CN116073453A - Alternating current-direct current hybrid power distribution network optimal scheduling method based on graph calculation - Google Patents

Alternating current-direct current hybrid power distribution network optimal scheduling method based on graph calculation Download PDF

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CN116073453A
CN116073453A CN202310115068.3A CN202310115068A CN116073453A CN 116073453 A CN116073453 A CN 116073453A CN 202310115068 A CN202310115068 A CN 202310115068A CN 116073453 A CN116073453 A CN 116073453A
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卫志农
马智刚
陈�胜
孙国强
臧海祥
朱瑛
黄蔓云
韩海腾
周亦洲
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Abstract

The invention discloses an alternating current-direct current hybrid power distribution network optimal scheduling method based on graph calculation. The method comprises the steps of abstracting equipment in an AC/DC hybrid power distribution network into a vertex of a graph, and establishing an object-oriented AC/DC hybrid power distribution network graph model so as to adapt to future power system data management based on a graph database; secondly, a collaborative optimization model of the AC/DC hybrid power distribution network with high proportion of optical storage is constructed based on the graph model, and an AC/DC hybrid power distribution network graph calculation method with vertexes as centers is deduced.

Description

Alternating current-direct current hybrid power distribution network optimal scheduling method based on graph calculation
Technical Field
The invention relates to an alternating current-direct current hybrid power distribution network optimal scheduling method based on graph calculation, and belongs to the field of operation and scheduling of alternating current-direct current hybrid power distribution networks.
Background
With large-scale access of distributed resources such as photovoltaic and energy storage to a power distribution network, power electronic devices in the power distribution network are increased, and the advantages of the AC/DC hybrid power distribution network in the aspects of efficient operation, flexible control and the like are obvious, so that the power distribution network has become a new trend of future power distribution network development. However, with large-scale access of distributed energy storage and photovoltaics, the scale of an operation optimization model of the ac-dc hybrid power distribution network is rapidly enlarged, the calculation efficiency and the resolvability of the traditional centralized algorithm are reduced, and the calculation requirement of the future large-scale distributed resource access of the ac-dc hybrid power distribution network is difficult to meet. Therefore, the method has important significance for searching an efficient model calculation method for the unified model of the AC/DC hybrid power distribution network.
The widely used distributed algorithms in the existing research, such as ATC and ADMM, are all based on distributed optimization of each sub-level or sub-area, centralized modeling is still adopted in each sub-level and area, and sub-level and area division also generally need human participation, so that modeling universality is poor. The graph calculation method based on the graph database has outstanding advantages in solving efficiency and expandability, can realize complete distributed calculation of vertexes and protect user privacy, but is mainly focused on aspects of tide calculation, power supply capacity evaluation and the like of an alternating current system at present, and is not fully applied in the aspect of optimizing operation of an alternating current-direct current hybrid power distribution network.
Aiming at the problems, the method abstracts equipment in the AC/DC hybrid power distribution network to be the vertex of the graph, and establishes an object-oriented AC/DC hybrid power distribution network graph model; the method has the advantages that the collaborative optimization model of the AC/DC hybrid power distribution network with the high-proportion optical storage is built based on the graph model, the efficient solution of the AC/DC hybrid power distribution network optimization model is realized based on the AC/DC hybrid power distribution network graph calculation method taking the top point as the center, the scheduling strategy of the equipment is rapidly acquired, meanwhile, the user privacy is protected, and the plug and play of the user equipment can be facilitated.
Disclosure of Invention
The invention aims to: in order to meet the optimization calculation requirement of the AC/DC hybrid distribution network under wide access of the optical storage, the invention provides an AC/DC hybrid distribution network optimization scheduling method based on graph calculation.
The technical scheme is as follows: in order to achieve the aim of the invention, the invention provides an alternating current/direct current hybrid power distribution network optimal scheduling method based on graph calculation, which comprises the following steps:
step 1: introducing a port concept, and establishing an alternating current-direct current hybrid power distribution network graph model;
step 2: associating state variables in the AC/DC hybrid power distribution network system with ports introduced in the graph model established in the step 1, associating decision variables in the AC/DC hybrid power distribution network system with devices, and establishing an AC/DC hybrid power distribution network coordination optimization model based on the graph model;
step 3: and (3) solving the optimization model constructed in the step (2) based on a graph calculation method taking the vertex as a center, acquiring an optimal scheduling strategy of the equipment, and carrying out optimal scheduling of the AC/DC hybrid power distribution network according to the optimal scheduling strategy.
Further, in the step 1, a concept of a port is introduced, and an ac/dc hybrid power distribution network graph model is built, and the specific method is as follows:
Introducing the concept of ports, regarding the ports as edges of a graph, regarding nodes and equipment as vertexes of the graph, and establishing a graph model of the alternating current-direct current hybrid power distribution network, wherein the vertexes in the graph model, namely the nodes, the equipment and the edges, namely the ports are expressed as follows:
the device comprises: the system comprises alternating current equipment, direct current equipment and coupling equipment, wherein an upper power grid, an alternating current line, an alternating current load and photovoltaic and energy storage accessed into the alternating current system in an alternating current system are all abstracted into the alternating current equipment; the direct current circuit, the direct current load and the energy storage and light Fu Jun connected into the direct current system are abstracted into direct current equipment; the coupling equipment is a voltage source type converter and is indicated by a subscript d;
and (3) node: the method is divided into an alternating current node and a direct current node, so that lossless energy exchange among similar associated ports is realized, and the lossless energy exchange is represented by a subscript n;
the port: each device comprises one or more ports, wherein the vertexes formed by the devices and the nodes are connected through the ports, the ports are divided into alternating current ports and direct current ports, and the alternating current ports and the direct current ports are also called edges and are denoted by subscript o;
ports in the alternating current-direct current hybrid power distribution network graph model are organized according to nodes or are organized according to equipment, when the ports are organized according to the nodes, intersections of ports connected with different nodes are empty, and a union of ports connected with all the nodes is a complete set; when the equipment is organized, the intersection sets of the ports connected with different equipment are empty, the union set of the ports connected with all the equipment is a complete set, and if the complete set of the ports is O, the above properties are expressed as follows:
Figure BDA0004078295160000021
Figure BDA0004078295160000022
Wherein, Γ n,r And Γ n,s Ports connected to nodes r and s, respectivelyAggregation, N n As the total number of nodes Γ d,e And Γ d,h N for the port set connected to device e and device h d As a total number of devices,
Figure BDA0004078295160000023
representing an empty set.
Further, in the step 2, the state variables in the system are all associated to the ports introduced in the graph model established in the step 1, the decision variables in the system are associated to the devices, and the optimization model of the ac/dc hybrid power distribution network based on the graph model is constructed as follows:
objective function: the aim is to minimize the sum of the running cost of each device in the AC/DC hybrid power distribution network;
Figure BDA0004078295160000031
wherein: x is x d C is a decision variable associated to device d d As a cost function of device d;
the cost function of each device is as follows:
Figure BDA0004078295160000032
wherein: t is a scheduling period subscript; t is the total scheduling period; c t The time-sharing electricity price is the electricity purchasing price of the upper-level power grid; p (P) sub,d,t The power purchasing power is the power purchasing power of the upper power grid; d (D) sub The method is a superior power grid equipment set;
Figure BDA0004078295160000033
maintaining a cost coefficient for energy storage operation; p (P) ch,d,t And P dis,d,t Respectively charging and discharging power of the energy storage equipment in the t period; lambda (lambda) ess,d A depreciated cost factor for the energy storage device; u (u) ess,d,t Switching state variables for energy storage charge and discharge in a t period; d (D) ESS Is an energy storage device set; d is a set of devices in the AC/DC hybrid power distribution network; wherein the cost of the superior power grid equipment is as follows The sum of time-period electricity purchase costs; the energy storage operation cost comprises operation maintenance cost and depreciation cost; the cost of other equipment is 0;
device operation constraints: the equipment operation constraint comprises an upper-level power grid purchase power constraint, an alternating current line and direct current line operation constraint, a voltage source type converter operation constraint, an energy storage operation constraint and a photovoltaic inverter reactive compensation constraint in an alternating current system;
1) Superior grid purchase power constraint
Figure BDA0004078295160000034
Figure BDA0004078295160000035
Wherein P is sub,d,t And Q sub,d,t Active and reactive power injection power of the upper power grid equipment in the period t are respectively;
Figure BDA0004078295160000036
and P sub,d Injecting upper and lower limits of active power into an upper power grid respectively; />
Figure BDA0004078295160000037
And Q sub,d Injecting reactive power upper and lower limits for the upper power grid respectively; p (P) ac,o,t And Q ac,o,t Active power and reactive power of the alternating current port o in the t period respectively; Γ -shaped structure sub,d Is a port set connected with an upper power grid;
2) Ac line operation constraints
When the device
Figure BDA0004078295160000041
When (I)>
Figure BDA0004078295160000042
For the AC line equipment set, if the ports at the two ends are i and j respectively, the second order cone form of the AC line based on the graph model is aboutThe bundles were as follows:
Figure BDA0004078295160000043
Figure BDA0004078295160000044
Figure BDA0004078295160000045
Figure BDA0004078295160000046
in the formula, v ac,i,t And v ac,j,t The square of the voltage amplitude of the port i and the port j of the alternating current line in the period t respectively; p (P) ac,i,t And Q ac,i,t Active power and reactive power of an alternating current line port i in a t period are respectively; p (P) ac,j,t And Q ac,j,t Active power and reactive power of an alternating current line port j in a t period are respectively; l (L) ac,d,t Squaring the amplitude of the alternating current line current in the t period; r is R ac,d And X ac,d The resistance and reactance of the alternating current line are respectively; l (L) ac,d,max The maximum current-carrying capacity of the alternating current line;
3) DC line operation constraints
When the device
Figure BDA0004078295160000047
When (I)>
Figure BDA0004078295160000048
For the set of direct current line equipment, the ports at the two ends of the set are respectively i and j, and the operation constraint of the direct current line is as follows:
Figure BDA0004078295160000049
/>
Figure BDA00040782951600000410
Figure BDA00040782951600000411
Figure BDA00040782951600000412
in the formula, v dc,i,t And v dc,j,t The square of the voltage amplitude of the port i and the port j of the direct current line in the period t respectively; p (P) dc,i,t And P dc,j,t Active power of the direct current line port i and the direct current line port j in the t period respectively; l (L) dc,d,t Squaring the current amplitude of the direct current line at the t period; r is R dc,d The resistance of the direct current circuit; l (L) dc,d,max The maximum current-carrying capacity of the direct current circuit;
4) Voltage source type converter row constraint
When device D e D vsc At time D vsc For the set of voltage source type converter devices, if the ac side port and the dc side port are i and j, respectively, there are:
Figure BDA0004078295160000051
Figure BDA0004078295160000052
Figure BDA0004078295160000053
Figure BDA0004078295160000054
Figure BDA0004078295160000055
Figure BDA0004078295160000056
Figure BDA0004078295160000057
in the formula, v ac,i,t And v dc,j,t The square of the voltage amplitude of the alternating current side port and the direct current side port of the voltage source type converter at the t period is respectively obtained; v vsc,d,t The square of the virtual port voltage amplitude of the voltage source type converter at the time period t; l (L) vsc,d,t The square of the equivalent branch current amplitude of the voltage source converter in the t period; r is R vsc,d And X vsc,d The equivalent resistance and reactance of the voltage source type converter are respectively; p (P) ac,i,t And Q ac,i,t Active power and reactive power of the alternating current side port in the t period respectively; p (P) vsc,d,t And Q vsc,d,t Active power and reactive power of virtual ports of the voltage source type converter at the t period respectively; p (P) dc,j,t Active power of a direct current side port of the voltage source type converter in the t period;
Figure BDA0004078295160000058
an upper reactive compensation power limit; mu is the voltage utilization rate of the voltage source type converter, and is commonly taken to be 0.866; m is M vsc,d For modulation ratio, value interval [0,1 ]]；S vsc,N The capacity of the alternating current side of the voltage source type converter; />
Figure BDA0004078295160000059
Is the upper limit value of the power at the direct current side;
5) Energy storage operation constraint
Figure BDA00040782951600000510
Figure BDA00040782951600000511
Figure BDA00040782951600000512
Figure BDA00040782951600000513
/>
Figure BDA0004078295160000061
Figure BDA0004078295160000062
Wherein P is ESS,d,max The upper limit of the charge and discharge power of the stored energy is set; beta ch,d,t And beta dis,d,t Respectively storing energy charging and discharging state variables in a t period; e (E) d,t And is the electric quantity at the beginning of the energy storage t period; Δt is the adjacent scheduling period time interval; η (eta) ch,d And eta dis,d Respectively charging and discharging efficiency of energy storage; e (E) N,d Is the rated capacity of energy storage; Γ -shaped structure ESS,d Is a port set connected with the energy storage;
Figure BDA0004078295160000069
the upper limit of the charge and discharge times of the stored energy is set; p (P) o,t Is a system active power state variable associated to port o;
6) Photovoltaic inverter operation constraints
Figure BDA0004078295160000063
Figure BDA0004078295160000064
Figure BDA0004078295160000065
Wherein D is PV Is a collection of photovoltaic devices;
Figure BDA0004078295160000066
the power factor angle corresponding to the lowest power factor of the photovoltaic system; p (P) PV,d,t Photovoltaic active power output is carried out for the period t; q (Q) PV,d,t Reactive power compensation of the photovoltaic system is carried out for a period t; s is S inv,d Is the apparent capacity of the photovoltaic inverter; Γ -shaped structure PV,d Is a port set connected with a photovoltaic system; q (Q) o,t Is a system reactive power state variable associated to port o;
node balancing constraints: node power balance constraints include power conservation constraints and state variable consistency constraints;
1) Conservation of power constraint
Figure BDA0004078295160000067
Figure BDA0004078295160000068
Wherein: Γ -shaped structure n,r Is a set of ports associated with node r; n (N) node Is a system node set;
2) State variable consistency constraints
Figure BDA0004078295160000071
Figure BDA0004078295160000072
Wherein:
Figure BDA0004078295160000073
is the average value of the square of the port voltage amplitude connected with the node r; i Γ n,r The I represents the number of ports connected with the node r; v o,t The state variable is squared for the system voltage magnitude associated to port o.
Further, in the step 3, the optimization model constructed in the step 2 is solved based on the graph calculation method with the vertex as the center, an optimal scheduling strategy of the equipment is obtained, and the optimal scheduling of the ac/dc hybrid power distribution network is performed according to the optimal scheduling strategy.
Defining a device extension cost function (1-35) and a node indication function (1-36):
Figure BDA0004078295160000074
Figure BDA0004078295160000075
in omega d Vector x composed of device d decision variables to satisfy device operation constraints d Vector y consisting of port state variables connected to device d d Is a feasible region of (2); psi n Vector y composed of port state variables connected to node n for satisfying node operation constraint n Is a feasible region of (2);
the optimization model of the alternating current-direct current hybrid power distribution network based on the graph model is equivalent to:
Figure BDA0004078295160000076
wherein y is a vector formed by all port state variables of the system;
based on the decomposition concept of ADMM, equation (1-37) is equivalent to:
Figure BDA0004078295160000077
where z is the mirror image of vector yA variable; z n A vector of mirror variables for ports associated with node n;
the equality constraint for relaxation formulas (1-38) is:
Figure BDA0004078295160000081
wherein x is a vector formed by decision variables of all equipment of the system; lambda is the system Lagrangian multiplier vector; l (·) is an augmented Lagrangian function, ρ is a penalty factor;
the alternating iterative solution formula based on ADMM to obtain the optimization problem formula (1-39) is:
{x k+1 ,y k+1 }＝argminL(x,y,z k ,λ k ) (1-40)
z k+1 ＝argminL(x k+1 ,y k+1 ,z,λ k ) (1-41)
λ k+1 ＝λ k +ρ(y k+1 -z k+1 ) (1-42)
wherein k is the current iteration solving times; x is x k+1 Solving vectors formed by all obtained equipment decision variables for the k+1st iteration; y is k+1 A vector of all port state variables updated for the k+1st iteration; z k+1 And z k Vectors composed of all mirror variables updated for the k+1th and k iterations respectively; lambda (lambda) k+1 And lambda (lambda) k The updated Lagrangian multiplier vector for the k+1th and k iterations;
decomposing the formulas (1-40) - (1-42) to the respective devices and the respective nodes according to the formulas (1-1) - (1-2):
Figure BDA0004078295160000082
Figure BDA0004078295160000083
/>
Figure BDA0004078295160000084
Wherein:
Figure BDA0004078295160000085
solving the vector formed by the obtained decision variables of the equipment d for the k+1st iteration; />
Figure BDA0004078295160000086
A vector of port state variables associated with device d updated for the k+1st iteration; />
Figure BDA0004078295160000087
And->
Figure BDA0004078295160000088
The vector is formed by mirror variables connected with the node n, which are updated for the k+1th iteration and the k iteration respectively; />
Figure BDA0004078295160000089
And->
Figure BDA00040782951600000810
The lagrangian multiplier vector associated with node n updated for the k+1th and k-th iterations, respectively; />
Figure BDA00040782951600000811
Updating the lagrangian multiplier vector associated with device d for the kth iteration;
because the associated port state variables of each device are independent of each other, equations (1-43) can be solved in parallel; the state variables of the ports associated with each node are mutually independent, so that the formulas (1-44) can be solved in parallel, and the formulas (1-45) can be calculated in parallel;
the node update optimization problem is a quadratic convex optimization problem, and constraint formulas (1-31) - (1-34) are equality constraints, so that an analytical solution of the node update optimization problem is obtained according to the Lagrangian multiplier method:
Figure BDA0004078295160000091
wherein: Γ -shaped structure n Is a set of ports associated with node n; i Γ n I represents the number of ports associated with node n;
Figure BDA0004078295160000092
Figure BDA0004078295160000093
the information of the active power, the reactive power and the voltage amplitude square state of the port o updated after parallel solving by each device in the formulas (1-43) is the k+1th iteration; />
Figure BDA0004078295160000094
The information of the port active power, reactive power and voltage amplitude square state updated after the parallel solution of each node of the formulas (1-44) is carried out for the (k+1) th iteration; / >
Figure BDA0004078295160000095
Figure BDA0004078295160000096
Lagrangian multiplier information updated by equations (1-45) for the kth iteration; alpha k+1 、β k+1 And gamma k+1 Intermediate parameters in the k+1st iteration solution;
vector y in formula (1-44) k+1 、z k+1 、λ k+1 And the scalar relationships in its analytical solutions (1-46) are as follows:
Figure BDA0004078295160000097
after solving the analytic solution formula (1-46) of the formula (1-44), carrying out parallel optimization calculation on each node by the formula (1-46) to accelerate the iterative solution process;
defining node original residual error after k+1 iterations
Figure BDA0004078295160000098
And k+1 iterations of dual residual +.>
Figure BDA0004078295160000099
As criteria for iterative convergence of equations (1-43), (1-46), (1-44):
Figure BDA00040782951600000910
/>
Figure BDA00040782951600000911
in the method, in the process of the invention,
Figure BDA00040782951600000912
solving the vector formed by the obtained equipment decision variables connected with the node n for the k+1st iteration;
when the original residual and the dual residual meet the formulas (1-50), the node is converged in an iteration mode, when all nodes of the system are converged, the system is converged, iteration is finished, and the optimal scheduling strategy of each device is output;
Figure BDA0004078295160000101
wherein: epsilon is iteration convergence precision;
in summary, the graph calculation steps of the graph structure-based alternating current-direct current hybrid power distribution network optimization model are as follows:
(1) Setting the iteration number k=0, giving the initial information z k And lambda (lambda) k ；
(2) Will z k And lambda (lambda) k Carrying in the formulas (1-43), solving the formulas (1-43) in parallel, and updating the vector x formed by the decision variables of the equipment decision k+1 Vector y composed of port state variables k+1 ；
(3) Will x k+1 And y k+1 Carrying in (1-46), calculating vector z formed by mirror variables updated by nodes k+1 ；
(4) Will y k+1 And z k+1 Carry-in (1-45), update Lagrangian multiplier vector lambda k+1 ；
(5) Will z k 、z k+1 And x k+1 Carrying out formulas (1-48) and (1-49), and calculating node convergence criterion
Figure BDA0004078295160000102
And->
Figure BDA0004078295160000103
(6) According to
Figure BDA0004078295160000104
And->
Figure BDA0004078295160000105
Judging whether all nodes of the system are converged, and if so, outputting an optimal scheduling strategy; otherwise, k=k+1, go (2).
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
1) The constructed AC/DC hybrid power distribution network graph model can completely represent equipment and network of the AC/DC hybrid power distribution network, realizes unified modeling, and is convenient for plug and play of user equipment;
2) The adopted second-order cone relaxation line equipment model has good cone relaxation precision in graph calculation, and can improve the solving efficiency of the model to a certain extent;
3) The graph calculation taking the vertex as the center can be suitable for the optimization calculation of the AC/DC hybrid power distribution network under the condition of large-scale photovoltaic energy storage access, the distributed calculation of each device is completely realized, the privacy of a user is protected, meanwhile, the solving efficiency and the resolvability of the model are improved, and the method has higher application value.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a topology diagram of an example of a 50-node AC/DC hybrid power distribution network with high-proportion optical storage;
FIG. 3 is a graph of the reactive power variation of the photovoltaic inverter;
FIG. 4 (a) is a graph showing the change of the stored energy using a charge-discharge strategy; (b) adopting a two-charge and two-discharge energy storage electric quantity change curve graph;
fig. 5 (a) voltage source converter reactive power variation curve; (b) a voltage source converter active power profile;
fig. 6 is a graph of iterative residual variation for the calculation method.
Detailed Description
The invention is further illustrated in the following, in conjunction with the accompanying drawings and detailed embodiments. It is to be understood that these examples are for illustrative purposes only and not for limiting the scope of the invention, and that various equivalent modifications to the invention will fall within the scope of the claims appended hereto, as viewed by a person skilled in the art.
As shown in fig. 1, the invention provides an ac/dc hybrid power distribution network optimization scheduling method based on graph calculation, which comprises the following steps:
step 1: introducing a port concept, and establishing an alternating current-direct current hybrid power distribution network graph model;
step 2: associating state variables in the AC/DC hybrid power distribution network system with ports introduced in the graph model established in the step 1, associating decision variables in the AC/DC hybrid power distribution network system with devices, and establishing an AC/DC hybrid power distribution network coordination optimization model based on the graph model;
Step 3: and (3) solving the optimization model constructed in the step (2) based on a graph calculation method taking the vertex as a center, acquiring an optimal scheduling strategy of the equipment, and carrying out optimal scheduling of the AC/DC hybrid power distribution network according to the optimal scheduling strategy.
Further, in the step 1, a concept of a port is introduced, and an ac/dc hybrid power distribution network graph model is built, and the specific method is as follows:
introducing the concept of ports, regarding the ports as edges of a graph, regarding nodes and equipment as vertexes of the graph, and establishing a graph model of the alternating current-direct current hybrid power distribution network, wherein the vertexes in the graph model, namely the nodes, the equipment and the edges, namely the ports are expressed as follows:
the device comprises: the system comprises alternating current equipment, direct current equipment and coupling equipment, wherein an upper power grid, an alternating current line, an alternating current load and photovoltaic and energy storage accessed into the alternating current system in an alternating current system are all abstracted into the alternating current equipment; the direct current circuit, the direct current load and the energy storage and light Fu Jun connected into the direct current system are abstracted into direct current equipment; the coupling equipment is a voltage source type converter and is indicated by a subscript d;
and (3) node: the method is divided into an alternating current node and a direct current node, so that lossless energy exchange among similar associated ports is realized, and the lossless energy exchange is represented by a subscript n;
The port: each device comprises one or more ports, wherein the vertexes formed by the devices and the nodes are connected through the ports, the ports are divided into alternating current ports and direct current ports, and the alternating current ports and the direct current ports are also called edges and are denoted by subscript o;
ports in the alternating current-direct current hybrid power distribution network graph model are organized according to nodes or are organized according to equipment, when the ports are organized according to the nodes, intersections of ports connected with different nodes are empty, and a union of ports connected with all the nodes is a complete set; when the equipment is organized, the intersection sets of the ports connected with different equipment are empty, the union set of the ports connected with all the equipment is a complete set, and if the complete set of the ports is O, the above properties are expressed as follows:
Figure BDA0004078295160000121
Figure BDA0004078295160000122
wherein, Γ n,r And Γ n,s Respectively, are port sets connected with a node r and a node s, N n As the total number of nodes Γ d,e And Γ d,h N for the port set connected to device e and device h d As a total number of devices,
Figure BDA0004078295160000123
representing an empty set.
Further, in the step 2, the state variables in the system are all associated to the ports introduced in the graph model established in the step 1, the decision variables in the system are associated to the devices, and the optimization model of the ac/dc hybrid power distribution network based on the graph model is constructed as follows:
objective function: the aim is to minimize the sum of the running cost of each device in the AC/DC hybrid power distribution network;
Figure BDA0004078295160000124
Wherein: x is x d C is a decision variable associated to device d d As a cost function of device d;
the cost function of each device is as follows:
Figure BDA0004078295160000125
wherein: t is a scheduling period subscript; t is the total scheduling period; c t The time-sharing electricity price is the electricity purchasing price of the upper-level power grid; p (P) sub,d,t The power purchasing power is the power purchasing power of the upper power grid; d (D) sub The method is a superior power grid equipment set;
Figure BDA0004078295160000126
maintaining a cost coefficient for energy storage operation; p (P) ch,d,t And P dis,d,t Respectively charging and discharging power of the energy storage equipment in the t period; lambda (lambda) ess,d A depreciated cost factor for the energy storage device; u (u) ess,d,t Switching state variables for energy storage charge and discharge in a t period; d (D) ESS Is an energy storage device set; d is a set of devices in the AC/DC hybrid power distribution network; the upper power grid equipment cost is the sum of the electricity purchasing cost of each period; the energy storage operation cost comprises operation maintenance cost and depreciation cost; the cost of other equipment is 0;
device operation constraints: the equipment operation constraint comprises an upper-level power grid purchase power constraint, an alternating current line and direct current line operation constraint, a voltage source type converter operation constraint, an energy storage operation constraint and a photovoltaic inverter reactive compensation constraint in an alternating current system;
1) Superior grid purchase power constraint
Figure BDA0004078295160000131
Figure BDA0004078295160000132
Wherein P is sub,d,t And Q sub,d,t Active and reactive power injection power of the upper power grid equipment in the period t are respectively;
Figure BDA0004078295160000133
And P sub,d Injecting upper and lower limits of active power into an upper power grid respectively; />
Figure BDA0004078295160000134
And Q sub,d Injecting reactive power upper and lower limits for the upper power grid respectively; p (P) ac,o,t And Q ac,o,t Active power and reactive power of the alternating current port o in the t period respectively; Γ -shaped structure sub,d Is a port set connected with an upper power grid;
2) Ac line operation constraints
When the device
Figure BDA0004078295160000135
When (I)>
Figure BDA0004078295160000136
For the AC line equipment set, if the ports at the two ends are i and j respectively, the second order cone form constraint of the AC line based on the graph model is as follows:
Figure BDA0004078295160000137
Figure BDA0004078295160000138
/>
Figure BDA0004078295160000139
Figure BDA00040782951600001310
in the formula, v ac,i,t And v ac,j,t The square of the voltage amplitude of the port i and the port j of the alternating current line in the period t respectively; p (P) ac,i,t And Q ac,i,t Active power and reactive power of an alternating current line port i in a t period are respectively; p (P) ac,j,t And Q ac,j,t Active power and reactive power of an alternating current line port j in a t period are respectively; l (L) ac,d,t Squaring the amplitude of the alternating current line current in the t period; r is R ac,d And X ac,d The resistance and reactance of the alternating current line are respectively; l (L) ac,d,max The maximum current-carrying capacity of the alternating current line;
3) DC line operation constraints
When the device
Figure BDA00040782951600001311
When (I)>
Figure BDA00040782951600001312
For the set of direct current line equipment, the ports at the two ends of the set are respectively i and j, and the operation constraint of the direct current line is as follows:
Figure BDA00040782951600001313
Figure BDA0004078295160000141
Figure BDA0004078295160000142
Figure BDA0004078295160000143
in the formula, v dc,i,t And v dc,j,t The square of the voltage amplitude of the port i and the port j of the direct current line in the period t respectively; p (P) dc,i,t And P dc,j,t Active power of the direct current line port i and the direct current line port j in the t period respectively; l (L) dc,d,t Squaring the current amplitude of the direct current line at the t period; r is R dc,d The resistance of the direct current circuit; l (L) dc,d,max The maximum current-carrying capacity of the direct current circuit;
4) Voltage source type converter row constraint
When device D e D vsc At time D vsc For the set of voltage source type converter devices, if the ac side port and the dc side port are i and j, respectively, there are:
Figure BDA0004078295160000144
Figure BDA0004078295160000145
Figure BDA0004078295160000146
Figure BDA0004078295160000147
Figure BDA0004078295160000148
Figure BDA0004078295160000149
Figure BDA00040782951600001410
in the formula, v ac,i,t And v dc,j,t The square of the voltage amplitude of the alternating current side port and the direct current side port of the voltage source type converter at the t period is respectively obtained; v vsc,d,t The square of the virtual port voltage amplitude of the voltage source type converter at the time period t; l (L) vsc,d,t The square of the equivalent branch current amplitude of the voltage source converter in the t period; r is R vsc,d And X vsc,d The equivalent resistance and reactance of the voltage source type converter are respectively; p (P) ac,i,t And Q ac,i,t Active power and reactive power of the alternating current side port in the t period respectively; p (P) vsc,d,t And Q vsc,d,t Active power and reactive power of virtual ports of the voltage source type converter at the t period respectively; p (P) dc,j,t Active power of a direct current side port of the voltage source type converter in the t period;
Figure BDA00040782951600001411
an upper reactive compensation power limit; mu is the voltage utilization rate of the voltage source type converter, and is commonly taken to be 0.866; m is M vsc,d For modulation ratio, value interval [0,1 ]]；S vsc,N The capacity of the alternating current side of the voltage source type converter; />
Figure BDA0004078295160000151
Is the upper limit value of the power at the direct current side;
5) Energy storage operation constraint
Figure BDA0004078295160000152
Figure BDA0004078295160000153
Figure BDA0004078295160000154
Figure BDA0004078295160000155
Figure BDA0004078295160000156
Figure BDA0004078295160000157
Wherein P is ESS,d,max The upper limit of the charge and discharge power of the stored energy is set; beta ch,d,t And beta dis,d,t Respectively storing energy charging and discharging state variables in a t period; e (E) d,t And is the electric quantity at the beginning of the energy storage t period; Δt is the adjacent scheduling period time interval; η (eta) ch,d And eta dis,d Respectively is stored energy charge and discharge efficiency; e (E) N,d Is the rated capacity of energy storage; Γ -shaped structure ESS,d Is a port set connected with the energy storage;
Figure BDA00040782951600001512
the upper limit of the charge and discharge times of the stored energy is set; p (P) o,t Is a system active power state variable associated to port o;
6) Photovoltaic inverter operation constraints
Figure BDA0004078295160000158
Figure BDA0004078295160000159
Figure BDA00040782951600001510
Wherein D is PV Is a collection of photovoltaic devices;
Figure BDA00040782951600001511
the power factor angle corresponding to the lowest power factor of the photovoltaic system; p (P) PV,d,t Photovoltaic active power output is carried out for the period t; q (Q) PV,d,t Reactive power compensation of the photovoltaic system is carried out for a period t; s is S inv,d Is the apparent capacity of the photovoltaic inverter; Γ -shaped structure PV,d Is a port set connected with a photovoltaic system; q (Q) o,t Is a system reactive power state variable associated to port o;
node balancing constraints: node power balance constraints include power conservation constraints and state variable consistency constraints;
1) Conservation of power constraint
Figure BDA0004078295160000161
/>
Figure BDA0004078295160000162
Wherein: Γ -shaped structure n,r Is a set of ports associated with node r; n (N) node Is a system node set;
2) State variable consistency constraints
Figure BDA0004078295160000163
Figure BDA0004078295160000164
Wherein:
Figure BDA0004078295160000165
is the average value of the square of the port voltage amplitude connected with the node r; i Γ n,r The I represents the number of ports connected with the node r; v o,t The state variable is squared for the system voltage magnitude associated to port o.
Further, in the step 3, the optimization model constructed in the step 2 is solved based on the graph calculation method with the vertex as the center, an optimal scheduling strategy of the equipment is obtained, and the optimal scheduling of the ac/dc hybrid power distribution network is performed according to the optimal scheduling strategy.
Defining a device extension cost function (1-35) and a node indication function (1-36):
Figure BDA0004078295160000166
Figure BDA0004078295160000167
in omega d Vector x composed of device d decision variables to satisfy device operation constraints d Vector y consisting of port state variables connected to device d d Is a feasible region of (2); psi n Vector y composed of port state variables connected to node n for satisfying node operation constraint n Is a feasible region of (2);
the optimization model of the alternating current-direct current hybrid power distribution network based on the graph model is equivalent to:
Figure BDA0004078295160000171
wherein y is a vector formed by all port state variables of the system;
based on the decomposition concept of ADMM, equation (1-37) is equivalent to:
Figure BDA0004078295160000172
wherein z is a mirror variable of vector y; z n A vector of mirror variables for ports associated with node n;
the equality constraint for relaxation formulas (1-38) is:
Figure BDA0004078295160000173
wherein x is a vector formed by decision variables of all equipment of the system; lambda is the system Lagrangian multiplier vector; l (·) is an augmented Lagrangian function, ρ is a penalty factor;
The alternating iterative solution formula based on ADMM to obtain the optimization problem formula (1-39) is:
{x k+1 ,y k+1 }＝argminL(x,y,z k ,λ k ) (1-40)
z k+1 ＝argminL(x k+1 ,y k+1 ,z,λ k ) (1-41)
λ k+1 ＝λ k +ρ(y k+1 -z k+1 ) (1-42)
wherein k is the current iteration solving times; x is x k+1 Solving vectors formed by all obtained equipment decision variables for the k+1st iteration; y is k+1 A vector of all port state variables updated for the k+1st iteration; z k+1 And z k Vectors composed of all mirror variables updated for the k+1th and k iterations respectively; lambda (lambda) k+1 And lambda (lambda) k The updated Lagrangian multiplier vector for the k+1th and k iterations;
decomposing the formulas (1-40) - (1-42) to the respective devices and the respective nodes according to the formulas (1-1) - (1-2):
Figure BDA0004078295160000174
Figure BDA0004078295160000175
Figure BDA0004078295160000181
wherein:
Figure BDA0004078295160000182
solving the vector formed by the obtained decision variables of the equipment d for the k+1st iteration; />
Figure BDA0004078295160000183
A vector of port state variables associated with device d updated for the k+1st iteration; />
Figure BDA0004078295160000184
And->
Figure BDA0004078295160000185
The vector is formed by mirror variables connected with the node n, which are updated for the k+1th iteration and the k iteration respectively; />
Figure BDA0004078295160000186
And->
Figure BDA0004078295160000187
The lagrangian multiplier vector associated with node n updated for the k+1th and k-th iterations, respectively; />
Figure BDA0004078295160000188
Updating the lagrangian multiplier vector associated with device d for the kth iteration;
because the associated port state variables of each device are independent of each other, equations (1-43) can be solved in parallel; the state variables of the ports associated with each node are mutually independent, so that the formulas (1-44) can be solved in parallel, and the formulas (1-45) can be calculated in parallel;
The node update optimization problem is a quadratic convex optimization problem, and constraint formulas (1-31) - (1-34) are equality constraints, so that an analytical solution of the node update optimization problem is obtained according to the Lagrangian multiplier method:
Figure BDA0004078295160000189
wherein: Γ -shaped structure n Is a set of ports associated with node n; i Γ n I represents the number of ports associated with node n;
Figure BDA00040782951600001810
Figure BDA00040782951600001811
the information of the active power, the reactive power and the voltage amplitude square state of the port o updated after parallel solving by each device in the formulas (1-43) is the k+1th iteration; />
Figure BDA00040782951600001812
The information of the port active power, reactive power and voltage amplitude square state updated after the parallel solution of each node of the formulas (1-44) is carried out for the (k+1) th iteration; />
Figure BDA00040782951600001813
Figure BDA00040782951600001814
Lagrangian multiplier information updated by equations (1-45) for the kth iteration; alpha k+1 、β k+1 And gamma k+1 Intermediate parameters in the k+1st iteration solution; />
Vector y in formula (1-44) k+1 、z k+1 、λ k+1 And the scalar relationships in its analytical solutions (1-46) are as follows:
Figure BDA00040782951600001815
after solving the analytic solution formula (1-46) of the formula (1-44), carrying out parallel optimization calculation on each node by the formula (1-46) to accelerate the iterative solution process;
defining node original residual error after k+1 iterations
Figure BDA0004078295160000191
And k+1 iterations of dual residual +.>
Figure BDA0004078295160000192
As criteria for iterative convergence of equations (1-43), (1-46), (1-44):
Figure BDA0004078295160000193
Figure BDA0004078295160000194
in the method, in the process of the invention,
Figure BDA0004078295160000195
solving the vector formed by the obtained equipment decision variables connected with the node n for the k+1st iteration;
When the original residual and the dual residual meet the formulas (1-50), the node is converged in an iteration mode, when all nodes of the system are converged, the system is converged, iteration is finished, and the optimal scheduling strategy of each device is output;
Figure BDA0004078295160000196
wherein: epsilon is iteration convergence precision;
in summary, the graph calculation steps of the graph structure-based alternating current-direct current hybrid power distribution network optimization model are as follows:
(1) Setting the iteration number k=0, giving the initial information z k And lambda (lambda) k ；
(2) Will z k And lambda (lambda) k Carrying in the formulas (1-43), solving the formulas (1-43) in parallel, and updating the vector x formed by the decision variables of the equipment decision k+1 Vector y composed of port state variables k+1 ；
(3) Will x k+1 And y k+1 Carrying in (1-46), calculating vector z formed by mirror variables updated by nodes k+1 ；
(4) Will y k+1 And z k+1 Carry-in (1-45), update Lagrangian multiplier vector lambda k+1 ；
(5) Will z k 、z k+1 And x k+1 Carrying out formulas (1-48) and (1-49), and calculating node convergence criterion
Figure BDA0004078295160000197
And->
Figure BDA0004078295160000198
(6) According to
Figure BDA0004078295160000199
And->
Figure BDA00040782951600001910
Judging whether all nodes of the system are converged, and if so, outputting an optimal scheduling strategy; otherwise, k=k+1, go (2).
Calculation case analysis
The 50-node ac/dc hybrid power distribution network with high-proportion optical storage shown in fig. 2 is taken as an example. The peak values of the active load and the reactive load of the system are 4945kW and 2300kVar respectively, and the voltage of the root node is 1.0pu; the upper limit of reactive compensation of the voltage source type converter is 300kVar, and the equivalent resistance and reactance are respectively 0.5 omega and 1.5 omega; for simulating a large-scale access scene of distributed photovoltaic and energy storage, 20 distributed photovoltaic are accessed in total, and the capacity of a total assembly unit is 2400kW; 24 distributed energy storage stations are connected, and the capacity of the total assembly machine is 1330kWh. The abstract graph model of the system contains 50 nodes, 144 devices, 193 ports in total, and total schedule period t=24.
The invention firstly analyzes the equipment scheduling strategy: setting the absolute convergence accuracy epsilon=0.001 of the iterative process, and converging by 295 iterations, wherein the controllable resource scheduling strategy is shown in fig. 3-5.
As can be seen from fig. 3, due to the limitation of the lowest power factor of the photovoltaic inverter, the reactive power of the photovoltaic inverter increases as the photovoltaic output increases, wherein most of the photovoltaic inverter emits reactive power to the ac system to achieve in-situ balancing of reactive power in the ac system; in order to ensure the transmission of the photovoltaic active power, a few photovoltaic inverters absorb part of reactive power from an alternating current system, so that the condition that the voltage of the photovoltaic grid-connected node is out of limit is avoided.
As can be seen from fig. 4, since the depreciation cost of the energy storage in the model is directly related to the energy storage capacity, most of the energy storage is operated by a one-charge-one-discharge mechanism, and only a small part of the energy storage with a smaller depreciation cost coefficient is operated by a two-charge-two-discharge mechanism. The energy storage is operated by adopting a 1 charge-1 discharge mechanism, the main charge time is concentrated between 2:00 and 4:00 in the early morning when the electricity purchasing price is lower, and the discharge time is mainly concentrated between 18:00 and 20:00 when the load demand is high and the electricity price is high; the energy storage operated by adopting the 2 charge and 2 discharge mechanism increases the discharge of 1 time in the midday electricity consumption peak 9:00-12:00 and the charge of 1 time of the photovoltaic output peak 14:00-16:00, so that the economical efficiency of the system operation is further improved.
As can be seen from fig. 5 (a), since the voltage source converters in the example are all relatively close to the feeder line end, the voltage source converters basically provide reactive power compensation for the ac system, so as to reduce the power transmission from the head end to the end, reduce the net loss, and improve the economical efficiency of the system operation; as can be seen from fig. 5 (b), in the period of 10:00-15:00 where the photovoltaic output is high, the dc system transmits excessive active power to the ac system through the voltage source converter; and in the period of low photovoltaic output, the alternating current system transmits active power to the direct current system so as to support the direct current load.
Next, when the absolute convergence accuracy epsilon=0.001 is taken, the dual residual of the original residual of the convergence process of the graph calculation method is shown in fig. 6, and the operation cost pair of the centralized calculation method is shown in table 1.
Table 1 comparison of operating costs for different calculation methods
Figure BDA0004078295160000201
As can be seen from fig. 6, the graph calculation converges after 295 iterations, and has better convergence as a whole; however, as the number of iterations increases, the convergence speed gradually decreases, especially after 150 times, and becomes very slow, and if the convergence speed needs to be increased, an improved method of adaptive step size ADMM may be adopted. As can be seen from table 1, the total running cost of the system calculated by the graph calculation is quite close to that of the centralized calculation, and the error is only 0.069%. And because the parallel computing capability of the graph computation makes the computation efficiency of the graph computation significantly higher than that of the centralized computation, and because the graph computation decomposes a large model, the resolvability of the graph computation is also significantly improved compared with that of the centralized computation.
Then, the graph calculation optimization costs and the solving efficiencies at different absolute convergence accuracies are shown in table 2.
Table 2 graph calculation optimization costs for different convergence accuracies
Figure BDA0004078295160000211
As can be seen from table 2, as the absolute convergence accuracy decreases, the model optimization cost gradually decreases, i.e., the optimality increases; meanwhile, as the absolute convergence accuracy decreases, the iteration number increases, the solving efficiency relatively decreases, but the solving efficiency of the graph calculation as a whole is significantly lower than that of the centralized calculation. Therefore, the graph calculation has wider application prospect under the condition of large-scale access of future distributed resources.
The intelligent bridge span design method based on the generation of the antagonistic neural network is used for completing intelligent span design of the overpass bridge and the navigation bridge. However, the above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereto, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention.

Claims (4)

1. The alternating current-direct current hybrid power distribution network optimal scheduling method based on graph calculation is characterized by comprising the following steps of:
Step 1: introducing a port concept, and establishing an alternating current-direct current hybrid power distribution network graph model;
step 2: associating state variables in the AC/DC hybrid power distribution network system with ports introduced in the graph model established in the step 1, associating decision variables in the AC/DC hybrid power distribution network system with devices, and establishing an AC/DC hybrid power distribution network coordination optimization model based on the graph model;
step 3: and (3) solving the optimization model constructed in the step (2) based on a graph calculation method taking the vertex as a center, acquiring an optimal scheduling strategy of the equipment, and carrying out optimal scheduling of the AC/DC hybrid power distribution network according to the optimal scheduling strategy.
2. The optimal scheduling method for the alternating current-direct current hybrid power distribution network based on graph calculation according to claim 1 is characterized in that in the step 1, a port concept is introduced, and an alternating current-direct current hybrid power distribution network graph model is built, wherein the method comprises the following steps:
introducing the concept of ports, regarding the ports as edges of a graph, regarding nodes and equipment as vertexes of the graph, and establishing a graph model of the alternating current-direct current hybrid power distribution network, wherein the vertexes in the graph model, namely the nodes, the equipment and the edges, namely the ports are expressed as follows:
the device comprises: the system comprises alternating current equipment, direct current equipment and coupling equipment, wherein an upper power grid, an alternating current line, an alternating current load and photovoltaic and energy storage accessed into the alternating current system in an alternating current system are all abstracted into the alternating current equipment; the direct current circuit, the direct current load and the energy storage and light Fu Jun connected into the direct current system are abstracted into direct current equipment; the coupling equipment is a voltage source type converter and is indicated by a subscript d;
And (3) node: the method is divided into an alternating current node and a direct current node, so that lossless energy exchange among similar associated ports is realized, and the lossless energy exchange is represented by a subscript n;
the port: each device comprises one or more ports, wherein the vertexes formed by the devices and the nodes are connected through the ports, the ports are divided into alternating current ports and direct current ports, and the alternating current ports and the direct current ports are also called edges and are denoted by subscript o;
ports in the alternating current-direct current hybrid power distribution network graph model are organized according to nodes or are organized according to equipment, when the ports are organized according to the nodes, intersections of ports connected with different nodes are empty, and a union of ports connected with all the nodes is a complete set; when the equipment is organized, the intersection sets of the ports connected with different equipment are empty, the union set of the ports connected with all the equipment is a complete set, and if the complete set of the ports is O, the above properties are expressed as follows:
Figure FDA0004078295150000011
Figure FDA0004078295150000012
wherein, Γ n,r And Γ n,s Respectively, are port sets connected with a node r and a node s, N n As the total number of nodes Γ d,e And Γ d,h N for the port set connected to device e and device h d As a total number of devices,
Figure FDA0004078295150000021
representing an empty set.
3. The method for optimal scheduling of ac/dc hybrid distribution network based on graph calculation according to claim 2, wherein in step 2, state variables in the system are all associated to ports introduced in the graph model established in step 1, decision variables in the system are associated to devices, and an ac/dc hybrid distribution network optimal model based on the graph model is constructed as follows:
Objective function: the aim is to minimize the sum of the running cost of each device in the AC/DC hybrid power distribution network;
Figure FDA0004078295150000022
/>
wherein x is d C is a decision variable associated to device d d As a cost function of device d;
the cost function of each device is as follows:
Figure FDA0004078295150000023
wherein t is a scheduling period subscript; t is the total scheduling period; c t The time-sharing electricity price is the electricity purchasing price of the upper-level power grid; p (P) sub,d,t The power purchasing power is the power purchasing power of the upper power grid; d (D) sub Is a superior power gridA set of devices;
Figure FDA0004078295150000024
maintaining a cost coefficient for energy storage operation; p (P) ch,d,t And P dis,d,t Respectively charging and discharging power of the energy storage equipment in the t period; lambda (lambda) ess,d A depreciated cost factor for the energy storage device; u (u) ess,d,t Switching state variables for energy storage charge and discharge in a t period; d (D) ESS Is an energy storage device set; d is a set of devices in the AC/DC hybrid power distribution network; the upper power grid equipment cost is the sum of the electricity purchasing cost of each period; the energy storage operation cost comprises operation maintenance cost and depreciation cost; the cost of other equipment is 0;
the equipment operation constraint comprises an upper-level power grid purchase power constraint, an alternating current line and direct current line operation constraint, a voltage source type converter operation constraint, an energy storage operation constraint and a photovoltaic inverter reactive compensation constraint in an alternating current system;
1) Superior grid purchase power constraint
Figure FDA0004078295150000025
Figure FDA0004078295150000031
Wherein P is sub,d,t And Q sub,d,t Active and reactive power injection power of the upper power grid equipment in the period t are respectively;
Figure FDA0004078295150000032
and P sub,d Injecting upper and lower limits of active power into an upper power grid respectively; />
Figure FDA0004078295150000033
And Q sub,d Injecting reactive power upper and lower limits for the upper power grid respectively; p (P) ac,o,t And Q ac,o,t Respectively t time interval alternating current portso active and reactive power; Γ -shaped structure sub,d Is a port set connected with an upper power grid;
2) Ac line operation constraints
When the device
Figure FDA0004078295150000034
When (I)>
Figure FDA0004078295150000035
For the AC line equipment set, if the ports at the two ends are i and j respectively, the second order cone form constraint of the AC line based on the graph model is as follows:
Figure FDA0004078295150000036
Figure FDA0004078295150000037
Figure FDA0004078295150000038
Figure FDA0004078295150000039
in the formula, v ac,i,t And v ac,j,t The square of the voltage amplitude of the port i and the port j of the alternating current line in the period t respectively; p (P) ac,i,t And Q ac,i,t Active power and reactive power of an alternating current line port i in a t period are respectively; p (P) ac,j,t And Q ac,j,t Active power and reactive power of an alternating current line port j in a t period are respectively; l (L) ac,d,t Squaring the amplitude of the alternating current line current in the t period; r is R ac,d And X ac,d The resistance and reactance of the alternating current line are respectively; l (L) ac,d,max The maximum current-carrying capacity of the alternating current line;
3) DC line operation constraints
When the device
Figure FDA00040782951500000310
When (I)>
Figure FDA00040782951500000311
For the set of direct current line equipment, the ports at the two ends of the set are respectively i and j, and the operation constraint of the direct current line is as follows:
Figure FDA00040782951500000312
Figure FDA00040782951500000313
Figure FDA00040782951500000314
Figure FDA0004078295150000041
in the formula, v dc,i,t And v dc,j,t The square of the voltage amplitude of the port i and the port j of the direct current line in the period t respectively; p (P) dc,i,t And P dc,j,t Active power of the direct current line port i and the direct current line port j in the t period respectively; l (L) dc,d,t Squaring the current amplitude of the direct current line at the t period; r is R dc,d The resistance of the direct current circuit; l (L) dc,d,max The maximum current-carrying capacity of the direct current circuit;
4) Voltage source type converter row constraint
When device D e D vsc At time D vsc For the set of voltage source type converter devices, if the ac side port and the dc side port are i and j, respectively, there are:
Figure FDA0004078295150000042
Figure FDA0004078295150000043
Figure FDA0004078295150000044
Figure FDA0004078295150000045
Figure FDA0004078295150000046
Figure FDA0004078295150000047
Figure FDA0004078295150000048
in the formula, v ac,i,t And v dc,j,t The square of the voltage amplitude of the alternating current side port and the direct current side port of the voltage source type converter at the t period is respectively obtained; v vsc,d,t The square of the virtual port voltage amplitude of the voltage source type converter at the time period t; l (L) vsc,d,t The square of the equivalent branch current amplitude of the voltage source converter in the t period; r is R vsc,d And X vsc,d The equivalent resistance and reactance of the voltage source type converter are respectively; p (P) ac,i,t And Q ac,i,t Active power and reactive power of the alternating current side port in the t period respectively; p (P) vsc,d,t And Q vsc,d,t Active power and reactive power of virtual ports of the voltage source type converter at the t period respectively; p (P) dc,j,t Active power of a direct current side port of the voltage source type converter in the t period;
Figure FDA0004078295150000049
an upper reactive compensation power limit; mu is the voltage utilization rate of the voltage source type converter, and is commonly taken to be 0.866; m is M vsc,d For modulation ratio, value interval [0,1 ]]；S vsc,N The capacity of the alternating current side of the voltage source type converter; />
Figure FDA00040782951500000410
Is the upper limit value of the power at the direct current side;
5) Energy storage operation constraint
Figure FDA0004078295150000051
Figure FDA0004078295150000052
Figure FDA0004078295150000053
Figure FDA0004078295150000054
Figure FDA0004078295150000055
Figure FDA0004078295150000056
Wherein P is ESS,d,max The upper limit of the charge and discharge power of the stored energy is set; beta ch,d,t And beta dis,d,t Respectively t time periods of energy storageCharge and discharge state variables; e (E) d,t And is the electric quantity at the beginning of the energy storage t period; Δt is the adjacent scheduling period time interval; η (eta) ch,d And eta dis,d Respectively charging and discharging efficiency of energy storage; e (E) N,d Is the rated capacity of energy storage; Γ -shaped structure ESS,d Is a port set connected with the energy storage;
Figure FDA0004078295150000057
the upper limit of the charge and discharge times of the stored energy is set; p (P) o,t Is a system active power state variable associated to port o;
6) Photovoltaic inverter operation constraints
Figure FDA0004078295150000058
Figure FDA0004078295150000059
Figure FDA00040782951500000510
Wherein D is PV Is a collection of photovoltaic devices;
Figure FDA00040782951500000511
the power factor angle corresponding to the lowest power factor of the photovoltaic system; p (P) PV,d,t Photovoltaic active power output is carried out for the period t; q (Q) PV,d,t Reactive power compensation of the photovoltaic system is carried out for a period t; s is S inv,d Is the apparent capacity of the photovoltaic inverter; Γ -shaped structure PV,d Is a port set connected with a photovoltaic system; q (Q) o,t Is a system reactive power state variable associated to port o;
node balancing constraints: node power balance constraints include power conservation constraints and state variable consistency constraints;
1) Conservation of power constraint
Figure FDA0004078295150000061
Figure FDA0004078295150000062
Wherein: Γ -shaped structure n,r Is a set of ports associated with node r; n (N) node Is a system node set;
2) State variable consistency constraints
Figure FDA0004078295150000063
Figure FDA0004078295150000064
/>
Wherein:
Figure FDA0004078295150000065
is the average value of the square of the port voltage amplitude connected with the node r; Γ -shaped structure n,r Representing the number of ports connected with the node r; v o,t The state variable is squared for the system voltage magnitude associated to port o.
4. The optimal scheduling method for the ac/dc hybrid power distribution network based on graph computation according to claim 3, wherein in the step 3, the optimal scheduling policy of the device is obtained based on the graph computation method with the vertex as the center to solve the optimal model constructed in the step 2, and the optimal scheduling of the ac/dc hybrid power distribution network is performed according to the optimal scheduling policy.
Defining a device extension cost function (1-35) and a node indication function (1-36):
Figure FDA0004078295150000066
Figure FDA0004078295150000067
in omega d Vector x composed of device d decision variables to satisfy device operation constraints d Vector y consisting of port state variables connected to device d d Is a feasible region of (2); psi n Vector y composed of port state variables connected to node n for satisfying node operation constraint n Is a feasible region of (2);
the optimization model of the alternating current-direct current hybrid power distribution network based on the graph model is equivalent to:
Figure FDA0004078295150000068
wherein y is a vector formed by all port state variables of the system;
based on the decomposition concept of ADMM, equation (1-37) is equivalent to:
Figure FDA0004078295150000071
Wherein z is a mirror variable of vector y; z n A vector of mirror variables for ports associated with node n;
the equality constraint for relaxation formulas (1-38) is:
Figure FDA0004078295150000072
wherein x is a vector formed by decision variables of all equipment of the system; lambda is the system Lagrangian multiplier vector; l (·) is an augmented Lagrangian function, ρ is a penalty factor;
the alternating iterative solution formula based on ADMM to obtain the optimization problem formula (1-39) is:
{x k+1 ,y k+1 }＝argminL(x,y,z k ,λ k ) (1-40)
z k+1 ＝argminL(x k+1 ,y k+1 ,z,λ k ) (1-41)
λ k+1 ＝λ k +ρ(y k+1 -z k+1 ) (1-42)
wherein k is the current iteration solving times; x is x k+1 Solving vectors formed by all obtained equipment decision variables for the k+1st iteration; y is k+1 A vector of all port state variables updated for the k+1st iteration; z k+1 And z k Vectors composed of all mirror variables updated for the k+1th and k iterations respectively; lambda (lambda) k+1 And lambda (lambda) k The updated Lagrangian multiplier vector for the k+1th and k iterations;
decomposing the formulas (1-40) - (1-42) to the respective devices and the respective nodes according to the formulas (1-1) - (1-2):
Figure FDA0004078295150000073
Figure FDA0004078295150000074
Figure FDA0004078295150000075
wherein:
Figure FDA0004078295150000076
solving the vector formed by the obtained decision variables of the equipment d for the k+1st iteration; />
Figure FDA0004078295150000077
A vector of port state variables associated with device d updated for the k+1st iteration; />
Figure FDA0004078295150000078
And->
Figure FDA0004078295150000079
The vector is formed by mirror variables connected with the node n, which are updated for the k+1th iteration and the k iteration respectively; / >
Figure FDA00040782951500000710
And->
Figure FDA00040782951500000711
The lagrangian multiplier vector associated with node n updated for the k+1th and k-th iterations, respectively; />
Figure FDA0004078295150000081
Updating the lagrangian multiplier vector associated with device d for the kth iteration;
because the associated port state variables of each device are independent of each other, equations (1-43) can be solved in parallel; the state variables of the ports associated with each node are mutually independent, so that the formulas (1-44) can be solved in parallel, and the formulas (1-45) can be calculated in parallel;
the node update optimization problem is a quadratic convex optimization problem, and constraint formulas (1-31) - (1-34) are equality constraints, so that an analytical solution of the node update optimization problem is obtained according to the Lagrangian multiplier method:
Figure FDA0004078295150000082
wherein: Γ -shaped structure n Is a set of ports associated with node n; Γ -shaped structure n Representing the number of ports associated with node n;
Figure FDA0004078295150000083
Figure FDA0004078295150000084
for the (k+1) th iteration, solving in parallel by the devices of formulas (1-43)Updated information of the active power, reactive power and voltage amplitude squared state of port o; />
Figure FDA0004078295150000085
The information of the port active power, reactive power and voltage amplitude square state updated after the parallel solution of each node of the formulas (1-44) is carried out for the (k+1) th iteration; />
Figure FDA0004078295150000086
Figure FDA0004078295150000087
Lagrangian multiplier information updated by equations (1-45) for the kth iteration; alpha k+1 、β k+1 And gamma k+1 Intermediate parameters in the k+1st iteration solution;
vector y in formula (1-44) k+1 、z k+1 、λ k+1 And the scalar relationships in its analytical solutions (1-46) are as follows:
Figure FDA0004078295150000088
after solving the analytic solution formula (1-46) of the formula (1-44), carrying out parallel optimization calculation on each node by the formula (1-46) to accelerate the iterative solution process;
defining node original residual error after k+1 iterations
Figure FDA0004078295150000089
And k+1 iterations of dual residual +.>
Figure FDA00040782951500000810
As criteria for iterative convergence of equations (1-43), (1-46), (1-44):
Figure FDA00040782951500000811
Figure FDA0004078295150000091
in the method, in the process of the invention,
Figure FDA0004078295150000092
solving the vector formed by the obtained equipment decision variables connected with the node n for the k+1st iteration;
when the original residual and the dual residual meet the formulas (1-50), the node is converged in an iteration mode, when all nodes of the system are converged, the system is converged, iteration is finished, and the optimal scheduling strategy of each device is output;
Figure FDA0004078295150000093
wherein: epsilon is iteration convergence precision;
in summary, the graph calculation steps of the graph structure-based alternating current-direct current hybrid power distribution network optimization model are as follows:
(1) Setting the iteration number k=0, giving the initial information z k And lambda (lambda) k ；
(2) Will z k And lambda (lambda) k Carrying in the formulas (1-43), solving the formulas (1-43) in parallel, and updating the vector x formed by the decision variables of the equipment decision k+1 Vector y composed of port state variables k+1 ；
(3) Will x k+1 And y k+1 Carrying in (1-46), calculating vector z formed by mirror variables updated by nodes k+1 ；
(4) Will y k+1 And z k+1 Carry-in (1-45), update Lagrangian multiplier vector lambda k+1 ；
(5) Will z k 、z k+1 And x k+1 Carrying out formulas (1-48) and (1-49), and calculating node convergence criterion
Figure FDA0004078295150000094
And->
Figure FDA0004078295150000095
(6) According to
Figure FDA0004078295150000096
And->
Figure FDA0004078295150000097
Judging whether all nodes of the system are converged, and if so, outputting an optimal scheduling strategy; otherwise, k=k+1, go (2). />
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117993740A (en) * 2024-04-03 2024-05-07 国网山西省电力公司营销服务中心 Multi-element power distribution network configuration method considering N-1 fault load loss cost

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