CN115276091B - Distributed power supply voltage control method based on full-pure function embedded voltage sensitivity - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The invention discloses a distributed power supply voltage control method based on full-pure function embedded voltage sensitivity. According to the method, HELM is utilized to calculate power flow of the power distribution network, and then sensitivity of voltage to injection power of each node is calculated according to a sensitivity calculation method based on HELM. And then using the sensitivity of the voltage to each step of the injection power of each node as a voltage stability criterion, and adding the voltage stability criterion into the constraint condition of the power distribution network voltage model. Finally, utilizing genetic algorithm to solve and determine control quantity P of distributed power supply according to objective function and constraint condition DGi . According to the invention, the HELM method is utilized to consider the nonlinear factors of the sensitivity, the nonlinear sensitivity of each order is calculated, HELM voltage stability index constraint is considered in a power distribution network voltage control model, and the voltage control effect is better.
Description
Technical Field
The invention belongs to the technical field of power information, and particularly relates to a distributed power supply voltage control method based on full-pure function embedded voltage sensitivity.
Background
With the development of related technologies such as power electronics and control technologies, a large number of distributed power sources (DG, distributed Generation) are possible to access to a power distribution network. At the same time, a series of problems are brought to the power distribution system: the DG is connected to change the power distribution system from a radial structure to an active structure and cause the internal power flow to change, so that the voltage is influenced to change, and the power distribution system has great influence on various aspects of the power distribution network; and the access position and the capacity of the DG have certain influence on the network loss, the voltage level and the stability of the power distribution network, the electric energy quality, the relay protection and the like of the power distribution network system.
Considering the influence of DG on the voltage level of a power distribution network, voltage sensitivity indexes are generally introduced to select, order and control DG, but the conventional sensitivity calculation method based on the jacobian matrix has the problem that the sick power 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, a 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 existing power flow with the maximum load, and consider the voltage stable if the existing power flow is smaller than the maximum load. This analytical method has the following problems: 1) The calculated amount of continuous calculation is large, the calculation time is long, and the real-time requirement of on-line voltage stability judgment and control is not met; 2) With DG or FACT access, and node load not increasing proportionally, the maximum load is changed, and the maximum load calculated by using the continuous power flow method is not accurate. In the last two years, a power flow calculation method based on Holomorphic embedding method full-pure function embedding is provided, the power flow method completely subverts the traditional cow pulling method, and whether a power flow solution exists can be determined without depending on node initial values.
In the prior art, other indexes are also 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, cannot consider a complex power distribution network load model accessed into DG or FACT equipment and the like, or neglect line resistance or grounding capacitance and the like, so that 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 full-pure function embedded voltage sensitivity, which is suitable for the voltage control problem containing DG, can solve the power flow and the voltage sensitivity under the pathological condition, and is simple and quick to calculate.
The distributed power supply voltage control method based on the full-pure function embedded voltage sensitivity specifically comprises the following steps:
step one, establishing a voltage control optimization model containing a distributed power supply distribution network
And s1.1 and DG are connected into the power distribution network, so that the flow of power flow of adjacent branches of the node can be reduced, and the network loss is reduced. However, if the capacity of the access DG is too large, reverse power flow occurs in the power distribution network, and network loss may also increase. The network loss after accessing DG is considered to establish the following objective function:
wherein P is loss Active loss of the power distribution network; n is the total number of nodes of the power distribution network; i and j are node numbers at two ends of the impedance branch k respectively; u (U) j The voltage amplitude at node j; r is R ij The resistance between the nodes i and j; p (P) j Active power, Q, of node j at the end of the impedance branch j For its reactive power.
s1.2, establishing constraint conditions, including a tide equation constraint, a node voltage constraint, a branch current constraint, a DG capacity constraint and a system voltage stability constraint:
(1) Constraint of tide equation
Wherein P is i 、Q i Active injection power and reactive injection power of the node i respectively; u (U) i The voltage amplitude of the node i; θ 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 is i,min 、U i,max The lower limit and the upper limit of the voltage amplitude of the node i are respectively defined.
(3) DG capacity constraint
Wherein P is DGi The DG active power accessed by the node i is represented; p (P) DGimax Maximum DG active power allowed to be accessed for the node i; omega represents DG installation node set; mu is permeability; p (P) Ltotal For the total active load of the system.
(4) System voltage stability constraints
An unreasonable 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 of voltage stability of the i-node, the coefficient of the fourth power exponent of s of the voltage of the i-node, and the coefficient of the 3 power exponent of s of the voltage of the i-node are respectively represented. When (when)The system voltage is stable; when (when)The system is unstable.
s1.3, substituting the constraint condition established in s1.2 into the objective function described in s1.1 to obtain an objective optimization function as follows:
wherein k is d Represents regional electricity price, τ represents the number of hours of maximum load utilization, U ilim 、U imin 、U imax Respectively represent extreme value and minimum value of i node voltageValue, maximum value, lambda V Represents a voltage out-of-limit penalty factor, lambda s Representing a voltage stability out-of-limit penalty factor:
k is a positive constant with a large value, and is usually 100 or more.
Step two, calculating power flow of power distribution network comprising distributed power supply by using HELM method
Assuming that no ground connection is arranged in the power distribution network, a root node is a balance node, a distributed power supply is a PQ node, and a node power equation is as follows:
wherein Y is ik Representing the admittance between the i node and the j node in the node admittance matrix, V k Represents the injection voltage at node k, k=1 to N;representing the conjugate of the i-node injection apparent power,/->Representing the conjugate of the i node injection voltage, m represents the number of PQ nodes in the network.
Constructing embedded pure virtual function V of node by utilizing pure function method i (s):
Wherein c i [n]An nth voltage sub-term representing the i node voltage in HELM load flow calculation, s being a frequency domain operator,s n N-th order terms representing the frequency domain operator s;
for the PQ node there is:
wherein,Y ii the self admittance of the i node in the node admittance matrix; y is Y ik The admittance between the i node and the k node in the node admittance matrix; y is Y i,shunt Is the ground admittance of the i node, Y when no ground branch exists i,shunt =0,Y ik,tran =Y ik 。
Assume that:
wherein d i [n]The nth voltage term, which represents the inverse of the i-node voltage.
The method comprises the following steps:
according to the equality of the coefficients of the s-series, the following can be obtained:
d i [k]the kth voltage component, c, representing the inverse of the voltage at the i-node i [n-k]N-k voltage components representing the i-node voltage. When the node is a PQ node, the expression (10) is taken into the expression (11) to obtain:
substituting formula (12) into formula (15) to obtain:
and then according to the coefficient equality of the s series, obtaining:
when s=0, there is:
thus:
d k [0]=1/c k [0] (19)
when the s-order is 1:
c is calculated to obtain k [1]. According to the equality of the coefficients of the s-series, the following can be obtained:
according to formula (14) there is:
thus, it is possible to obtain:
when s=1, a solution to the power flow can be obtained. On the basis, calculate the objective functionActive loss P of power distribution network loss 。
Step three, calculating sensitivity of voltage to node injection power by using HELM method
To solve the sensitivity of voltage to node injection active power and reactive power, the following is required:
wherein P is j Representing the active power injected by node j, Q j Representing the reactive power injected by node j.
From the calculation of equation (18), c i [0]Independent of the injection power of node i, and therefore,all 0. On both sides of equation (20) for P j 、Q j The deviation is calculated, and the following steps are obtained:
when j=i:
when j+.i:
the simultaneous equations (25) and (26) can be solvedFrom the solving process, it can be seen +.>Andindependent of the system power flow distribution, and dependent only on the network structure and electrical distance, and is therefore referred to as a voltage junctionStructure sensitivity.
From equation (14):
from this, it is deduced that:
similarly, P is found on both sides of equation (21) j 、Q j The deviation is calculated, and the following steps are obtained:
when j=i:
when j+.i:
can be found out
From equation (22), it can be deduced that:
the cyclic calculation formulas (27) to (31) are solved to obtain allThen, the total nonlinear sensitivity of the voltage to the injection power is calculated by substituting the calculated sensitivity into equation (24).
It was found by analysis that,to the first power of the loadProportional because the first term on the right of equation (39) is constant when n=2, and the second term is proportional to the load; />Proportional to the load squared and so on. In general, the number of the devices used in the system,and->And becomes smaller as the value of n increases. Total voltage sensitivity->And->Can be obtained from formula (24).
Using HELM to calculate to obtain voltage sensitivity of each order, then subtracting high-order sensitivity from low-order sensitivity, wherein the difference value is positive when the low-order sensitivity is larger than the high-order sensitivity under normal conditions; when the load is increased, if the difference value is negative, judging that the voltage is unstable; 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 unstable, and the voltage prevention control is started.
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 。
The invention has the following beneficial effects:
the power distribution network voltage based on the HELM voltage sensitivity stability criterion can be used for on-line voltage control of the power distribution network, solves the problem that the power distribution network voltage stability criterion is not easy to calculate, is high in calculation speed and simple in calculation, and has higher theoretical significance and application value. When the power distribution network comprising the distributed power supply is subjected to voltage control, the nonlinear factor of sensitivity is considered, the influence of the distributed power supply on the voltage stability of the power distribution network is considered in an objective function, and the voltage control effect is better.
Drawings
FIG. 1 is a flow chart of a distributed power supply voltage control method based on full pure function embedded voltage sensitivity;
FIG. 2 is a schematic diagram of a 33 node grid used in the examples;
FIG. 3 is a schematic diagram comparing HELM tide calculation results with forward-push substitution results;
FIG. 4 is a graph of the difference between the HELM load flow calculation result and the forward-push-back method result;
FIG. 5 is a plot of voltage versus reactive power sensitivity calculated using HELM at base tidal current;
FIG. 6 is a graph of the difference between the calculated voltage reactive sensitivity results of HELM and the calculated voltage reactive sensitivity results of perturbation;
FIG. 7 is a lambda V curve for node 30 in a 33-node system;
FIG. 8 is a plot of the sensitivity of each portion of the 30 node voltage to reactive power;
FIG. 9 is a graph of the active and reactive loads of the system;
FIG. 10 is a DG active output;
FIG. 11 is a graph showing the active loss results of the system 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 power distribution network voltage stability determination method based on the hellm voltage sensitivity includes the following steps:
step one, a mathematical model of the power distribution network is built according to the data of the 33-node power grid shown in fig. 2.
And step two, carrying out load flow calculation by using the HELM, wherein the result is shown in a figure 3, and the difference is shown in a figure 4. As can be seen from fig. 3 and fig. 4, the result of the load flow calculation based on the help is substantially identical to the result of the calculation by the push-back method, and the method of using the help to perform load flow calculation is proved to be feasible.
And step three, calculating the voltage sensitivity by using the HELM, wherein the result is shown in fig. 5. Fig. 6 is a graph of the difference between the voltage reactive sensitivity results calculated by the help and the voltage reactive sensitivity results calculated by the perturbation method. From fig. 5 and 6, it can be seen that the voltage reactive sensitivity results calculated by the help are substantially identical to the voltage reactive sensitivity results calculated by the perturbation method, and it has been proved that the voltage sensitivity using the help is feasible.
Using a Matpower drawn λv plot for a 33-node system, the abscissa λ is the load growth factor. As can be seen 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 plot of the sensitivity of each portion of the voltage at node 30 as the full network load increases proportionally.
As can be seen from fig. 8, the reactive power sensitivity of the C (2), C (3), C (4), C (5), and C (6) parts of the voltage gradually increases with the load increase ratio, and when the load value is about 2.5 times the initial value, the reactive power sensitivity of the C (5) and C (6) parts of the voltage first crosses, at this time, the reactive power sensitivity of the C (6) part of the voltage starts to exceed the reactive power sensitivity of the C (5) part of the voltage, and the reactive power sensitivity of the C (6) part of the voltage increases with the load. After this crossing load point, the voltage sensitivity of the voltage parts to reactive power is increasing and the system voltage has been destabilized. This point is very close to the voltage inflection point obtained according to fig. 7, and is taken as a judgment point of voltage stability destabilization when calculating the voltage sensitivity.
Taking outWhen->The system voltage is stable; when (when)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 and reactive loads of the system. The DG access nodes are 7, 14, 18, 25, 30 and 32, the maximum capacity of the nodes is 750kW, and the DG active output is shown in fig. 10 according to the present distributed power supply voltage control method. The active network loss results of the system before and after DG control are shown in fig. 11. The results of the system voltage stability index before and after DG control are shown in fig. 12. As can be seen from the figure, the distributed power supply voltage control is performed by adopting the method, so that the network loss is reduced more, and the voltage stability is improved.
Claims (4)
1. The distributed power supply voltage control method based on full-pure function embedded voltage sensitivity is characterized by comprising the following steps of: the method specifically comprises the following steps:
step one, establishing a voltage control optimization model containing a distributed power supply distribution network
s1.1, establishing the following objective function by considering the network loss after accessing DG:
wherein P is loss Active loss of the power distribution network; n is the total number of nodes of the power distribution network; i and j are node numbers at two ends of the impedance branch k respectively; u (U) j The voltage amplitude at node j; r is R ij The resistance between the nodes i and j; p (P) j Active power, Q, of node j at the end of the impedance branch j Reactive power thereof;
s1.2, establishing constraint conditions, including load flow equation constraint, node voltage constraint, branch current constraint, DG capacity constraint and system voltage stability constraint; the difference value of the low-order voltage sensitivity and the high-order voltage sensitivity is used as an evaluation index of the real-time voltage stability, and the system voltage stability constraint is as follows:
wherein VSI i 、c i [4]、c i [3]Respectively represent voltage stability index of i node and i nodeA coefficient of the fourth power exponent of s of the voltage of the point, a coefficient of the 3 power exponent of s of the voltage of the inode;
s1.3, substituting the constraint condition established in s1.2 into the objective function described in s1.1 to obtain an objective optimization function as follows:
wherein k is d Represents regional electricity price, τ represents the number of hours of maximum load utilization, U ilim 、U imin 、U imax Respectively represent the extreme value, the minimum value and the maximum value of the i node voltage lambda V Represents a voltage out-of-limit penalty factor, lambda s Representing a voltage stability out-of-limit penalty factor:
k is a constant, and K is more than 100;
step two, calculating power flow of power distribution network comprising distributed power supply by using HELM method
Assuming that no ground connection is arranged in the power distribution network, a root node is a balance node, a distributed power supply is a PQ node, and a node power equation is as follows:
wherein Y is ik Representing the admittance between the i node and the j node in the node admittance matrix, V k Represents the injection voltage at node k, k=1 to N;representing inode injection viewsAt the conjugation of power, V i * Representing the conjugate of the i node injection voltage, m representing the number of PQ nodes in the network;
constructing embedded pure virtual function V of node by utilizing pure function method i (s):
Wherein c i [n]An nth voltage sub-term representing the i node voltage in HELM load flow calculation, s is a frequency domain operator, s n N-th order terms representing the frequency domain operator s;
for the PQ node there is:
wherein,Y ii the self admittance of the i node in the node admittance matrix; y is Y ik The admittance between the i node and the k node in the node admittance matrix; y is Y i,shunt Is the ground admittance of the i node, Y when no ground branch exists i,shunt =0,Y ik,tran =Y ik ;
When s=1, calculating to obtain a solution of the power flow; thereby calculating the active loss P of the power distribution network in the objective function loss ;
Step three, calculating sensitivity of voltage to node injection power by using HELM method
Solving to obtain the voltage sensitivity of each step by HELM methodThen substituting formula (9) to calculate the total nonlinear sensitivity of voltage to injection 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 full-pure function embedded voltage sensitivity according to claim 1, wherein: the specific method for calculating the power flow of the power distribution network comprising the distributed power supply by utilizing the HELM method comprises the following steps:
bringing formula (7) into formula (8) gives:
assume that:
wherein d i [n]An nth voltage sub-term representing the inverse of the voltage of the i node;
the method comprises the following steps:
according to the equality of the coefficients of the s-series, the following can be obtained:
d i [k]representing the inverse of the i-node voltageThe kth voltage component, c i [n-k]N-k voltage sub-terms representing the i-node voltage;
substituting formula (11) into formula (10) to obtain:
and then according to the coefficient equality of the s series, obtaining:
when s=0, there is:
thus:
d k [0]=1/c k [0] (17)
when the s-order is 1:
c is calculated to obtain k [1]The method comprises the steps of carrying out a first treatment on the surface of the According to the equality of the coefficients of the s-series, the following can be obtained:
according to equation (13) there is:
thus, it is possible to obtain:
when s=1, a solution to the power flow is obtained.
3. The distributed power supply voltage control method based on full-pure function embedded voltage sensitivity according to claim 2, wherein: the method for calculating the sensitivity of the voltage to the 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 following is required:
wherein P is j Representing the active power injected by node j, Q j Representing reactive power injected by the node j;
from the calculation of equation (16), c i [0]Independent of the injection power of node i, and therefore,are all 0; p on both sides of equation (18) j 、Q j The deviation is calculated, and the following steps are obtained:
when j=i:
when j+.i:
simultaneous equations (23), (24) solve And->Independent of the system power flow distribution, only related to the network structure and the electrical distance, so it is called voltage structure sensitivity;
from equation (13):
from this, it is deduced that:
similarly, P is found on both sides of equation (19) j 、Q j The deviation is calculated, and the following steps are obtained:
when j=i:
when j+.i:
can be found out
Can be deduced from formula (20):
circulation calculation type (25) to (29)Solving to obtain allThen, the total nonlinear sensitivity of the voltage to the injection power is calculated by substituting the total nonlinear sensitivity into equation (22).
4. The distributed power supply voltage control method based on full-pure function embedded voltage sensitivity according to claim 3, wherein: the flow equation constraint is as follows:
wherein P is i 、Q i Active injection power and reactive injection power of the node i respectively; u (U) i The voltage amplitude of the node i; θ 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 is i,min 、U i,max The lower limit and the upper limit of the voltage amplitude of the node i are respectively set;
the DG capacity constraint is:
wherein P is DGi The DG active power accessed by the node i is represented; p (P) DGimax Maximum DG active power allowed to be accessed for the node i; omega represents DG installation node set; mu is permeability; p (P) Ltotal For the total active load of the system.
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