CN111242513B - Consistency theory-based distributed economic dispatching method for power system - Google Patents

Consistency theory-based distributed economic dispatching method for power system Download PDF

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CN111242513B
CN111242513B CN202010128975.8A CN202010128975A CN111242513B CN 111242513 B CN111242513 B CN 111242513B CN 202010128975 A CN202010128975 A CN 202010128975A CN 111242513 B CN111242513 B CN 111242513B
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周帅
肖敏
周映江
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides a distributed economic dispatching method of a power system based on a consistency theory, which comprises the steps of selecting power generating sets according to user required power, selecting leader power generating sets from the power generating sets, and constructing strong connection communication of the power generating sets; performing mathematical modeling on economic dispatching of a distributed power system, and providing an optimized unit iteration rule and an optimized iteration initial value based on the mathematical modeling and a strong connection communication topology; and iterating according to the iteration rule and the iteration initial value until the sum of the mismatching powers of all the leader machine sets is smaller than a set threshold value, and judging that the economic dispatching reaches supply and demand balance. In the iterative process, each set not only feeds the mismatch power of the set back to the consistency variables of the set, but also feeds the mismatch power of all neighbor sets communicated with the set back to the consistency variables of the set, so that the economic dispatching of the power system is more sensitive to the error perception of each set, and the supply and demand balance of the power system is realized more quickly.

Description

Consistency theory-based distributed economic dispatching method for power system
Technical Field
The invention belongs to the field of economic dispatching of power systems, and particularly relates to a distributed economic dispatching method of a power system based on a consistency theory.
Background
The economic dispatching is one of the basic problems of the power system, and the aim of carrying out the economic dispatching on the power system is to coordinate each unit to meet the power consumption requirement of a user and the safe and stable operation of the whole power grid under the condition of considering various constraint conditions of the generator set, so that the lowest economic cost consumed by the power grid dispatching is realized. The traditional economic dispatching scheme mostly adopts a centralized dispatching scheme, the scheme needs a control center, each unit in the power system needs to transmit own state information to the control center, and the control center dispatches each unit according to the power required by a user and the output condition of each unit at present.
With the development of society, the topological structure of the power system is more and more huge and complex, which brings communication pressure and calculation and allocation pressure to the traditional control center of centralized economic dispatch. Under the background, a distributed economic dispatching scheme is generated, a control center is not needed in the distributed economic dispatching scheme, each unit is communicated with adjacent units around, and an iteration rule of economic dispatching of the power system is given through a consistency algorithm. However, the distributed economic dispatch iterative algorithm needs a long iteration time to iterate to satisfy supply and demand balance because no control center uniformly issues a dispatch instruction, and therefore how to accelerate the iteration speed of the distributed economic dispatch is an urgent problem to be solved.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a distributed economic dispatching method of a power system based on a consistency theory, which is used for overcoming the defect that the iteration time of the current distributed economic dispatching method is longer so as to accelerate the dispatching process of the distributed power system.
The technical scheme is as follows: the method comprises the following specific steps:
(S1) selecting a plurality of generator sets according to the power required by the user, carrying out strong communication topology construction on the generator sets, and selecting one or more generator sets from the generator sets as leader sets; the leader unit can acquire the user power demand, and each of the multiple generator sets can communicate with an adjacent generator set to mutually transmit state information according to the constructed strong communication topology; wherein, the strong communication means that each unit has a neighbor unit to communicate with it.
(S2) mathematically modeling the plurality of gensets, including constructing an objective function that targets a minimization of each genset cost, and determining constraints on each genset contribution based on the user demand power;
(S3) according to the mathematical modeling and the constructed strong communication topology, setting iterative updating rules of gain cost, output and mismatch power of each unit, and setting initial values of the output and mismatch power of each unit;
(S4) iteration is carried out by utilizing the iterative updating rules of the gain cost, the output and the mismatch power based on the initial values of the gain cost, the output and the mismatch power of each unit until the sum of the mismatch power of each leader unit is less than the set threshold value, and the distributed economic dispatch is judged to reach the supply and demand balance and the output of each unit is optimal.
Further, in the step (S2), the process of mathematically modeling the plurality of generator sets is as follows:
firstly, assuming that all units participating in scheduling are thermal generator units, the energy consumption cost function can be approximated as a quadratic function as follows:
Figure BDA0002395282210000021
wherein C is i (P i ) Represents the output of the ith unit as P i Time consuming costs; alpha is alpha i ＜0，β i >0，γ i And (5) less than 0, wherein the three parameters are constants and are determined by the characteristic attributes of each generator set.
The economic dispatching problem of the unit can be converted into a convex optimization problem, and a mathematical model of the following economic dispatching is established:
Figure BDA0002395282210000022
Figure BDA0002395282210000023
Figure BDA0002395282210000024
wherein N represents the number of all units participating in economic dispatch,
Figure BDA0002395282210000025
and
Figure BDA0002395282210000026
respectively represent the upper limit and the lower limit of the ith unit output, P D Representing the power demand of the user.
Further, in step (S3), the present invention optimizes the solving of the mathematical model. Specifically, for the convex optimization problem, the lagrangian function is defined as follows:
Figure BDA0002395282210000027
we can get from the lagrange multiplier method:
Figure BDA0002395282210000028
wherein
Figure BDA0002395282210000029
The gain cost of the unit i is represented and lambda represents a multiplier. Based on the Lagrange multiplier principle, the optimal solution is obtained by the optimization problem when the unit gain cost is the same. That is, when the following equation holds
Figure BDA00023952822100000210
The convex optimization problem has an optimal solution, and the economic dispatching of the power system realizes the balance of supply and demand with the lowest cost.
The economic dispatching problem is completed through an algorithm in practical application, and the distributed economic dispatching algorithm is realized through mutually coordinating and exchanging state information among the units. For distributed economic dispatching, a unit needs to transmit the output, the gain cost and the error power of the current state of the unit to a neighbor node. From the principle of solving the mathematical model of the economic dispatching problem, it can be known that the optimal solution of the economic dispatching problem is realized when the gain cost of each unit is equal. Therefore, the gain cost of each unit is used as a consistency variable, the mismatch power of each unit is used as a feedback state quantity to correct the gain cost of the unit, the output of the unit is continuously updated, and when the gain cost of each unit is the same as the gain cost of a neighbor unit, the distributed economic dispatching algorithm is optimal. Accordingly, the present invention presents the following improved and innovative iteration rules to find the optimal solution for mathematical modeling in step (S2):
Figure BDA0002395282210000031
Figure BDA0002395282210000032
Figure BDA0002395282210000033
wherein
Figure BDA0002395282210000034
And the number of the first and second electrodes,
Figure BDA0002395282210000035
λ i (k)、P i (k)、e i (k) respectively representing the gain cost, the output and the mismatch power of the ith unit during the kth iteration;
Figure BDA0002395282210000036
is the set of all the units sending information to unit i,
Figure BDA0002395282210000037
is the set of all the units requiring the unit j to transmit information, wherein
Figure BDA0002395282210000038
And is
Figure BDA0002395282210000039
I.e. each unitThe information can be sent to the user or transmitted to the user;
Figure BDA00023952822100000310
indicating the number of all nodes sending information to the inode,
Figure BDA00023952822100000311
representing the number of all nodes needing j nodes to send state information; theta is an order of magnitude of 10 -4 A positive number of (d); n is a radical of i + 、N j - 、
Figure BDA00023952822100000312
All determined by the constructed strongly connected communication topology.
Further, in the step (S3), the setting of initial values of the output and the mismatch power of each unit specifically includes:
a) initial output P of unit i i (0) Should satisfy the capacity constraint P of the unit i m ≤P i (0)≤P i M Because the economic dispatching work is a continuous process, the initial output of the unit is the output of the unit when the previous round of economic dispatching is finished, and P is taken for the unit which is newly added to participate in dispatching i (0)＝P i m (ii) a And the initial value of the gain variable is taken as lambda i (0)＝(P i (0)-α i )/β i 。
b) Initial value e of mismatch power of unit i i (0) Satisfies the following conditions:
Figure BDA00023952822100000313
wherein
Figure BDA00023952822100000314
The number of leader groups.
c) The mismatch power sum of each unit can measure the error between the current output of all units and the power required by the user. The requirement power of the user is equal to the sum of the initial output and the mismatch power of all the units, and the sum of the output and the mismatch rate of the units is known to be equal to the requirement power of the user in each algorithm iteration process according to the rule of the mismatch power, namely the requirement power of the user is equal to the requirement power of the user
Figure BDA0002395282210000041
Further, regarding the iteration in step (S4), before the scheduling of the unit starts (i.e., the supply and demand balance between the required power of the user and the output of each unit is achieved through the iteration), the information center reasonably selects a leader unit (i.e., a leader node) and informs the leader unit of the required power of the user, then the information center sends identity (leader and non-leader) information to all the units participating in the scheduling, and the unit (node) receiving the identity information resets its initial mismatch power value according to its identity to prepare for starting the scheduling.
After iteration starts, the leader node sends the mismatching power of the leader node to the information center, and the information center judges the sum of absolute values of the mismatching powers of all the leader nodes
Figure BDA0002395282210000042
And judging whether the dispatching process of the power system is finished or not according to whether the dispatching process is within the range of the constraint threshold value T or not. When in use
Figure BDA0002395282210000043
And judging that the distributed economic dispatching achieves balance of supply and demand and the output of each unit achieves the optimal value.
Has the advantages that: compared with the prior art, the invention has the following advantages:
a) compared with the traditional distributed economic scheduling algorithm, the gain cost lambda of the algorithm provided by the invention i (k) In the iterative process, not only can the self mismatch power be collected, but also the mismatch power of the neighbor nodes is taken into account, so that each set is more sensitive to the error induction between the current output and the target output, and the supply and demand balance can be realized more quickly.
b) The method provided by the invention does not need to collect the mismatch power of all the units, thereby reducing the communication pressure.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of a topology relationship of the unit communication in the power system according to the present invention.
FIG. 3 is a diagram illustrating an iterative effect of a unit update rule in the method of the present invention.
Detailed Description
The invention will be explained in more detail below with reference to specific embodiments and the accompanying drawings.
Referring to fig. 1, the distributed economic dispatch method of the present application includes steps S1 to S4. The steps are respectively as follows:
s1: selecting a plurality of generator sets according to user required power, carrying out strong communication topology construction on the generator sets, and selecting one or more generator sets from the generator sets as leader sets.
Distributed economic dispatch requires strong communication between each unit, i.e., each unit has a neighbor unit to communicate with it. The leader unit can acquire the user power demand, and each of the plurality of generator units can communicate with an adjacent unit to send or transmit state information according to the constructed strong communication topology. In this embodiment, 6 nodes of five units and one information center are selected for distributed economic scheduling description. The topological relationship of the nodes is shown in fig. 2, where node 0 is an information center capable of sending identity information (leader or non-leader) to each generator group node. The remaining nodes represent 5 gensets, respectively. Since the information center (node 0) reasonably selects the leader nodes (nodes 1 and 5) and informs the leader nodes of the required power, the nodes 1 and 5 are the leaders of the distributed economic dispatching, and the nodes know the required power of the users. The communication topology is shown in fig. 2.
S2: and carrying out mathematical modeling on the economic dispatch of each generator set.
Firstly, it is assumed that all units participating in scheduling are thermal generator units, and the energy consumption cost function thereof can be approximated as a quadratic function as follows:
Figure BDA0002395282210000051
wherein C is i (P i ) Represents the ith unit output as P i Time consuming costs; alpha is alpha i ＜0，β i >0，γ i And (5) less than 0, wherein the three parameters are constants and are determined by the characteristic attributes of each generator set. In this embodiment, each parameter for setting five units is shown in table 1.
TABLE 1
Figure BDA0002395282210000052
The economic dispatching problem of the unit can be converted into a convex optimization problem, and a mathematical model of the following economic dispatching is established:
Figure BDA0002395282210000053
Figure BDA0002395282210000054
Figure BDA0002395282210000055
wherein, P D 1800MW represents the power demand of the user, N5 represents the number of all units which participate in the economic dispatch and are selected by the parameter information center,
Figure BDA0002395282210000056
and
Figure BDA0002395282210000057
the distribution represents the upper and lower limits of the ith fleet force.
S3: and setting iterative updating rules of gain cost, output and mismatch power of each unit according to the mathematical modeling and the constructed strong communication topology, and setting initial values of the output and mismatch power of each unit.
The iterative update rule for setting the output and the mismatch power of each unit specifically includes:
for the convex optimization problem, the lagrangian function is defined as follows:
Figure BDA0002395282210000058
we can get from the lagrange multiplier method:
Figure BDA0002395282210000059
thus, when the following equation is established
Figure BDA0002395282210000061
Wherein
Figure BDA0002395282210000062
Representing the gain cost λ of a unit i i And λ represents a multiplier. The convex optimization problem has an optimal solution, namely the electric power system economic dispatching realizes the lowest cost and completes the dispatching task of each unit. Accordingly, the present invention provides the following improved and innovative iterative algorithm:
Figure BDA0002395282210000063
Figure BDA0002395282210000064
Figure BDA0002395282210000065
wherein
Figure BDA0002395282210000066
Figure BDA0002395282210000067
Figure BDA0002395282210000068
Is the set of all the units sending information to unit i,
Figure BDA0002395282210000069
is the set of all the units requiring the unit j to transmit information, wherein
Figure BDA00023952822100000610
And is
Figure BDA00023952822100000611
Namely, each unit can send information to itself or transmit information to itself;
Figure BDA00023952822100000612
indicating the number of all nodes sending information to the inode,
Figure BDA00023952822100000613
indicating the number of all nodes that need j nodes to send status information. θ is a learning gain parameter, and in this embodiment, θ is 6.26 × 10 -4 。N i + 、N j - 、
Figure BDA00023952822100000614
Are determined by the strongly connected communication topology constructed in step (S1). As shown in FIG. 2, if P, Q, C are respectively the elements p ij 、q ij 、c ij The formed matrix has:
Figure BDA00023952822100000615
setting initial values of the output and the mismatch power of each unit specifically comprises the following steps:
(a) initial output P of unit i (0) Should satisfy the capacity constraint P of the unit i m ≤P i (0)≤P i M Because the economic dispatching work is a continuous process, the initial output of the unit is the output of the unit when the previous round of economic dispatching is completed, and because the initial power of each unit is assumed to be the first economic dispatching of the unit, the lower limit of the output capacity constraint of each unit is set. And the initial value of the gain variable is taken as lambda i (0)＝(P i (0)-α i )/β i 。
(b) Initial value e of mismatch power of unit i i (0) Satisfies the following conditions:
Figure BDA0002395282210000071
wherein
Figure BDA0002395282210000072
The number of leader groups.
(c) The mismatch power can measure the error between the current output of all the units and the power required by the user. The sum of the output and the mismatch rate of all the units is known from the initial setting, and the sum of the output and the mismatch rate of the units is known from the rule of the mismatch power to be kept equal to the required power of the user in each iteration of the algorithm, that is to say
Figure BDA0002395282210000073
And finally, referring to table 2 for the initial value of the distributed economic scheduling iterative algorithm.
TABLE 2
Figure BDA0002395282210000074
S4: and iterating by using an iteration updating rule of the gain cost, the output power and the mismatch power based on the initial values of the gain cost, the output power and the mismatch power of each unit until the sum of the mismatch power of each leader unit is less than a set threshold value, and judging that the distributed economic dispatching achieves supply and demand balance and the output power of each unit is optimal.
The scheduling process is a process for achieving supply and demand balance of user required power and output of each unit through iteration. Before the scheduling starts, the information center sends identity information (the nodes 1 and 5 are leader nodes, and the other nodes are non-leader nodes) to all the nodes, and the nodes receiving the identity information reset the initial mismatch power values according to the identities of the nodes to prepare for starting the scheduling. After the dispatching is started, the leader node sends the mismatch power of the leader node to the information center, and the information center judges the sum of absolute values of the mismatch power of all the leader nodes (1 and 5 nodes)
Figure BDA0002395282210000075
Whether the economic dispatching process of the power system meets the supply and demand balance is judged according to whether the economic dispatching process of the power system is within the constraint range.
Compared with the traditional distributed economic dispatching method, the method provided by the invention has the advantage that the gain cost lambda of the ith unit is i (k) In the iterative process, not only can the self mismatch power be collected, but also the mismatch power of the neighbor nodes is taken into account, so that each unit is more sensitive to the error induction between the current output and the target output, the supply and demand balance can be realized more quickly, and the comparison of the iterative effect of the method of the invention and the traditional method is shown in fig. 3.

Claims (4)

1. A distributed economic dispatching method of a power system based on a consistency theory is characterized by comprising the following steps:
(S1) selecting a plurality of generator sets according to the power required by the user, carrying out strong communication topology construction on the generator sets, and selecting one or more generator sets from the generator sets as leader sets; the leader unit can obtain the power required by the user, and each of the multiple generator units can communicate with an adjacent generator unit to mutually transmit state information according to the constructed strong communication topology;
(S2) mathematically modeling economic dispatch for the plurality of gensets, including constructing an objective function targeting minimization of cost for each genset, and determining constraints on output of each genset based on the user demand power;
(S3) according to the mathematical modeling and the constructed strong communication topology, setting iterative updating rules of gain cost, output and mismatch power of each unit, and setting initial values of the output and mismatch power of each unit;
(S4) based on the initial values of the gain cost, the output power and the mismatch power of each unit, utilizing the iteration updating rules of the gain cost, the output power and the mismatch power to iterate until the sum of the mismatch power of each leader unit is smaller than a set threshold value, and judging that the distributed economic dispatch reaches supply and demand balance and the output power of each unit reaches the optimum;
in the step (S3), the iterative update rules of the gain cost, the output power, and the mismatch power of each unit are respectively:
Figure FDA0003738929320000011
Figure FDA0003738929320000012
Figure FDA0003738929320000013
wherein
Figure FDA0003738929320000014
And the number of the first and second electrodes,
Figure FDA0003738929320000015
λ i (k)、P i (k)、e i (k) respectively representing the gain cost, the output and the mismatch power of the ith unit in the kth iteration;
Figure FDA0003738929320000016
is the set of all the units sending information to unit i,
Figure FDA0003738929320000017
is the set of all the units requiring the unit j to transmit information, wherein
Figure FDA0003738929320000018
And is provided with
Figure FDA0003738929320000019
Figure FDA00037389293200000110
Indicating the number of all units sending information to unit i,
Figure FDA00037389293200000111
representing the number of all the units needing the unit j to send the state information; theta is a learning gain parameter and is an order of magnitude of 10 -4 A positive number of;
Figure FDA00037389293200000112
all determined by the constructed strongly connected communication topology.
2. The distributed economic dispatching method of the power system based on the consistency theory as claimed in claim 1, wherein in the step (S2), the objective function is:
Figure FDA0003738929320000021
Figure FDA0003738929320000022
in the formula, N represents the number of units participating in economic dispatch and P represents the number of all the output units i Representing the output of the ith unit; c i (P i ) Represents the ith unit output as P i Time consuming costs; alpha is alpha i <0，β i >0，γ i <0, all three parameters are constants and are determined by the characteristic attributes of each generator set;
the unit attribute and output constraint conditions are as follows:
Figure FDA0003738929320000023
Figure FDA0003738929320000024
Figure FDA0003738929320000025
wherein the content of the first and second substances,
Figure FDA0003738929320000026
and
Figure FDA0003738929320000027
respectively representing the upper limit and the lower limit of the ith unit output, P D Representing the power demanded by the user.
3. The distributed economic dispatching method of the power system based on the consistency theory as claimed in claim 1, wherein in the step (S3),
a) initial output P of unit i i (0) Is set to P i (0)＝P i m (ii) a The initial value of the i gain variable of the unit is taken as lambda i (0)＝(P i (0)-α i )/β i ；
b) Initial value e of mismatch power of unit i i (0) Satisfies the following conditions:
Figure FDA0003738929320000028
wherein
Figure FDA0003738929320000029
Number of leader groups;
c) the required power of the user is equal to the sum of the initial output values and the initial mismatch power values of all the units, and the sum of the output values and the mismatch power of all the units is kept equal to the required power of the user in each iteration process, namely
Figure FDA00037389293200000210
4. The distributed economic dispatching method of the power system based on the consistency theory as claimed in claim 3, characterized in that in the step (S4), the sum of the mismatch powers of the leader groups is smaller than a set threshold value, and is expressed by the following equation:
Figure FDA00037389293200000211
wherein T is the threshold.
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