left(29\right);$

$res2\left(L_l\right)=\frac{1}{(Ls-1)}\·\frac{P_t}{S_{\mathrm{\Δ}base}}---\left(30\right);$

In formula (29)-(30): p (*) is event L_lMThe probability of system crash when generation; (L_s-1) be that circuit transmission limit is abundantDegree; P_tFor circuit sending end amount of power transfer; S_baseFor power reference value.

Compared with existing static electric voltage stability methods of risk assessment, of the present invention based on the uncertain modeling of loadElectrical network static voltage stability methods of risk assessment possess following advantage: one, compared with certainty appraisal procedure, institute of the present inventionThe electrical network static voltage stability methods of risk assessment based on the uncertain modeling of load of stating has been taken into account multiple uncertain factorProbability distribution, make thus assessment result can reflect objective, all sidedly the actual operating state of electrical network, thus make assessmentResult is more accurate. Its two, compared with probability assessment method, of the present invention based on load uncertain modeling electrical network quietState voltage stabilization methods of risk assessment, taking historical load Changing Pattern as basis, has been taken into account and has been present in original negative accurately, all sidedlyUncertainty in node serial number and load growth situation that increasing appears in lotus consumption, load, has possessed thus and has had physics meaningJustice, can be from the risk indicator of reflection static voltage stability degree at all levels, thereby make assessment result more accurate.

The present invention efficiently solves the inaccurate problem of existing static electric voltage stability methods of risk assessment assessment result, suitableFor the static electric voltage stability risk assessment of electrical network.

Brief description of the drawings

Fig. 1 is the electrical network static voltage stability methods of risk assessment flow chart based on the uncertain modeling of load.

Fig. 2 is " mutual information-relevant the closing of describing Taiyuan 110kV electrical network the whole network payload node load variations othernessSystem ".

Fig. 3 is the load stochastic growth model of Taiyuan 110kV grid nodes 15,18 and 47.

Fig. 4 is the circuit through-put power situation of change under constant power load model in certain trend computing of Taiyuan 110kV electrical network.

Fig. 5 is the circuit through-put power situation of change under integrated load model in certain trend computing of Taiyuan 110kV electrical network.

Fig. 6 be Taiyuan 110kV electrical network under three kinds of load increases, the core probability of network limit load level value-at-riskDensity Distribution.

Detailed description of the invention

Based on the electrical network static voltage stability methods of risk assessment of the uncertain modeling of load, the method is to adopt following stepRapid realization:

1) set up load uncertainty models; Described load uncertainty models comprises: first lotus fluctuation probability Distribution Model,There is the node cluster model of cognition, the load stochastic growth model that increase in load;

2) set up trend operational model: first determine in electrical network and occur according to the node cluster model of cognition of load appearance growthThe node serial number of load growth, afterwards based on monte carlo simulation methodology gather respectively in just lotus fluctuation probability Distribution Model at the beginning ofLoad increment sample in lotus consumption sample and load stochastic growth model, finally takes into account synthetic load spy based on sample valueThe continuous tide computing of property;

3) set up risk assessment index, and use the high operation risk region in risk indicator identification electrical network; Described riskEvaluation index comprises network limit load level risk indicator, the low compressive load risk indicator of node, circuit through-put power accounting windDanger index, line threshold transmission nargin risk indicator.

Described step 1) in,

The method of setting up just lotus fluctuation probability Distribution Model specifically comprises the steps:

1.1) getting clusters number is 2, generates at random one group of initial value that is subordinate to matrix element;

1.2) historical load data are carried out to fuzzy C-means clustering for the first time;

1.3) calculate the interior Classification Index BWP of class between the class of evaluating this cluster result; Specific formula for calculation is as follows:

$BWP(j,i)=\frac{b(j,i)-w(j,i)}{b(j,i)+w(j,i)}---\left(1\right);$

$b(j,i)=\underset{1\≤k\≤m,k\≠j}{\min }\left(\frac{1}{n_k}\underset{p=1}{\overset{n_k}{\Σ}}\right||x_p^k-x_i^j|{|}^2)---\left(2\right);$

$w(j,i)=\frac{1}{n_j-1}\underset{q=1,q\≠i}{\overset{n_j}{\Σ}}\left|\right|x_q^j-x_i^j|{|}^2---\left(3\right);$

In formula (1)-(3): BWP (j, i) is the interior Classification Index of class between class; B (j, i) is the infima species of i sample of j classSpacing; W (j, i) is the inter-object distance of i sample of j class; J and k are class mark; I, p and q are specimen number; M is cluster numbersOrder; n_kIt is the number of samples in k class; n_jIt is the number of samples of j class;Be p sample of k class;Be j class iIndividual sample;Be q sample of j class;

1.4) again produce at random one group and be subordinate to matrix element initial value, repeating step 1.2)-1.3), until cluster number of times reachesTill historical load data length 1/2;

1.5) make clusters number add 1, generate at random one group of initial value that is subordinate to matrix element, repeating step 1.2)-1.4), straightTill clusters number reaches the evolution value of historical load data length;

1.6) add up the interior Classification Index of class between whole classes; Select the interior Classification Index maximum of class between class to be BWP_optTime correspondenceCluster result, the period dividing mode as to load power consumption time graph:

${\mathrm{BWP}}_{opt}=max\left\{\frac{1}{n}\underset{j=1}{\overset{m}{\Σ}}\underset{i=1}{\overset{n_j}{\Σ}}BWP(j,i)\right\},2\≤m\≤Csize---\left(4\right);$

In formula (4): BWP_optFor Classification Index in class between the class of corresponding optimum cluster result; N is total sample number; Csize isThe evolution value of load sample total length;

1.7), to every type load power consumption period, calculate the coefficient correlation of all payload node power consumptions of the whole network and form phase relationMatrix number;

1.8) utilize Cholesky method decomposition step 1.7) in every correlation matrix corresponding to type load power consumption period,Obtain obeying the load power consumption sample of multidimensional normal distribution; So far, the modeling of first lotus fluctuation probability Distribution Model is complete;

Load occurs that the node cluster model of cognition increasing is specifically expressed as follows:

${\mathrm{\ρ}}_{xy}=\frac{\mathrm{cov}(x,y)}{\sqrt{D\left(x\right)\·D\left(y\right)}}---\left(5\right);$

$I_{xy}={\∫}_x{\∫}_{y}p(x,y)\·ln\left(\frac{p(x,y)}{p\left(x\right)\·p\left(y\right)}\right)dxdy---\left(6\right);$

In formula (5)-(6): ρ_xyFor the coefficient correlation of x and y; I_xyFor the mutual information of x and y; Cov (x, y) is the association of x and yVariance; D (x) and D (y) are respectively the variance of x, y; P (x) and p (y) are respectively the marginal probability density of x, y; P (x, y) is x and yJoint probability density;

Load stochastic growth model is specifically expressed as follows:

$\mathrm{\θ}=ar\cos \left(\frac{D1\·D0}{\left|D1\right|\·\left|D0\right|}\right)---\left(9\right);$

In formula (7)-(9): the reference direction that D0 is load growth; D1 is the actual growing direction of load; (S₁,S₂,...,S_Nload) one-dimensional vector of the each payload node apparent energy of serving as reasons composition; Nload is payload node number;Being i carriesThe power factor (1≤i≤Nload) of lotus point; S_ΔbaseFor the power reference value of system; k_LiFor load growth coefficient, k_LiValueSet can be by step 1) described method determines, also can be determined by the approximating method of probability distribution.

Described step 2) in,

First, according to given threshold values ρ₁、ρ₂And I₁、I₂, determine the node serial number that occurs load growth in electrical network:

ρ₁≤ρ_xy≤ρ₂(10)；

I₁≤I_xy≤I₂(11)；

In formula (10)-(11): x and y are node serial number; ρ₁And ρ₂Be respectively lower limit and the upper limit of coefficient correlation; I₁And I₂Be respectively lower limit and the upper limit of mutual information;

Afterwards, utilize step 1) method introduced, try to achieve first lotus consumption sample in just lotus fluctuation probability Distribution Model andLoad increment sample in load stochastic growth model, determines k_LiValue set;

Trend operational model is specifically expressed as follows:

$\left\{\begin{array}{c}{P}_{Gi}(1+{\mathrm{\λk}}_{Gi})-P_{Li0}-P_{Li}-U_i\underset{j=1}{\overset{j=n}{\mathrm{\Σ}}}{U}_j(G_{ij}{\mathrm{cos\δ}}_{ij}+B_{ij}{\mathrm{sin\δ}}_{ij})=0\\ Q_{Gi}-Q_{Li0}-Q_{Li}-U_i\underset{j=1}{\overset{j=n}{\Σ}}{U}_j(G_{ij}{\mathrm{sin\δ}}_{ij}-B_{ij}{\mathrm{cos\δ}}_{ij})=0\end{array}\right.---\left(12\right);$

In formula (12)-(13): the sustainable growth factor that λ is load; P_Li0、Q_Li0Be respectively initial meritorious, the nothing of node iMerit power load amount;For the power factor of node i; δ_ijFor the phase angle difference of node i and j voltage; In the time of i=j, Y_ii＝G_ii+jB_iiFor node self-admittance; In the time of i ≠ j, Y_ij＝G_ij+jB_ijFor node transadmittance; S_ΔbaseFor the power reference value of system; k_LiForLoad growth coefficient, k_GiFor the exert oneself growth factor relevant with power generation dispatching strategy; Integrated load model is commonly used constant current, constant-resistanceAnti-, permanent power-type is loaded and the static equivalent model of induction conductivity represents, while taking into account integrated load model, and bus admittance matrixBuilding method be:

Y_ij＝Y_In+Y_Zn+Y_Mn(14)；

Y_In＝I_n0/V_n0(15)；

Y_Zn＝1/Z_n(16)；

Y_Mn＝1/(R+jX)(17)；

$R=\frac{r_m{(r_2/s)}^2+(r_m^2+x_m^2)(r_2/s)+r_m{x}_2^2}{Z_{2m}}---\left(18\right);$

$X=\frac{x_2(r_m^2+x_m^2)+x_m({(r_2/s)}^2+x_2^2)}{Z_{2m}}---\left(19\right);$

Z_2m＝(r_m+r₂/s)²+(x_m+x₂)²(20)；

T_m＝l·(α+(1-α)(1-s)^p)(21)；

$T_e=\frac{V_i^2\·r_2/s}{{(r_1+r_2/s)}^2+{(x_1+x_2)}^2}---\left(22\right);$

In formula (14)-(22): Y_In、Y_ZnAnd Y_MnBe respectively the equivalence of constant current type, constant-impedance type and induction motor loadAdmittance value; S, r_m+jx_mAnd r₂/s+jx₂Be respectively revolutional slip, excitation impedance and the secondary equiva lent impedance of induction conductivity; V_iFor jointThe voltage magnitude of point i; L, α and p are respectively induction motor load rate, repose resistance square and mechanical load performance index;

Based on step 1) set up load uncertainty models, utilize one group of load sample of the every collection of DSMC,Just the trend operational model that synthetic load is taken into account in application calculates, until gathered whole load samples.

Described step 3) in,

Network limit load level risk indicator is specifically expressed as follows:

$P_{collapse}=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{P}_{Ltotal}\left(M_i\right)p\left(M_i\right)---\left(23\right);$

$Q_{collapse}=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{Q}_{Ltotal}\left(M_i\right)p\left(M_i\right)---\left(24\right);$

In formula (23)-(24): m is total simulation number of times; P_Ltotal(M_i) and p (M_i) be respectively the system of i kind load scenariosThe probability of ultimate load amount and appearance thereof, the implication of idle parameter and meritorious situation are similar, repeat no more;

The low compressive load risk indicator of node is specifically expressed as follows:

${\left(busrisk\right)}_i=\underset{j=1}{\overset{ai}{\Σ}}p\left(collapse\right|A_{ij})\·res\left(A_{ij}\right)---\left(25\right);$

$res\left(A_{ij}\right)=\frac{1}{{\left(P_{collapse}\right)}_j/{\left(P_{collapse}\right)}_{mean}}---\left(26\right);$

In formula (25)-(26):For i node voltage is the event sets that the whole network is minimum; P (*) is event A_ijWhen generationThe probability of system crash; Event result res (*) is the system maximum load amount after ultimate load desired value normalized;

Circuit through-put power accounting risk indicator is specifically expressed as follows:

${\left(linerisk1\right)}_l=\underset{k=1}{\overset{Kl}{\Σ}}p\left(collapse\right|L_{lk})\·res1\left(L_{lk}\right)---\left(27\right);$

$res1\left(L_{lk}\right)=\frac{{(p\_transfer)}_{lk}}{{\left(pcollapse\right)}_k}\·100\%---\left(28\right);$

In formula (27)-(28):For the limit transmitted power of circuit l in the whole network and the ratio of system load amount the highestEvent sets; P (*) is event L_lkThe probability of system crash when generation; (p_transfer)_lk(pcollapse)_kBe respectively thingUpper active power and the system limits load capacity transmitting of circuit l when part k occurs;

Line threshold transmission nargin risk indicator is specifically expressed as follows:

${\left(linerisk2\right)}_l=\underset{m=1}{\overset{LM}{\Σ}}p\left(collapse\right|L_{lM})\·res2\left(L_{lM}\right)---\left(29\right);$

$res2\left(L_l\right)=\frac{1}{(Ls-1)}\·\frac{P_t}{S_{\mathrm{\Δ}base}}---\left(30\right);$

In formula (29)-(30): p (*) is event L_lMThe probability of system crash when generation; (L_s-1) be that circuit transmission limit is abundantDegree; P_tFor circuit sending end amount of power transfer; S_baseFor power reference value.

When concrete enforcement, taking Taiyuan 57 node 110kV electrical networks as example, technical scheme of the present invention is done further specificallyBright:

1) set up load uncertainty models:

By step 1) described flow process, at the beginning of obtaining, lotus fluctuation probability Distribution Model is: the part of first payload node is lotus justSample value is (47.53 ,-46.9 ,-58.5 ,-62.5 ,-50.5 ,-55.7 ,-43.2 ,-58.5), the portion of second payload nodeAt the beginning of point, lotus sample value is (2.2 ,-2.7 ,-3.4 ,-4.0 ,-3.5 ,-2.8 ,-3.1 ,-3.9), and other payload nodes are lotus sample justBe omitted. By step 1) method introduced, the time graph of load power consumption is divided into two time periods, in first time period, theOne and the coefficient correlation of the second payload node sample be 0.77; Second time period, the first and second payload nodes relevantCoefficient is 0.74;

By step 1) described flow process, load is occurred to the node cluster model of cognition increasing is expressed as Fig. 2: abscissa is for describingThe whole network is the mutual information of the node load difference in change opposite sex between two, and ordinate is to describe the whole network node load difference in change opposite sex between twoCoefficient correlation. Artificially the threshold values of given " mutual information-coefficient correlation " is respectively 1.5-0.9,1-0.8, and 0-0, obtains following threeCategory node group, the possibility that same class node load increases is simultaneously larger: first kind node cluster, threshold values 1.5-0.9 to 3-1 itBetween node serial number be 2,6,9,12,13,14,15,16,19,25,29,30,38,41,49,51,52,53,54,56,57; TheTwo category node groups, the node serial number of threshold values between 1-0.8 to 1.5-0.9 is 1,3,5,8,20,27,28,32,35,47,50;The 3rd category node group, the node serial number of threshold values between 0-0 to 1-0.8 is 10,17,18,23,31,33,42,43,44,55;

By step 1) described flow process, the load stochastic growth model obtaining as an example of node 15,18,47 example is expressed as Fig. 3;

2) set up trend operational model, take into account the continuous tide computing of synthetic load characteristic, record each circuit and passDefeated power and the whole network node voltage. In trend computing, make in integrated load model induction conductivity, constant-impedance, constant current and perseveranceThe ratio that power load accounts for total initial load power is respectively 0.5,0.2,0.1,0.2, and induction conductivity model is all chosen domesticTypical case's induction conductivity numerical value calculates (r1=0.04, x1=0.18, r2=0.02, x2=0.12, rm=0.35, xm=3.5, α=0.15, p=2). Statistics only increases first kind node cluster, increases by one or two category node groups and increases by three class joints simultaneously respectivelyTrend operation result in three kinds of situations of point group. Only show in certain continuous tide computing the merit of transmission on circuit 1 and 15 hereinRate size, as Fig. 4-Fig. 5;

3) set up risk assessment index, and based on risk assessment index, continuous tide operation result is carried out to risk assessment.Three kinds of horizontal risk indicator P of ultimate load that load increase is corresponding_collapseBe respectively 2312.3,2434.2,2447.7MW,Q_collapseBe respectively 1050.6,1315.2,1400.1MVar, P_collapseCore probability density distribution as shown in Figure 6. Three kinds negativeThe low compressive load risk indicator of node operation result under lotus growth pattern is in table 1; Circuit transmission under three kinds of load increasesPower accounting risk indicator and line threshold transmission nargin risk indicator operation result are in table 2;

The low compressive load value-at-risk of table 1 node

；

Table 2 line power transmission risk

；

Analysis indexes operation result is known, and from causing system generation collapse of voltage angle, 31 and 33 nodes are all risky,And the value-at-risk of 31 nodes is far above 33 nodes; Circuit 1 and 15 is heavy duty elevated track through-put power accounting risk circuit, butThe line threshold transmission nargin risk of circuit 1 is very low, just the opposite with circuit 15.

Claims (4)

1. the electrical network static voltage stability methods of risk assessment based on the uncertain modeling of load, is characterized in that: the partyMethod is to adopt following steps to realize:

1) set up load uncertainty models; Described load uncertainty models comprises: first lotus fluctuation probability Distribution Model, loadThere is the node cluster model of cognition, the load stochastic growth model that increase;

2) set up trend operational model: the node cluster model of cognition that first appearance increases according to load is determined appearance load in electrical networkThe node serial number increasing, gathers respectively the first lotus consumption in just lotus fluctuation probability Distribution Model based on monte carlo simulation methodology afterwardsAmount sample and the load increment sample of load in stochastic growth model, finally take into account synthetic load characteristic based on sample valueContinuous tide computing;

3) set up risk assessment index, and use the high operation risk region in risk indicator identification electrical network; Described risk assessmentIndex comprises that network limit load level risk indicator, the low compressive load risk indicator of node, circuit through-put power accounting risk refer toMark, line threshold transmission nargin risk indicator.

2. the electrical network static voltage stability methods of risk assessment based on the uncertain modeling of load according to claim 1,It is characterized in that: described step 1) in,

The method of setting up just lotus fluctuation probability Distribution Model specifically comprises the steps:

1.1) getting clusters number is 2, generates at random one group of initial value that is subordinate to matrix element;

1.2) historical load data are carried out to fuzzy C-means clustering for the first time;

1.3) calculate the interior Classification Index BWP of class between the class of evaluating this cluster result; Specific formula for calculation is as follows:

$BWP\left(j,i\right)=\frac{b(j,i)-w(j,i)}{b(j,i)+w(j,i)}---\left(1\right);$

$b(j,i)=\underset{1\≤k\≤m,k\≠j}{min}\left(\frac{1}{n_k}\underset{p=1}{\overset{n_k}{\Σ}}\right||x_p^k-x_i^j|{|}^2)---\left(2\right);$

$w(j,i)=\frac{1}{n_j-1}\underset{q=1,q\≠i}{\overset{n_j}{\Σ}}\left|\right|x_q^j-x_i^j|{|}^2---\left(3\right);$

In formula (1)-(3): BWP (j, i) is the interior Classification Index of class between class; B (j, i) is the infima species spacing of i sample of j classFrom; W (j, i) is the inter-object distance of i sample of j class; J and k are class mark; I, p and q are specimen number; M is clusters number;n_kIt is the number of samples in k class; n_jIt is the number of samples of j class;Be p sample of k class;Be i sample of j classThis;Be q sample of j class;

1.4) again produce at random one group and be subordinate to matrix element initial value, repeating step 1.2)-1.3), go through until cluster number of times reachesHistory load data length 1/2 till;

1.5) make clusters number add 1, generate at random one group of initial value that is subordinate to matrix element, repeating step 1.2)-1.4), until poly-Till class number reaches the evolution value of historical load data length;

1.6) add up the interior Classification Index of class between whole classes; Select the interior Classification Index maximum of class between class to be BWP_optTime corresponding poly-Class result, the period dividing mode as to load power consumption time graph:

${\mathrm{BWP}}_{opt}=max\left\{\frac{1}{n}\underset{j=1}{\overset{m}{\Σ}}\underset{i=1}{\overset{n_j}{\Σ}}BWP(j,i)\right\},2\≤m\≤Csize---\left(4\right);$

In formula (4): BWP_optFor Classification Index in class between the class of corresponding optimum cluster result; N is total sample number; Csize is loadThe evolution value of sample total length;

1.7), to every type load power consumption period, calculate the coefficient correlation of all payload node power consumptions of the whole network and form coefficient correlation squareBattle array;

1.8) utilize Cholesky method decomposition step 1.7) in every correlation matrix corresponding to type load power consumption period, obtainObey the load power consumption sample of multidimensional normal distribution; So far, the modeling of first lotus fluctuation probability Distribution Model is complete;

Load occurs that the node cluster model of cognition increasing is specifically expressed as follows:

${\mathrm{\ρ}}_{xy}=\frac{\mathrm{cov}(x,y)}{\sqrt{D\left(x\right)\·D\left(y\right)}}---\left(5\right);$

$I_{xy}={\∫}_x{\∫}_{y}p(x,y)\·ln\left(\frac{p(x,y)}{p\left(x\right)\·p\left(y\right)}\right)dxdy---\left(6\right);$

In formula (5)-(6): ρ_xyFor the coefficient correlation of x and y; I_xyFor the mutual information of x and y; Cov (x, y) is the covariance of x and y;D (x) and D (y) are respectively the variance of x, y; P (x) and p (y) are respectively the marginal probability density of x, y; P (x, y) is the connection of x and yClose probability density;

Load stochastic growth model is specifically expressed as follows:

$\mathrm{\θ}=ar\cos \left(\frac{D1\·D0}{\left|D1\right|\·\left|D0\right|}\right)---\left(9\right);$

In formula (7)-(9): the reference direction that D0 is load growth; D1 is the actual growing direction of load; (S₁,S₂,...,S_Nload) beThe one-dimensional vector being formed by each payload node apparent energy; Nload is payload node number;It is the merit of i the point of loadRate factor (1≤i≤Nload); S_ΔbaseFor the power reference value of system; k_LiFor load growth coefficient, k_LiThe set of value can be byStep 1) described method determines, also can be determined by the approximating method of probability distribution.

3. the electrical network static voltage stability methods of risk assessment based on the uncertain modeling of load according to claim 1,It is characterized in that: described step 2) in,

First, according to given threshold values ρ₁、ρ₂And I₁、I₂, determine the node serial number that occurs load growth in electrical network:

ρ₁≤ρ_xy≤ρ₂(10)；

I₁≤I_xy≤I₂(11)；

In formula (10)-(11): x and y are node serial number; ρ₁And ρ₂Be respectively lower limit and the upper limit of coefficient correlation; I₁And I₂RespectivelyFor lower limit and the upper limit of mutual information;

Afterwards, utilize step 1) method introduced, try to achieve first lotus consumption sample and load in just lotus fluctuation probability Distribution ModelLoad increment sample in stochastic growth model, determines k_LiValue set;

Trend operational model is specifically expressed as follows:

$\left\{\begin{array}{c}{P}_{Gi}(1+{\mathrm{\λk}}_{Gi})-P_{Li0}-P_{Li}-U_i\underset{j=1}{\overset{j=n}{\Σ}}{U}_j(G_{ij}{\mathrm{cos\δ}}_{ij}+B_{ij}{\mathrm{sin\δ}}_{ij})=0\\ Q_{Gi}-Q_{Li0}-Q_{Li}-U_i\underset{j=1}{\overset{j=n}{\Σ}}{U}_j(G_{ij}{\mathrm{sin\δ}}_{ij}-B_{ij}{\mathrm{cos\δ}}_{ij})=0\end{array}\right.---\left(12\right);$

In formula (12)-(13): the sustainable growth factor that λ is load; P_Li0、Q_Li0Be respectively initial meritorious, the idle merit of node iRate load;For the power factor of node i; δ_ijFor the phase angle difference of node i and j voltage; In the time of i=j, Y_ii＝G_ii+jB_iiFor node self-admittance; In the time of i ≠ j, Y_ij＝G_ij+jB_ijFor node transadmittance; S_ΔbaseFor the power reference value of system; k_LiFor negativeLotus growth factor, k_GiFor the exert oneself growth factor relevant with power generation dispatching strategy; Integrated load model is commonly used constant current, constant-resistanceAnti-, permanent power-type is loaded and the static equivalent model of induction conductivity represents, while taking into account integrated load model, and bus admittance matrixBuilding method be:

Y_ij＝Y_In+Y_Zn+Y_Mn(14)；

Y_In＝I_n0/V_n0(15)；

Y_Zn＝1/Z_n(16)；

Y_Mn＝1/(R+jX)(17)；

$R=\frac{r_m{(r_2/s)}^2+(r_m^2+x_m^2)(r_2/s)+r_m{x}_2^2}{Z_{2m}}---\left(18\right);$

$X=\frac{x_2(r_m^2+x_m^2)+x_m({\left(r_2/s\right)}^2+x_2^2)}{Z_{2m}}---\left(19\right);$

Z_2m＝(r_m+r₂/s)²+(x_m+x₂)²(20)；

T_m＝l·(α+(1-α)(1-s)^p)(21)；

$T_e=\frac{V_i^2\·r_2/s}{{(r_1+r_2/s)}^2+{(x_1+x_2)}^2}---\left(22\right);$

In formula (14)-(22): Y_In、Y_ZnAnd Y_MnBe respectively the equivalent admittance of constant current type, constant-impedance type and induction motor loadValue; S, r_m+jx_mAnd r₂/s+jx₂Be respectively revolutional slip, excitation impedance and the secondary equiva lent impedance of induction conductivity; V_iFor node iVoltage magnitude; L, α and p are respectively induction motor load rate, repose resistance square and mechanical load performance index;

Based on step 1) set up load uncertainty models, utilize one group of load sample of the every collection of DSMC, just shouldCalculate with the trend operational model of taking into account synthetic load, until gathered whole load samples.

4. the electrical network static voltage stability methods of risk assessment based on the uncertain modeling of load according to claim 1,It is characterized in that: described step 3) in,

Network limit load level risk indicator is specifically expressed as follows:

$P_{collapse}=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{P}_{Ltotal}\left(M_i\right)p\left(M_i\right)---\left(23\right);$

$Q_{collapse}=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{Q}_{Ltotal}\left(M_i\right)p\left(M_i\right)---\left(24\right);$

In formula (23)-(24): m is total simulation number of times; P_Ltotal(M_i) and p (M_i) be respectively the system limits of i kind load scenariosThe probability of load capacity and appearance thereof, the implication of idle parameter and meritorious situation are similar, repeat no more;

The low compressive load risk indicator of node is specifically expressed as follows:

${\left(busrisk\right)}_i=\underset{j=1}{\overset{ai}{\Σ}}p\left(collapse\right|A_{ij})\·res\left(A_{ij}\right)---\left(25\right);$

$res\left(A_{ij}\right)=\frac{1}{{\left(P_{collapse}\right)}_j/{\left(P_{collapse}\right)}_{mean}}---\left(26\right);$

In formula (25)-(26):For i node voltage is the event sets that the whole network is minimum; P (*) is event A_ijSystem when generationThe probability of collapse; Event result res (*) is the system maximum load amount after ultimate load desired value normalized;

Circuit through-put power accounting risk indicator is specifically expressed as follows:

${\left(linerisk1\right)}_l=\underset{k=1}{\overset{Kl}{\Σ}}p\left(collapse\right|L_{lk})\·res1\left(L_{lk}\right)---\left(27\right);$

$res1\left(L_{lk}\right)=\frac{{\left(p\_transfer\right)}_{lk}}{{\left(pcollapse\right)}_k}\·100\%---\left(28\right);$

In formula (27)-(28):For the limit transmitted power of circuit l in the whole network event set the highest with the ratio of system load amountClose; P (*) is event L_lkThe probability of system crash when generation; (p_transfer)_lk(pcollapse)_kThe event k of being respectively sends outUpper active power and the system limits load capacity transmitting of circuit l when raw;

Line threshold transmission nargin risk indicator is specifically expressed as follows:

${\left(linerisk2\right)}_l=\underset{m=1}{\overset{LM}{\Σ}}p\left(collapse\right|L_{lM})\·res2\left(L_{lM}\right)---\left(29\right);$

$res2\left(L_l\right)=\frac{1}{(Ls-1)}\·\frac{P_t}{S_{\mathrm{\Δ}base}}---\left(30\right);$

In formula (29)-(30): p (*) is event L_lMThe probability of system crash when generation; (L_s-1) be circuit transmission limit nargin; P_tFor circuit sending end amount of power transfer; S_baseFor power reference value.