Optimal power distribution network derivation system and optimal power distribution network derivation method

Abstract

To provide an optimal power distribution network derivation system capable of deriving a configuration of a power distribution network which optimizes an open / closed state of a switch and suppresses a power loss to a minimum, and an optimal power distribution network derivation method.SOLUTION: A network analysis section 11 extracts a tree structure representing a connection relation between a supply point and a demand point of power. A power loss condition calculation section 13 calculates a power loss condition using the tree structure. A voltage drop condition calculation section 15 calculates a voltage drop condition using the tree structure. A current capacity condition calculation section 17 calculates a current capacity condition using the tree structure. An uninterruptible power condition calculation section 19 calculates an uninterruptible power condition using the tree structure. A radial condition calculation section 21 calculates a radial condition using the tree structure. An order reduction condition calculation section 23 calculates an order reduction condition on which orders of five constraint conditions are reduced to second-order. A constraint condition integration section 25 constructs an evaluation function from six constraint conditions. An optimal power distribution network calculation section 26 delivers the evaluation function to a quantum computer and causes the quantum computer to derive an optimal power distribution network.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an optimal power distribution network extraction system and an optimal power distribution network extraction method. [Background technology]

[0002] Traditionally, constructing a power distribution network involves dividing the distribution lines into multiple sections using sectionalizing switches, and then connecting or disconnecting each section with other adjacent sections using switches to find the optimal network configuration that satisfies constraints such as keeping the current within the permissible limit and maintaining a specified voltage.

[0003] Patent Document 1 discloses a technique in which sections separated by switches are represented as blocks, the open / closed states of multiple switches are represented as binary variables {a,b} with arbitrary integers a and b, an evaluation function for power loss is formulated using binary variables, and this is applied to an annealing machine to find a supply path using a combination of switches that minimizes power loss. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Patent No. 6736787 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] Patent Document 1 assumes that power will not be supplied from supply points located more than four blocks apart. However, when considering actual power distribution networks, this condition is too restrictive and has the problem of not being applicable to most power distribution networks.

[0006] In Patent Document 1, as shown in FIG. 10, taking blocks B1 to B6 each containing a plurality of supply points as one unit, the power loss is calculated on the premise that an electric resistance and a current value are assigned to each of blocks B1 to B6. Therefore, for links q 12 , q 14 , q 23 , q 25 , q 36 , q 46 , q 56 for which an electric resistance and a current value are given respectively, the technique according to Patent Document 1 cannot be applied. For example, within the illustrated block B4, currents and resistances (I 41 , R 41 ), (I 42 , R 42 ), (I 43 , R 43 )...(I 4k , R 4k ) are given for each interval, but not given in units of blocks (connected components) such as current and resistance (I4, R4).

[0007] Specifically, since the calculation of power loss uses the current value accumulated from the end point as seen from the supply point, the calculation of power loss depends on the connection method between demand points within the block (which is upstream and which is downstream as seen from the supply point). The relationship between supply points within the block (which is upstream and which is downstream) changes depending on the open / closed state of the switch connecting the blocks. Therefore, there is a problem that the power loss cannot be obtained simply by summing up the electric resistance and current value within the block respectively.

[0008] Figure 11 is a conceptual diagram illustrating the problems arising in Patent Document 1. In the illustrated example, the upstream / downstream directions are reversed when switch C1 is closed (Case 1) and when switch C2 is closed (Case 2), resulting in different contributions from block B2 in power loss calculations. In other words, if we assume the use of numerical values ​​assigned to each block, such as the sum of electrical resistance and current values ​​included in block B2, it becomes impossible to calculate power loss. Therefore, there is a problem in that technologies that assume resistance and current values ​​are given on a block-by-block basis cannot be applied.

[0009] Furthermore, Patent Document 1 states that for the maximum current condition and the maximum allowable voltage condition, an L-power operation is performed for a sufficiently large L. However, in order to perform the calculation using a quantum annealing machine, it is necessary to define the evaluation function in quadratic form, and in this case, the order reduction method must be applied at least (L-2) times. Since one constraint term is added each time the order reduction method is applied, when L is large, the number of constraint terms becomes enormous, and in practice, it becomes difficult to derive the optimal solution by applying quantum annealing.

[0010]

number

[0011] However, here, I i 11 , V i This is a polynomial with open / closed state 0 / 1 as a variable. Since it is raised to the power of L, P current and P high The degree of this expression becomes extremely large. Applying a method to reduce the degree until it becomes a quadratic expression in this state results in a problem where the number of constraint terms swells to an enormous number. Furthermore, while combinatorial optimization methods such as the Quantum Approximate Optimization Algorithm (QAOA) have been proposed for general-purpose quantum computers (gate-based), even with general-purpose quantum computers, when the dimensionality of the evaluation function is high, a large number of CNOT gates, which bridge bits, are required. This leads to the problem that quantum circuits containing many CNOT gates are prone to noise. Therefore, in both quantum annealing machines and general-purpose quantum computers, deriving the optimal solution becomes difficult when the dimensionality of the evaluation function is high.

[0012] Therefore, the object of the present invention is to provide an optimal power distribution network derivation system and an optimal power distribution network derivation method that can derive a power distribution network configuration that optimizes the opening and closing state of switches and minimizes power loss. [Means for solving the problem]

[0013] To solve the above problems, the present invention employs the following means. In other words, the optimal power distribution network derivation system of the present invention is an optimal power distribution network derivation system that optimizes a power distribution network using a quantum computer, comprising: a network analysis unit that analyzes power distribution network data and extracts a tree structure with all supply points included in the power distribution network as roots, representing the connection / disconnection of links between supply points that supply power and demand points that receive power; a power loss condition calculation unit that calculates power loss conditions within the power distribution network by summing the "resistance value" × "square of the current value" of the links using the tree structure obtained by the network analysis unit; a voltage drop condition calculation unit that calculates voltage drop conditions to ensure that none of the links in the power distribution network exceed a certain voltage value using the tree structure obtained by the network analysis unit; a current capacity condition calculation unit that calculates current capacity conditions to ensure that the amount of current flowing through each of the links in the power distribution network is less than or equal to a certain value using the tree structure obtained by the network analysis unit; and the tree structure obtained by the network analysis unit The system is characterized by comprising: an uninterruptible power condition calculation unit that calculates an uninterruptible power condition that guarantees no power outages will occur at any demand point within the power distribution network; a radial condition calculation unit that uses the tree structure of the network analysis unit to calculate a radial condition that power should not be supplied from two or more supply points within the power distribution network; an order reduction condition calculation unit that reduces the order of third-order or higher terms included in the power loss condition, voltage drop condition, current capacity condition, uninterruptible power condition, and radial condition to second order and calculates an order reduction condition that defines the relationships between variables that arise as a result; a constraint integration unit that derives an evaluation function to be passed to the quantum computer from the power loss condition, voltage drop condition, current capacity condition, uninterruptible power condition, radial condition, and order reduction condition; and an optimal power distribution network calculation unit that passes the evaluation function derived by the constraint integration unit to the quantum computer to derive an optimal power distribution network that minimizes power loss.

[0014] Furthermore, the optimal power distribution network derivation method of the present invention is an optimal power distribution network derivation method that optimizes the power distribution system using a quantum computer, and comprises: analyzing power distribution network data, representing the connection / disconnection of links between supply points that supply power and demand points that receive power, extracting a tree structure with all supply points included in the power distribution network as roots, calculating power loss conditions within the power distribution network by summing the "resistance value" × "square of the current value" of the links using the tree structure, calculating voltage drop conditions to ensure that none of the links in the power distribution network exceed a certain voltage value using the tree structure, calculating current capacity conditions to ensure that the amount of current flowing through each of the links in the power distribution network is less than or equal to a certain value using the tree structure, and using the tree structure within the power distribution network The method is characterized by including: calculating an uninterrupted power condition that guarantees no power outages will occur at any demand point; using the tree structure, calculating a radial condition that power cannot be supplied from two or more supply points within the distribution network; reducing the order of third-order or higher terms included in the power loss condition, voltage drop condition, current capacity condition, uninterrupted power condition, and radial condition down to the second order, and calculating an order reduction condition that defines the resulting relationships between variables; deriving an evaluation function from the power loss condition, voltage drop condition, current capacity condition, uninterrupted power condition, radial condition, and order reduction condition to be passed to the quantum computer; and passing the derived evaluation function to the quantum computer to derive an optimal distribution network that minimizes power loss. [Effects of the Invention]

[0015] According to this invention, it is possible to derive a power distribution network configuration that optimizes the opening and closing state of switches and minimizes power loss. [Brief explanation of the drawing]

[0016] [Figure 1] This is a block diagram showing the configuration of the optimal power distribution network extraction system 1 according to an embodiment of the present invention. [Figure 2]This is a flowchart illustrating the operation of the optimal power distribution network derivation system 1 according to this embodiment. [Figure 3] This is a conceptual diagram illustrating the network analysis of the power distribution network in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 4] This is a conceptual diagram showing the tree structure when focusing only on the relationships between blocks in the method for extracting the tree structure of the power distribution network in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 5] This is a conceptual diagram illustrating the method for extracting the tree structure of the power distribution network in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 6] This is a conceptual diagram illustrating the method for extracting the tree structure of the power distribution network in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 7] This is a conceptual diagram showing the correspondence between the tree structure extracted from the entire power distribution network and the tree structure within each block in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 8] This is a conceptual diagram illustrating the method for calculating power loss in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 9] This is a conceptual diagram showing the constraint terms used in calculating the order reduction conditions in the optimal power distribution network derivation system 1 according to this embodiment. [Figure 10] This is a conceptual diagram illustrating a conventional method for determining power loss. [Figure 11] This is a conceptual diagram to explain the problems caused by conventional technology. [Modes for carrying out the invention]

[0017] Embodiments of the present invention will be described below with reference to the attached drawings. This invention provides a method for deriving a power distribution network that minimizes power loss using a quantum computer. As mentioned above, the term "quantum computer" is not limited to either an annealing machine or a general-purpose quantum computer. In the case of an annealing machine, it refers to quantum annealing; in the case of a general-purpose quantum computer, it refers to derivation using combinatorial optimization algorithms such as quantum approximation optimization algorithms. A power distribution network is a large network composed of supply points that supply electricity and demand points that receive the transmitted electricity. Hereafter, supply points and demand points will be collectively referred to as nodes, and the edges connecting the nodes will be referred to as links. Links have switches that can control whether they are "connected" or "disconnected," and these switches are scattered throughout the network. The objective of this invention is to optimize the open / closed states of these switches and derive a network configuration that minimizes power loss.

[0018] Figure 1 is a block diagram showing the configuration of the optimal power distribution network derivation system 1 according to an embodiment of the present invention. The optimal power distribution network derivation system 1 comprises a power distribution system data storage unit 10, a network analysis unit 11, a network analysis result storage unit 12, a power loss condition calculation unit 13, a power loss condition storage unit 14, a voltage drop condition calculation unit 15, a voltage drop condition storage unit 16, a current capacity condition calculation unit 17, a current capacity condition storage unit 18, an uninterrupted power supply condition calculation unit 19, an uninterrupted power supply condition storage unit 20, a radial condition calculation unit 21, a radial condition storage unit 22, an order reduction condition calculation unit 23, an order reduction condition storage unit 24, a constraint condition integration unit 25, and an optimal power distribution network calculation unit (quantum combinatorial optimization) 26.

[0019] The power distribution system data storage unit 10 stores information about the power distribution network as power distribution network data 30, including node numbers representing supply and demand points of the power distribution network, resistance (electrical resistance), reactance, current capacity value (active current / reactive current) of each link connecting the nodes, a flag indicating whether each link is operable (switchable) (an operable link is a switch), and the distribution (supply point (source): 1, demand point: 0). Based on the power distribution network data 30, the network analysis unit 11 extracts a tree structure representing the connection relationships between nodes and blocks within the power distribution network, with the supply point as the root. The network analysis result storage unit 12 stores the tree structure (analysis result) extracted by the network analysis unit 11.

[0020] The power loss condition calculation unit 13 calculates the power loss condition (condition 1) using the tree structure (network analysis results) stored in the network analysis result storage unit 12. The power loss condition storage unit 14 stores the power loss condition (condition 1) calculated by the power loss condition calculation unit 13. The voltage drop condition calculation unit 15 calculates the voltage drop condition (condition 2) using the tree structure (network analysis results) stored in the network analysis result storage unit 12. The voltage drop condition storage unit 16 stores the voltage drop condition (condition 2) calculated by the voltage drop condition calculation unit 15.

[0021] The current capacity condition calculation unit 17 uses the tree structure (network analysis results) stored in the network analysis result storage unit 12 to calculate the current capacity condition (condition 3) (the condition in which the amount of current flowing through each link is less than or equal to a certain value). The current capacity condition storage unit 18 stores the current capacity condition (condition 3) calculated by the current capacity condition calculation unit 17. The uninterrupted power condition calculation unit 19 uses the tree structure (network analysis results) stored in the network analysis result storage unit 12 to calculate the uninterrupted power condition (condition 4) that guarantees no power outages will occur (that every demand point is connected to at least one supply point). The uninterrupted power condition storage unit 20 stores the uninterrupted power condition (condition 4) calculated by the uninterrupted power condition calculation unit 19.

[0022] The radial condition calculation unit 21 uses the tree structure (network analysis results) stored in the network analysis result storage unit 12 to calculate radial conditions (condition 5) that guarantee no cycles occur in the network (one demand point cannot be supplied by more than two edges). The radial condition storage unit 22 stores the radial conditions (condition 5) calculated by the radial condition calculation unit 21.

[0023] The order reduction condition calculation unit 23 calculates an order reduction condition (condition 6) that defines the relationships between variables that arise when it reduces the order of terms of order 3 or higher, which are included in the five constraint conditions stored in the power loss condition storage unit 14, voltage drop condition storage unit 16, current capacity condition storage unit 18, uninterrupted power supply condition storage unit 20, and radial condition storage unit 22, respectively. In the following explanation, we will use the case where we reduce the order of terms of order 3 or higher included in the five constraint conditions to the second order and calculate an order reduction condition (condition 6) that defines the relationships between variables that arise when it is done. The order reduction condition storage unit 24 stores the order reduction condition (condition 6) that arises as a result of the order reduction calculated by the order reduction condition calculation unit 23.

[0024] The constraint integration unit 25 constructs an evaluation function from the six constraint conditions (conditions 1 to 6) stored in the order reduction condition storage unit 24, which is then passed to the quantum computer (not shown). The optimal power distribution network calculation unit 26 passes the evaluation function to the quantum computer (not shown) to calculate the optimal power distribution network. The quantum computer (not shown) then optimizes the open / closed states of the switches and calculates the optimal power distribution network 40 that minimizes power loss.

[0025] In order to have a quantum computer perform calculations, an evaluation function must be defined. The defined evaluation function is sent to the quantum computer, for example, via the cloud. The quantum computer searches for combinations of open / closed states of switches in the power distribution network that minimize the received evaluation function, and returns the result.

[0026] Here, the evaluation function is a mathematical expression in which the state of the switch is the variable. The state of the switch is represented by a binary value, such as open: 0 / closed: 1, and the evaluation function itself is expressed as a quadratic polynomial in which these open / closed states are the variables. This invention demonstrates how to construct this quadratic polynomial.

[0027] Figure 2 is a flowchart illustrating the operation of the optimal power distribution network derivation system 1 according to this embodiment. First, the network analysis unit 11 analyzes the network based on the power distribution network data 30 and extracts a tree structure 31 representing the connection relationships between nodes and blocks within the power distribution network, with the supply points as the root (step S10).

[0028] Next, the optimal power distribution network derivation system 1 calculates five constraint conditions (power loss (condition 1), voltage drop condition (condition 2), current capacity condition (condition 3), uninterrupted power condition (condition 4), and radial condition (condition 5))32 using the power loss condition calculation unit 13, voltage drop condition calculation unit 15, current capacity condition (condition 3), uninterrupted power condition (condition 4), and radial condition (condition 5) 32 (step S12).

[0029] Specifically, the power loss condition calculation unit 13 calculates the power loss condition (condition 1) using the network analysis results (tree structure) 31. The voltage drop condition calculation unit 15 calculates the voltage drop condition (condition 2) using the network analysis results (tree structure) 31. The current capacity condition calculation unit 17 calculates the current capacity condition (condition 3) using the network analysis results (tree structure) 31. The uninterrupted power condition calculation unit 19 calculates the uninterrupted power condition (condition 4), which guarantees that no power outages occur at any demand point, using the network analysis results (tree structure) 31. The radial condition calculation unit 21 calculates the radial condition (condition 5), which guarantees that no cycles occur in the network, using the network analysis results (tree structure) 31.

[0030] Next, the optimal power distribution network derivation system 1 uses the order reduction condition calculation unit 23 to reduce the order of terms of order 3 or higher included in the five constraint conditions (power loss condition (condition 1), voltage drop condition (condition 2), current capacity condition (condition 3), uninterrupted power condition (condition 4), radial condition (condition 5)) 32 to the order 2, and calculates a constraint condition (order reduction condition; condition 6) 33 that defines the relationship between the variables that arise as a result (step S14).

[0031] Next, the optimal power distribution network derivation system 1, using the constraint integration unit 25, derives an evaluation function 34 that is ultimately passed to the quantum computer (not shown) from the five constraint conditions (conditions 1 to 5) 32 and the constraint condition (order reduction condition; condition 6) 33 (a total of six constraint conditions) (step S16). Next, the optimal power distribution network derivation system 1, using the optimal power distribution network calculation unit 26, passes the evaluation function 34 to the quantum computer (not shown) to calculate the optimal power distribution network, and the quantum computer (not shown) derives an optimal power distribution network 40 that optimizes the opening and closing states of the switches and minimizes power loss (step S18).

[0032] Furthermore, the process of deriving the optimal power distribution network 40 that minimizes power loss using the optimal power distribution network derivation system 1 described above may be calculated on an hourly, periodic, or seasonal basis.

[0033] The details of each component are described below. (1) Network analysis of the power distribution network Figure 3 is a conceptual diagram illustrating the network analysis of the power distribution network in the optimal power distribution network derivation system 1 according to this embodiment. The power distribution network has a network structure with supply points and demand points as nodes. Links between nodes on the power distribution network include links that are fixed to be connected and links whose connection status can be changed by opening and closing switches. A set of nodes connected by links that are fixed to be connected can be considered as one block. In the case shown in Figure 3, B1 to B6 correspond to that block. Also, q 14 ,q 24 ,q 34 ,q 15 ,q 36 This is a switch that connects blocks.

[0034] In the network analysis process, a network structure is first extracted, representing the connections between blocks, with switches as edges and blocks as points. In Figure 3, focusing only on the relationships between blocks results in the structure shown in Figure 4. This allows for later reference of which blocks contain supply points, which switches connect the blocks, the paths connecting blocks containing supply points, and the paths from blocks without supply points to blocks containing supply points. The results of the analysis of the relationships between blocks will later be used to calculate the uninterrupted power supply condition and the radial power supply condition.

[0035] (2) Extraction of tree structure In calculating power loss, the precise expression will be explained later, but in general terms, it is calculated as the sum of "resistance value" × "square of current value" as follows.

[0036]

number

[0037] Here, A is the set of all power supply points, and F(a) is a tree structure with supply point a as the root node. Also, R l The resistance value of link l is I l [F(a)] is the cumulative current value from the downstream link to link l on the tree structure F(a) with supply point a as the root, i.e., I l [F(a)] is given by the following:

[0038]

number

[0039] Here I l The value of the current flowing through link l is

[0040]

number

[0041] This means that in the tree structure F(a) with supply point a as the root, link i is located downstream of link l. In other words, in calculating power loss, it is necessary to accumulate the current value from downstream of the tree structure with the supply point as the root. However, until the results of quantum combinatorial optimization are obtained, it is not determined which supply point will supply power to each demand point (it is not determined which tree structure with which supply point as the root on which the current value should be accumulated). For this reason, it is necessary to extract a tree structure with each supply point as the root for all supply points included in the distribution network in advance. Figure 5 shows the extracted tree structure for the distribution network shown in Figure 3.

[0042] From the power distribution network shown in Figure 3, as shown in Figure 5, F(a8), F(a5), F(a 10 Three tree structures are obtained. It is important to note here that each demand point in the distribution network must satisfy the radial condition that "power cannot be supplied from more than one supply point." Therefore, each tree structure contains only one supply point, the root node. In other words, the result of extracting the tree structure is up to the point just before reaching the block containing the supply point. For example, in the tree structure F(a5) shown in Figure 5, node a5 is the supply point, but switch q 15 ,q 36 If we close the block and connect blocks B5 and B6, it violates the radial condition, so blocks B5 and B6 are not included in tree structure F(a5) (the extracted tree structure will only go up to block B1 before block B5 and up to block B3 before block B6). F(a8), F(a 10 The same applies to ).

[0043] ■ Tree structure between nodes within a block To calculate power loss later, we introduce symbols for the tree structure representing the relationships between nodes within each block. As can be seen from Figure 5, the tree structure representing the relationships between nodes within a block changes depending on where the block is supplied with power. For example, if we focus on block B4 shown in Figure 5, in F(a8) s1 is the root node, but in F(a5) s2 is F(a 10In this case, s3 is the root node.

[0044] Here, within block B, a tree structure is defined with the supply point or the endpoint s of the switch as the root, T B (s) will be used as a descriptive term. For example, the tree structure within block B4 will be as shown in Figure 6.

[0045] Figure 5 shows the results of extracting the tree structure, including the tree structure F(a) extracted from the entire power distribution network and the tree structure T within each block. B The correspondence of (s) is summarized in Figure 7. As can be seen from Figure 7, the tree structure F(a) extracted from the entire power distribution network is the tree structure T within each block. B It consists of (s). In the case shown in Figure 7, F(a8) is

[0046]

number

[0047] It consists of F(a5)

[0048]

number

[0049] It consists of F(a 10 )teeth

[0050]

number

[0051] It consists of.

[0052] (3) Calculation of power loss conditions The power loss conditions are calculated using the analysis results of the above network, particularly the extraction of the tree structure. As mentioned earlier, power loss is basically calculated as the sum of the "resistance value" × "square of the current value" of the links connecting the nodes (see Equation 1), and the current value used in this calculation is the cumulative value obtained by moving from downstream to upstream of the tree structure with the power supply point as the root, as shown in (Equation 2). At this time, the tree structure along which the cumulative value should be calculated depends on where each block is supplied with power, and therefore changes depending on how it is connected to surrounding blocks (open / closed state of switches).

[0053] The following explains how to calculate power loss. Figure 8 is a conceptual diagram illustrating the method for calculating power loss in the optimal power distribution network derivation system 1 according to this embodiment. Figure 8 shows the power distribution network shown in Figure 3 with information on resistance, active current, and reactive current values ​​for each link.

[0054]

number

[0055] The equation represents (resistance, active current, and reactive current). There are two types of current values, active and reactive, and both must be considered when calculating power loss. In other words, to write Equation 1 more precisely, power loss can be expressed as the sum of the active current component and the reactive current component, as follows:

[0056]

number

[0057] However, I l [F(a)],J l [F(a)] represents the cumulative value of active current and reactive current, respectively, along the tree structure F(a) from downstream to link l. Here,

[0058]

number

[0059] If we define it as follows,

[0060]

number

[0061] It can be expressed as follows. For example, in the case of the power distribution network shown in Figure 3, the supply points are a8, a5, a 10 These are the three points,

[0062]

number

[0063] This is the result.

[0064] Therefore, the following explains how to determine the power loss evaluation function P(F(a)) along the tree structure F(a) extracted from the power distribution network. Here, we will explain using the block tree structure F(a8) shown in Figure 7 as an example.

[0065] When calculating power loss along the tree structure F(a8) of the power distribution network, the supply point a8 in block B5 becomes the root node. Consequently, s7 becomes the root in block B1, s1 in block B4, and s6 in block B3. In other words, within each block,

[0066]

number

[0067] The current value will be accumulated according to this.

[0068] Here, we introduce the following symbols: Tree structure T within block B B In (s), the value of the active current accumulated from the end downstream of node n shall be represented by the following symbol.

[0069]

number

[0070] Here,

[0071]

number

[0072] is a wooden structure T B (s) means that link l is downstream from node n. Similarly, for reactive current,

[0073]

number

[0074] This is defined as follows. For example, in block B4 shown in Figure 8, the tree structure in Figure 6

[0075]

number

[0076] When the current values ​​are accumulated according to this method,

[0077]

number

[0078] This can be calculated as follows. For example, the analysis results shown in Figure 6.

[0079]

number

[0080] Accordingly, when the current values ​​within block B4 are accumulated,

[0081]

number

[0082] And so on. Furthermore, here, in order to simplify the symbols,

[0083]

number

[0084] If the node n in the argument is the endpoint s of the switch itself, the tree structure T is omitted. That is,

[0085]

number

[0086] We will express it as follows. After defining the cumulative current values ​​along the tree structure within each block as described above, we use them to calculate the power loss P(F(a)) along the tree structure F(a) between blocks. Below, we will show the calculation method using P(F(a8)) as an example. The function P(F(a)) represents the part of the evaluation function that expresses the case where each demand point in the distribution network is supplied with power from supply point a8 in block B5. For all nodes n from the terminal n9,s9 belonging to block B3 to the supply point a8 in block B5, we accumulate the loss calculation using the cumulative current values ​​from downstream to node n and the resistance values. Therefore, in order to show the calculation process, we will explain below how the cumulative current values ​​are calculated in the links within block B4 in particular.

[0087] F(a8) is a tree structure

[0088]

number

[0089] The blocks are composed of B3→B4→B1→B5, arranged from downstream to upstream. Therefore, when calculating the cumulative current value of link s3n3 within block B4 according to the tree structure F(a8), all links included in block B3 are downstream from link s3n3. Therefore, switch q 34 If it is closed, the cumulative current value for the entire block B3 must be added, and switch q 34 If it is open, it will not contribute. The cumulative value of the current up to just before block B3 connects to block B4 is in the tree structure

[0090]

number

[0091] The cumulative current value within block B3 according to the above

[0092]

number

[0093] Since it is expressed as, the cumulative current value of link s3n3 is

[0094]

number

[0095] It is expressed as follows. However, here, q 34 I is a binary variable that is 1 if the switch between B3 and B4 is closed, and 0 if it is open. l If you use the symbol [F(a)],

[0096]

number

[0097] This means that, similarly, the cumulative current value of links n1 and n3 is

[0098]

number

[0099] This is the result. Furthermore, the cumulative current value of link s1n1 also includes the current value I2+I4 from s2 to n1,

[0100]

number

[0101] This is expressed as follows. This value is the cumulative value of the active current from block B3 to block B4 along the tree structure F(a8). Furthermore, when tracing back through the tree structure F(a8) to find the cumulative value for the links within block B1, for example, the cumulative current value of link s4n4 within block B1 is given by switch q 14 If it is closed, all the current values ​​accumulated up to that point will be added together,

[0102]

number

[0103] It is expressed as follows. Similarly, the cumulative current value up to the link connecting s8a8 in block B5 is

[0104]

number

[0105] Thus, the cumulative current value is represented by a binary variable q (0 / 1) that represents the open / closed state each time it passes through a switch along the tree structure from downstream. ij The multiplication is expressed in a form where it appears recursively. Finally, the power loss evaluation function P(F(a8)) along the tree structure F(a8) is calculated as described above.

[0106]

number

[0107] Using this, the calculation is performed as follows:

[0108]

number

[0109] Here, it is important to note that since P(F(a)) above is calculated recursively from downstream, the binary variable q represents the opening and closing of the switch. ij The point is that the degree can be 3 or higher. In fact, when we expand equation 4,

[0110]

number

[0111] Like q ij A third-order term appears in this expression. In quantum combinatorial optimization, it is common to deal with this using a second-order polynomial. The solution to this order will be explained later in section (8) Calculation of the Order Reduction Condition.

[0112] (4) Calculation of conditions for no power outage Next, the calculation of the uninterrupted power supply condition will be explained with reference to Figure 4. The uninterrupted power supply condition is a condition that guarantees that every demand point is connected to at least one supply point. Demand points included in blocks B2, B5, and B6, which contain supply points, are already connected to supply points and therefore do not have to worry about power outages. However, blocks B1, B3, and B4, which do not contain supply points, must be connected to one of the blocks B2, B5, or B6 that contain supply points. For example, in the case of block B4, in order to be connected to block B2, switch q 24 It needs to be closed, and in order to connect to block B6, switch q 34 ,q 36 Both must be closed. Also, to connect to block B5, switch q 14 ,q 15Both sides must be closed. Since a quantum computer returns the combination that minimizes the evaluation function as the solution, to represent the above state, it is necessary to define the evaluation function so that it is 0 if the condition is met and a positive number if it is not. Therefore, to represent the uninterrupted condition for block B4, the evaluation function can be defined as follows.

[0113]

number

[0114] In fact, if block B4 is connected to any one of the supply points, the result is 0; if none of the conditions are met, the result is C. penalty This is the evaluation function when focusing on block B4, but the same logic can be applied to blocks B1 and B3. This can be expressed in general terms as follows:

[0115]

number

[0116] Here, A is the set of all blocks that include the supply point, A C Let be the complement of A, i.e., the set of all blocks that do not contain a supply point; Ω(b,a) be the set of all paths connecting block b and block a (without a supply point in between); and Q(p) be the set of switches on path p. Here, it should be noted that, similar to the power loss condition,

[0117]

number

[0118] This part may be of order 3 or higher. The solution to this order will be explained later in (8) Calculation of Order Reduction Conditions.

[0119] (5) Calculation of radial conditions Next, the calculation of the radial condition will be explained with reference to Figure 4. The radial condition is that each demand point must not be supplied with power from two or more supply points. It is necessary to restrict the opening and closing of switches so that blocks containing the supply points of blocks B2, B5, and B6 are not connected to each other. For example, the switch on the path connecting block B2 and block B5 is q 24 ,q 14 ,q 15 Therefore, if all of these are in a closed state, the radial condition is violated. Thus, switch q 24 ,q 14 ,q 15 The evaluation function needs to be designed so that a penalty is imposed if both conditions become 1 simultaneously. This can be done, for example, as follows:

[0120]

number

[0121] In fact, switch q 24 ,q 14 ,q 15 If any one of these is 0 (open), then the above equation becomes 0, and switch q 24 ,q 14 ,q 15 C is only available when all of them are 1 (all closed). penalty This is the result. If we consider blocks B5 and B6, and blocks B2 and B6 in the same way, the evaluation function representing the radial condition in the case of Figure 4 is as follows.

[0122]

number

[0123] In a generalized form, this can be expressed as follows:

[0124]

number

[0125] However, here, A represents the set of all blocks containing the supply point, Ω(a,a') represents the set of all paths connecting two elements a and a' of A (the paths do not contain the supply point), and Q(p) represents the set of switches on path p. Here again,

[0126]

number

[0127] As shown above, if there are three or more switches on path p, a term of order 3 or higher may appear in the evaluation function. However, in the same way as in the calculation of the power loss condition in (3) and the calculation of the no-interruption condition in (4) above, the order can be reduced to 2nd order by the method described in the calculation of the order reduction condition in (8) below.

[0128] (6) Calculation of current capacity conditions The current capacity condition is a constraint that specifies that the current flowing through each link must be below a certain value. For example, in the power distribution network shown in Figure 8, the active current flowing through the link connecting s8a8 in block B5 is expressed as follows.

[0129]

number

[0130] The same applies to reactive currents.

[0131]

number

[0132] This is how it is calculated. Here, for example, if the current capacity is 300[A], the following must be satisfied.

[0133]

number

[0134] In other words, switch q satisfies the above conditions. 15 ,q 14 , q 34 It is necessary to determine the open / closed state. Therefore,

[0135]

number

[0136] In that case, we design the evaluation function to impose a penalty. Here,

[0137]

number

[0138] This is defined as follows: For example, when all switches are in the closed state (q 15 =1,q 14 =1,q 34 Assuming that = 1,

[0139]

number

[0140] It was calculated as follows:

[0141]

number

[0142] In that case, the current capacity will be exceeded, so switch q 15 ,q 14 , q 34 One of these must always be in an open state. Therefore, the evaluation function is

[0143]

number

[0144] It is defined as follows. In fact, if the evaluation function is defined in this way, the switch q15 ,q 14 , q 34 If all of them are 1 (closed state), then C penalty Therefore, if even one of the states is open, the result is 0. Generalizing this, we get the following:

[0145] I l As defined in (Equation 2), [F(a)] is the cumulative effective current value from the end to link l along the tree structure F(a), J l Similarly, [F(a)] is the reactive current value accumulated from the end to link l along the tree structure F(a). The binary variables representing the opening and closing of the switches included in the tree structure [F(a)] are

[0146]

number

[0147] Represented by,

[0148]

number

[0149] This is defined as follows. (6-1) Assuming all switches are in the closed position

[0150]

number

[0151] The value of the current capacity θ of link l is l For links exceeding a certain limit, the set of switches on the link

[0152]

number

[0153] Go and get it.

[0154] When all of those switches are in the closed state, define an evaluation function as follows to impose a penalty.

[0155]

Number

[0156] (7) Calculation of voltage drop condition In the voltage drop condition, using the current value accumulated from the downstream, the voltage on each link is accumulated from the upstream instead of the downstream. A method of accumulation along the tree structure F(a8) shown in FIG. 7 will be described. When the resistance, reactance, active current value, and reactive current value of the link a8n8 are given by (R 15 , S 15 , I 15 , J 15 ), the voltage drop V 15 [F(a8)] up to the link a8n8 is

[0157]

Number

[0158] When it is

[0159]

Number

[0160] given by

[0161] Next, the voltage drop V7[F(a8)] of the link s7n4 is similarly

[0162]

Number

[0163] using

[0164]

Number

[0165] when

[0166] [Number]

[0167] is given. When this is repeated up to link n6s9, the voltage drop of link n6s9 is

[0168] [Number]

[0169] is used to

[0170] [Number]

[0171] is expressed as. Thus, the voltage drop recursively accumulated from upstream to downstream

[0172] [Number]

[0173] is a function of the binary variable representing the open / closed state of the switch on the tree structure F(a)

[0174] [Number]

[0175] is. Therefore, V l [F(a)] is

[0176] [Number]

[0177] If we write it as such, the voltage drop condition, like the current capacity condition, is expressed as follows.

[0178] [Number]

[0179] Here, θ l is the voltage threshold for link l.

[0180] [Number]

[0181] Since there are terms of..., it can become cubic or higher, which is the same as the current capacity condition.

[0182] (8) Calculation of the degree reduction condition Regarding the terms of degree three or higher that appear in the evaluation function from the calculation of the above (1) power loss condition to the calculation of the (7) voltage drop condition, a method for reducing the degree to quadratic will be explained. In quantum combinatorial optimization, it is common to handle the evaluation function as a quadratic polynomial. However, recently, a method has also been proposed to directly optimize the evaluation function of a polynomial with terms of degree three or higher in the form of HUBO (Higher Order Unconstrained Binary Optimization), and it is not necessarily necessary to reduce the dimension to quadratic. When handling the evaluation function as a quadratic polynomial, for terms of degree three or higher such as q A q B q C the degree is reduced by the following variable transformation.

[0183] [Number]

[0184] q D = q A q B is set, and the variable q DWe reduced it to a second order by adding one more, but this substitution alone is insufficient. q D q is not a variable that can freely take 0 or 1 in a purely independent manner, D =q A q B The following constraint must be satisfied. Therefore, q D =q A q B To impose a penalty that restricts us, we consider the following constraints.

[0185]

number

[0186] This constraint term takes the values ​​shown in Figure 9. That is, q D =q A q B The value is 0 when the condition is met, and 1 or greater otherwise. Therefore, when this constraint term is added to the evaluation function, the solution obtained by minimizing the evaluation function is q D =q A q B This will result in obtaining something that satisfies the requirements.

[0187] In higher-order cases, this transformation is repeated to reach the second order. For example, as seen in power loss conditions,

[0188]

number

[0189] A third-order term like this can be reduced to a second-order term by applying this method once. q that appeared under the radial condition 15 q 14 q 34 q 36 If there is a fourth-degree term like this, the degree can be reduced to second degree by applying the method twice. However, this method adds one constraint condition each time it is applied, and when applied to relatively high-degree polynomials, the number of constraint terms becomes enormous, leading to a situation where an optimal solution cannot be obtained in practice.

[0190] (9) Integration of constraints Finally, we integrate the power loss conditions, voltage drop conditions, current capacity conditions, uninterrupted power supply conditions, radial conditions, and order reduction conditions, all of which have been reduced to the second order, to construct an overall evaluation function to pass to the quantum computer.

[0191]

number

[0192] Quantum computers use this evaluation function

[0193]

number

[0194] An optimal power distribution network to minimize [the problem]

[0195]

number

[0196] The following decision is made:

[0197]

number

[0198] According to the embodiment described above, when determining the power loss conditions, a tree structure with the supply point as the root is first extracted, and then addition is performed "recursively" from downstream to upstream of the supply point. Therefore, unlike existing technologies, there is no need to impose a limit on the number of connected blocks. For this reason, it can be applied to actual large-scale power distribution networks.

[0199] Furthermore, according to the embodiment described above, since a tree structure with each supply point as a root is extracted in advance for all supply points included in the power distribution network, it is possible to respond to changes in the contribution of each block to power loss that change depending on the open / closed state of the switch.

[0200] Furthermore, according to the above-described embodiment, in particular, when calculating the voltage drop condition and current capacity condition, the constraints are defined in such a way that it is guaranteed that the voltage and current values ​​do not exceed the threshold without increasing the order. Therefore, even if the order is reduced to the second order so that it can be passed to a quantum annealing machine, it is possible to prevent the number of constraint terms from becoming enormous. Also, when calculations are performed on a general-purpose quantum computer, the number of CNOT gates included in the quantum circuit can be reduced.

[0201] In the above explanation, we used the example of using a second-order polynomial for the evaluation function, but the order of the evaluation function is not limited to second order. For example, methods have been proposed to optimize evaluation functions that are polynomials with terms of order 3 or higher, in the form of HUBO (Higher Order Unconstrained Binary Optimization), so it is not always necessary to reduce the dimensionality to second order. Therefore, as long as the evaluation function can handle the order, it is possible to construct an overall evaluation function to be passed to the quantum computer by integrating the power loss condition, voltage drop condition, current capacity condition, uninterrupted power condition, radial condition, and order reduction condition, all of which include terms of order 3 or higher, without reducing the dimensionality to second order. In other words, the order reduction condition calculation unit may reduce the order of terms included in the power loss condition, voltage drop condition, current capacity condition, uninterrupted power condition, and radial condition to an order that the evaluation function can handle, and calculate an order reduction condition that defines the resulting relationship between variables. [Explanation of symbols]

[0202] 1. Optimal Power Distribution Network Derivation System 10. Distribution System Data Storage Unit 11 Network Analysis Department 12 Network Analysis Result Storage Unit 13 Power loss condition calculation section 14 Power loss condition storage section 15. Voltage drop condition calculation unit 16 Voltage drop condition storage unit 17 Current capacity condition calculation section 18 Current capacity condition storage section 19. Unit for calculating uninterrupted power supply conditions 20 Uninterruptible Condition Storage Unit 21 Radial Condition Calculation Unit 22 Radial condition accumulation section 23 Order reduction condition calculation unit 24 Order reduction condition storage unit 25 Constraint Integration Unit 26. Optimal Power Distribution Network Calculation Unit (Quantum Combinatorial Optimization) 30 Power distribution network data 31 Analysis results (tree structure) 32 Constraints 33 Order reduction conditions 34. Evaluation Function 40 Optimal Power Distribution Network

Claims

1. An optimal power distribution network derivation system that uses a quantum computer to optimize the power distribution network, A network analysis unit analyzes power distribution network data, represents the connection / disconnection of links between power supply points and power demand points, and extracts a tree structure with all supply points included in the power distribution network as roots. A power loss condition calculation unit calculates the power loss conditions within the power distribution network by summing the "resistance value" × "square of the current value" of the links using the tree structure generated by the network analysis unit, A voltage drop condition calculation unit calculates voltage drop conditions to ensure that none of the links in the power distribution network exceed a certain voltage value, using the tree structure of the network analysis unit. A current capacity condition calculation unit that uses the tree structure of the network analysis unit to calculate current capacity conditions for keeping the amount of current flowing through each of the links in the power distribution network below a certain value, An uninterruptible power condition calculation unit calculates uninterruptible power conditions that guarantee no power outages will occur at any demand point within the distribution network, using the tree structure of the network analysis unit. A radial condition calculation unit calculates a radial condition that power must not be supplied from two or more supply points within the power distribution network, using the tree structure of the network analysis unit. An order reduction condition calculation unit calculates order reduction conditions that define the relationships between variables that arise as a result of reducing the order of third-order or higher terms included in the power loss condition, voltage drop condition, current capacity condition, uninterrupted power condition, and radial condition to second order, A constraint integration unit that derives an evaluation function to be ultimately passed to the quantum computer from the power loss condition, the voltage drop condition, the current capacity condition, the no-interruption condition, the radial condition, and the order reduction condition, An optimal power distribution network calculation unit provides the evaluation function derived by the constraint integration unit to the quantum computer to derive an optimal power distribution network that minimizes power loss, An optimal power distribution network derivation system characterized by comprising the following features.

2. The optimal power distribution network derivation system according to claim 1, characterized in that the derivation of the optimal power distribution network is performed hourly, seasonally, and periodically.

3. The optimal power distribution network derivation system according to claim 1, characterized in that the power loss condition calculation unit calculates a power loss condition expressed as the sum of an active current component and a reactive current component based on the current value accumulated from downstream to upstream of a tree structure with the supply point as the root.

4. The optimal power distribution network derivation system according to claim 1, characterized in that the voltage drop condition calculation unit calculates the voltage drop condition by accumulating the voltage from upstream to downstream of the tree structure using the current value accumulated from downstream to upstream of the tree structure with the supply point as the root.

5. A method for deriving an optimal power distribution network that optimizes the power distribution system using a quantum computer, The process involves analyzing power distribution network data to represent the connection / disconnection of links between power supply points and power demand points, and extracting a tree structure with all supply points included in the power distribution network as roots. Using the aforementioned tree structure, the power loss conditions within the power distribution network are calculated by summing the "resistance value" × "square of the current value" of the links. Using the aforementioned tree structure, calculate the voltage drop conditions such that none of the links within the power distribution network exceed a certain voltage value. Using the aforementioned tree structure, calculate the current capacity conditions required to keep the amount of current flowing through each of the links in the power distribution network below a certain value. Using the aforementioned tree structure, calculate the conditions for no power outages, which guarantee that no power outages will occur at any demand point within the distribution network. Using the aforementioned tree structure, calculate the radial condition that power cannot be supplied from two or more supply points within the power distribution network. The process involves reducing the order of terms of third order or higher included in the aforementioned power loss condition, voltage drop condition, current capacity condition, uninterrupted power condition, and radial condition to the second order, and calculating the order reduction conditions that define the resulting relationships between the variables. To derive an evaluation function to be ultimately passed to the quantum computer from the aforementioned power loss conditions, voltage drop conditions, current capacity conditions, uninterrupted power conditions, radial conditions, and order reduction conditions, The derived evaluation function is passed to the quantum computer to derive the optimal power distribution network that minimizes power loss. A method for deriving an optimal power distribution network, characterized by including the following:

Images