CN101609989B - System for calculating power supply abundance of urban power network - Google Patents

Abstract

The invention relates to a system for calculating power supply abundance of a urban power network, which is characterized by comprising an equivalent model fitting module, a trust domain subproblem solution module, a target function real descend value solution module, a target function searching step-length searching direction adjusting module and an alternating current power flow calculating module; the network basic data and the calculated initial value of the city electric network are input into a calculating system; in the equivalent model fitting module, the equivalent second-order model of the target function is output according to the basic data and calculated initial value; when the HESSEN matrix norm value of the equivalent second-order model is smaller than permissible error, namely the abundance value of power supply capability of the power network is output finally by the target function real descend value solution module. The system for calculating power supply abundance of the urban power network fully exerts the advantages of effectiveness and local superlinear convergence when the trust domain method is used for solving morbidity optimization problem, simultaneously the alternating current power flow algorithm reflects the influence of voltage level of the system, transmission capability of branches and reactive power flow to the power supply capability of the network precisely, and the voltage constraint of all nodes in the network can be calculated.

Description

A kind of system for calculating power supply abundance of urban power network

Technical field

The present invention relates to a kind of electric power system computing system, especially in regard to a kind of system for calculating power supply abundance of urban power network.

Background technology

Urban power network power supply capacity abundant intensity assessment is mainly by finding the solution urban network max power supply capability, and then compares the power supply nargin of assessment electrical network with electrical network present situation electric load level.The assessment of urban distribution network power supply capacity abundant intensity relates to city power transmission network, high voltage distribution network and low-voltage network, and the expression formula of its target function is as follows:

$\mathrm{UNPSAI}=\frac{\mathrm{MNSPL}}{\mathrm{MPL}}---\left(1\right)$

Equation (1) expression urban distribution network power supply abundant intensity value UNPSAI is the ratio of the horizontal MPL of peak load of electrical network peak load deliverability MNSPL and present situation electrical network, and the reflection electrical network adapts to the ability that electric load changes.The calculating of electrical network peak load deliverability MNSPL can be regarded as a problem of finding the solution extreme value on mathematics, promptly generating equipment and transmission line all are no more than under the condition of constraint such as rated capacity in satisfying network, ask for the maximum of all load point burden with power sums in the network.Its target function is:

$\mathrm{MNSPL}=f\left(x\right)=\max \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_{\mathrm{Li}}---\left(2\right)$

In the formula: P _LiBe the active power of i load bus, n is the load point sum.The constraints of equation (2) is: the constraint of power supply capacity bound; The thermally-stabilised capacity-constrained of circuit; The thermally-stabilised transmission capacity constraint of physical components such as transformer; The busbar voltage constraint.Reach relevant constraints as can be seen from target function, the existence of constraints in the network although the expression formula of target function is fairly simple, but presents very strong nonlinear characteristic near extreme point.At present, the assessment of the power supply capacity abundant intensity of urban distribution network does not also have the accurate method of a kind of comparatively science.The main method of traditional evaluation urban distribution network power supply capacity abundant intensity has balance of electric power and ener method, trial-and-error method, peak load method of multiplicity and network max-flow method etc.

1) balance of electric power and ener method and power transformation capacitance balance method are power supply capacity abundant intensity appraisal procedures commonly used in the urban power network planning design.The planning personnel at first adopts balance of electric power and ener method and power transformation capacitance balance to assess the power supply capacity of urban distribution network in the Electric Power Network Planning course of work, passes through the reliability of network configuration under the N-1 condition in trend calculation check varying level year then.The greatest drawback of the method is, it can't obtain the net capability of the electric network composition in planning level year, therefore whether overload of all the other elements in the mode verification electrical network that can only stop transport by the N-1 of network element, thereby carry out qualitative evaluation, and can't draw the quantitative evaluation result of urban distribution network power supply abundant intensity and reliability urban distribution network power supply capacity abundant intensity.Therefore when the load forecast deviation of electrical network greatly the time, obvious deficiency will appear in the adaptive of planning network.

2) trial-and-error method is by given certain system loading, and according to certain sharing of load coefficient sharing of load is arrived each load point, again it is carried out trend and calculates; If there is not branch road generation power to get over line, then increase system loading, carry out trend and calculate, will cause the branch road through-put power above till the thermally-stabilised limit of branch road up to increasing very little load.The accuracy of this method evaluation result depends on the reasonability of sharing of load coefficient, and computational process is more loaded down with trivial details.

3) the peak load method of multiplicity is based on the existing load of network, and the peak load multiple that can reach by computing network comes the evaluating network power supply capacity.The evaluation result of this method is subjected to the influence of the existing Load distribution situation of network to a great extent.

4) network max-flow method at first is converted into equivalent network with supply network, i.e. system mode flow chart is determined the net capability of network again according to the minimal cut set capacity of the capacity-constrained of branch road and equivalent network.This method is applicable to the net capability of finding the solution localized network, and is not suitable for finding the solution the target function of the net capability of urban electric power network.

In sum, the power supply capacity nargin of urban distribution network is evaluated at the following aspects to be needed to break through: (1) manually by AC power flow carry out power supply capacity evaluates calculation amount huge, take time and effort, and computational accuracy is difficult to hold.(2) the power supply capacity analysis carried out in conjunction with optimization method of DC power flow method can't be taken into account the reactive voltage constraint of network, and the gained result still needs the calculation check by AC power flow.(3) there is tangible nonlinear characteristic in the target function of finding the solution urban network max power supply capability, need find the solution ability algorithm model preferably to nonlinear problem.Therefore, the computational analysis of mains supply ability abundant intensity needs precision and the higher algorithm model of efficient, and the AC power flow algorithm is to calculate the developing direction of urban distribution network power supply capacity abundant intensity in conjunction with optimized Algorithm.

The research of trust region method originates from Powell work in 1970, and he has proposed an algorithm of finding the solution unconstrained optimization problem, and the distance between iteration point that this algorithm will be looked for novelty when each iteration and the current iteration point is no more than a controlled numerical value.Introducing the control step-length is because traditional linear search method usually causes the algorithm failure owing to step-length is excessive, particularly particularly like this when problem is morbid state.The control step-length is equivalent in fact in the neighborhood that with the current iteration point is the center asks extreme value to a naive model that is similar to former problem.This skill can be regarded as the only trust of pairing approximation model in a neighborhood, so this neighborhood is called as trusted zones (trust region), corresponding method also just is called as the trusted zones method.

Summary of the invention

At the problems referred to above, the purpose of this invention is to provide in a kind of voltage constraint, branch power constraint and generating constraint in the reflection electrical network, can effectively find the solution the system for calculating power supply abundance of urban power network of the target function of urban network max power supply capability.

For achieving the above object, the present invention takes following technical scheme: a kind of system for calculating power supply abundance of urban power network is characterized in that: it comprises that Equivalent Model fitting module, trusted zones subproblem are found the solution module, the true drop-out value of target function is found the solution module, target function step-size in search direction of search adjusting module and AC power flow computing module; In described Equivalent Model fitting module, basic data and calculating initial value according to input, the equivalent second-order model of export target function, when the HESSEN of described equivalent second-order model matrix norm value during less than permissible error, promptly find the solution the value that module is calculated described target function, finally export mains supply ability abundant intensity value by the true drop-out value of described target function; When the HESSEN of described equivalent second-order model matrix norm value during more than or equal to described permissible error, find the solution in the module described trusted zones subproblem, in conjunction with described basic data with calculate initial value and described equivalent second-order model, export the drop-out value of estimating that the difference of the extreme value of described current goal functional value and equivalent second-order model tries to achieve; Find the solution in the module in the true drop-out value of described target function, by the true drop-out value of the described target function of AC power flow technology export; In described execution direction of search adjusting module, by the ratio of described future prices depreciation and true drop-out value, adjust the step-size in search and the direction of search of described target function value, export new search point and trusted zones border in described Equivalent Model fitting module.

Described equivalent second-order model is $q^{\left(k\right)}\left(s\right)=f\left(x_k\right)+g_k^{T}s+0.5s^T{G}_{k}s,$ F (x wherein _k) put x for described target function at current search _kNumerical value, g _kBe the broad sense first derivative matrix of described target function f (x), G _kBe the Hessen matrix of described target function f (x), s is an operator.

The extreme value that described trusted zones subproblem is found the solution the described equivalent second-order model in the module is:

$\min q\left(d_k\right)=f\left(x_k\right)+g_k^T{d}_k+0.5{d_k}^T{G}_k{d}_k$

s.t.‖d _k‖＜h _k

Wherein, d _kBe current search step-length, h _kFor current trusted zones border, try to achieve minq (d _k) after, and then calculating target function estimate drop-out value.

In the described execution direction of search adjusting module, adjust the step-size in search of described target function value and the method for the direction of search and be, when described ratio＞0, upgrade the current search point, even the new search point; Otherwise be start point search with the current search point again; When described ratio＜0.25, dwindle the trusted zones border; When described ratio 〉=0.75,, then amplify the trusted zones border, otherwise in original trusted zones, search for if when step-size in search reaches described current trusted zones border.

The present invention is owing to take above technical scheme, it has the following advantages: 1, urban distribution network power supply capacity abundant intensity algorithm of the present invention, not only can be used to assess the adaptability of urban distribution network to the electric load fluctuation, and can be by the reasonability of power supply capacity abundant intensity difference assessment electric network composition under the contrast heterogeneous networks structural condition, therefore significant to urban power network planning.2, system for calculating power supply abundance of urban power network of the present invention asking in the process in the power distribution network power supply capacity, because the algorithm that the iterative process of load point and target function adopts trusted zones method and AC power flow to combine, the iteration step length of load point can in time be adjusted according to AC power flow result calculated and subspace function matching degree, and the convergence that algorithm is good has obtained representing fully.3, system for calculating power supply abundance of urban power network of the present invention has been given full play to the trusted zones method and has been found the solution the advantage of ill optimization problem validity and local superlinear convergence, the convergence that target function is found the solution is better, the AC power flow algorithm has reflected the influence to the network power supply ability of system voltage level, branch road transmittability and reactive power flow accurately simultaneously, can take into account each the node voltage constraint in the network.

Description of drawings

Fig. 1 is the schematic flow sheet of system for calculating power supply abundance of urban power network of the present invention

Fig. 2 is the network topology structure and the network basic parameter schematic diagram in A district in the embodiment of the invention

Fig. 3 is that power factor is 0.99 o'clock a target function iterative process schematic diagram in the embodiment of the invention

Fig. 4 is that power factor is 0.99 o'clock a load point iterative process schematic diagram in the embodiment of the invention

Fig. 5 is that power factor is 0.90 o'clock a target function iterative process schematic diagram in the embodiment of the invention

Fig. 6 is that power factor is 0.90 o'clock a load point iterative process schematic diagram in the embodiment of the invention

Embodiment

The present invention makes up system for calculating power supply abundance of urban power network in conjunction with trusted zones method and AC power flow computing method, and main contents comprise: the equivalent second-order model of target function is found the solution, and the actual value of target function calculates, and target function search drop-out value is calculated.Wherein target function minimum search end mark is that the HESSEN norm of matrix value of the equivalent second order Equivalent Model of target function is less than assigned error.

Computing system of the present invention comprises following four basic modules: Equivalent Model fitting module 1, and the trusted zones subproblem is found the solution module 2, and the true drop-out value of target function is found the solution module 3, target function step-size in search and direction of search adjusting module 4.Wherein, the major function of Equivalent Model fitting module 1 is to adopt nonlinear least square method, asks for the parameter value of the second order Equivalent Model of the controlled neighborhood internal object function of searching for point; The major function that the trusted zones subproblem is found the solution module 2 is to find the solution the minimum of Equivalent Model in controlled neighborhood of target function; The major function that the true drop-out value of target function is found the solution module 3 is to finish the calculating of the target function value of mains supply ability by the AC power flow computing module; The major function of target function step-size in search and direction of search adjusting module 4 is to find the solution the prediction drop-out value of the target function that module 2 calculates by the trusted zones subproblem, the true drop-out value of combined objective function is found the solution the true drop-out value of target function that module 3 calculates, and adjusts the direction of search and the step-size in search of the maximum of target function.

As shown in Figure 1, algorithm flow of the present invention is as follows:

1) sets up the network configuration of urban distribution network, network foundation data such as the thermally-stabilised transmission capacity constraint of physical components such as clear and definite power supply capacity bound constraint, the thermally-stabilised capacity-constrained of circuit, transformer and busbar voltage constraint.Simultaneously given calculating initial value is prepared, for example the current search point x of current time k _k, load point electric load initial value, target function initial ranging step-length d ₀, the Hessen matrix norm permissible error ξ and trusted zones border initial value h ₀Deng, trusted zones border initial value h wherein ₀Get Hessen matrix initial value g ₀Norm.

2) use Equivalent Model fitting module 1, at current search point x _kTrusted zones h _kIn, ask for the target function f (x) of equation (2) expression at current search point x=x by numerical perturbation method and least-square fitting approach _kEquivalent second-order model and parameter.Wherein target function is put x at current search _kThe equivalent second-order model expression formula launched of Taylor (Taylor) be:

$q^{\left(k\right)}\left(s\right)=f\left(x_k\right)+g_k^{T}s+0.5s^T{G}_{k}s---\left(3\right)$

F (x wherein _k) put x for target function at current search _kNumerical value, g _kBe the broad sense first derivative matrix of target function f (x), G _kBe the Hessen matrix of target function f (x), s is the Taylor operator.

3) the HESSEN matrix G of the equivalent second-order model of calculating _kNorm value, and with step 1) in given permissible error ξ compare, as HESSEN matrix G _kNorm value during less than permissible error ξ, turn to step 8); As HESSEN matrix G _kNorm value during more than or equal to permissible error ξ, then continue the search that step 4) is carried out the target function extreme value.

4) find the solution module 2 by the trusted zones subproblem, the extreme value of the equivalent second-order model of the expression of accounting equation (3):

$\min q\left(d_k\right)=f\left(x_k\right)+g_k^T{d}_k+0.5{d_k}^T{G}_k{d}_k---\left(4\right)$

s.t.‖d _k‖＜h _k

Wherein, d _kBe current search step-length, h _kBe current trusted zones border, try to achieve min q (d _k) after, and then calculating target function estimate drop-out value.Estimate drop-out value and be target function current search point x _kCurrent goal functional value f (x _k) with the minimizing difference of equivalent second-order model, estimate the drop-out value expression formula and be:

Pred _k＝f(x _k)-min?q(d _k) (5)。

5) find the solution module 3 by the true drop-out value of target function, according to the current search step-length d of equivalent second-order model _k, by AC power flow technique computes target function f (x _k) and f (x _k+ d _k), and obtain the actual drop-out value of target function, actual drop-out value expression formula is:

Ared _k＝f(x _k)-f(x _k+d _k) (6)

6) carry out direction of search adjusting module 4, by calculating actual drop-out value Ared _kWith estimate drop-out value Pred _kRatio r _k, adjust the step-size in search d in search procedure next time of target function _kAnd the direction of search.R wherein _kCharacterize the approximation ratio of target function second-order model equivalent, r with it _kThe approximation ratio that shows equivalent second-order model more greatly is bigger, should consider suitably to amplify search border h _K+1r _kLittler, then should consider to dwindle trusted zones border h _K+1Pass through r _kValue and dependent thresholds contrast can accomplish to adjust the step-size in search d in search procedure next time of target function in good time _kAnd the direction of search.r _kExpression formula as follows:

r _k＝Ared _k/Pred _k (7)

The process of the concrete step-size in search and the direction of search is as follows:

Work as r _k＞0, upgrade the current search point, even new search point x _K+1=x _k+ d _kOtherwise again with current search point x _kBe start point search, promptly get new search point x _K+1=x _k

Work as r _k, dwindle trusted zones border h at＜0.25 o'clock _K+1Even, trusted zones border h _K+1=‖ h _k‖/4;

Work as r _k〉=0.75 o'clock, if step-size in search reaches the trusted zones border, i.e. ‖ d _k‖=h _kThe time, even then suitably amplify trusted zones border h _K+1=2h _kOtherwise, in original trusted zones, search for, even h _K+1=h _k

7) upgrade the new search point x that obtains _K+1With trusted zones border h _K+1After, return step 2), ask for the equivalent second-level model of current search point by using Equivalent Model fitting module 1, and continue to repeat above-mentioned steps 4) to the iterative process of step 6), iterative process is until HESSEN matrix G _kNorm value less than permissible error ξ till.

8) as the HESSEN of equivalent second-order model matrix G _kNorm during less than permissible error ξ, find the solution the MNSPL value of module 3 calculating target function equations (2) by the true drop-out value of target function, ask for mains supply ability abundant intensity value UNPSAI according to equation (1) then, power supply capacity abundant intensity calculating process finishes.

When carrying out the calculating of urban distribution network power supply capacity abundant intensity UNPSAI, required master data is as follows:

I) power supply, the power supply in the urban distribution network can be divided into power plant and power supply transformer station two classes.Wherein power supply transformer station is meant 220kV, 330kV or the 500kV step-down substation in the urban distribution network, specifically comprises: subregion under the power supply transformer station; The electric pressure of power supply transformer station; Platform number, the total capacity of step-down transformer in the power supply transformer station; The model of each step-down transformer in the power supply transformer station; Each step-down transformer inserts the position in the urban distribution network in the power supply transformer station, and promptly transformer high, medium and low voltage side joint is gone into the nodename of urban distribution network.

II) high-tension distributing line, its Back ground Information comprises: the electric pressure of high-tension distributing line; Each high-tension distributing line inserts head, the endpoint node of urban distribution network; The length of each high-tension distributing line; The wire type of each high-tension distributing line and thermoae limited capacity amount thereof.

III) high tension substation, its Back ground Information comprises: the affiliated subregion of each high tension substation; Platform number, the total capacity of transformer in each high tension substation; The model of each high voltage power distribution transformer, rated capacity; Each high voltage power distribution transformer inserts the high, medium and low voltage side gusset title of urban distribution network.

IV) workload demand of electrical network, its Back ground Information comprises: electric load curve, to determine load power constraint upper and lower limit; Load point inserts the node name of urban distribution network; The predicted value of present situation electric load and distant view electric load.

Present invention is described below in conjunction with accompanying drawing and example:

I) present embodiment is an example with China's A district power transmission network, in order to simplify calculating, has kept the ring network structure of regional power grid in the present embodiment, and with the bus of radial network reduction value transformer station.It below is the basic condition of this electric network composition.

As shown in Figure 2, the highest voltage level of A district electrical network is 220kV, is the strong point in the power supply area periphery with three 220kV transformers, forms 220kV dual-ring network structure node.BUS 1～BUS6 is the node on the bus, and wherein the voltage of Node B US 1～BUS5 is 220V, and the voltage of BUS6 is 110V.Circuit Line1～Line10 is a transmission line, and wherein circuit Line1, Line2, Line3 and Line4 form 2 220kV power supply passways for transmitting electricity, and parameter is 2 * 400mm ²/ 20km; The parameter of Line5 and Line6 is 400mm ²/ 20km; The parameter of Line7 and Line8 is 400mm ²/ 25km; The parameter of Line9 and Line10 is 300mm ²/ 35km.Load point load1～load4 is the load that is articulated on Node B US3, BUS4, BUS5 and the BUS6.

The ii) target function of present embodiment and constraints: according to correlation analysis, the target function of the electrical network peak load deliverability MNSPL of system is:

$\mathrm{MNSPL}=f\left(x\right)=\max \underset{i=1}{\overset{4}{\mathrm{\Σ}}}{P}_{\mathrm{Li}}---\left(8\right)$

Constraints comprises node voltage constraint, the constraint of circuit conveying capacity, load point initial value and power factor.It is as shown in table 1 that the upper and lower limit of the node voltage of present embodiment is taken as 0.9 ~ 1.1 times of node nominal voltage temporarily:

The constraint of table 1 node voltage

Nodename	Electric pressure	The node voltage upper limit	The node voltage lower limit
				BUS1	220	242	198
BUS2	220	242	198
				BUS3	220	242	198
BUS4	220	242	198
				BUS5	220	242	198
BUS6	110	121	99

The constraint of circuit conveying capacity mainly refers to the lasting thermally-stabilised transmission capacity of transmission line and the rated capacity of transformer, as the conductor cross-section of circuit and the main transformer capacity of transformer station.The transmission capacity limit value of the line related of present embodiment and transformer station is as shown in table 2.

The transmission capacity limit value of table 2 circuit and transformer station

The circuit sequence number	Headend node	Endpoint node	Electric pressure (kV)	Transmission capacity (MVA)
					Line1	BUS?1	BUS?3	220	643.98
Line?2	BUS?1	BUS?3	220	643.98
					Line?3	BUS?2	BUS?4	220	643.98
Line?4	BUS?2	BUS?4	220	643.98
					Line?5	BUS?3	BUS?4	220	321.99
Line?6	BUS?3	BUS?4	220	321.99
					Line?7	BUS?3	BUS?5	220	321.99
Line?8	BUS?3	BUS?5	220	321.99
					Line?9	BUS?4	BUS?5	220	270.55
Line?10	BUS?4	BUS?5	220	270.55
					The circuit sequence number	Headend node	Endpoint node	Electric pressure (kV)	Transmission capacity (MVA)
Line?11	BUS?5	BUS?6	220	540.00

The initial value of load point is as shown in table 3 in the present embodiment:

The meritorious electric load of table 3 electric load point

The load point sequence number	Node ID	Burden with power (MW)
			Load1	BUS?3	450
Load2	BUS?4	420
			Load3	BUS?5	300
Load4	BUS?6	375

The iii) result of calculation of electrical network peak load deliverability MNSPL

Power factor is the result of calculation under 0.99 condition:

The peak load deliverability value MNSPL of A district electric power networks is 2160.94MW, and the peak load deliverability of system is subject to the lower limit of busbar voltage of the conveying capacity Node B US6 of transformer branch road BUS5-BUS6.Following form and curve have provided the iterative process of finding the solution of the result of calculation of result of calculation, AC power flow of result of calculation, the node voltage of network peak load deliverability and electric load.Then, the result of calculation of peak load deliverability is as shown in table 4, and node voltage result of calculation is as shown in table 5, and the result of calculation of AC power flow is as shown in table 6, electric load find the solution iterative process as shown in Figure 3, Figure 4.

The result of calculation of table 4 peak load deliverability

The load point sequence number	Node ID	Burden with power (MW)
			Load1	BUS?3	629.40
Load2	BUS?4	587.44
			Load3	BUS?5	419.60
Load4	BUS?6	524.50
			Add up to	--	2160.94

The result of calculation of table 5 node voltage

Node ID	Voltage magnitude (pu)	Angle (rad)
			BUS1	1.01	0
BUS2	1.01	-2.07
			BUS?3	0.975	-6.34

BUS?4	0.981	-6.1
			BUS?5	0.953	-9.38
BUS?6	0.984	-15

Table 6 AC power flow result calculated

The circuit sequence number	Headend node	Endpoint node	Meritorious (pu)	Idle (pu)	Apparent power (pu)
						The circuit sequence number	Headend node	Endpoint node	Meritorious (pu)	Idle (pu)	Apparent power (pu)
Line?1	BUS?1	BUS?3	5.59	1.44	5.77
						Line?2	BUS?1	BUS?3	5.59	1.44	5.77
Line?3	BUS?2	BUS?4	5.40	1.74	5.67
						Line?4	BUS?2	BUS?4	5.40	1.74	5.67
Line?5	BUS?3	BUS?4	-0.33	-0.34	0.48
						Line?6	BUS?3	BUS?4	-0.33	-0.34	0.48
Line?7	BUS?3	BUS?5	2.70	0.68	2.78
						Line?8	BUS?3	BUS?5	2.70	0.68	2.78
Line?9	BUS?4	BUS?5	2.09	0.55	2.16
						Line?10	BUS?4	BUS?5	2.09	0.55	2.16
Line?11	BUS?5	BUS?6	5.24	1.28	5.40
						Line?1	BUS?3	BUS?1	-5.52	-0.79	5.57
Line?2	BUS?3	BUS?1	-5.52	-0.79	5.57
						Line?3	BUS?4	BUS?2	-5.36	-1.32	5.51
Line?4	BUS?4	BUS?2	-5.36	-1.32	5.51
						Line?5	BUS?4	BUS?3	0.33	0.35	0.48
Line?6	BUS?4	BUS?3	0.33	0.35	0.48

Line?7	BUS?5	BUS?3	-2.67	-0.52	2.72
						Line?8	BUS?5	BUS?3	-2.67	-0.52	2.72
Line?9	BUS?5	BUS?4	-2.05	-0.42	2.10
						Line?10	BUS?5	BUS?4	-2.05	-0.42	2.10
Line?11	BUS?6	BUS?5	-5.24	-0.75	5.30

Power factor (PF) is the result of calculation under 0.90 condition:

The peak load deliverability value MNSPL of A district electric power networks is 1897.84MW, and the peak load deliverability of system is subject to the lower limit of the busbar voltage of the conveying capacity of transformer branch road BUS5-BUS6 and Node B US6.Following form and curve have provided the iterative process of finding the solution of the result of calculation of result of calculation, AC power flow of result of calculation, the node voltage of network peak load deliverability and electric load.Then, the result of calculation of peak load deliverability is as shown in table 7, and node voltage result of calculation is as shown in table 8, and the result of calculation of AC power flow is as shown in table 9, electric load find the solution iterative process such as Fig. 5, shown in Figure 6.

The result of calculation of table 7 peak load deliverability

Sequence number	Node ID	Burden with power (MW)
			Load1	BUS?3	552.77
Load2	BUS?4	515.92
			Sequence number	Node ID	Burden with power (MW)
Load3	BUS?5	368.51
			Load4	BUS?6	460.64
Add up to	--	1897.84

The result of calculation of table 8 node voltage

Node ID	Voltage magnitude (pu)	Angle (rad)
			BUS1	1.01	0
BUS2	1.01	-1.97
			BUS?3	0.9481	-5.55
BUS?4	0.9584	-5.41

BUS?5	0.9112	-8.21
			BUS?6	0.9091	-13.8

Table 9 AC power flow result calculated

The circuit sequence number	Headend node	Endpoint node	Meritorious (pu)	Idle (pu)	Apparent power (pu)
						Line1	BUS?1	BUS?3	4.94	2.79	5.67
Line?2	BUS?1	BUS?3	4.94	2.79	5.67
						Line?3	BUS?2	BUS?4	4.74	3.50	5.90
Line?4	BUS?2	BUS?4	4.74	3.50	5.90
						Line?5	BUS?3	BUS?4	-0.26	-0.59	0.64
Line?6	BUS?3	BUS?4	-0.26	-0.59	0.64
						Line?7	BUS?3	BUS?5	2.36	1.41	2.75
Line?8	BUS?3	BUS?5	2.36	1.41	2.75
						Line?9	BUS?4	BUS?5	1.86	1.20	2.21
Line?10	BUS?4	BUS?5	1.86	1.20	2.21
						Line?11	BUS?5	BUS?6	4.61	2.82	5.40
Line1	BUS?3	BUS?1	-4.87	-2.16	5.32
						Line?2	BUS?3	BUS?1	-4.87	-2.16	5.32
Line?3	BUS?4	BUS?2	-4.69	-3.04	5.59
						Line?4	BUS?4	BUS?2	-4.69	-3.04	5.59
Line?5	BUS?4	BUS?3	0.26	0.59	0.65
						Line?6	BUS?4	BUS?3	0.26	0.59	0.65
Line?7	BUS?5	BUS?3	-2.33	-1.25	2.64
						Line?8	BUS?5	BUS?3	-2.33	-1.25	2.64

Line?9	BUS?5	BUS?4	-1.82	-1.06	2.10
						Line?10	BUS?5	BUS?4	-1.82	-1.06	2.10
The circuit sequence number	Headend node	Endpoint node	Meritorious (pu)	Idle (pu)	Apparent power (pu)
						Line?11	BUS?6	BUS?5	-4.61	-2.23	5.12

Sample calculation analysis:

From the result of calculation of above embodiment as can be seen:

1. the power supply abundant intensity value UNPSAI of A district electrical network is 1.4.Because the power supply capacity abundant intensity is greater than 1, so the urban distribution network in A district can satisfy the demand that has the electrical network power load now, and possesses certain adaptive capacity.

2. the peak load power supply capacity of A district electrical network mainly is subjected to the restriction of the busbar voltage of the conveying capacity of transformer branch road BUS5-BUS6 and BUS6, decline along with power factor of electric network, system's power supply capacity descends to some extent, and in the embodiments of the invention, the decline amount is about 10%.Therefore, can predict, reduce the idle transmission of branch road, improve the system power factor, will improve the conveying capacity of power distribution network active power by optimizing reactive power compensation.

3. the network configuration in A district is very unreasonable, as: the trend of the double-circuit line of BUS3-BUS4 is lighter in the network.

4. the iterative process of asking for load point and target function in the process of making a general survey of the power distribution network power supply capacity as seen, the algorithm that trusted zones method and AC power flow combine combines the advantage of algorithm separately, the iteration step length of load point can in time be adjusted according to AC power flow result calculated and subspace function matching degree, and the convergence that algorithm is good has obtained representing fully; The AC power flow algorithm has reflected the influence to the network power supply ability of system voltage level, branch road transmittability and reactive power flow accurately simultaneously.

Claims (1)

1. urban distribution network power supply abundant intensity appraisal procedure, it may further comprise the steps:

1) sets up a urban distribution network power supply abundant intensity evaluating system, this urban distribution network power supply abundant intensity evaluating system comprises the Equivalent Model fitting module, the trusted zones subproblem is found the solution module, and the true drop-out value of target function is found the solution module, target function step-size in search and direction of search adjusting module;

2) set up the network configuration of urban distribution network, the thermally-stabilised transmission capacity constraint and the busbar voltage constraint of clear and definite power supply capacity bound constraint, the thermally-stabilised capacity-constrained of circuit, transformer; Simultaneously given calculating initial value is prepared, and comprises the current search point x of current time k _k, load point electric load initial value, target function initial ranging step-length d ₀, the Hessen matrix norm permissible error ξ and trusted zones border initial value h ₀, trusted zones border initial value h wherein ₀Get Hessen matrix initial value g ₀Norm;

3) use the Equivalent Model fitting module, at current search point x _kTrusted zones h _kIn, ask for target function by numerical perturbation method and least-square fitting approach

At current search point x=x _kEquivalent second-order model and parameter, P wherein _LiBe the active power of i load bus, n is the load point sum; Wherein target function is put x at current search _kThe equivalent second-order model expression formula launched of Taylor be:

$q^{\left(k\right)}\left(s\right)=f\left(x_k\right)+g_k^{T}s+{0.5s}^T{G}_{k}s---\left(1\right)$

In the formula (1), f (x _k) put x for target function at current search _kNumerical value, g _kBe the broad sense first derivative matrix of target function f (x), G _kBe the Hessen matrix of target function f (x), s is the Taylor operator;

4) the HESSEN matrix G of the equivalent second-order model of calculating _kNorm value, and with step 2) in given permissible error ξ compare, as HESSEN matrix G _kNorm value during less than permissible error ξ, turn to step 9); As HESSEN matrix G _kNorm value during more than or equal to permissible error ξ, then continue the search that step 5) is carried out the target function extreme value;

5) find the solution module by the trusted zones subproblem, the extreme value of the equivalent second-order model of calculating formula (1):

$\min q\left(d_k\right)=f\left(x_k\right)+g_k^T{d}_k+0.5{d_k}^T{G}_k{d}_k$ (2)

s.t.‖d _k‖＜h _k

In the formula (2), d _kBe current search step-length, h _kFor current trusted zones border, try to achieve minq (d _k) after, advance

And calculating target function estimate drop-out value; Estimate drop-out value and be target function current search point x _kCurrent goal functional value f (x _k) with the minimizing difference of equivalent second-order model, estimate the drop-out value expression formula and be:

Pred _k＝f(x _k)-minq(d _k) (3)；

6) find the solution module by the true drop-out value of target function, according to the current search step-length d of equivalent second-order model _k, by AC power flow technique computes target function f (x _k) and f (x _k+ d _k), and obtain the actual drop-out value of target function, actual drop-out value expression formula is:

Ared _k＝f(x _k)-f(x _k+d _k) (4)；

7) carry out direction of search adjusting module, by calculating actual drop-out value Ared _kWith estimate drop-out value Pred _kRatio r _k, adjust the step-size in search d in search procedure next time of target function _kAnd the direction of search; The process of the concrete adjustment step-size in search and the direction of search is as follows:

Work as r _k＞0, upgrade the current search point, make new search point x _K+1=x _k+ d _kOtherwise again with current search point x _kBe start point search, get new search point x _K+1=x _k

Work as r _k, dwindle trusted zones border h at＜0.25 o'clock _K+1, make trusted zones border h _K+1=‖ h _k‖/4;

Work as r _k〉=0.75 o'clock, if step-size in search reaches the trusted zones border, ‖ d _k‖=h _kThe time, then suitably amplify the trusted zones border, make h _K+1=2h _kOtherwise, in original trusted zones, search for, make h _K+1=h _k

8) upgrade the new search point x that obtains _K+1With trusted zones border h _K+1After, return step 3), ask for the equivalent second-order model of current search point by using the Equivalent Model fitting module, and continue to repeat above-mentioned steps 5) to the iterative process of step 7), iterative process is until HESSEN matrix G _kNorm value less than permissible error ξ till;

9) as the HESSEN of equivalent second-order model matrix G _kNorm during less than permissible error ξ, find the solution the MNSPL value of module calculating target function by the true drop-out value of target function, then according to equation

Ask for mains supply ability abundant intensity value UNPSAI, wherein MNSPL represents electrical network peak load deliverability, and MPL represents the peak load level of present situation electrical network;

10) according to the adaptability of the mains supply ability abundant intensity value UNPSAI assessment urban distribution network of asking for, simultaneously by contrasting the reasonability of power supply capacity abundant intensity difference assessment electric network composition under the heterogeneous networks structural condition to the electric load fluctuation.

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