CN108493985A - Identification method for out-of-limit weak link of voltage of power distribution network containing distributed power supply - Google Patents

Abstract

The invention discloses a method for identifying a distribution network voltage out-of-limit weak link containing a distributed power supply, which comprises the steps of obtaining a reference voltage and a topological structure of a distribution network, a feeder line parameter and a head end voltage, a load access position and capacity, a reactive compensation device access position and capacity, and a DG access position and capacity, calculating the DG maximum access capacity of each node, identifying the voltage out-of-limit according to the difference between DG output active power of each node and the DG maximum access capacity of the node if DG is intensively grid-connected, converting into the active power of a DG at the tail end if DG is dispersedly grid-connected, and comparing with the DG maximum access capacity of the tail node to identify the voltage out-of-limit. The method can guide a power worker to quickly and accurately judge the out-of-limit reasons of the voltage, identify the weak links of the voltage and adopt a corresponding voltage regulation method, is favorable for realizing safe grid connection and voltage regulation of the distributed power supply, and has popularization prospect and practical significance.

Description

Identification method of voltage out-of-limit weak link in distribution network with distributed generation

technical field

The invention relates to a method for identifying a weak link in which the voltage of a distribution network with a distributed power source exceeds the limit, and belongs to the technical field of distribution network voltage protection.

Background technique

Voltage is an important indicator to measure the normal operation of the power grid. If the voltage exceeds the limit, some user equipment will not operate normally, and even endanger the safety of the system. As the end link of power distribution, the distribution network is closely related to users, and the large-scale fluctuation of user demand will directly cause the voltage limit of the distribution network feeder. With the rapid development of the global economy, energy shortages and environmental pollution are driving the transformation of the world's energy systems to clean, intelligent and low-carbon. More and more distributed generation (DG) mainly in the form of wind power, photovoltaic, and small hydropower is incorporated into the distribution network, which will also have a great impact on the voltage of the distribution network. For the transmission system with a small impedance ratio, in addition to using the on-load tap changer to adjust the voltage, the output adjustment of the reactive power supply can also effectively improve the voltage quality, and its voltage control equipment is more concentrated. However, the distribution network has dense users, diverse equipment, and complex system parameters. In many cases, the reactive power compensation of the capacitor bank does not significantly improve the voltage. Reasonable planning and control of the output power of distributed power in the distribution network can also alleviate the low voltage problem when the feeder is long and the load is heavy, but the intermittent output power of distributed power also restricts its ability to solve voltage problems. There are many factors that cause the distribution network voltage to exceed the limit, some of which are fluctuating, random and uncontrollable. The access of intermittent distributed power sources and the demand for time-varying random loads may amplify the randomness and variation of the power flow of the distribution network, making the distribution network more prone to light-load and heavy-load operating conditions. The feeder voltage tends to exceed the lower limit when the load is heavy, and usually the lower limit limit will appear at the end of the feeder; the feeder voltage will easily exceed the upper limit when the feeder is lightly loaded, and the voltage will easily exceed the upper limit limit at the first section of the feeder or the DG access point. Therefore, overvoltage is also One of the main reasons for limiting the access capacity of distributed power. At present, there is a lack of methods and tools to directly identify the weak links and causes of voltage violations in the distribution network, and it is impossible to provide effective distribution network planning and control references for avoiding voltage violations.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the defects of the prior art, provide a method for identifying the weak links of distribution network with distributed power supply, and calculate the maximum load access capacity, maximum DG Access capacity, by comparing the actual feeder access conditions to identify the weak links of voltage over-limit, so as to provide effective guidance for voltage over-limit governance.

In order to solve the above-mentioned technical problems, the present invention provides a method for identifying weak links in distribution network voltages with distributed power sources, which includes the following steps:

1) Obtain the reference voltage and topological structure of the distribution network, feeder parameters and head-end voltage U ₀ , load connection location and capacity, reactive power compensation device connection location and capacity, DG connection location and capacity, among which, feeder parameters Including active power P _1,i and reactive power Q _{1,i transmitted on feeder 1,i} , resistance R _{1,i of feeder 1,i} , reactance X 1,i of feeder _1,i ; where, 1,i are the first and last nodes of the feeder, i=1,2,...,n;

2) Calculate the maximum DG access capacity of each node;

3) If the DGs are centralized and connected to the grid, then go to step 4), if the DGs are scattered and connected to the grid, then go to step 5);

4) Compare the DG output active power of each node with the maximum DG admission capacity of the node. When P _DG,k >P _DG,kmax , the voltage at the grid-connected DG exceeds the upper limit; when P _DG,k <P When _DG,kmax is connected to the front end of the feeder when the output of DG is insufficient, the terminal voltage exceeds the lower limit, and the identification ends. Among them, P _DG,k is the DG output active power of node k, and P _DG,kmax is the maximum DG access of node k capacity; for node k on the feeder, k=1,2,...,n, definition: the node k∈(1,n/3) is the front end of the feeder, and the node k∈(n/3,2n/3) is The node at the middle end of the feeder and k∈(2n/3,n) is the end of the feeder;

5) convert the active power of all DGs that are distributed into the active power P'DG _,nall of the DG at the end of the feeder;

6) Comparing P' _DG,nall with the maximum DG admission capacity P _DG,nmax of the terminal node n, when P' _DG,nall ≤ P _DG,nmax , the total DG output power of the feeder will not cause the node voltage to exceed the upper limit, However, if the net load active power of all nodes is positive, the terminal voltage is easy to exceed the lower limit. If the net load active power of all nodes is negative or zero, the voltage of each node of the line is normal, otherwise the node voltage is easy to exceed the lower limit; when P' _DG,nall When ＞PDG _,nmax , the voltage of DG grid-connected nodes is easy to exceed the upper limit.

In the aforementioned step 2), the calculation method of the maximum access capacity of each node DG connected to the grid is:

First, calculate the active power output by DG on each node:

Among them, P _DG,k is the active power output by DG on node k, Q _DG,k is the reactive power output by DG on node k, P _L,j is the active power of connected load on node j, Q _L,j is the reactive power of the connected load on node j, λ _G is the power factor of DG, satisfying γ _G is the ratio of the vertical component of voltage drop caused by network loss caused by DG only to the vertical component of voltage drop caused by load, and γL is the ratio of the vertical component of voltage drop caused by network loss caused by load only to the voltage caused by load The ratio of the longitudinal component of drop, U _N is the rated voltage, PL _,i and Q _L,i are, ΔU _0,k ∈ (-0.07,0.07), n is the number of nodes on the feeder;

Then, take ΔU _0,k =-0.07 and put it into formula (14) to obtain the maximum DG admission capacity P _DG,kmax of node k.

In the aforementioned step 4), when P _DG,k >P _DG,kmax , when DG is connected to the front end of the feeder, if the end load is too heavy or the line is too long, it is easy to cause the voltage at the end of the line to exceed the lower limit; when DG is connected to the feeder At the terminal, if the load in the front and middle of the line is too heavy, the terminal voltage will be higher than the upper limit and the middle terminal voltage will be lower than the lower limit.

In the aforementioned step 4), when P _DG,k < P _DG,kmax , when DG is connected to the front end of the feeder, if the line is too long and the load at the end is too heavy, it is easy to cause the voltage at the end of the line to exceed the lower limit. When DG is connected to the feeder At the middle end, if the end load is too heavy, the voltage at the end of the line will easily exceed the lower limit. When DG is connected to the end of the feeder line, the voltage at the node before the DG access point will easily exceed the lower limit.

In the aforementioned step 5), the calculation method of the converted active power P' _{DG, nall} is:

Wherein, η _i is a conversion coefficient, η _i =P _DG,nmax /PDG _,imax , P _DG,i is the active power output by DG on node i, i=1,2,...,n.

As mentioned above, within the allowable range of the reactive power compensation device and DG output, if the voltage of all nodes still cannot be qualified, the reason for the voltage exceeding the limit is that the newly added load is too heavy. The difference between the load capacity and the maximum admitted load capacity identifies the load nodes that are prone to voltage violations;

The additional load capacity allowed by each node is:

Among them, P _L,k is the newly added load capacity of node k, λ _L,k is the newly added load power factor, which satisfies: Q _L,k is the new load reactive power of node k;

The maximum admission load capacity of node k is: take ΔU _0,k as 0.07-(U _k -min(U _i )), put it into formula (17) to calculate the maximum admission load capacity PL of node k _{, kmax} , where U _i is the voltage value of node i, k≤i≤n.

The beneficial effect that the present invention reaches:

The present invention aims at the characteristics of many influencing factors of the distribution network voltage, according to the obtained reference voltage and topology structure of the distribution network, feeder parameters and head-end voltage, load access position and capacity, reactive power compensation device access position and capacity, The access location and capacity of distributed power supply provide a method for identifying voltage exceeding the limit, which can guide electric power workers to quickly and accurately judge the cause of voltage exceeding the limit, identify weak links of voltage and adopt corresponding voltage regulation methods, which is conducive to realizing distributed power supply. Safe grid connection and voltage regulation of power supply have promotional prospects and practical significance.

Description of drawings

Fig. 1 is the voltage drop mechanism analysis circuit diagram of the present invention;

Fig. 2 is a multi-node voltage drop circuit diagram of the present invention;

Fig. 3 is a flowchart of the method of the present invention.

Detailed ways

The present invention will be further described below. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.

The identification method of the weak link of the distribution network containing the distributed power supply voltage of the present invention, the specific process is shown in Figure 3, including the following steps:

1) Obtain the reference voltage and topological structure of the distribution network, feeder parameters and head-end voltage, load access location and capacity, reactive power compensation device access location and capacity, distributed generation (DG) access location and capacity.

2) According to the topological structure of the distribution network, analyze the mechanism of voltage drop in the distribution network and the reasons that affect the voltage limit.

Referring to Figure 1, the expression of the terminal voltage on the feeder simply caused by the load is as follows:

Among them, U ₀ is the voltage at the head end of the feeder, U ₁ is the voltage at the low-voltage side of the transformer, U _i is the voltage value of node i; K is the transformation ratio of the on-load tap changer transformer; P _1,i , Q _1,i are the feeder 1 ,i (1,i are the first and last nodes of the feeder respectively, i=1,2,…,n) the active and reactive power transmitted on; R _1,i is the resistance of feeder 1,i, X _1,i is the reactance of feeder 1,i.

It can be seen from formula (1) that the voltage at the head end of the feeder, impedance and transmission power will cause the voltage to exceed the limit, and the specific voltage regulation methods that may be used are as follows:

2a) Generator voltage regulation: For small power grids that directly supply power without boosting, when the power supply radius is not long and the network loss is not large, the voltage quality can be improved by changing the generator terminal voltage; and for power supply systems with multi-level voltage control , the use of generator voltage regulation has little effect on improving the voltage at the end of the feeder. In the case of insufficient reactive power in the system, it is easy to cause reactive power redistribution on the feeder, and conflicts with the economical distribution of reactive power.

2b) Voltage regulation by controlling the number of switched capacitor banks: When the reactive power required by the load is heavy and the reactive power of the feeder is short, reactive power can be compensated by switching capacitor banks, as shown in Figure 1 Q _C,i , reactive power compensation The methods include centralized compensation in the substation, distributed reactive power compensation of the line and local reactive power compensation of the electrical equipment.

The expression of reactive power compensation to improve terminal voltage is:

In the formula, Q _C,i is the reactive power of switching capacitor bank on node i.

2c) Reducing the impedance of the feeder can reduce the power loss on the transmission path and thus increase the voltage at the end of the feeder. To transform the distribution network feeder, shorten the power supply radius, and increase the cross-sectional area of the wire, but this method has a large investment cost and is not easy to implement.

2d) The reactance on the feeder line of the transmission network is much larger than the resistance, and the reactive power compensation device is more sensitive to improving the voltage at the end of the feeder line. However, when the resistance of the feeder line of the distribution network is greater than the reactance, the active power transmitted on the feeder line is less sensitive to the voltage drop. Large, see Figure 1, the expression of DG compensation for voltage improvement terminal voltage is:

In the formula, P _DG,i is the active power output by DG on node i, and Q _DG,i is the reactive power output by DG on node i.

3) Referring to Figure 2, considering the influence of network loss on the longitudinal component of voltage drop, the power flow of the feeder is calculated by the forward push-back method:

From formula (4)-(7) can get:

In formulas (4)-(7), ΔP _k-1,k is the active power loss of feeder k-1,k, ΔQ _k-1,k is the reactive power loss of feeder k-1,k; P” _k is the node The active power flowing in from k, Q” _k is the reactive power flowing in from node k; P’ _k is the active power flowing out from node k, Q’ _k is the reactive power flowing out from node k; P _L,i is the connected The active power entering the load, Q _L,i is the reactive power connected to the load on node i; R _k-1,k is the resistance of the feeder k-1,k, X _k-1,k is the feeder k-1, The reactance of k; U _k is the current voltage value of node k, ΔU _0,k is the longitudinal component of the voltage drop of feeder 0,k, feeder node k=1,2,...,n. In Figure 2, is the apparent power flowing into node k. is the apparent power flowing out of node k.

Considering that the voltage drop of the power distribution system in normal operation is generally not large, the voltage of each node of the feeder is represented by the rated voltage U _N , and the longitudinal component of the voltage drop caused by the network loss on the feeder 0,k is recorded as The vertical component of the voltage drop caused by the load is recorded as ΔU _L,0,k , then the vertical component of the voltage drop of the feeder 0,k can be expressed as:

in,

Considering that in formula (10), the values of ΔP _m,m+1 , ΔQ _m,m+1 are small relative to ΔP _L,m , ΔQ _L,m and can be ignored in the calculation, then formula (10) can be further Simplifies to:

The ratio of the vertical component of voltage drop caused by network loss to the vertical component of voltage drop caused by load is defined as the voltage drop ratio coefficient:

According to the data analysis of the actual system, under normal circumstances, γ is about 0.02-0.06.

4) According to the allowable voltage limit of each node, when the load of each node is constant, the longitudinal component of the voltage drop of the feeder 0,k including DG connected to the distribution network is:

Among them, P _DG,j is the DG output active power on node j (j=1,2,…,n), γ _L is the vertical component of the voltage drop caused by the network loss caused by the load only to the voltage caused by the load The ratio of the longitudinal component of the drop; γG is the ratio of the vertical component of the voltage drop caused by the network loss caused by DG only to the vertical component of the voltage drop caused by the load.

4a) When only one node k is connected to DG, according to formula (13), the expression of DG output active power on node k is:

In the formula, P _DG,k is the active power output by DG on node k, Q _DG,k is the reactive power output by DG on node k; λ _G is the power factor of DG, then Typically ΔU _0,k ∈(-0.07,0.07) according to the operating specification.

4b) When multiple nodes are connected to the DG at the same time, referring to Figure 2, n nodes are all connected to the DG, and the DG power conversion coefficient _ηk is defined, which can be calculated by the following formula:

η _k = P _DG,nmax /P _{DG,k max} (15)

Among them, P _DG,nmax and P _DG,kmax are the maximum admission capacity allowed by DG on feeder end node n and any node k, respectively, within the allowable range of feeder voltage drop. The smaller the value of ηk, the smaller the sensitivity of the DG output power on node k to the voltage drop, and the greater the DG capacity that these nodes can access without causing the upper limit of the voltage constraint.

When ΔU _0,k =-0.07, calculate the maximum DG admission capacity P _DG,nmax of node n according to formula (14).

The DG active power injected by any node on the feeder is converted to the end node of the feeder through _ηk , and aggregated into an equivalent DG, so that the voltage problem caused by the decentralized access of the feeder DG is transformed into the voltage caused by the centralized access of the end node Problem, the DG active power converted and aggregated to the end node n of the feeder is:

And compare the actual total DG output capacity converted by formula (16) to judge whether the entire feeder may exceed the upper limit. When P' _DG,nall ≤ P _DG,nmax , the total DG output power of the feeder will not cause the node voltage The higher the upper limit; when P' _DG,nall >P _DG,nmax , the DG grid-connected point voltage is easy to exceed the upper limit.

5) Within the allowable range of the reactive power compensation device and DG output, if the voltage of all nodes still cannot be qualified, the reason for the voltage exceeding the limit may be that the load is remotely connected or the feeder is running under heavy load. Let the load be a PQ node model. Consider In the case of network loss, under the condition that the feeder already has a load, the additional load capacity allowed by each load node is:

In the formula, P _L,k is the active power of the newly added load at node k, and λ _L,k is the power factor of the newly added load, that is,

In order to ensure that the new load node voltage and the node voltage after the new load node do not exceed the limit, the maximum value of ΔU _0,k at this time is 0.07-(U _k -min(U _i )), where k≤i≤ n, the lowest node voltage just reaches the critical minimum value at this time, the calculated new load capacity is the maximum admission load capacity to ensure that the voltage does not exceed the limit, denoted as _PL,kmax , and then use the actual load capacity and the maximum The difference in admitted load capacity identifies load nodes that are prone to voltage overruns.

6) For specific implementation, see Fig. 3, step 4) can be used to calculate the maximum access capacity of DG grid-connected, and instruct electric power workers to judge whether the node voltage exceeds the upper limit according to whether the actual DG access capacity meets the maximum DG access capacity. When DG is centrally connected to the grid, when P _DG,k >P _DG,kmax , the voltage at the DG grid connection exceeds the upper limit, and according to the position where DG is connected to the feeder, there are also the following situations: When DG is connected to the front end of the feeder, if the end Heavy load or too long line will easily cause the voltage at the end of the line to exceed the lower limit. When DG is connected to the rear end of the feeder, if the load in the front and middle of the line is heavy, the voltage at the end will exceed the upper limit and the voltage at the middle end will exceed the lower limit; when P _DG,k <P _{DG, kmax} , when the DG is connected to the front end of the feeder when the output is insufficient, the terminal voltage will exceed the lower limit. The load is heavy, and it is easy to cause the voltage at the end of the line to exceed the lower limit. When the DG is connected to the middle end of the feeder, if the end load is heavy, the voltage at the end of the line is likely to exceed the lower limit. When the DG is connected to the end of the feeder, the node voltage before the DG access point May be lower limit. For node i on the feeder, i=1, 2,..., n are defined in the present invention: i∈(1,n/3) is the front end of the feeder, i∈(n/3,2n/3) is the middle end of the feeder, i∈(2n/3,n) is the feeder end.

When the DGs are connected to the power grid in a decentralized manner, the active power output of all DGs that are connected in a decentralized manner is converted into the active power P' _DG,nall of the DGs at the end of the feeder by Equation (16), and then compared with the maximum DG admission capacity P _{DG, nmax} compares and judges the voltage exceeding the limit, so as to identify weak DG grid-connected nodes, specifically: when P' _DG,nall ≤ P _DG,nmax , the total DG output power of the feeder will not cause the node voltage to exceed the upper limit, but if all nodes If the net load active power is positive, the terminal voltage may exceed the lower limit. If the net load active power of all nodes is negative or zero, the voltage of each node of the line is normal, otherwise the node voltage may exceed the lower limit. When P' _DG,nall >P _DG,nmax , the voltage of DG grid-connected nodes is easy to exceed the upper limit.

Finally, within the allowable range of the reactive power compensation device and DG output, calculate the maximum load capacity allowed by each node according to the above step 5), and compare the uniform distribution of the load, and the terminal voltage drop when the distribution is concentrated at the front, middle and rear ends Different, instruct electric power workers to identify weak load nodes that are prone to voltage lower limit based on the actual new node load.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made. It should also be regarded as the protection scope of the present invention.

Claims (6)

1. The identification method of the out-of-limit weak link of the voltage of the power distribution network containing the distributed power supply is characterized by comprising the following steps of:

1) obtaining reference voltage and topological structure of power distribution network, feeder line parameters and head end voltage U₀The load access position and capacity, the reactive compensation device access position and capacity and the DG access position and capacity, wherein the feeder line parameters comprise active power P transmitted on the feeder lines 1 and i_1,iAnd reactive power Q_1,iResistance R of the feed line 1, i_1,iReactance X of the feeder 1, i_1,i(ii) a Wherein 1, i are respectively a feedThe first and last nodes of the line, i ═ 1,2, …, n;

2) calculating the DG maximum admittance capacity of each node;

3) if the DGs are intensively grid-connected, the step 4) is carried out, and if the DGs are dispersedly grid-connected, the step 5) is carried out;

4) comparing the DG output active power of each node with the DG maximum admission capacity of the node, and when P is reached_DG,k＞P_DG,kmaxWhen the grid voltage of the DG is higher, the grid voltage of the DG is higher; when P is present_DG,k＜P_DG,kmaxWhen the DG output is insufficient, the lower limit of the terminal voltage is increased by connecting the front end of the feeder line under the condition that the DG output is insufficient, and the identification is finished, wherein P_DG,kActive power, P, is output for DG of node k_DG,kmaxMaximum admission capacity of DG for node k; for node k, k ═ 1,2, …, n on the feeder, define: the node of k belonging to (1, n/3) is the front end of the feeder line, the node of k belonging to (n/3,2n/3) is the middle end of the feeder line, and the node of k belonging to (2n/3, n) is the tail end of the feeder line;

5) the active power of all DGs which are dispersedly accessed is converted into the active power P 'of the DGs at the end of the feeder line'_DG,nall；

6) Prepared from P'_DG,nallDG maximum admission capacity P with the end node n_DG,nmaxComparison, when P'_DG,nall≤P_DG,nmaxIn the process, the total DG output power of the feeder line does not cause the node voltage to exceed the upper limit, but if all the node net loads are positive, the tail end voltage is easy to exceed the lower limit, if all the node net loads are negative or zero, the voltage of each node of the line is normal, otherwise, the node voltage is easy to exceed the lower limit; when P'_DG,nall＞P_DG,nmaxIn this case, the DG grid connection node voltage tends to be higher.

2. The method for identifying the out-of-limit weak link of the voltage of the power distribution network with the distributed power supply according to claim 1, wherein in the step 2), the method for calculating the maximum access capacity of the DG grid-connection of each node comprises the following steps:

firstly, calculating the active power output by DGs on each node:

wherein, P_DG,kActive power, Q, output for DG on node k_DG,kFor reactive power, P, output by DG on node k_L,jActive power, Q, for the access load on node j_L,jReactive power, λ, for a load connected to node j_GIs the power factor of DG, satisfiesγ_GGamma is the ratio of the longitudinal component of the voltage drop due to the grid loss caused by DG alone to the longitudinal component of the voltage drop caused by the load_LThe ratio of the longitudinal component of the voltage drop caused by the network loss caused by the load alone to the longitudinal component of the voltage drop caused by the load, U_NAt rated voltage, P_L,iAnd Q_L,iIs, Δ U_0,kThe epsilon is (-0.07,0.07), and n is the number of nodes on the feeder line;

then, take Δ U_0,kSubstituting equation (14) for-0.07, the maximum allowable DG capacity P for node k is obtained_DG,kmax。

3. The method for identifying the out-of-limit weak link of the voltage of the power distribution network with the distributed power supply according to claim 2, wherein in the step 4), when P is reached_DG,k＞P_DG,kmaxWhen the DG is connected to the front end of the feeder line, if the load at the tail end is too heavy or the line is too long, the lower limit of the voltage at the tail end of the line is easy to be caused; when the DG is connected to the rear end of the feeder, if the front middle part of the line is overloaded, the end voltage is caused to exceed the upper limit, and the middle end voltage is caused to exceed the lower limit.

4. The method for identifying the out-of-limit weak link of the voltage of the power distribution network with the distributed power supply according to claim 2, wherein in the step 4), when P is reached_DG,k＜P_DG,kmaxWhen DG is connected to the front end of the feeder line, if the line is too long and the load at the tail end is too heavy, the lower limit of the voltage at the tail end of the line is easily caused, and when DG is connected to the middle end of the feeder line, if the load at the tail end is too heavy, the lower limit of the voltage at the tail end of the line is easily caused, and when DG is connected to the middleWhen a DG is connected to the end of a feeder, the lower limit of the node voltage before the DG is connected to the point is easily caused.

5. The method for identifying the out-of-limit weak link of the voltage of the power distribution network with the distributed power supplies according to claim 2, wherein in the step 5), the converted active power P'_DG,nallThe calculation method comprises the following steps:

wherein, η_iTo reduce the coefficient, η_i＝P_DG,nmax/P_DG,imax，P_DG,iThe active power output by DG at node i, i ═ 1,2, …, n.

6. The method for identifying the voltage out-of-limit weak link of the power distribution network with the distributed power supply as claimed in claim 2, wherein in the output allowable range of the reactive power compensation device and the DG, if the voltages of all nodes cannot be qualified, the voltage out-of-limit reason is that newly increased loads are too heavy, the calculation of each node allows additional load increase, and then the difference between the newly increased load capacity of each node and the maximum allowable load capacity of each node is used for identifying the load node which is easy to have voltage out-of-limit;

the allowed additional load capacity of each node is:

wherein, P_L,kNew load capacity, λ, for node k_L,kFor newly increasing the load power factor, the following requirements are met:Q_L,knewly adding load reactive power for the node k;

the maximum admissible load capacity for node k is: taking Delta U_0,kIs 0.07- (U)_k-min(U_i) Bring it intoThe maximum admissible load capacity P of the node k is obtained by calculation of the formula (17)_L,kmaxWherein, U_iThe voltage value of the node i is represented by k which is not less than i and not more than n.