CN115276091A - Distributed power supply voltage control method based on all-pure-function embedded voltage sensitivity - Google Patents
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Abstract
The invention discloses a distributed power supply voltage control method based on holomorphic embedded voltage sensitivity. According to the method, firstly, the power flow of the power distribution network is calculated by using the HELM, and then the sensitivity of voltage to the injection power of each node is calculated according to a sensitivity calculation method based on the HELM. And then using the sensitivity of the voltage to each step of the injected power of each node as a voltage stability criterion to be added into the constraint condition of the voltage model of the power distribution network. Finally, solving and determining the control quantity P of the distributed power supply according to the objective function and the constraint condition by utilizing a genetic algorithm DGi . According to the invention, the HELM method is utilized to consider the nonlinear factors of the sensitivity, calculate the nonlinear sensitivity of each order, consider the HELM voltage stability index constraint in the power distribution network voltage control model, and have better voltage control effect.
Description
Technical Field
The invention belongs to the technical field of electric power information, and particularly relates to a distributed power supply voltage control method based on holomorphic embedded voltage sensitivity.
Background
With the development of related technologies such as power electronics and control technologies, it is possible to access a large number of Distributed Generation (DG) into a power distribution network. Meanwhile, a series of problems are brought to the power distribution system: the access of DG changes the distribution system from a radiation structure to an active structure and causes the change of the internal tide, thereby influencing the voltage and changing the voltage, and generating great influence on various aspects of the distribution network; and the access position and capacity of the DG have certain influence on the network loss of the power distribution network system, the voltage level and stability of the power distribution network, the power quality, the relay protection and the like.
Considering the influence of the DGs on the voltage level of the power distribution network, a voltage sensitivity index is usually introduced to select, sequence and control the DGs, but the conventional sensitivity calculation method based on the Jacobian matrix has the problem that the sick load flow cannot be calculated. Considering the influence of DG on the voltage stability of the power distribution network, a voltage stability margin needs to be introduced into an objective function, the conventional static voltage stability analysis and judgment method of the power distribution network is to calculate the maximum load causing voltage instability according to a continuous power flow method, compare the current power flow with the maximum load, and consider the voltage stability if the current power flow is smaller than the maximum load. This analysis method has the following problems: 1) The calculation amount of continuous calculation is large, the calculation time is long, and the real-time requirements of online voltage stability judgment and control are not met; 2) As the DG or FACT access and the node load are not increased proportionally, the maximum load is changed, and the maximum load calculated by using the continuous power flow method is not accurate. A load flow calculation method based on the embedding of Holomorphic embedding method pure functions is proposed in the last two years, the load flow method completely subverts the traditional cow pulling method, and whether a load flow solution exists or not can be determined without depending on node initial values.
In the prior art, other indexes are provided for judging whether the voltage of the power distribution network is stable, such as a line breakdown index, a line voltage stability L index and the like, but the indexes are derived based on a two-machine system, a complex power distribution network load model accessed into DG or FACT equipment and the like cannot be considered, or line resistance or grounding capacitance and the like are ignored, and the evaluation is not accurate enough.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a distributed power supply voltage control method based on the all-pure function embedded voltage sensitivity, which is suitable for the voltage control problem containing DG, can solve the load flow and voltage sensitivity under the pathological condition, and has simple and quick calculation.
The distributed power supply voltage control method based on the all-pure-function embedded voltage sensitivity specifically comprises the following steps:
step one, establishing a voltage control optimization model of a power distribution network containing distributed power supplies
s1.1, DG accessing the distribution network may reduce the flow of power flow in the adjacent branches of the node, network loss is reduced. However, if the capacity of the access DG is too large, the reverse power flow of the power distribution network can occur, and the network loss can also be increased. The following objective function is established by considering the network loss after the DG is accessed:
wherein, P loss Is the active loss of the distribution network; n is the total number of nodes of the power distribution network; i and j are respectively the node numbers at the two ends of the impedance branch k; u shape j Is the voltage amplitude of node j; r ij Is the resistance between nodes i, j; p j Active power, Q, of node j at the end of the impedance branch j Is its reactive power.
s1.2, establishing constraint conditions including a power flow equation constraint, a node voltage constraint, a branch current constraint, a DG capacity constraint and a system voltage stabilization constraint:
(1) Flow equation constraints
Wherein, P i 、Q i Respectively the active injection power and the reactive injection power of the node i; u shape i Is the voltage amplitude of node i; theta ij Is the voltage phase angle; g ij 、B ij Branch conductance and susceptance, respectively.
(2) Node voltage constraint
U i,min ≤U i ≤U i,max (3)
Wherein, U i,min 、U i,max Respectively, the lower limit and the upper limit of the voltage amplitude of the node i.
(3) DG capacity constraints
Wherein, P DGi Representing DG active power accessed by the node i; p DGimax The maximum DG active power allowed to be accessed for the node i; Ω represents a DG installation node set; mu is permeability; p Ltotal Is the total active load of the system.
(4) System voltage stability constraint
An improper DG configuration may affect the stability of the voltage level of the distribution network, and even the stability of the distribution network. The difference obtained by subtracting the higher-order sensitivity from the lower-order sensitivity is used as an evaluation index of the real-time voltage stability:
wherein, VSI i 、c i [4]、c i [3]The index indicates the voltage stability of the i-node, the coefficient of the power of s of the voltage of the i-node, and the coefficient of the power of 3 of the voltage of the i-node. When in use
The system voltage is stable; when the temperature is higher than the set temperature
The system is unstable.
s1.3, substituting the constraint condition established by s1.2 into the objective function stated in s1.1 to obtain an objective optimization function as follows:
wherein k is d Denotes regional electricity prices,. Tau.denotes the maximum load utilization hours, U ilim 、U imin 、U imax Respectively represent the extreme value, the minimum value, the maximum value and lambda of the voltage of the i node V Representing a voltage out-of-limit penalty factor, λ s And representing a voltage stability out-of-limit penalty factor:
k is a normal number with a large value, and is usually more than 100.
Step two, calculating the power flow of the power distribution network comprising the distributed power supply by using an HELM method
Supposing that no grounding branch exists in the power distribution network, the root node is a balance node, the distributed power supply is a PQ node, and a node power equation is as follows:
wherein, Y ik Representing the mutual admittance, V, between the i-node and the j-node in the nodal admittance matrix k Represents the injection voltage at node k, k = 1-N;
indicating that the inode injects the conjugate of the apparent power,
represents the conjugate of the i-node injection voltage and m represents the number of PQ nodes in the network.
Embedded pure virtual function V for constructing node by using full pure function method i (s)：
Wherein, c i [n]The nth voltage subentry of the voltage of the i node in the HELM power flow calculation is represented, s is a frequency domain operator, and s is n An n-th term representing a frequency domain operator s;
for PQ nodes there are:
wherein the content of the first and second substances,
Y ii self-admittance of an i-node in a node admittance matrix; y is ik The mutual admittance between the i and k nodes in the node admittance matrix is obtained; y is i,shunt For the ground admittance of the i-node, Y when there is no ground branch i,shunt ＝0，Y ik,tran ＝Y ik 。
Suppose that:
wherein d is i [n]The nth voltage component representing the reciprocal of the voltage at the i-node.
Comprises the following steps:
from the equality of the coefficients of the s series, one can obtain:
d i [k]the kth voltage component representing the reciprocal of the i-node voltage, c i [n-k]N-k voltage components representing the i-node voltage. When the node is a PQ node, the formula (10) is taken into the formula (11) to obtain:
substituting formula (12) for formula (15) to obtain:
and then obtaining the following result according to the equality of coefficients of s series:
when s =0 there is:
thus:
d k [0]＝1/c k [0] (19)
when the order of s is 1:
is calculated to obtain c k [1]. The coefficients according to the s series are equal, so that:
according to equation (14) there is:
thereby, it is possible to obtain:
when s =1, a solution of the trend can be obtained. On the basis, the active loss P of the power distribution network in the objective function is calculated loss 。
Step three, calculating the sensitivity of voltage to node injection power by using a HELM method
To solve the sensitivity of voltage to the injection of active and reactive power into a node, the following requirements are required:
wherein P is j Representing active power, Q, injected at node j j Representing the reactive power injected at node j.
As can be seen from the calculation of equation (18), c i [0]Independent of the injected power at node i, and therefore,
are all 0. On both sides of equation (20) to P j 、Q j Calculating the partial derivative, obtaining:
when j = i:
when j ≠ i:
simultaneous equations (25) and (26) can be solved
From the solving process, it can be seen that
And
independent of the system power flow distribution, only the network structure and the electrical distance, and therefore it is called the voltage structure sensitivity.
As can be seen from equation (14):
thereby deducing:
similarly, P is paired on both sides of equation (21) j 、Q j Calculating the partial derivative, obtaining:
when j = i:
when j ≠ i:
can find out
This can be derived from equation (22):
the loop calculation formulas (27) to (31) are calculated, and all the formulas are obtained by solving
Then, the total nonlinear sensitivity of the voltage to the injected power is calculated in equation (24).
The analysis finds that the raw materials are mixed with the raw materials,
proportional to the load first power, since the first term on the right of equation (39) is constant and the second term is proportional to the load when n = 2;
proportional to the load squared, and so on. In general,
and
and becomes smaller as the value of n increases. Total voltage sensitivity
And
can be obtained from the formula (24).
Obtaining voltage sensitivity of each order by using HELM calculation, and then subtracting high-order sensitivity from low-order sensitivity, wherein the low-order sensitivity is larger than the high-order sensitivity under the normal condition, namely the difference value is positive; when the load is increased, if the difference value is negative, the voltage instability is judged; in the actual voltage stabilization prevention control, a difference threshold may be set, and if the calculated difference exceeds the threshold, the voltage is considered to be about to be destabilized, and the voltage prevention control is started.
Step four, solving the solution according to the objective function and the constraint condition by using the genetic algorithmDetermining a control quantity P of a distributed power supply DGi 。
The invention has the following beneficial effects:
the distribution network voltage based on the HELM voltage sensitivity stability criterion can be used for online voltage control of the distribution network, the problem that the distribution network voltage stability criterion is not easy to calculate is solved, the calculation speed is high, the calculation is simple, and the method has high theoretical significance and application value. When voltage control is carried out on the power distribution network containing the distributed power supply, the nonlinear factor of sensitivity is considered, the influence of the distributed power supply on the voltage stability of the power distribution network is also considered in the objective function, and the voltage control effect is better.
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FIG. 1 is a flow chart of a distributed power supply voltage control method based on an all-pure-function embedded voltage sensitivity;
FIG. 2 is a schematic diagram of a 33-node grid used in an embodiment;
FIG. 3 is a schematic diagram showing a comparison between the results of the HELM power flow calculation and the results of the forward-backward substitution;
FIG. 4 is a comparison difference chart of the results of the HELM power flow calculation and the result of the forward-backward substitution;
FIG. 5 is a graph of voltage versus reactive power sensitivity calculated using a HELM under a base tidal stream;
FIG. 6 is a graph of the difference between the voltage reactive sensitivity results calculated by the HELM and the voltage reactive sensitivity results calculated by the perturbation method;
FIG. 7 is a λ V curve for node 30 in a 33-node system;
FIG. 8 is a plot of reactive power sensitivity for each portion of 30 node voltage;
FIG. 9 is a graph of the active and reactive load of the system;
fig. 10 is DG active output;
fig. 11 shows the system active network loss results before and after DG control;
fig. 12 shows the system voltage stability index results before and after DG control.
Detailed Description
The invention is further explained below with reference to the drawings;
as shown in fig. 1, the method for determining the voltage stability of the power distribution network based on the voltage sensitivity of the HELM comprises the following steps:
step one, establishing a mathematical model of the power distribution network according to data of the 33-node power grid shown in fig. 2.
And step two, performing load flow calculation by using the HELM, wherein the result is shown in figure 3, and the difference value is shown in figure 4. As can be seen from fig. 3 and 4, the results of the load flow calculation based on the HELM are substantially consistent with the results of the forward-backward substitution calculation, which proves that the load flow calculation method using the HELM is feasible.
And step three, calculating the voltage sensitivity by using the HELM, wherein the result is shown in figure 5. Fig. 6 is a graph of the difference between the voltage reactive sensitivity results calculated by HELM and the voltage reactive sensitivity results calculated by perturbation. From fig. 5 and 6, it can be seen that the voltage reactive sensitivity results calculated by the HELM are substantially consistent with the voltage reactive sensitivity results calculated by the perturbation method, which proves that voltage sensitivity is feasible by using the HELM.
The graph of λ V for a 33 node system plotted using Matpower, with λ on the abscissa being the load increase factor. As is clear from fig. 7, the breakdown voltage of the node 30 is about 0.5, and the active load at this time is about 2.4 times the initial value.
Fig. 8 is a graph showing the sensitivity of each portion of the voltage at the 30 node as the total grid load increases proportionally.
As can be seen from fig. 8, the reactive sensitivities of the voltage parts C (2), C (3), C (4), C (5) and C (6) are gradually increased along with the increase of the load, and when the load value is about 2.5 times of the initial value, the voltage-reactive sensitivities of the voltage parts C (5) and C (6) are crossed first, and at this time, the voltage-reactive sensitivity of the voltage part C (6) starts to exceed the voltage-reactive sensitivity of the voltage part C (5), and is increased along with the increase of the load. After this crossed load point, the voltage sensitivity of the voltage components to reactive power increases and the system voltage has already become unstable. This point is very close to the voltage inflection point obtained from fig. 7, and this point is taken as a determination point of voltage stabilization and instability in calculating the voltage sensitivity.
Get the
When in use
The system voltage is stable; when the temperature is higher than the set temperature
The system is unstable.
Step four, solving and determining the control quantity P of the distributed power supply according to the objective function and the constraint condition by utilizing a genetic algorithm DGi 。
Fig. 9 is a graph of the active load and the reactive load of the system. The DG access nodes are 7, 14, 18, 25, 30 and 32, the maximum capacity of the node is 750kW, and the DG active output is shown in fig. 10 according to the distributed power supply voltage control method. The system active network loss results before and after DG control are shown in fig. 11. Fig. 12 shows the system voltage stability index results before and after DG control. It can be seen from the figure that the voltage control of the distributed power supply by adopting the method reduces the network loss more and improves the voltage stability.
Claims (4)
1. A distributed power supply voltage control method based on the all-pure-function embedded voltage sensitivity is characterized by comprising the following steps: the method specifically comprises the following steps:
step one, establishing a voltage control optimization model of a power distribution network containing distributed power supplies
s1.1, establishing the following objective function in consideration of the network loss after accessing the DG:
wherein, P loss Is the active loss of the distribution network; n is the total number of nodes of the power distribution network; i and j are respectively the node numbers at the two ends of the impedance branch k; u shape j Is the voltage amplitude of node j; r is ij Is the resistance between nodes i, j; p j Active power, Q, of node j at the end of the impedance branch j Is its reactive power;
s1.2, establishing constraint conditions including a power flow equation constraint, a node voltage constraint, a branch current constraint, a DG capacity constraint and a system voltage stability constraint; and using the difference value of the sensitivity of the low-order voltage and the sensitivity of the high-order voltage as an evaluation index of the real-time voltage stability, wherein the system voltage stability is constrained as follows:
wherein, VSI i 、c i [4]、c i [3]A voltage stability index of the i node, a coefficient of the power of the fourth of the s of the voltage of the i node, and a coefficient of the power of the 3 of the s of the voltage of the i node, respectively;
s1.3, substituting the constraint condition established by s1.2 into the objective function stated in s1.1 to obtain an objective optimization function as follows:
wherein k is d Denotes regional electricity prices,. Tau.denotes the maximum load utilization hours, U ilim 、U imin 、U imax Respectively represent the extreme value, the minimum value, the maximum value and lambda of the voltage of the i node V Representing a voltage out-of-limit penalty factor, λ s And representing a voltage stability out-of-limit penalty factor:
k is a constant and is greater than 100;
step two, calculating the power flow of the power distribution network comprising the distributed power supply by using an HELM method
Supposing that no grounding branch circuit exists in the power distribution network, the root node is a balance node, the distributed power supply is a PQ node, and a node power equation is as follows:
wherein, Y ik Representing the mutual admittance, V, between the i-node and the j-node in the nodal admittance matrix k Represents the injection voltage at node k, k = 1-N;
representing the conjugate of the injected apparent power at the i-node, V i * Represents the conjugate of the i-node injection voltage, and m represents the number of PQ nodes in the network;
embedded pure virtual function V for constructing node by using all pure function method i (s)：
Wherein, c i [n]The nth voltage subentry of the i-node voltage in the HELM power flow calculation is represented, s is a frequency domain operator, s n An n-th term representing a frequency domain operator s;
for PQ nodes there are:
wherein the content of the first and second substances,
Y ii self-admittance of an i-node in a node admittance matrix; y is ik The mutual admittance between the i node and the k node in the node admittance matrix is obtained; y is i,shunt For the ground admittance of the i-node, Y when there is no ground branch i,shunt ＝0，Y ik,tran ＝Y ik ；
When s =1, calculating a solution of the power flow; thereby calculating the power distribution network active loss in the objective functionConsumption P loss ；
Step three, calculating the sensitivity of voltage to node injection power by using a HELM method
Solving by HELM method to obtain voltage sensitivity of each order
Then substituting into formula (9), calculating the total nonlinear sensitivity of voltage to injected power
And
step four, solving and determining the control quantity P of the distributed power supply according to the objective function and the constraint condition by utilizing a genetic algorithm DGi 。
2. The distributed power supply voltage control method based on holo-pure function embedded voltage sensitivity of claim 1, wherein: the specific method for calculating the power flow of the power distribution network comprising the distributed power supply by using the HELM method comprises the following steps:
substituting formula (7) into formula (8) yields:
suppose that:
wherein, d i [n]An nth voltage component representing the reciprocal of the i-node voltage;
consists of:
the coefficients according to the s series are equal, so that:
d i [k]the kth voltage component representing the reciprocal of the i-node voltage, c i [n-k]N-k voltage components representing the i-node voltage;
obtained by substituting formula (11) for formula (10):
and then obtaining the following result according to the equality of coefficients of s series:
when s =0 there is:
thus:
d k [0]＝1/c k [0] (17)
when the order of s is 1:
is calculated to obtain c k [1](ii) a The coefficients according to the s series are equal, so that:
according to equation (13) there is:
thereby, it is possible to obtain:
when s =1, a solution of the trend is obtained.
3. The distributed power supply voltage control method based on the holo-pure function embedded voltage sensitivity of claim 2, wherein: the method for calculating the sensitivity of voltage to node injection power by using the HELM method comprises the following steps:
to solve the sensitivity of voltage to node injection active power and reactive power, the requirements are as follows:
wherein P is j Representing active power, Q, injected at node j j Represents the reactive power injected at node j;
as can be seen from the calculation process of equation (16), c i [0]Independent of the injected power at node i, and therefore,
are all 0; in the two sides of the formula (18) to P j 、Q j Calculating the partial derivative, obtaining:
when j = i:
when j ≠ i:
the simultaneous formulas (23) and (24) are solved
And
independent of the system power flow distribution, only the network structure and the electrical distance, and therefore it is called the voltage structure sensitivity;
as can be seen from equation (13):
thereby deducing:
similarly, P is paired on both sides of equation (19) j 、Q j Calculating the partial derivative, obtaining:
when j = i:
when j ≠ i:
can find out
This can be derived from equation (20):
the loop calculation formulas (25) to (29) are calculated, and all the equations are obtained by solving
Then, the total nonlinear sensitivity of the voltage to the injected power is calculated in equation (22).
4. The distributed power supply voltage control method based on holo-pure function embedded voltage sensitivity of claim 3, wherein: the power flow equation constraint is as follows:
wherein, P i 、Q i Respectively the active injection power and the reactive injection power of the node i; u shape i Is the voltage amplitude of node i; theta ij Is the voltage phase angle; g ij 、B ij Branch conductance and susceptance respectively;
the node voltage constraint is:
U i,min ≤U i ≤U i,max (31)
wherein, U i,min 、U i,max The lower limit and the upper limit of the voltage amplitude of the node i are respectively;
the DG capacity constraint is:
wherein, P DGi Representing DG active power accessed by the node i; p DGimax The maximum DG active power allowed to be accessed for the node i; Ω represents a DG installation node set; mu is permeability; p is Ltotal Is the total active load of the system.
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| CN117239770A (en) * | 2023-11-15 | 2023-12-15 | 广东电网有限责任公司中山供电局 | Distributed power supply voltage real-time control method and system |
| CN117728448A (en) * | 2024-02-08 | 2024-03-19 | 北京智芯微电子科技有限公司 | Dynamic regulation and control method, device, equipment and medium for active power distribution network |
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