JP6417150B2 - Power management system, management apparatus, power purchase plan generation method, and computer program - Google Patents

Description

  The present invention relates to a power management system, a management device, a power purchase plan generation method, and a computer program.

  Patent Document 1 describes a supply and demand control device that obtains power supply and demand prediction data from power consumption and obtains control parameters for performing operation control of the power storage system.

International Publication No. 2011/086866

As a prediction model for probabilistically predicting power consumption and the like, it is possible to use a model assuming Gaussianity.
However, the present inventors have found that a prediction model assuming Gaussianity may not always be appropriate.
Therefore, a new method capable of generating a power purchase plan is desired not only for a prediction model assuming Gaussianity but also for a non-Gaussian stochastic prediction model.

(1) A power management system according to one aspect of the present invention includes a power storage device that charges purchased power and discharges the power for supplying power to a power consuming device, and a management device that generates a power purchase plan. Prepare.
The management device includes a storage unit that stores a prediction model that includes a probability distribution of a predicted value of a net load in the power storage device for each of a plurality of time zones within a target period that is a target of a power purchase plan, and a Markov determination process. And a processing unit that performs a power purchase plan process for generating the power purchase plan by solving.
The Markov determination process has a plurality of first states that discretely indicate the amount of power stored in the power storage device at each of a plurality of discrete times dividing the target period into a plurality of time zones.
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process.
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. This is a process of determining the amount of electricity purchased in each.

(2) The Markov decision process can be changed when power is purchased from the first state at a certain first time, and a plurality of second states that can be changed to the first state at the next time after the first time. The second state further includes two states, and the second state includes a state indicating at least one of overcharge and shortage of power storage in the power storage device, and the second state when power is purchased from the first state. The transition probability may be given based on the prediction model.

(3) It is preferable that the cost includes a loss due to occurrence of at least one of overcharge and insufficient storage in the power storage device.

(4) The probability distribution in the prediction model is preferably a non-Gaussian distribution.

(5) The power purchase planning process preferably includes a selection process for selecting the prediction model used to solve the Markov decision process. The selection process is a process of selecting one of a first prediction model whose probability distribution is a normal distribution and a second prediction model whose probability distribution is a nonparametric distribution as the prediction model.

(6) Another aspect of the present invention is a management device that generates a power purchase plan, wherein the predicted value of the net load in the power storage device for each of a plurality of time zones within a target period that is a target of the power purchase plan. A storage unit that stores a prediction model including a probability distribution; and a processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process.

(7) Another aspect of the present invention is a method of generating a power purchase plan by a computer, and a predicted value of a net load in a power storage device for each of a plurality of time zones within a target period that is a target of the power purchase plan. Storing a prediction model composed of the probability distribution in the storage unit, and performing a power purchase plan process for generating the power purchase plan by solving a Markov decision process.

(8) In another aspect of the present invention, the computer stores a prediction model including a probability distribution of predicted values of net load in the power storage device for each of a plurality of time zones within a target period that is a target of a power purchase plan. It is a computer program for functioning as a storage unit and a processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process.
The computer program can be recorded on a computer-readable recording medium.

It is a block diagram of a power management system. (A) shows net load performance data, (b) shows prediction model data. It is a flowchart which shows a power purchase plan process. It is a histogram of power consumption. (A) shows the normality test result of the power consumption amount, (b) shows the normality test result of the generated power amount, and (c) shows the normality test result of the net load amount. It is a figure which shows Weibull distribution with an average value and a standard deviation equal to normal distribution and average distribution. It is a network representation of a Markov decision process. It is a network representation of a Markov decision process having an intermediate state. (A) is a net load amount prediction model (non-parametric distribution), and (b) a net load amount prediction model (Gaussian distribution). It is a figure which shows the time transition of a power purchase price. It is the distribution of daily power payments. It is a flowchart which shows a power purchase plan process. It is a block diagram which shows the other example of an electric power system.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

[1. Configuration of power management system]
As shown in FIG. 1, the power management system 100 includes a power storage device 1 and a management device 4. In the present embodiment, the power management system 100 is installed at each site where power consumption is performed, such as a home or office. A base where power consumption is performed can purchase power from outside the base (for example, power supplied from an electric power company), generate power, and consume the purchased power or generated power. Power generation does not have to be performed at the site. The management device 4 may manage the power sale to the outside of the base, but does not consider the power sale in this embodiment.

  The base has a power consuming device (load) 2 and a power generation device 3. The power consuming device 2 is, for example, an electrical device installed at home. The power generation device 3 is, for example, a solar power generation device.

  The power storage device 1 is charged with purchased power or generated power, and is discharged to supply power to the power consuming device 2. The management device 4 is configured as a power router that manages charging / discharging of the power storage device 1, power supply to the power consuming device 2, power purchase from the outside, and the like. The management device 4 is connected to the power storage device 1, the power consuming device 2, the power generation device 3, and the power system outside the base via the power line 5.

  The management device 4 includes a power control unit 6 and a processing device (computer) 7. The power control unit 6 performs power control among the power storage device 1, the power consuming device 2, the power generation device 3, and the external power system. In the power control, the power supplied from the power generation device 3 is given to the power storage device 1 or the power consuming device 2, the purchased power is given to the power storage device 1 or the power consuming device 2, or the power stored in the power storage device 1 is stored. To the power consuming device 2 is included. The processing device 7 is configured as a computer including a processing unit 7a and a storage unit 7b. The computer 7 performs necessary information processing (power purchase plan processing, prediction model data generation processing, power control processing, etc., which will be described later) by executing the installed computer program.

  The storage unit 7b of the processing device 7 stores an area for storing the predicted model data 71 of the net load amount of the power storage device 1 and a region for storing the power purchase plan data 72 at the site where the power storage device 1 is installed. And have. The net load amount is an amount obtained by subtracting the power consumption amount at the base from the power generation amount at the base where the power storage device 1 is installed. The net load amount is a positive value when the generated power amount is larger than the consumed power amount, and is a negative value when the consumed power amount is larger than the generated power amount.

  The processing device 7 generates power purchase plan data 72 and stores the generated power purchase plan data 72 in the storage unit 7b. The power control unit 6 performs power purchase based on the power purchase plan data stored in the storage unit 7b. The power purchase plan data 72 is generated so as to minimize the future power purchase price based on the predicted model data 71 of the net load obtained from the future power consumption and power generation amount at the base. In this embodiment, the period (target period) that is the target of the power purchase plan is one day (24 hours), but the length of the target period of the power purchase plan is not particularly limited. The power purchase plan is generated before the start of the target period (for example, the day before the day that is the target period).

  The prediction model data 71 of the net load amount is a probability distribution of the net load for each hour period of one day (24 hours) that is the target period. The prediction model data 71 is generated based on past net load performance data. The prediction model data 71 is generated by normalizing the frequency distribution of the net load amount generated in the same time zone of each day within the past period (past d days).

  As shown in FIG. 2A, the net load performance data is data indicating the net load amount in each time zone (every hour) on each of a plurality of days (d days). As shown in FIG. 2 (b), the prediction model data 71 includes time zones for a plurality of time zones in a day (from 0 o'clock to 1 o'clock, 1 o'clock to 2 o'clock, ..., 23 o'clock to 24 o'clock). The number of data (24) corresponding to the number of time zones of the day is included. Each time zone data is a set of occurrence probabilities for each net load amount obtained by normalizing the frequency for each net load amount that occurred in the same time zone on the past d days by the total number of occurrences (d).

  For example, in the time zone data 71a from 0:00 to 1 o'clock shown in FIG. 2B, the net load amount is generated for each of a plurality of net load amounts in the time zone from 0:00 to 1 o'clock in the past d days. Frequency and probability of occurrence. In the time zone data 71a from 0 o'clock to 1 o'clock shown in FIG. 2 (b), for example, for a net load amount of 3.9 kWh, the occurrence frequency (number of occurrences) in the past d days is 2, and the occurrence probability is 2 / d.

  The time zone data 71a from 0 o'clock to 1 o'clock indicates the probability distribution of each net load amount range in the time zone from 0 o'clock to 1 o'clock. Other time zone data 71b, 71c,... Also show probability distributions of the respective net load amount ranges in the corresponding time zone.

  Here, the net load amount in the net load record data shown in FIG. 2A is a continuous value, whereas the net load amount in the prediction model data 71 shown in FIG. 2B is a discrete value. . In FIG. 2B, the discretization width Δ of the net load value is 0.1 kWh. For example, in the time zone data 71a of FIG. 2B, a class having a net load amount of 3.9 kWh indicates a range of the net load amount indicated by the left closed half-open section [3.9, 4.0). When the prediction model data 71 is generated from the net load actual data, the continuous net load amount in the net load actual data is projected to a discrete value indicating a section (class) to which the net load amount belongs. For example, if the net load actually generated is 3.91 kWh, it is counted in the prediction model data 71 as the occurrence of a net load with a net load of 3.9 kWh.

The processing unit 7a of the processing device 7 uses the Markov decision process to minimize the future power purchase price based on the prediction model data 71 generated based on the net load actual data, and the amount of power purchased in each time zone. The power purchase planning process is performed.
As shown in FIG. 3, in the power purchase planning process, the prediction model data 71 stored in the storage unit 71 is acquired (step S11), and the power purchase amount in each time zone is determined by solving the Markov decision process (step S12). ). The determined power purchase amount for each time period is stored in the storage unit 7b as the power purchase plan data 72 (step S13).
The processing unit 7a performs power purchase control and other power control by the power control unit 6 based on the power purchase plan data 72 set in the storage unit 7b (power control process).

[2. Non-Gaussianity of Prediction Model]
When the present inventors examined the net load actual result data, they discovered that it would not be appropriate if a Gaussian property was assumed for the net load occurrence probability distribution. Accordingly, if Gaussianity is assumed as the prediction model data, an appropriate power purchase plan may not be performed.
However, since the prediction model data shown in FIG. 2 (b) is a probability distribution indicating the occurrence probability of each discrete net load amount, it is not necessary to assume Gaussianity for the occurrence probability of the net load in each time zone. Good. That is, the prediction model data 71 can represent not only a probability distribution that is a Gaussian distribution (normal distribution) but also a non-Gaussian distribution such as a multimodal distribution.
In the present embodiment, both Gaussian and non-Gaussian can be handled as the probability distribution. Therefore, when non-Gaussian prediction model data is appropriate, non-Gaussian prediction model data can be used.

  Hereinafter, it will be described that any occurrence probability distribution of power consumption, generated power, and net load cannot assume Gaussianity.

  Here, as the actual data of power consumption, 35 households of power consumption data and power generation data for one year measured in Higashi-Omi City, Shiga Prefecture from October 1, 2010 to September 30, 2011. Use minutes.

  FIG. 4 shows a histogram of power consumption in a time zone from 7:30 to 8:00 on each day of one year in one of the 35 households. The horizontal axis in FIG. 4 indicates the power consumption [Wh] (Consumption of electricity), and the vertical axis indicates the frequency distribution. In FIG. 4, it is a bimodal distribution in which peaks occur at two locations, around 1000 Wh and between 3000 and 4000 Wh, and non-Gaussianity is confirmed. This bimodality occurs because there is a period when relatively little power is used and a period when relatively much power is used during the year from 7:30 to 8:00. It is presumed that

  FIG. 5 shows the result of confirming by the normality test that non-Gaussianity (non-normality) occurs even in a period shorter than one year (here, 30 days).

  The normality test determines the frequency distribution of power consumption, generated power, and net load for each time period from the data for the last 30 days of each household, and determines whether the frequency distribution has normality. Is called. Since the number of data in the frequency distribution in each time zone is 30, the Shapiro-Wilk test was performed as a normality test method for a small number of data. At the time of the verification, the frequency distribution for each time zone (every hour) was obtained from the data for 30 days immediately before each reference day as the reference day for each household for 320 days in one year. Therefore, the number of tests for one household is 24 hours × 320 days = 7680 times.

In each graph of FIG. 5, the horizontal axis is the household id (house id), indicating the identifier (id) of each of the 35 households, and the vertical axis is normality (Gaussian) for each household as a result of the normal test. The number determined to be not (frequency) is shown.
FIG. 5A shows the number of households determined (rejected) that the frequency distribution of power consumption is not Gaussian. The average number of rejects is 6528.
FIG. 5B shows the number of households determined (rejected) that the frequency distribution of the amount of generated power is not Gaussian, and the average number of rejects is 7437.
FIG. 5C shows the number of households determined (rejected) that the frequency distribution of the net load (power generation amount-power consumption amount) has no Gaussianity, and the average number of rejections is 5196. .

As a result of 7680 trials, whether or not the number of rejections as shown in FIG. As a result of performing a two-sided test using a binomial test at the significance level α = 0.05, the null hypothesis that all of the power consumption, the generated power, and the net load were accidental events was rejected.
Thus, when the past (30 days) frequency distribution is constructed, normality is rejected.

  Therefore, it can be seen that it is desirable that the prediction model data 71 based on past performance data can have a non-Gaussian distribution.

Here, since the Gaussian distribution is described by an average value and variance, the prediction model data assuming the Gaussian distribution may be simple data consisting of the average value and variance.
However, if the Gaussian distribution is used, there is a risk that the predicted value will increase or decrease as will be understood from the comparison with the Weibull distribution in FIG. Such an upside risk and downside risk lead to an under-evaluation of an overdischarge risk or an overcharge risk of the power storage device, and easily deteriorate the power storage device.
From this point of view, the assumption of Gaussianity in the prediction model data 71 is not appropriate, and it is desirable that a non-Gaussian distribution be possible.

[3. Electricity purchase planning method considering non-Gaussian property]
[3.1 Outline of Electricity Purchase Planning Method]
Even if the probability distribution of the prediction model data 71 is a non-Gaussian distribution, the processing device 7 generates a power purchase plan using a Markov decision assumption that can handle such prediction model data 71.
In the present embodiment, the processing unit 7a uses the net load actual data (power consumption actual data and generated power actual data) on the d day immediately before the power purchase plan creation date, the next day ( Prediction model data 71 for the power purchase plan) is generated and stored in the storage unit 7b (see FIG. 2). The processing device 7 monitors the net load (power consumption and generated power) and stores the monitoring result in the storage unit 7b as actual data.

The processing unit 7a plans the power purchase amount at each time on the next day (planning target date) that is the planning target period from the prediction model data 71 and the Markov decision process. On the day of the plan (plan target date), the processing unit 7a purchases power from the power system side according to the power purchase plan.
Since the consumption amount and the power generation amount on the day are actually different from the predicted values, the power storage device 1 and the power generation device 3 (or power system) are shut off when overcharging occurs. If overdischarge occurs and additional power is required, additional power will be purchased from the power system.

[3.2 Modeling of storage status and amount of electricity purchased]
In order to formulate the Markov decision process, the power storage state (power storage amount) and the power purchase amount of the power storage device 1 are discretized and modeled.

[3.2.1 Discrete storage amount]
The storage amount (charge amount) of the power storage device 1 at each time on the planning target date is the storage amount set Ω: = {0, Δ,. . . , NΔ} elements. N is a natural number, Δ indicates a discretization width, and Δ: = S _max / N [Wh]. S _max is the storage capacity of the power storage device 1. Thus, the amount of power stored in the power storage device 1 is 0, Δ,. . . , NΔ (= S _max ).
The discretization width Δ of the storage amount is the same value as the discretization width Δ of the net load value in the prediction model data.

[3.2.2 Discrete time]
A set of discrete times h (time set) of the planning target date is represented by {0, 1,. . . H}. If the time set is a set of times every hour, H is “24” indicating 24 hours, and if the time set is a set of times every 30 minutes, H is “48” indicating 24 hours. It becomes.
The discretization width of each time included in the time set is set to be the same as the time zone width of each time zone data 71a, 71b, 71c constituting the prediction model data 71 of FIG. That is, the time h is a plurality of discrete times dividing one day (target period) into a plurality of time zones in the prediction model data 71.
In the following, it is assumed that the discretization width of each time included in the time set is 1 hour and H = 24, in alignment with FIG.

[3.2.3 State indicating first storage amount at each time (first state)]
S _{(h, i)} is defined as a symbol indicating a state (event) in which the charged amount at each time h becomes the i-th element of the charged amount set Ω.
As shown in FIG. 7, a set (state set) of states (power storage states) indicating storage amounts (0 to N) at respective times h from 0 to H is represented as S _h = {s _{(h, i)} } _{i. = 0,. . , N.}

[3.2.4 Electricity purchase amount]
The amount of power purchased (the amount of power purchased ₎ from each storage state s _{(h, i)} is represented by a _{(h, i)} . The power purchase amount a _{(h, i)} is the power purchase amount set {0, Δ,. . . , AΔ} element values. A is a natural number, Δ is a discretization width, and AΔ is an upper limit of purchased electric energy per unit time (time corresponding to the discretization width at each time = 1 hour).
The discretization width Δ of the power purchase amount is the same value as the discretization width Δ of the storage amount and the discretization width Δ of the net load value in the prediction model data. Thus, the amount of stored electricity, the amount of purchased power a _{(h, i)} , and the net load amount in the prediction model data are all expressed as discrete values of the same discretization width Δ.

[3.2.5 Probability distribution of net load]
Let Pr (l _h ) be the probability distribution of the predicted value l _h of the net load that occurs in the time zone [h, h + 1) indicated by time h. The time zone indicated by time h is defined by the left closed half-open section [h, h + 1). For example, if time h = 0, Pr (l ₀ ) is the probability of the predicted value l ₀ of the net load amount occurring in the time zone from 0 o'clock to 1 o'clock (time zone including 0 o'clock but not 1 o'clock). The distribution is shown (see FIG. 2 (b)).

A set (h = 0 to _H ) of probability distributions Pr (l _h ) for each time within the planning target period constitutes the prediction model data 71. Hereinafter, the “prediction model data 71” may be referred to as “prediction model Pr (l _h )”.

The prediction model Pr (l _h ) is generated by normalizing the frequency distribution of the net load amount in the time period [h, h + 1) in the past d days, assuming that the net load amount between the times is independent.
As described above with reference to FIG. 2B, in the frequency distribution of the net load amount, each class (net load amount range) is defined as a left closed half-open section b _k : = [kΔ, (k + 1) Δ). . However, for each time h, k is assumed to take the value of the element of the integer subset K _h. Integer subset K _h, for each time h, becomes the value of the number and elements of the element are different. This is because the frequency distribution of the net load amount differs in the distribution of the generated net load amount at each time h.

[3.2.6 Lower and upper limits of class in frequency distribution]
In the probability distribution Pr (l _h ) of the net load amount occurring in the time zone [h, h + 1) indicated by time h, the lower limit class is represented by m ^h Δ among all classes of the probability distribution Pr (l _h ). The upper limit class is represented by M ^h Δ. In the subset K _h , the number of elements and the value of the elements are different at each time h, so the lower limit class m ^h Δ and the upper limit class M ^h Δ are different at each time h.

[3.2.7 Transition probability]
A Markov decision process is a stochastic process having a set of states and a set of actions, and the probability of transition to the next state when a certain action is taken in each state is Pr.
In the present embodiment, the set of states in the Markov decision process is the above-described accumulation amount set S _h = {s _{(h, i)} } _{i = 0,. . Is N,} the set _{S h} element in a state _s of _{(h, i)} represents the charged amount of time h the (i × Δ).
In the present embodiment, the set of actions in the Markov decision process is the power purchase amount set {0, Δ,. . . , AΔ}, and the power purchase amount a _{(h, i),} which is an element of the power purchase amount set, indicates the power purchase amount when the storage amount is i × Δ at time h.

State _{s (h, i)} of the time h transition probability from the next time h + 1 state _{s (h + 1, j),} the state _{s (h, i)} purchased in electrodeposition _{a (h, i)} when subjected to , The probability Pr (s _{(h + 1, j)} | s _{(h, i} ), a _{(h, i)} ) for transition to the next state s _{(h + 1, J)} (see FIG. 7A). J is a natural number from 0 to N, similarly to i.

The power storage amount (power storage state) in the power storage device 1 varies depending on the net load amount including power generation and consumption in addition to the power purchase amount. Here, since the prediction model Pr (l _h ) indicates a probability distribution of the predicted value l _h of the net load amount occurring in the time zone [h, h + 1) corresponding to each time h, the state s _(h, power purchase _a in _{i) (h, i)} when subjected to, probability of transition to the state _{s (h + 1, j)} Pr (s (h + 1, j) | s (h, i), a (h, i) ) Is given based on the prediction model Pr (l _h ) and the power purchase amount a _{(h, i)} .

[3.2.8 Intermediate state (second state)]
Depending on the predicted net load amount, the power storage device 1 is overcharged (when the storage amount reaches the storage capacity _Smax ) or overdischarged (discharge is required even when the storage amount reaches 0). ) May occur. In this case, charge / discharge control such as shutting off the power generation device 3 and the power storage device 1 or purchasing additional power from an external power system is required.

In the Markov decision process of the present embodiment, in order to generate a power purchase plan that takes into account the costs associated with charge / discharge control for coping with overcharge or overdischarge, an intermediate state (first) in each time zone [h, h + 1) is used. 2 _{state) {z (h, k)} } k = m h,. _{. . , (N + A + M} ^h ₎ . That is, the intermediate state _{z (h, k),} each time h (where h is 0 to H-1 to the take values) states in _{s (h, i)} and the state at the next time h + 1 _{s (} defined as an intermediate state between _{h + 1, i)} . (See FIG. 7B). In other words, to the intermediate state _{z (h, k),} the first state _{s (h, i)} at time h are possible transition from the intermediate state _{z (h, k)} from the first state s at the next time h + 1 Transition to _{(h + 1, i)} is possible.

In each time zone [h, h + 1), ((N + A + M _h ) −m ^h +1) intermediate states z _{(h, k} ) are provided. Here, m ^h is a value obtained by dividing the lower limit class m ^h Δ in the probability distribution Pr (l _h ) of the net load occurring in the time zone [h, h + 1) indicated by time ^h by the discretization width Δ. is there.
As shown in FIG. 7B, in the state s _{(h, 0)} where the amount of electricity stored at time h is 0, when power consumption occurs in the time zone [h, h + 1) (when a negative net load amount occurs) Over discharge (insufficient power storage) occurs. In this case, based on the prediction model Pr (l _h ), additional power purchase of −m ^h Δ is required at the maximum. Z _{(h, m} ^h ₎ in FIG. 7B is one of intermediate states indicating such a shortage of power storage.

M _h is a value obtained by dividing the upper limit class M ^h Δ in the probability distribution Pr (l _h ) of the net load generated in the time zone [h, h + 1) indicated by the time ^h by the discretization width Δ.
As shown in FIG. 7B, in the state s _{(h, N)} where the amount of electricity stored at time h is N, when power generation by the power generator 3 occurs in the time zone [h, h + 1) (a positive net load amount occurs). In such a case, an overcharge of NΔ (power storage capacity) + AΔ (upper limit of power purchase) + M ^h Δ (power generation amount) occurs in the power storage device 1 at the maximum. In this case, it is necessary to shut off the power generation device 3 and the power storage device 1 so that charging exceeding the power storage capacity is not performed. In FIG. 7B, z _{(h, M} ^h ₎ is one of intermediate states indicating overcharge.

The intermediate state z _{(h, k)} may be omitted when the cost associated with charge / discharge control for dealing with overcharge or overdischarge (insufficient power storage) is not taken into consideration. Further, even in the case where the intermediate state z _{(h, k)} is provided, if the shortage of power storage is not considered as the cost, the intermediate state z _{(h, k)} indicating the shortage of power storage may be omitted, and overcharging is considered as a cost. If not considered, the intermediate state z _{(h, k)} indicating overcharge may be omitted.

The intermediate state z _{(h, k)} transitions to the next state (first state; storage state) according to the transition function ξ shown in the following equation (1).

The first expression (the uppermost expression) in Expression (1) is an intermediate state z _{(h, k)} , and no constraint violation (overcharge (k> N) or overdischarge (k <0)) occurs. It represents a state transition (0 ≦ k ≦ N).
The second equation (the second equation from the top) of the equation (1) avoids the overcharge state (k> N) in the intermediate state z _{(h, k)} by shutting off the power generation device 3 and the power storage device 1. Represents the state transition of the case.
The third expression (the lowermost expression) of Expression (1) represents a state transition when overdischarge (insufficient storage; k <0) in the intermediate state z _{(h, k)} is compensated by additional power purchase.

[3.2.9 Transition probability from storage state (first state) to intermediate state (second state)]
The transition probability Pr (z _{(h, k)} | s _{(h, i)} , a _{(h, i)} ) from the storage state s _{(h, i)} to the intermediate state z _{(h, k)} Is given based on the prediction model Pr (l _h ). Specifically, it is as the following formula (2).

[3.2.10 Transition probability from state at time h to state at time h + 1]
According to the above, in the state s (h, i) at the time h, the probability Pr (s _{(h + 1, j)} | s that makes a transition to the state s (h + 1, j) when the power purchase a (h, i) is performed. _{(H, i} ), a _{(h, i)} ) is expressed by the following equation (3).

[3.3 Formulation of Markov Decision Process]
Based on the above, the Markov decision process for determining the amount of electricity purchased is formulated as follows.
Each time zone [h, the system power selling price of h + 1) and ^{_{p H G [yen / Wh]}} . Reward functions r (s _{(h, i)} , a _{(h, i)} , z _{(h, k )} when a _{(h, i)} [Wh] is purchased from the storage state s _{(h, i) at} each time ₎ ) Is defined by the following equation (4).

In the formula ^{_{(3), p H G a}} (h, i) _{shows a (h,} i) purchase price of electricity when the power purchase [Wh] [yen]. min {kΔ, 0} is a function that selects the smaller of kΔ and 0, and max {kΔ−S _max , 0} is a function that selects the larger of kΔ−S _max and 0.
^{_{p H G ω m min {kΔ}} , 0} is constraint violation; indicates the cost of the (power storage shortage ^{_{k <0), p H G}} ω M max {kΔ-S max, 0} constraint violation (overcharge The cost in the case of k> N). The cost of constraint violation can be adjusted by adjusting the weight parameters ω _m and ω _M. By including the constraint violation cost in the reward function r, it is possible to express the deterioration cost of the storage battery and the additional power selling cost when overcharge occurs.
Note that at least one of the two constraint violation costs may be omitted.

[3.4 Algorithms for solving Markov decision processes]
The purpose of the Markov decision process of the present embodiment is to minimize the cost including the power purchase price of one day (the target period of the power purchase plan) (in this embodiment, the cost includes the loss cost due to constraint violation). This is a plan for the amount of electricity purchased in each state s _{(h, i)} .

State _{s (h, i)} the optimal state-value function of _{^{V * (s (h, i}} )) , the function _{Q (s (h, i)} , a (h, i)) shown by the following formula (5) It is calculated using.

The function of Equation (4) is expressed as V ^* (ξ (z _{(h, k,)} indicating the state value from the terminal state s _{(H, i) at} time H to the state ξ (z _{(h, k)} ) at the next time h + 1 _{. k)} It is defined recursively using)).

State _{s (h, i)} the optimal state-value function of _{^{V * (s (h, i}} )) , the function _{Q (s (h, i)} , a (h, i)) using the following formula (6 ) As the solution of the Bellman equation.

Further, the optimum amount of power purchase in each state s _{(h, i)} is determined by the following equation (7).

argmax {Q (s _{(h, i)} , a _{(h, i)} )}
Formula (6) is the minimum power purchase amount a ^{* of} one or a plurality of power purchase amounts a _{(h, i)} = a ′ that maximizes Q (s _{(h, i)} , a _{(h, i)} ) ^. _This is an expression for obtaining _{(h, i)} . Dependence on the external power system by selecting the minimum power purchase amount a ^* _{(h, i)} out of the power purchase amount that realizes the same minimum cost (cost including power purchase price and loss cost due to constraint violation) Can be minimized, leading to efficient use of renewable energy (for example, electric power energy by solar power generation).
In Markov decision process shown in FIG. 7A, the time state of _{H s (H, i),} that is, the former are all end states of _{S H.} An arbitrary state s _{(H-1, i)} at time H-1 is set as a starting point, and power purchase and a net load are added, so that a terminal state s _{(H, i)} is reached, and the Markov determination process ends.

[3.5 Generation of electricity purchase plan and operation based on electricity purchase plan]
The processing unit 7 solves the Markov decision process formulated as described above based on the prediction model Pr (l _h ), and plans the optimum power purchase amount a ^* _{(h, i)} in each state. Processing is performed (see FIG. 3).
The algorithm for solving the Markov decision process is as follows. The Markov decision process is solved by a backward induction.

In the above algorithm, the state values V ^* (s _{(h, i)} ) of all the states s _{(h, i} ) are initialized in the first to third lines.
Next, the state value V ^* (s _{(h, i)} ) of each state s _{(h, i} ) is updated in the sixth to eighth lines.
As described above, the state s _{(H, i)} at the time H is all treated as the terminal state, and the state value V ^* (s _{(h, i)} ) is obtained until the state s _{(0, i)} at the time 0. . In line 9, the optimum power purchase amount ^a _{* (h, i)} of each state _{s (h, i)} is determined.
As described above, the processing unit 7a determines the optimal power purchase amount of each state s _{(h, i)} by solving the Markov determination process. The processing unit 7a causes the storage unit 7b to store the determined optimum power purchase amount a ^* _{(h, i)} in each state s _{(h, i) as} the power purchase plan data 72.

Since the power purchase plan data 72 is configured by the optimum power purchase amount a ^* _{(h, i) of} each state s _{(h, i)} , the power _h at the day when the power purchase plan is executed and the power storage device at that time h. 1 actual storage amount iΔ and power purchase amount a ^* _{(h, i)} are associated with each other. Therefore, when the processing unit 7a refers to the power purchase plan data 72 based on the time h on the day when the power purchase plan is executed and the actual power storage amount iΔ of the power storage device 1 at the time h, the power purchase amount a ^* _{( h, i)} = a _h can be obtained.

  Such a power purchase plan process is performed at the end of the previous day of the target date (the current day) of the power purchase plan. In the present embodiment, the processing unit 7a also performs the prediction model data generation process described above prior to the power purchase planning process.

The processing unit 7a performs power control processing including power purchase control processing based on the generated power purchase plan data 72. Processing portion 7a, as purchased power control process, monitors the storage amount of the power storage device 1, based on the current time h and the power storage amount, determines a power purchase amount a _h until the next time h + 1. Then, the processing unit 7a to the power control unit 6 outputs a command for purchasing the determined power purchase amount a _h, to perform the power control unit 6 two power purchase.

Here, the net load amount in the prediction model is a discrete value, whereas the actual net load amount on the day of plan execution is a continuous value. Thus, planning run day time h of course also charged amount s _h of the power storage device 1 in, it varies continuously. Therefore, the processing unit 7a, the monitored accumulation amount _{s h,} obtaining a charge state _{s (h, i) s} were projected into discrete storage amount corresponding to ^{h *.} Processing unit 7a, based on the current time h and discrete storage amount s _h ^*, determines a power purchase amount a _h.

Projection from the continuous storage amount _{s h} into discrete storage amount _s ^{h *} correspond to a plurality of charge state _{s (h, i)} at time h plurality of power storage amount iΔ (= 0, Δ, .. ., of N), it is performed by the absolute value of the closest value (a difference in continuous storage amount s _h is the smallest charge amount).

The storage amount s h of continuous values in place of projecting the discrete storage amount s h *, the storage amount s h from purchased electric quantity a * (h, i) of the continuous value to allow determine, a discrete The discrete power purchase amount a * (h, i) determined for the power storage state s (h, i) may be converted in advance into a continuous power purchase amount by interpolation.

When the net load amount l _h generated in the time zone [h, h + 1) is insufficient for storage (s _h + a _h + l _h <0) or overcharge (s _h + a _h + l _h > S _max ), the processing unit 7a Performs a charge / discharge control process (shut-off of the power generation apparatus 3 or additional power purchase) for the power control unit 6 so that 0 <s _h + a _h + l _h <S _max .

[4. Evaluation]
The result of having evaluated the power management system 100 concerning this embodiment is shown.
For evaluation, we used actual data (power consumption data and generated power amount data) for 35 households per year measured in Higashi-Omi-shi, Shiga Prefecture during the period from October 1, 2010 to September 30, 2011. .

FIG. 8A illustrates a prediction model Pr (l _h ) for a certain day of a certain household constructed under the condition of d = 30 in the method illustrated in FIG. In FIG. 8A, the horizontal axis is time [h], and shows a total of 24 time zones per hour. In FIG. 8A, the vertical axis represents the net load amount l _h [Wh]. The scale at the left end of FIG. 8A shows the occurrence probability of the net load amount l _{h at} a certain time h, and the occurrence probability is shown in the range of 0.00 to 0.50. The occurrence probability = 0.50 indicates that the corresponding net load amount has occurred with a probability of 0.50 on the 30th (d = 30), that is, has occurred 15 times.
FIG. 8A shows a non-Gaussian probability distribution.

FIG. 8B shows a prediction model Pr (l _h ) constructed as a Gaussian distribution under the condition of d = 30, not the method shown in FIG. The construction of the prediction model Pr (l _h ) as a Gaussian distribution is based on the average net load μ _{h for} each time zone [h, h + 1) and the standard from the net load (power generation amount—power consumption amount) in the past d days. It is obtained by calculating the deviation σ _h .
In FIG. 8B, the meanings of the horizontal and vertical axes and the scale at the left end are the same as those in FIG.

  Power purchase shall be performed every hour. That is, the power purchase amount for 24 times from the power storage state at 0:00 to the power storage state at 24:00 is planned. For this reason, H = 25. The power price of the external system was set as shown in FIG. 9 with reference to the power price “Hapi e Plan” by time of Kansai Electric Power. In FIG. 9, the horizontal axis represents time, and the vertical axis represents the power purchase price.

The case where the storage capacity _Smax of the power storage device 1 was set to 2000 Wh, 4000 Wh, 6000 Wh, 8000 Wh, 10000 Wh, and 15000 Wh was evaluated. Also in this case, the division number N-1 is given so that the discretization width Δ = 10 [Wh]. The purchase plan target period for which evaluation was performed is each day of 200 days from November 1, 2010, and immediately before the forecast model Pr (l _h ) is generated on each day as the purchase plan target period. 30 days worth of data is available.

  The evaluation uses a frequency distribution (nonparametric distribution) that may be non-Gaussian as shown in FIG. 8A as a prediction model, and a normal distribution (Gaussian distribution) as shown in FIG. 8B. In each case, the amount of electricity purchased for 200 days was compared for each household.

Two cases of (ω _m , ω _M ) = (1, 0) and (ω _m , ω _M ) = ( ₁₀ , 0) are considered as weights for the cost when the constraint is violated. In the former case, ω _m = 1 is set on the assumption that no extra cost is required even if additional power is purchased to avoid overdischarge (insufficient storage). When shutting down the power generation device 3 to avoid overcharge, additional cost may be considered due to opportunity loss, but not considered here, and ω _M = 0 in both cases. In the latter case, ω _m = 10. In this case, when overdischarge progresses to the extent that additional power purchase is required, the power storage device 1 is deteriorated due to overdischarge, and a cost corresponding to the deterioration is set.

FIG. 10 shows the distribution of the amount of electricity purchased when the power storage device 1 having a power storage capacity of 6000 [Wh] is installed in a household with household id = 3. Figure 10 (a) is a case of the prediction model Pr _{(l h)} assuming a Gaussian, a case of FIG. 10 (b) is a predictive model Pr nonparametric distribution _{(l h).}
In FIG. 10, the horizontal axis represents the power purchase payment amount per day, and the vertical axis represents the frequency of occurrence of the corresponding power purchase payment amount for 200 days. FIG. 10 shows a case where ω _m = 1.

In order to determine whether or not the purchase payment amount in each of FIGS. 10A and 10B has a statistically significant difference, the normality of the payment amount distribution shown in FIGS. 10A and 10B was tested by the Shapiro-Wilk test. The results of the Shapiro-Wilk test are shown in Table 1.

  Table 1 shows the number of households whose normality was rejected among 35 households under various storage capacity conditions. Since normality was rejected in the distribution of 70% or more from the results shown in Table 1, the Wilcoxon signed rank sum test, which is a non-parametric test for judging whether there is a significant difference in the representative value with respect to the data with correspondence, is performed. Adopted. The test was a one-sided test. In other words, against the null hypothesis that there is no significant difference in the representative value, an alternative hypothesis that the representative value of the nonparametric distribution is smaller than the representative value of the normal distribution was tested. The significance level was α = 0.05.

The result of Wilcoxon signed rank sum one-sided test is shown in the second column of Table 2. Each row in the second column of Table 2 shows the number of households out of 35 households whose null hypothesis was rejected. For the result that the payment amount was small in n out of 35 households, the null hypothesis that this is a coincidence event and the alternative hypothesis that the payment amount in non-parametric distribution becomes small, the significance level α = 0 A one-sided test by binomial test (sign test) was performed at .05. The asterisk (*) in the second column is attached to those confirmed to have a significant difference as a result of the binomial test. In both weights ω _m = 1 and ω _m = 10, as the storage capacity increases, the number of households whose annual payment is smaller is increased by using the nonparametric distribution. The third column of Table 2 is the average of the ratio of the annual payment when using the non-parametric distribution and the annual payment when using the normal distribution for each household.

In summary, it was confirmed that the annual payment amount decreased with the increase of the storage capacity by using the nonparametric distribution in both the weights ω _m = 1 and ω _m = 10. Specifically, when ω _m = 1, the storage capacity is 1% to 2% when the storage capacity is 6000 [Wh] or more, and when ω _m = 10, the storage capacity is 8000 [Wh] and the saving is 3% to 10%. Was shown to be expected on average.

[5. Selection of non-parametric distribution prediction model and normal distribution prediction model]
FIG. 11 shows a non-parametric distribution that is a frequency distribution as shown in FIGS. 2B and 8A and a normal distribution (Gaussian as shown in FIG. 8B) as the prediction model Pr (l _h ). The power purchase plan process including the prediction model selection process (step S10) for selecting either one of the distribution) is shown.

  As described above, even if the prediction model is based on the net load actual data, a difference occurs in the power purchase amount depending on whether the prediction model has a non-parametric distribution or a normal distribution. In particular, in the evaluation results described above, the non-parametric distribution is advantageous when the storage capacity is large, but the normal distribution is advantageous when the storage capacity is small.

In the power purchase planning process of FIG. 11, the processing unit 7a can select any one of the nonparametric distribution normal distributions as the prediction model Pr (l _h ), so that the degree of freedom is widened.

  The processing unit 7a selects the prediction model based on, for example, the storage capacity of the power storage device 1 installed at the base, or based on an input of a user instruction indicating which one to select, It can be made based on the determination as to which one can be selected based on the actual amount data to reduce the power purchase payment.

  In the prediction model acquisition in step S11 of FIG. 11, the selected prediction model is acquired. Step S12 and step S13 are the same as those in FIG.

[6. Management server]
FIG. 12 shows a management system 100 configured to perform a power purchase plan not on the management device 4 provided at the base, but on the management server 200 provided on a network such as the Internet.

  The management server 200 includes a processing unit 210 and a storage unit 220. The storage unit 220 stores the net load amount prediction model 221 applied to each site, and the net transmitted from the management device 4 at each site. An area for storing actual load amount data (power consumption actual result data and generated power amount actual data) 223 and an area for storing power purchase plan data 222 transmitted to the base are provided.

  The management server 200 performs a prediction model data generation process for generating a prediction model (prediction model data) 221 based on the net load amount result data 223 transmitted from the management device 4 at each site. The prediction model data generation processing in the management server 200 is the same as the prediction model data generation processing described above that is performed by the management device 4.

  In addition, the management server 200 performs the same power purchase plan process as the power purchase plan process described above as performed by the management apparatus 4 to generate the power purchase plan data 222. The management server 200 transmits the generated power purchase plan data 222 to the management device 4 at each site.

The management device 4 in FIG. 12 includes a communication unit 9 for transmitting net load amount actual data to the management server 200 and receiving power purchase plan data 222 from the management server 200.
In the management system 100 of FIG. 1, the management server 200 functions as a management device that generates a power purchase plan on behalf of the management device 4 at each site, and performs prediction model data generation processing and power purchase plan processing. The management apparatus 4 does not need to perform the prediction model data generation process and the power purchase planning process, and only needs to perform the power control process for the power control unit 6.

[6. Addendum]
The present invention is not limited to the above embodiment, and can be appropriately changed within the scope described in the claims.

DESCRIPTION OF SYMBOLS 1 Electric power storage apparatus 2 Electric power consumption apparatus 3 Electric power generation apparatus 4 Management apparatus 5 Power line 6 Electric power control part 7 Computer (processing apparatus)
7a processing unit 7b storage unit 9 communication unit 71 prediction model 71a time zone data 71b time zone data 71c time zone data 72 power purchase plan data 100 management system 200 management server (management device)
210 Processing Unit 220 Storage Unit 221 Prediction Model 222 Power Purchase Plan Data 223 Actual Data

Claims (12)

A power storage device that charges the purchased power and discharges it to supply power to a power consuming device; and
A management device for generating a power purchase plan;
With
The management device
A storage unit that stores a prediction model including a probability distribution of a predicted value of a net load in the power storage device for each of a plurality of time zones within a target period that is a target of a power purchase plan;
A processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
With
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The Markov decision process can transition when a power purchase is performed from a first state at a certain first time, and a plurality of second states that can transition to a first state at a time next to the first time. In addition,
The second state includes a state indicating at least one of overcharge and insufficient storage in the power storage device,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The probability of transition to the second state when purchasing power from the first state is given based on the prediction model,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A power management system that determines the amount of electricity purchased. A power storage device that charges the purchased power and discharges it to supply power to a power consuming device; and
A management device for generating a power purchase plan;
With
The management device
A storage unit that stores a prediction model including a probability distribution of a predicted value of a net load in the power storage device for each of a plurality of time zones within a target period that is a target of a power purchase plan;
A processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
With
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. Ri processing der to determine the power purchase amount in each
The power purchase planning process includes a selection process for selecting the prediction model used to solve the Markov decision process,
The selection process, the as prediction model, first prediction model and power management system processing der Ru for selecting one of the second prediction model the probability distribution is non-parametric distribution probability distribution is a normal distribution. A power generator,
A power storage device that charges the purchased power or the power generated by the power generation device and discharges the power to supply power to the power consuming device; and
A management device for generating a power purchase plan;
With
The management device
Prediction of net load in the power storage device, which is an amount obtained by subtracting the power consumption amount in the power consuming device from the power generation amount in the power generation device, for each of a plurality of time zones within a target period to be a target of the power purchase plan A storage unit for storing a prediction model including a probability distribution of values;
A processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
With
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A power management system that determines the amount of electricity purchased. A management device for generating a power purchase plan,
A storage unit that stores a prediction model including a probability distribution of predicted values of net load in the power storage device for each of a plurality of time zones within a target period to be a target of a power purchase plan;
A processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
With
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The Markov decision process can transition when a power purchase is performed from a first state at a certain first time, and a plurality of second states that can transition to a first state at a time next to the first time. In addition,
The second state includes a state indicating at least one of overcharge and insufficient storage in the power storage device,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The probability of transition to the second state when purchasing power from the first state is given based on the prediction model,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A management device that is a process for determining the amount of electricity purchased in each. A management device for generating a power purchase plan,
A storage unit that stores a prediction model including a probability distribution of predicted values of net load in the power storage device for each of a plurality of time zones within a target period to be a target of a power purchase plan;
A processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
With
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. Ri processing der to determine the power purchase amount in each
The power purchase planning process includes a selection process for selecting the prediction model used to solve the Markov decision process,
The selection process, the as prediction model, a probability distribution is the first prediction model and process der Ru management system that selects one of the second prediction model the probability distribution is nonparametric distribution is a normal distribution. A power purchase plan included in a power management system including a power generation device and a power storage device that charges the purchased power or the power generated by the power generation device and discharges the power to supply power to the power consuming device is generated. A management device,
The predicted value of the net load in the power storage device, which is the amount obtained by subtracting the power consumption amount in the power consuming device from the power generation amount in the power generation device, for each of a plurality of time zones within the target period subject to the power purchase plan A storage unit for storing a prediction model composed of a probability distribution of
A processing unit that performs a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
With
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A management device that is a process for determining the amount of electricity purchased in each. A method of generating a power purchase plan by a computer,
Storing a prediction model including a probability distribution of a predicted value of a net load in a power storage device for each of a plurality of time zones within a target period to be a target of a power purchase plan,
A power purchase plan process for generating the power purchase plan by solving a Markov decision process;
Including
The Markov determination process has a plurality of first states that discretely indicate a storage amount of the power storage device for each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The Markov decision process can transition when a power purchase is performed from a first state at a certain first time, and a plurality of second states that can transition to a first state at a time next to the first time. In addition,
The second state includes a state indicating at least one of overcharge and insufficient storage in the power storage device,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The probability of transition to the second state when purchasing power from the first state is given based on the prediction model,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A method that is a process of determining the amount of electricity purchased in each. A method of generating a power purchase plan by a computer,
Storing a prediction model including a probability distribution of a predicted value of a net load in a power storage device for each of a plurality of time zones within a target period to be a target of a power purchase plan,
A power purchase plan process for generating the power purchase plan by solving a Markov decision process;
Including
The Markov determination process has a plurality of first states that discretely indicate a storage amount of the power storage device for each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. Ri processing der to determine the power purchase amount in each
The power purchase planning process includes a selection process for selecting the prediction model used to solve the Markov decision process,
The selection process, as the prediction model, Ru processing der the first prediction model and the probability distribution probability distribution is a normal distribution selects one of the second prediction model is a nonparametric distribution methods. A computer generates a power purchase plan in a power management system including a power generation device and a power storage device that charges the purchased power or the power generated by the power generation device and discharges the power to supply power to a power consuming device. A method,
The predicted value of the net load in the power storage device, which is the amount obtained by subtracting the power consumption amount in the power consuming device from the power generation amount in the power generation device, for each of a plurality of time zones within the target period subject to the power purchase plan A prediction model consisting of a probability distribution of
A power purchase plan process for generating the power purchase plan by solving a Markov decision process;
Including
The Markov determination process has a plurality of first states that discretely indicate a storage amount of the power storage device for each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A method that is a process of determining the amount of electricity purchased in each. Computer
A storage unit that stores a prediction model including a probability distribution of predicted values of net load in the power storage device for each of a plurality of time zones within a target period to be a target of a power purchase plan;
A processing unit for performing a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
A computer program for functioning as
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The Markov decision process can transition when a power purchase is performed from a first state at a certain first time, and a plurality of second states that can transition to a first state at a time next to the first time. In addition,
The second state includes a state indicating at least one of overcharge and insufficient storage in the power storage device,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The probability of transition to the second state when purchasing power from the first state is given based on the prediction model,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A computer program that determines the amount of electricity purchased. Computer
A storage unit that stores a prediction model including a probability distribution of predicted values of net load in the power storage device for each of a plurality of time zones within a target period to be a target of a power purchase plan;
A processing unit for performing a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
A computer program for functioning as
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. Ri processing der to determine the power purchase amount in each
The power purchase planning process includes a selection process for selecting the prediction model used to solve the Markov decision process,
The selection process, the as prediction model, first prediction model and processes der Ru computer program the probability distribution selects one of the second prediction model is a non-parametric distribution probability distribution is a normal distribution. Generating a power purchase plan in a power management system including a power generation device and a power storage device that charges the purchased power or the power generated by the power generation device and discharges the power to supply power to a power consuming device. for,
The predicted value of the net load in the power storage device, which is the amount obtained by subtracting the power consumption amount in the power consuming device from the power generation amount in the power generation device, for each of a plurality of time zones within the target period subject to the power purchase plan A storage unit for storing a prediction model composed of a probability distribution of
A processing unit for performing a power purchase plan process for generating the power purchase plan by solving a Markov decision process;
A computer program for functioning as
The Markov determination process has a plurality of first states that discretely indicate the storage amount of the power storage device at each of a plurality of discrete times dividing the target period into a plurality of the time zones,
The prediction model is for giving a transition probability from the first state at each time to the first state at the next time in the Markov decision process,
The power purchase planning process uses a plurality of first states to solve the Markov decision process using the prediction model stored in the storage unit and to minimize the cost including the power purchase price within the target period. A computer program that determines the amount of electricity purchased.