CN112467735A - D-PMU (direct-measurement unit) and RTU (remote terminal unit) configuration method considering vulnerability of power distribution network structure - Google Patents

D-PMU (direct-measurement unit) and RTU (remote terminal unit) configuration method considering vulnerability of power distribution network structure Download PDF

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CN112467735A
CN112467735A CN202011386171.4A CN202011386171A CN112467735A CN 112467735 A CN112467735 A CN 112467735A CN 202011386171 A CN202011386171 A CN 202011386171A CN 112467735 A CN112467735 A CN 112467735A
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rtu
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CN112467735B (en
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吴红斌
李诗伟
胡斌
朱刘柱
徐子方
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Hefei University of Technology
Economic and Technological Research Institute of State Grid Anhui Electric Power Co Ltd
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Economic and Technological Research Institute of State Grid Anhui Electric Power Co Ltd
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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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

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Abstract

The invention discloses a D-PMU and RTU configuration method for considering the vulnerability of a power distribution network structure, which comprises the following steps: 1, collecting parameter information of an active power distribution network; 2, calculating the importance of each node; 3 initializing discrete particle swarm parameters and D-PMU and RTU position sequences; 4, calculating a fitness value of the coverage and state estimation error of the power distribution network node based on the D-PMU; 5, comparing the fitness values to obtain the optimal D-PMU and RTU position sequences of the particle individuals and the globally optimal D-PMU and RTU position sequences of the population, and updating the next generation of population; and 6, continuously searching the global optimal D-PMU and RTU position sequence of the new generation of population until the iteration termination condition is met. The method can effectively identify the fragile links of the power distribution network, improve the measurement configuration efficiency, and improve the monitoring degree of the D-PMU on the power distribution network while accurately sensing the running state of the power distribution network, thereby better maintaining the safe and stable running of the power distribution network.

Description

D-PMU (direct-measurement unit) and RTU (remote terminal unit) configuration method considering vulnerability of power distribution network structure
Technical Field
The invention relates to the field of intelligent sensing and identification of a power distribution network, in particular to a D-PMU and RTU configuration method considering the vulnerability of a power distribution network structure.
Background
With the development of new energy and the continuous improvement of the grid-connected proportion thereof, the active power distribution network needs to adaptively adjust the network, the power supply, the load and the like according to the actual running state of the power system, and the measurement system is used as an important part of intelligent sensing identification of the power distribution network, so that a data basis is provided for state estimation. However, it is increasingly difficult for the advanced measurement system and Remote Terminal Unit (RTU) in the existing data acquisition and monitoring system to meet the requirements of power distribution network situation awareness on measurement data real-time performance and accuracy, a GPS-based novel low-cost and high-efficiency power distribution network synchronized phasor measurement device (D-PMU) provides a new means for monitoring the active power distribution network due to its advantages of real-time measurement, phasor measurement, small measurement error, etc., and installation of a D-PMU device on an important node in the active power distribution network in the future has great feasibility and necessity, but due to the limitations of technology and cost, the overall configuration coverage of the D-PMU and the RTU is low. Therefore, how to identify the key nodes of the power distribution network and optimize and configure the limited D-PMU and RTU makes the configuration result not only meet the precision requirement of state estimation, but also improve the coverage rate of the D-PMU on the key nodes in the power distribution network becomes an important problem to be solved urgently.
The optimization directions of the current optimized configuration scheme of the measuring device are mostly only two, the number of the measuring devices is minimum, and the state estimation precision is highest; the nodes at different positions are treated equally, and the influence of the difference between the nodes at different topological positions and the access of a Distributed Generation (DG) on the importance degree of the nodes is not considered, so that some fragile nodes in the power distribution network are not configured with a measuring device with a fault monitoring function, such as a D-PMU; most of the configuration objects are single measurement, which is not in line with the current situation of long-term coexistence of RTU and D-PMU in the measurement system of the actual power distribution network, and even if the configuration is carried out aiming at mixed measurement, a staged configuration method is adopted for different measurements, and the configuration process is complex.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides the configuration method of the D-PMU and the RTU, which takes the vulnerability of the power distribution network structure into consideration, so that the vulnerable links of the power distribution network can be effectively identified, the measurement configuration efficiency is improved, the monitoring degree of the D-PMU on the power distribution network is improved while the operation state of the power distribution network is accurately sensed, and the safe and stable operation of the power distribution network is better maintained.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention relates to a D-PMU and RTU configuration method for considering the vulnerability of a power distribution network structure, which is characterized by comprising the following steps:
step one, collecting parameter information of an active power distribution network:
step 1.1, constructing a topology structure diagram G ═ N, E } of the active power distribution network according to nodes and lines in the active power distribution network, wherein N ═ N1,n2,…,nMIs the set of nodes, E ═ E1,e2,…,eLIs the set of lines; wherein n isMDenotes the Mth node, eLRepresenting the L-th line, M representing the total number of nodes, and L representing the total number of lines;
step 1.2, collecting the number S of distributed power DGs and historical data of the output of each distributed power DG, and simulating the output of each distributed power DG by using a Gaussian mixture model to obtain the mean value of the output of the S-th distributed power DG
Figure BDA0002809756490000021
Figure BDA0002809756490000022
Step two, calculating the importance of each node of the active power distribution network:
step 2.1, obtaining by using the formula (1)To the jth node n in the active distribution networkjDegree of connection De(j)：
Figure BDA0002809756490000023
In formula (1): delta1(i, j) represents the connection condition of any node in the topology structure diagram G, if the ith node niAnd the jth node njAdjacent, then let δ1(i, j) is equal to 1, otherwise, let δ1(i,j)＝0；δ2(j) Showing the connection condition between the node in the topology structure graph G and the distributed power supply DG if the jth node njConnecting distributed power DG, then make delta2(j) On the contrary, let δ2(j)＝0，i≠j,i,j＝1,2,…,M；
Step 2.2, obtaining the adjacent ith node n by using the formula (2)iAnd the jth node njInter-line eijImportance of IE(i,j)：
Figure BDA0002809756490000024
In formula (2): t is tijIs a line eijThe number of triangles which can be formed;
step 2.3, obtaining the jth node n by using the formula (3)jTo line eijContribution of importance NE (i, j):
Figure BDA0002809756490000025
step 2.4, obtaining the jth node n by using the formula (4)jBridge length B ofr(j)：
Figure BDA0002809756490000026
In formula (4):
Figure BDA0002809756490000027
is the jth node njA set of neighboring nodes;
step 2.5, obtaining the jth node n by using the formula (5)jNode importance of IN(j)：
Figure BDA0002809756490000028
In formula (6):
Figure BDA0002809756490000029
the mean value of the output of the S distributed generation DG, S is the total number of distributed generation DGs connected to the active power distribution network, and N is the total number of distributed generation DGs connected to the active power distribution networkGIs a set of nodes connected with a distributed power supply DG, and NG＝{nG1,nG2,…,nGS}；nGSDenotes the S-th node to which a distributed power supply DG is connected, LjGsIs the jth node njAnd the s-th node n connected with a distributed power supply DGGsShortest path distance between;
step three, initializing a D-PMU and RTU position sequence:
step 3.1, initializing particle swarm parameters:
setting a population of m particles
Figure BDA0002809756490000031
The particle dimension is the total number M of nodes of the active power distribution network, and the maximum iteration number is KmaxThe position vector of the t-th particle in the population is
Figure BDA0002809756490000032
xtdIs composed of
Figure BDA0002809756490000033
D-th dimension element of (1), and xtdBelongs to { -1,0,1} and corresponds to the D-th node n in the position sequence of the t-th D-PMU and RTUdMeasurement configuration of (2): x is the number oftd1 stands for the d-th node ndConfigure D-PMU, xtd-1 represents the d-th node ndConfiguring RTU, x td0 represents the d-th node ndThe D-PMU or RTU is not configured,
Figure BDA0002809756490000034
position X of corresponding t-th discrete particlet＝{Xt1,Xt2,...,XtB·MIs a B.M-dimensional vector, XtB·MIs XtB is the binary digit of the particle, t is 1,2, …, M, d is 1,2, …, M;
step 3.2, defining and initializing the current iteration number k to be 0; initializing D-PMU and RTU position sequences: generating speed V (k) of k-th generation particle swarm and position sequence of D-PMU and RTU
Figure BDA0002809756490000035
Step four, calculating the fitness value of the kth generation of particle swarm:
step 4.1, obtaining coverage D of the kth generation particle swarm D-PMU to the node by using the formula (6)MON(k)：
Figure BDA0002809756490000036
In the formula (6), DMON,t(k) Representing the coverage of D-PMU to nodes in the t-th D-PMU and RTU position sequence of the k-th generation of particle swarm, xtj(k) The position sequences of the t-th D-PMU and RTU in the k-th generation particle swarm
Figure BDA0002809756490000037
The j-th dimension element of (1);
step 4.2, calculating the state estimation error E of the kth generation populationr(k)：
Step 4.2.1, according to the position sequence of the D-PMU and the RTU
Figure BDA0002809756490000038
Generating measurement data z consisting of measured values and pseudo-measured values of D-PMU and RTUk,tSetting the initial value of the current state quantity formed by the real part and the imaginary part of the branch current as
Figure BDA0002809756490000039
The termination condition is set by equation (7):
Figure BDA00028097564900000310
in formula (7):
Figure BDA00028097564900000311
a u-th current state correction for the τ -th state estimation iteration for the t-th particle in the k-th generation of particles, u being 1,2, …, l2，l2The current state quantity is the number, and zeta is the calculation precision;
step 4.2.2, setting the state estimation iteration time tau as 0;
step 4.2.3, obtaining a Jacobian matrix of the tth particle in the kth generation particle swarm for the state estimation iteration of the tth time by using the formula (8)
Figure BDA0002809756490000041
Figure BDA0002809756490000042
In the formula (8), the reaction mixture is,
Figure BDA0002809756490000043
to represent
Figure BDA0002809756490000044
With respect to item l1Measurement of quantities
Figure BDA0002809756490000045
Is measured as a function of the non-linear measure of,
Figure BDA0002809756490000046
a current state estimator for the τ th state estimation iteration of the tth particle in the kth generation of particle swarm;
step 4.2.4, using the formula (9) Obtaining an information matrix of the t-th particle in the kth generation particle swarm for the state estimation iteration of the t-th time
Figure BDA0002809756490000047
Figure BDA0002809756490000048
In formula (9): wk,tMeans in the k-th generation-based particle swarm
Figure BDA0002809756490000049
A measure weight matrix is generated, and the main diagonal elements are
Figure BDA00028097564900000410
Diagonal matrix of σvIs the standard deviation of the measurement error of the v-th quantity, v-1, 2, …, l1，l1Measuring the number of the samples;
step 4.2.5, obtaining the current state variable correction quantity of the t-th state estimation iteration of the t-th particle in the k-th generation particle swarm by using the formula (10)
Figure BDA00028097564900000411
Figure BDA00028097564900000412
4.2.6, obtaining the current state estimator of the t +1 th state estimation iteration of the t particle in the kth generation particle swarm by using the formula (11)
Figure BDA00028097564900000413
Figure BDA00028097564900000414
Step 4.2.7, determining the current state variable correction for the τ th iteration
Figure BDA00028097564900000415
Whether a termination condition is satisfied; if yes, stopping iteration and outputting a state estimation result
Figure BDA00028097564900000416
Otherwise, assigning tau +1 to tau, and skipping to the step 4.2.3 to continue execution;
step 4.2.8, obtaining the state estimation relative error E of the kth generation particle swarm by using the formula (12)r(k)：
Figure BDA00028097564900000417
In formula (12): er,t(k)、
Figure BDA00028097564900000418
Respectively show the position sequence according to D-PMU and RTU
Figure BDA00028097564900000419
The total state estimation error and the u-th current state estimation value x obtained by state estimation calculationuThe real value of the u current state quantity;
step 4.3, obtaining the population fitness value F (k) of the kth generation by using the formula (13):
F(k)＝Er(k)-DMON(k) (13)
step five, updating the D-PMU and RTU position sequence:
step 5.1, particle swarm encoding:
initializing B-2; the position sequences of the t-th D-PMU and RTU in the k-th generation of particle swarm
Figure BDA0002809756490000051
D-th dimension position element x in (1)td(k) Converting into 2-bit binary number to obtain the binary position vector X of the t-th particle in the k-th generation of discrete particle swarmt(k) 2d-1, 2d elements: xt,2d-1(k)、Xt,2d(k)；
Step 5.2, updating the individual optimal D-PMU and RTU position sequence Popt(k)：
Comparing historical fitness values of the t-th particle in k iterations, and assigning the minimum fitness value to the individual extreme value FPopt,t(k) Individual extremum FPopt,t(k) The corresponding position vector is the individual optimal position P of the t particle in the k generation particle swarmopt,t(k) And obtaining the individual optimal D-PMU and RTU position sequences of the kth generation of particle swarm: popt(k)＝{Popt,1(k),Popt,2(k),…,Popt,t(k),…,Popt,m(k)}；
Step 5.3, updating the global optimal D-PMU and RTU position sequence Gopt(k)：
Obtaining a global extreme FG of the kth generation particle swarm by using the formula (14)opt(k)，FGopt(k) The corresponding binary position vector is the global optimal position G of the kth generation particle swarmopt(k)；
FGopt(k)＝min{Popt,1(k),Popt,2(k),…,Popt,m(k)},t＝1,2,…,m (14)
Step 5.4, calculating the difference | FG between the global extreme values of two adjacent iterationsopt(k-1)-FGopt(k) And judging whether a termination condition is met; if yes, jumping to step 6.2; otherwise, executing step 5.5; k is 1,2, …, Kmax；
Step 5.5, updating the flight speed V of the b-dimensional element of the t-th particle in the k + 1-th generation particle swarm by using the formula (15)tb(k+1)：
Vtb(k+1)＝ω(k)Vtb(k)+c1r1(Ptb(k)-Xtb(k))+c2r2(Gb(k)-Xtb(k)) (15)
In the formula (17), Ptb(k) For the individual optimal position P of the tth particle in the kth generation particle swarmopt,t(k) The b-th element of (1), Gb(k) Global optimum position G for k generation particle swarmopt(k) ω (k) is an inertia weight factor of the k-th generation, c1、c2Is an acceleration factor；r1、r2Is [0,1 ]]The above random numbers, b ═ 1,2, …, 2M;
step 5.6, updating the b-dimensional element X at the t-th particle position in the k + 1-th generation particle swarm by using the formula (16)tb(k+1)：
Figure BDA0002809756490000052
In the formula (18), utb(k +1) is [0,1 ]]Average number of inner uniform distributions;
step 5.7, particle swarm decoding:
converting the discrete particle position X (k +1) of the k +1 generation particle swarm into a D-PMU and RTU position sequence of the k +1 generation particle swarm
Figure BDA0002809756490000061
The position vector X of the t discrete particle in the k +1 generation particle groupt2d-1 d, 2d element X oft,2d-1、Xt,2dCombine to form a 2-bit binary number and combine Xt,2d-1The formed 2-bit binary number is converted into decimal number as sign bit, thereby obtaining the t-th D-PMU and RTU position sequence in the k +1 th generation particle swarm
Figure BDA0002809756490000062
D-th dimension element x of (2)td；
Step six, outputting the optimal configuration result of the D-PMU and the RTU:
step 6.1, judge whether to satisfy k<Kmax(ii) a If yes, assigning k +1 to k, and then skipping to the step 4.1 for execution; otherwise, executing step 6.2;
step 6.2, according to the particle decoding mode, the global optimal position G of the kth generation populationopt(k) And converting the position sequences into D-PMU and RTU position sequences to obtain the optimal D-PMU and RTU configuration results.
Compared with the prior art, the invention has the beneficial effects that:
the invention introduces the topological criticality of the bridge degree description node, defines the node importance degree by combining the influence of DG on the basis, and utilizes the index to measure the importance degree of each node of the active power distribution network, thereby avoiding the limitation of only considering the topological characteristic of the power distribution network or only considering the electrical characteristic, further assisting the power grid staff to identify the fragile link on the power distribution network structure and strengthening the protection of the key node.
Aiming at the fault monitoring function that the D-PMU is often ignored in the configuration process, the invention describes the monitoring degree of the measuring system on the vulnerable link of the power distribution network by using the coverage rate of the D-PMU on the key node, describes the state estimation precision of the measuring system by using a state estimation error, and generates an optimal D-PMU and RTU position sequence by adopting an improved discrete particle swarm algorithm by comprehensively considering the two aspects; the D-PMU is preferentially installed at the key node while the state estimation precision of the configuration result is ensured, so that the operation state of the power distribution network is accurately sensed, the structural weak link of the power distribution network is effectively monitored, and the method has important significance for maintaining the safe and stable operation of the power distribution network.
3 the improved discrete particle swarm algorithm adopted by the invention enables each two dimensions of the discrete particles to be combined into 2-bit binary numbers by improving the encoding mode of the particle swarm, and the different values of the binary numbers correspond to three different measurement installation states on each node of the power distribution network, thereby realizing the parallel configuration of the D-PMU and the RTU, overcoming the problem of complicated configuration steps caused by different measurement batch configurations in the traditional mixed measurement configuration method, and improving the efficiency of measurement configuration.
Drawings
FIG. 1 is a flow chart of the position selection of a D-PMU and an RTU based on an improved discrete particle swarm optimization of the invention;
Detailed Description
In the embodiment, a D-PMU and RTU configuration method considering the vulnerability of a power distribution network structure identifies the vulnerable links of the power distribution network by combining the influence definition node importance of the topology structure and DG of the power distribution network; establishing a state estimator based on a minimum weighted quadratic multiplication algorithm; and generating an optimal D-PMU and RTU position sequence by adopting an improved discrete particle swarm algorithm. Specifically, as shown in fig. 1, the method comprises the following steps:
1. a D-PMU and RTU configuration method considering the vulnerability of a power distribution network structure is characterized by comprising the following steps:
step one, collecting parameter information of an active power distribution network:
step 1.1, constructing a topology structure diagram G ═ N, E } of the active power distribution network according to nodes and lines in the active power distribution network, wherein N ═ N1,n2,…,nMIs the set of nodes, E ═ E1,e2,…,eLIs the set of lines; wherein n isMDenotes the Mth node, eLRepresenting the L-th line, M representing the total number of nodes, and L representing the total number of lines;
in the topological graph of the power distribution network, DGs are attached to nodes connected with the DGs and are not counted as an independent node in N;
step 1.2, collecting the number S of distributed power DGs and historical data of the output of each distributed power DG, and simulating the output of each distributed power DG by using a Gaussian mixture model to obtain the mean value of the output of the S-th distributed power DG
Figure BDA0002809756490000071
Figure BDA0002809756490000072
Step two, calculating the importance of each node of the power distribution network:
node importance INThe basic idea of establishment is as follows: combined node bridge degree BrAnd the influence of the DG on the node importance degree is obtained; the influence degree depends on the DG output and the shortest path distance L between the DG output and each nodejGs，
Figure BDA0002809756490000073
The degree of influence of the s-th DG on the importance of other nodes is described. Therefore, the problem of weak link identification of the active power distribution network is converted into the problem of identifying high INProblem of value nodes.
Step 2.1, obtaining the jth node n in the active power distribution network by using the formula (1)jDegree of connection De(j)：
Figure BDA0002809756490000074
In formula (1): delta1(i, j) represents the connection condition of any node in the topology structure diagram G, if the ith node niAnd the jth node njAdjacent, then let δ1(i, j) is equal to 1, otherwise, let δ1(i,j)＝0；δ2(j) Showing the connection condition between the node in the topology structure graph G and the distributed power supply DG if the jth node njConnecting distributed power DG, then make delta2(j) On the contrary, let δ2(j)＝0，i≠j,i,j＝1,2,…,M；
Step 2.2, obtaining the adjacent ith node n by using the formula (2)iAnd the jth node njInter-line eijImportance of IE(i,j)：
Figure BDA0002809756490000075
In formula (2): t is tijIs a line eijThe number of triangles which can be formed;
step 2.3, obtaining the jth node n by using the formula (3)jTo line eijContribution of importance NE (i, j):
Figure BDA0002809756490000081
step 2.4, obtaining the jth node n by using the formula (4)jBridge length B ofr(j)：
Figure BDA0002809756490000082
In formula (4):
Figure BDA0002809756490000083
is the jth node njA set of neighboring nodes;
step 2.5, obtaining the jth node n by using the formula (5)jNode importance of IN(j)：
Figure BDA0002809756490000084
In formula (6):
Figure BDA0002809756490000085
the mean value of the output of the S distributed generation DG, S is the total number of distributed generation DGs connected to the active power distribution network, and N is the total number of distributed generation DGs connected to the active power distribution networkGIs a set of nodes connected with a distributed power supply DG, and NG＝{nG1,nG2,…,nGS}；nGSDenotes the S-th node to which a distributed power supply DG is connected, LjGsIs the jth node njAnd the s-th node n connected with a distributed power supply DGGsShortest path distance between;
step three, initializing D-PMU and RTU position sequences
Step 3.1, initializing particle swarm parameters:
setting a population of m particles
Figure BDA0002809756490000086
The particle dimension is the total number M of nodes of the active power distribution network, and the maximum iteration number is KmaxThe position vector of the t-th particle in the population is
Figure BDA0002809756490000087
xtdIs composed of
Figure BDA0002809756490000088
D-th dimension element of (1), and xtdBelongs to { -1,0,1} and corresponds to the D-th node n in the position sequence of the t-th D-PMU and RTUdMeasurement configuration of (2): x is the number oftd1 stands for the d-th node ndConfigure D-PMU, xtd-1 represents the d-th node ndConfiguring RTU, xtd0 represents the d-th node ndThe D-PMU or RTU is not configured,
Figure BDA0002809756490000089
position X of corresponding t-th discrete particlet＝{Xt1,Xt2,...,XtB·MIs a B.M-dimensional vector, XtB·MIs XtB is the binary digit of the particle, t is 1,2, …, M, d is 1,2, …, M;
step 3.2, defining and initializing the current iteration number k to be 0; initializing D-PMU and RTU position sequences: generating speed V (k) of k-th generation particle swarm and position sequence of D-PMU and RTU
Figure BDA00028097564900000810
Step four, calculating the fitness value of the kth generation population:
step 4.1, obtaining coverage D of the kth generation particle swarm D-PMU to the node by using the formula (6)MON(k)：
Figure BDA0002809756490000091
In the formula (6), DMON,t(k) Representing the coverage of D-PMU to nodes in the t-th D-PMU and RTU position sequence of the k-th generation of particle swarm, xtj(k) The position sequences of the t-th D-PMU and RTU in the k-th generation particle swarm
Figure BDA0002809756490000092
The j-th dimension element of (1);
in formula (6): by xtj·(xtj+1)/2 denotes D-PMU at node njThe mounting state of (2): if node njConfigure D-PMU, then xtd1, corresponding to xtj·(xtj+1)/2 ═ 1, if node njWithout D-PMU, xtd-1/0, corresponding to xtj·(xtj+1)/2＝0；
Step 4.2, calculating the state estimation error E of the kth generation populationr(k)：
In the state estimation, the relation between a measurement z consisting of the measured values and the pseudo-measured values of the D-PMU and the RTU and a current state variable x consisting of the real part and the imaginary part of the branch current is shown as the formula (A):
z＝h(x)+ε (A)
in formula (7):
Figure BDA0002809756490000093
Figure BDA0002809756490000094
is the first1Measurement of quantity, /)1The number of the measured data is measured,
Figure BDA0002809756490000095
Figure BDA0002809756490000096
is the first2A current state quantity of2Is the number of state quantities;
Figure BDA0002809756490000097
describing a nonlinear mathematical relationship between a current state variable x and a quantity measurement z for measuring a function phasor, wherein epsilon is a measurement error phasor;
step 4.2.1, according to the position sequence of the D-PMU and the RTU
Figure BDA0002809756490000098
Generating measurement data z consisting of measured values and pseudo-measured values of D-PMU and RTUk,tSetting the initial value of the current state quantity formed by the real part and the imaginary part of the branch current as
Figure BDA0002809756490000099
The termination condition is set by equation (7):
Figure BDA00028097564900000910
in formula (7):
Figure BDA00028097564900000911
a u-th current state correction for the τ -th state estimation iteration for the t-th particle in the k-th generation of particles, u being 1,2, …, l2，l2The current state quantity is the number, and zeta is the calculation precision;
step 4.2.2, setting the state estimation iteration time tau as 0;
step 4.2.3, obtaining a Jacobian matrix of the tth particle in the kth generation particle swarm for the state estimation iteration of the tth time by using the formula (8)
Figure BDA00028097564900000912
Figure BDA0002809756490000101
In the formula (8), the reaction mixture is,
Figure BDA0002809756490000102
to represent
Figure BDA0002809756490000103
With respect to item l1Measurement of quantities
Figure BDA0002809756490000104
Is measured as a function of the non-linear measure of,
Figure BDA0002809756490000105
estimating the current state of the kth generation of particles in the kth generation of particle swarm;
step 4.2.4, obtaining an information matrix of the t-th particle in the k-th generation particle swarm for the state estimation iteration for the t time by using the formula (9)
Figure BDA0002809756490000106
Figure BDA0002809756490000107
In formula (9): wk,tMeans in the k-th generation-based particle swarm
Figure BDA0002809756490000108
Generated measurementsA weight matrix of which the main diagonal elements are
Figure BDA0002809756490000109
Diagonal matrix of σvIs the standard deviation of the measurement error of the v-th quantity, v-1, 2, …, l1，l1Measuring the number of the samples;
step 4.2.5, obtaining the current state variable correction quantity of the t-th state estimation iteration of the t-th particle in the k-th generation particle swarm by using the formula (10)
Figure BDA00028097564900001010
Figure BDA00028097564900001011
4.2.6, obtaining the current state estimator of the t +1 th state estimation iteration of the t particle in the kth generation particle swarm by using the formula (11)
Figure BDA00028097564900001012
Figure BDA00028097564900001013
Step 4.2.7, determining the current state variable correction for the τ th iteration
Figure BDA00028097564900001014
Whether a termination condition is satisfied; if yes, stopping iteration and outputting a state estimation result
Figure BDA00028097564900001015
Otherwise, assigning tau +1 to tau, and skipping to the step 4.2.3 to continue execution;
step 4.2.8, obtaining the state estimation relative error E of the kth generation particle swarm by using the formula (12)r(k)：
Figure BDA00028097564900001016
In formula (12): er,t(k)、
Figure BDA00028097564900001017
Respectively show the position sequence according to D-PMU and RTU
Figure BDA00028097564900001018
The total state estimation error and the u-th current state estimation value x obtained by state estimation calculationuThe real value of the u current state quantity;
step 4.3, obtaining the population fitness value F (k) of the kth generation by using the formula (13):
the fitness function determines the optimization direction of the D-PMU and RTU position sequences, and in order to consider the state estimation precision and the monitoring degree of the measurement system on the power distribution network, the state estimation relative error E is usedrMeasuring the state estimation accuracy, the smaller the value is, the better the value is, and the coverage D of the D-PMU is usedMON(k) The monitoring degree of the measuring system on the fragile link of the power distribution network is measured, the larger the value is, the better the value is, and therefore, the fitness value function is set as:
F(k)＝Er(k)-DMON(k) (13)
step five, updating the D-PMU and RTU position sequence:
step 5.1, particle swarm encoding:
initializing B-2; the position sequences of the t-th D-PMU and RTU in the k-th generation of particle swarm
Figure BDA0002809756490000111
D-th dimension position element x in (1)td(k) Converting into 2-bit binary number to obtain the binary position vector X of the t-th particle in the k-th generation of discrete particle swarmt(k) 2d-1, 2d elements: xt,2d-1(k)、Xt,2d(k)，Xt(k) The dimension of (D) is changed from D to 2D accordingly;
in the first case: x is the number oftd(k) 1, i.e. node ndConfigure D-PMU, then Xt,2d-1(k)＝0、Xt,2d(k) 1 is ═ 1; first, theTwo conditions are as follows: x is the number oftd(k) 1, i.e. node ndConfigure RTU, then Xt,2d-1(k)＝1、Xt,2d(k) 1 is ═ 1; in the third case: x is the number oftd(k) 0, i.e. node ndWithout D-PMU or RTU, then Xt,2d-1(k)＝0、Xt,2d(k)＝0；
Step 5.2, updating the individual optimal D-PMU and RTU position sequence Popt(k)：
Comparing historical fitness values of the t-th particle in k iterations, and assigning the minimum fitness value to the individual extreme value FPopt,t(k) Individual extremum FPopt,t(k) The corresponding position vector is the individual optimal position P of the t particle in the k generation particle swarmopt,t(k) And obtaining the individual optimal D-PMU and RTU position sequences of the kth generation of particle swarm: popt(k)＝{Popt,1(k),Popt,2(k),…,Popt,t(k),…,Popt,m(k)}；
Step 5.3, updating the global optimal D-PMU and RTU position sequence Gopt(k)：
Obtaining a global extreme FG of the kth generation particle swarm by using the formula (14)opt(k)，FGopt(k) The corresponding binary position vector is the global optimal position G of the kth generation particle swarmopt(k)；
FGopt(k)＝min{Popt,1(k),Popt,2(k),…,Popt,m(k)},t＝1,2,…,m (14)
Step 5.4, calculating the difference | FG between the global extreme values of two adjacent iterationsopt(k-1)-FGopt(k) And judging whether a termination condition is met; if yes, jumping to step 6.2; otherwise, executing step 5.5; k is 1,2, …, Kmax；
Step 5.5, updating the flight speed V of the b-dimensional element of the t-th particle in the k + 1-th generation particle swarm by using the formula (15)tb(k+1)：
Vtb(k+1)＝ω(k)Vtb(k)+c1r1(Ptb(k)-Xtb(k))+c2r2(Gb(k)-Xtb(k)) (15)
In the formula (17), Ptb(k) For the individual optimal position P of the tth particle in the kth generation particle swarmopt,t(k) The b-th element of (1), Gb(k) Global optimum position G for k generation particle swarmopt(k) ω (k) is an inertia weight factor of the k-th generation, c1、c2Is an acceleration factor; r is1、r2Is [0,1 ]]The above random numbers, b ═ 1,2, …, 2M;
in the formula (17), the inertial weight factor ω (k) generally has a value range of [0.4,0.9], the larger the value of the inertial weight factor ω (k) is, the larger the search range of the particle to the solution space is, so as to avoid falling into the local optimum, the ω (k) is reduced in an exponential trend, and the formula (B) is used to obtain ω (k):
Figure BDA0002809756490000121
step 5.6, updating the b-dimensional element X at the t-th particle position in the k + 1-th generation particle swarm by using the formula (16)tb(k+1)：
Figure BDA0002809756490000122
In the formula (18), utb(k +1) is [0,1 ]]Average number of inner uniform distributions;
step 5.7, particle swarm decoding:
converting the discrete particle position X (k +1) of the k +1 generation particle swarm into a D-PMU and RTU position sequence of the k +1 generation particle swarm
Figure BDA0002809756490000123
The position vector X of the t discrete particle in the k +1 generation particle groupt2d-1 d, 2d element X oft,2d-1、Xt,2dCombine to form a 2-bit binary number and combine Xt,2d-1The formed 2-bit binary number is converted into decimal number as sign bit, thereby obtaining the t-th D-PMU and RTU position sequence in the k +1 th generation particle swarm
Figure BDA0002809756490000124
D-th dimension element x of (2)td；
In the first case: xt,2d-1(k+1)＝0、Xt,2d(k +1) is 1, then xtd(k) 1, stands for node ndConfiguring a D-PMU; in the second case: xt,2d-1(k)＝1、Xt,2d(k) X is 1td(k) Under-1, stands for node ndConfiguring an RTU; in the third case: xt,2d-1(k)＝0、Xt,2d(k) 0 or Xt,2d-1(k+1)＝1、Xt,2d(k +1) is 0, then xtd(k) 0, represents a node ndD-PMU or RTU is not installed;
step six, outputting the optimal configuration result of the D-PMU and the RTU:
step 6.1, judge whether to satisfy k<Kmax(ii) a If yes, assigning k +1 to k, and then skipping to the step 4.1 for execution; otherwise, executing step 6.2;
step 6.2, according to the particle decoding mode, the global optimal position G of the kth generation populationopt(k) And converting the position sequences into D-PMU and RTU position sequences to obtain the optimal D-PMU and RTU configuration results.
In summary, the present invention first collects parameter information of the power distribution network; weak links of the power distribution network are identified by introducing node importance which can comprehensively reflect topological characteristics and electrical characteristics of the power distribution network; combining the D-PMU with the RTU position sequence to define a coverage index of the D-PMU to describe the monitoring degree of the measuring system on the fragile links of the power distribution network; the coverage degree and the state estimation precision of the D-PMU are taken as the optimization direction, the optimal D-PMU and RTU position sequences are generated by adopting the improved discrete particle swarm algorithm, the parallel configuration of the D-PMU and the RTU is realized, the state estimation precision is ensured while the coverage rate of the D-PMU on key nodes is improved, the operation state of the power distribution network is accurately sensed, the weak links of the power distribution network structure are well monitored, the safe and stable operation of the power distribution network is maintained, and the method has wide engineering application value.

Claims (1)

1. A D-PMU and RTU configuration method considering the vulnerability of a power distribution network structure is characterized by comprising the following steps:
step one, collecting parameter information of an active power distribution network:
step 1.1, constructing a topology structure diagram G ═ N, E } of the active power distribution network according to nodes and lines in the active power distribution network, wherein N ═ N1,n2,…,nMIs the set of nodes, E ═ E1,e2,…,eLIs the set of lines; wherein n isMDenotes the Mth node, eLRepresenting the L-th line, M representing the total number of nodes, and L representing the total number of lines;
step 1.2, collecting the number S of distributed power DGs and historical data of the output of each distributed power DG, and simulating the output of each distributed power DG by using a Gaussian mixture model to obtain the mean value of the output of the S-th distributed power DG
Figure FDA0002809756480000011
Step two, calculating the importance of each node of the active power distribution network:
step 2.1, obtaining the jth node n in the active power distribution network by using the formula (1)jDegree of connection De(j)：
Figure FDA0002809756480000012
In formula (1): delta1(i, j) represents the connection condition of any node in the topology structure diagram G, if the ith node niAnd the jth node njAdjacent, then let δ1(i, j) is equal to 1, otherwise, let δ1(i,j)＝0；δ2(j) Showing the connection condition between the node in the topology structure graph G and the distributed power supply DG if the jth node njConnecting distributed power DG, then make delta2(j) On the contrary, let δ2(j)＝0，i≠j,i,j＝1,2,…,M；
Step 2.2, obtaining the adjacent ith node n by using the formula (2)iAnd the jth node njInter-line eijImportance of IE(i,j)：
Figure FDA0002809756480000013
In formula (2): t is tijIs a line eijThe number of triangles which can be formed;
step 2.3, obtaining the jth node n by using the formula (3)jTo line eijContribution of importance NE (i, j):
Figure FDA0002809756480000014
step 2.4, obtaining the jth node n by using the formula (4)jBridge length B ofr(j)：
Figure FDA0002809756480000015
In formula (4):
Figure FDA0002809756480000016
is the jth node njA set of neighboring nodes;
step 2.5, obtaining the jth node n by using the formula (5)jNode importance of IN(j)：
Figure FDA0002809756480000021
In formula (6):
Figure FDA0002809756480000022
the mean value of the output of the S distributed generation DG, S is the total number of distributed generation DGs connected to the active power distribution network, and N is the total number of distributed generation DGs connected to the active power distribution networkGIs a set of nodes connected with a distributed power supply DG, and NG＝{nG1,nG2,…,nGS}；nGSDenotes the S-th node to which a distributed power supply DG is connected, LjGsIs the jth node njAnd the s-th node n connected with a distributed power supply DGGsThe most important of the twoShort path distance;
step three, initializing a D-PMU and RTU position sequence:
step 3.1, initializing particle swarm parameters:
setting a population of m particles
Figure FDA0002809756480000023
The particle dimension is the total number M of nodes of the active power distribution network, and the maximum iteration number is KmaxThe position vector of the t-th particle in the population is
Figure FDA0002809756480000024
xtdIs composed of
Figure FDA0002809756480000025
D-th dimension element of (1), and xtdBelongs to { -1,0,1} and corresponds to the D-th node n in the position sequence of the t-th D-PMU and RTUdMeasurement configuration of (2): x is the number oftd1 stands for the d-th node ndConfigure D-PMU, xtd-1 represents the d-th node ndConfiguring RTU, xtd0 represents the d-th node ndThe D-PMU or RTU is not configured,
Figure FDA0002809756480000026
position X of corresponding t-th discrete particlet＝{Xt1,Xt2,...,XtB·MIs a B.M-dimensional vector, XtB·MIs XtB is the binary digit of the particle, t is 1,2, …, M, d is 1,2, …, M;
step 3.2, defining and initializing the current iteration number k to be 0; initializing D-PMU and RTU position sequences: generating speed V (k) of k-th generation particle swarm and position sequence of D-PMU and RTU
Figure FDA0002809756480000027
Step four, calculating the fitness value of the kth generation of particle swarm:
step 4.1, obtaining the kth generation particle swarm D-P by using the formula (6)Coverage D of MU to nodeMON(k)：
Figure FDA0002809756480000028
In the formula (6), DMON,t(k) Representing the coverage of D-PMU to nodes in the t-th D-PMU and RTU position sequence of the k-th generation of particle swarm, xtj(k) The position sequences of the t-th D-PMU and RTU in the k-th generation particle swarm
Figure FDA0002809756480000029
The j-th dimension element of (1);
step 4.2, calculating the state estimation error E of the kth generation populationr(k)：
Step 4.2.1, according to the position sequence of the D-PMU and the RTU
Figure FDA00028097564800000210
Generating measurement data z consisting of measured values and pseudo-measured values of D-PMU and RTUk,tSetting the initial value of the current state quantity formed by the real part and the imaginary part of the branch current as
Figure FDA00028097564800000211
The termination condition is set by equation (7):
Figure FDA00028097564800000212
in formula (7):
Figure FDA0002809756480000031
a u-th current state correction for the τ -th state estimation iteration for the t-th particle in the k-th generation of particles, u being 1,2, …, l2，l2The current state quantity is the number, and zeta is the calculation precision;
step 4.2.2, setting the state estimation iteration time tau as 0;
step 4.2.3 obtaining the kth generation particle swarm by using the formula (8)Jacobian matrix for the tth particle to perform the state estimation iteration t
Figure FDA0002809756480000032
Figure FDA0002809756480000033
In the formula (8), the reaction mixture is,
Figure FDA0002809756480000034
to represent
Figure FDA0002809756480000035
With respect to item l1Measurement of quantities
Figure FDA0002809756480000036
Is measured as a function of the non-linear measure of,
Figure FDA0002809756480000037
a current state estimator for the τ th state estimation iteration of the tth particle in the kth generation of particle swarm;
step 4.2.4, obtaining an information matrix of the t-th particle in the k-th generation particle swarm for the state estimation iteration for the t time by using the formula (9)
Figure FDA0002809756480000038
Figure FDA0002809756480000039
In formula (9): wk,tMeans in the k-th generation-based particle swarm
Figure FDA00028097564800000310
A measure weight matrix is generated, and the main diagonal elements are
Figure FDA00028097564800000311
Diagonal matrix of σvIs the standard deviation of the measurement error of the v-th quantity, v-1, 2, …, l1，l1Measuring the number of the samples;
step 4.2.5, obtaining the current state variable correction quantity of the t-th state estimation iteration of the t-th particle in the k-th generation particle swarm by using the formula (10)
Figure FDA00028097564800000312
Figure FDA00028097564800000313
4.2.6, obtaining the current state estimator of the t +1 th state estimation iteration of the t particle in the kth generation particle swarm by using the formula (11)
Figure FDA00028097564800000314
Figure FDA00028097564800000315
Step 4.2.7, determining the current state variable correction for the τ th iteration
Figure FDA00028097564800000316
Whether a termination condition is satisfied; if yes, stopping iteration and outputting a state estimation result
Figure FDA00028097564800000317
Otherwise, assigning tau +1 to tau, and skipping to the step 4.2.3 to continue execution;
step 4.2.8, obtaining the state estimation relative error E of the kth generation particle swarm by using the formula (12)r(k)：
Figure FDA0002809756480000041
In formula (12): er,t(k)、
Figure FDA0002809756480000042
Respectively show the position sequence according to D-PMU and RTU
Figure FDA0002809756480000043
The total state estimation error and the u-th current state estimation value x obtained by state estimation calculationuThe real value of the u current state quantity;
step 4.3, obtaining the population fitness value F (k) of the kth generation by using the formula (13):
F(k)＝Er(k)-DMON(k) (13)
step five, updating the D-PMU and RTU position sequence:
step 5.1, particle swarm encoding:
initializing B-2; the position sequences of the t-th D-PMU and RTU in the k-th generation of particle swarm
Figure FDA0002809756480000044
D-th dimension position element x in (1)td(k) Converting into 2-bit binary number to obtain the binary position vector X of the t-th particle in the k-th generation of discrete particle swarmt(k) 2d-1, 2d elements: xt,2d-1(k)、Xt,2d(k)；
Step 5.2, updating the individual optimal D-PMU and RTU position sequence Popt(k)：
Comparing historical fitness values of the t-th particle in k iterations, and assigning the minimum fitness value to the individual extreme value FPopt,t(k) Individual extremum FPopt,t(k) The corresponding position vector is the individual optimal position P of the t particle in the k generation particle swarmopt,t(k) And obtaining the individual optimal D-PMU and RTU position sequences of the kth generation of particle swarm: popt(k)＝{Popt,1(k),Popt,2(k),…,Popt,t(k),…,Popt,m(k)}；
And 5. step 5.3. Updating global optimum D-PMU, RTU position sequence Gopt(k)：
Obtaining a global extreme FG of the kth generation particle swarm by using the formula (14)opt(k)，FGopt(k) The corresponding binary position vector is the global optimal position G of the kth generation particle swarmopt(k)；
FGopt(k)＝min{Popt,1(k),Popt,2(k),…,Popt,m(k)},t＝1,2,…,m (14)
Step 5.4, calculating the difference | FG between the global extreme values of two adjacent iterationsopt(k-1)-FGopt(k) And judging whether a termination condition is met; if yes, jumping to step 6.2; otherwise, executing step 5.5; k is 1,2, …, Kmax；
Step 5.5, updating the flight speed V of the b-dimensional element of the t-th particle in the k + 1-th generation particle swarm by using the formula (15)tb(k+1)：
Vtb(k+1)＝ω(k)Vtb(k)+c1r1(Ptb(k)-Xtb(k))+c2r2(Gb(k)-Xtb(k)) (15)
In the formula (17), Ptb(k) For the individual optimal position P of the tth particle in the kth generation particle swarmopt,t(k) The b-th element of (1), Gb(k) Global optimum position G for k generation particle swarmopt(k) ω (k) is an inertia weight factor of the k-th generation, c1、c2Is an acceleration factor; r is1、r2Is [0,1 ]]The above random numbers, b ═ 1,2, …, 2M;
step 5.6, updating the b-dimensional element X at the t-th particle position in the k + 1-th generation particle swarm by using the formula (16)tb(k+1)：
Figure FDA0002809756480000051
In the formula (18), utb(k +1) is [0,1 ]]Average number of inner uniform distributions;
step 5.7, particle swarm decoding:
the (k +1) th generation particleThe discrete particle position X (k +1) of a subgroup is converted into a D-PMU, RTU position sequence of the k +1 th generation particle swarm
Figure FDA0002809756480000052
The position vector X of the t discrete particle in the k +1 generation particle groupt2d-1 d, 2d element X oft,2d-1、Xt,2dCombine to form a 2-bit binary number and combine Xt,2d-1The formed 2-bit binary number is converted into decimal number as sign bit, thereby obtaining the t-th D-PMU and RTU position sequence in the k +1 th generation particle swarm
Figure FDA0002809756480000053
D-th dimension element x of (2)td；
Step six, outputting the optimal configuration result of the D-PMU and the RTU:
step 6.1, judge whether to satisfy k<Kmax(ii) a If yes, assigning k +1 to k, and then skipping to the step 4.1 for execution; otherwise, executing step 6.2;
step 6.2, according to the particle decoding mode, the global optimal position G of the kth generation populationopt(k) And converting the position sequences into D-PMU and RTU position sequences to obtain the optimal D-PMU and RTU configuration results.
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