JP2021052588A - Electric power demand forecasting device and electric power demand forecasting method - Google Patents

Abstract

To predict the electricity demand of consumers by simple processing using data on the electricity consumption of past consumers.SOLUTION: An electric energy demand forecasting device 1 includes a model parameter determination unit 17 that determines model parameters of a mathematical model that predicts electric energy demand on the basis of past electric energy consumption information and weather information of consumers, and a power demand calculation unit 21 that applies weather forecast information to a mathematical model to calculate power demand, and the power demand includes a first term based on the past power consumption obtained by excluding a portion that depends on the weather, a second term based on the amount of electricity used depending on the past weather, and a third term of an error term.SELECTED DRAWING: Figure 1

Description

The present invention relates to a power demand prediction device and a power demand prediction method for predicting the power demand of a consumer.

Conventionally, electric power companies such as new electric power companies procure electric power from the one-day market (spot market) or the same-day market (hourly market) on the Japan Wholesale Electric Power Exchange (electric power trading market), and the procured electric power. Is supplied to consumers (residents who use electricity demand facilities, etc.). In the procurement of such electric power, if the amount of electricity procured does not match the actual amount of electric power demand, a penalty charge (imbalance charge) or waste (provided free of charge to the electric power company) will occur. It is required to accurately predict the amount of demand. For example, when procuring electric power from the market, an electric power company is known to predict the amount of electric power demand based on the past (the day before or the day before the previous day) consumer power consumption (power consumption).

On the other hand, the power consumption of consumers includes power consumption that fluctuates according to weather conditions such as outside temperature and humidity. It is difficult to accurately match the actual power demand. Further, it is conceivable to modify the forecast of the electric power demand as appropriate based on the predicted value of the outside air temperature, but manual work by a skilled operator is required, and the workload is large.

On the other hand, there is known a power demand forecasting system that predicts the power consumption of a consumer at a forecasting target time based on a power consumption forecasting model and an outside temperature at the forecasting target time point (see Patent Document 1). This power demand prediction system extracts the outside temperature power relationship (relationship between the outside temperature and the outside temperature fluctuation power that fluctuates according to the outside temperature among the power consumption), and based on the extracted outside temperature power relationship. , Create a power consumption prediction model for predicting the power consumption of consumers according to the outside temperature.

Japanese Patent No. 6193400

In the prior art described in Patent Document 1, the electric power used by the consumer is a constant base electric power in a predetermined period, an outside temperature fluctuating electric power that fluctuates according to the outside temperature, and the behavior of the consumer (resident, etc.). It is separated into details consisting of action power that fluctuates according to. Then, in creating the power consumption prediction model, the outside temperature power relationship is extracted based on the past power consumption value data of the time zone when the correlation between the outside temperature and the power consumption is high, and based on the outside temperature power relationship, The behavioral state, which is the power usage state of the consumer, is estimated, and based on the estimated behavioral state, a behavioral state prediction model for predicting the behavioral state of the consumer according to the outside temperature is created, and the consumer Calculate the action power, which is the remaining power excluding the outside temperature fluctuation power and the reference base power, and calculate the action power of the consumer in each action state based on the action power and the action state. Predict.

Therefore, the above-mentioned conventional technique has a problem that the data processing for creating the power consumption prediction model is complicated.

The present invention has been devised in view of the problems of the prior art, and makes it possible to predict the electric power demand of the consumer by a simple process using the data on the electric energy used by the consumer in the past. The main purpose is to provide an electric energy demand forecasting device and an electric energy demand forecasting method.

The electric energy demand forecasting device of the present invention is an electric energy demand forecasting device that predicts the electric energy demand of a consumer based on a mathematical model, and acquires the electric energy consumption in the past by the consumer. A unit, a weather information acquisition unit that acquires past weather information of the area where the customer is located, and a plurality of model parameters included in the mathematical model based on the information on the amount of power used and the past weather information. The electric energy demand amount for calculating the electric energy demand amount of the consumer by applying the model parameter determination unit to be determined respectively and the forecast information of the weather on the prediction target date to the mathematical model in which the plurality of model parameters are determined. A calculation unit is provided, and in the mathematical model, the predicted electric energy of the consumer includes a function based on the past electric energy excluding the electric energy depending on the past weather. The configuration includes a first term, a second term including a function based on the amount of power consumption depending on the weather on the prediction target day, and a third term as an error term.

The electric energy forecasting method of the present invention is an electric energy forecasting method using an electric energy forecasting device that predicts an electric energy demand of a consumer based on a mathematical model, and obtains information on past electric energy consumption by the consumer. Acquire, acquire the past weather information of the area where the consumer is located, determine and predict each of a plurality of model parameters included in the mathematical model based on the information on the amount of electric energy used and the past weather information. By applying the forecast information of the weather on the target day to the mathematical model in which the plurality of model parameters are determined, the electric energy demand of the consumer is calculated, and the predicted electric energy of the consumer in the mathematical model is calculated. The electric energy demand is based on the first term including a function based on the past electric energy excluding the electric energy depending on the past weather, and the electric energy depending on the weather on the forecast target day. The configuration includes a second term including a function and a third term as an error term.

According to the present invention, it is possible to predict the electric power demand of a consumer by a simple process using the data on the electric power consumption of the past consumer.

Functional block diagram of the power demand forecasting device according to the first embodiment Hardware configuration diagram of the power demand forecasting device according to the first embodiment A flow chart showing the flow of power demand prediction processing by the power demand prediction device according to the first embodiment. A flow chart showing details of the model parameter determination process (step ST101) in FIG.

The first invention made to solve the above problem is a power demand prediction device that predicts a consumer's power demand based on a mathematical model, and acquires information on the past power consumption by the consumer. It is included in the mathematical model based on the power consumption acquisition unit, the weather information acquisition unit that acquires the past weather information of the area where the consumer is located, the power consumption information, and the past weather information. By applying the model parameter determination unit that determines each of the plurality of model parameters and the forecast information of the weather on the prediction target date to the mathematical model in which the plurality of model parameters are determined, the electric energy demand of the consumer can be obtained. A power demand calculation unit for calculating is provided, and in the mathematical model, the predicted power demand of the consumer is obtained by excluding the power consumption depending on the past weather from the past power consumption. The configuration includes a first term including a function based on the above, a second term including a function based on the amount of power consumption depending on the weather on the prediction target day, and a third term as an error term.

According to this, past consumers do not need to perform complicated processing such as extracting data that is highly correlated with the outside temperature in the past consumer power consumption data and predicting the behavioral state of the consumer. It is possible to predict the electric energy demand of consumers by simple processing using the data related to the electric energy consumption of.

Further, in the second invention, the plurality of model parameters include the first to third model parameters included in the first to third terms, respectively, and the second model parameter is the second model parameter. The configuration is constrained to a non-negative value so that the term is positive.

This facilitates the interpretation of weather-dependent power consumption in a mathematical model.

Further, in the third invention, the plurality of model parameters include the first to third model parameters included in the first to third terms, respectively, and the model parameter determining unit includes the first to third models. By fixing any two of the first to third model parameters and determining the remaining one model parameter so as to maximize a predetermined log-likelihood function containing the three model parameters. , The first to third model parameters are sequentially determined.

According to this, it is possible to predict the electric power demand of the consumer by a simpler process using the data on the electric power consumption of the past consumer.

Further, in the fourth invention, the model parameter determining unit clusters the data constituting the past weather information, and based on the plurality of clusters generated by the clustering, the amount of power consumption depending on the past weather. The configuration is such that the function based on is determined.

According to this, it is possible to accurately predict the electric power demand of the consumer by a simple process.

Further, in the fifth invention, the past weather information is configured to include at least one data of outside air temperature, humidity, weather, and precipitation.

According to this, it is possible to predict the electricity demand of the consumer by simple processing based on the easily available weather information.

Further, in the sixth invention, the past weather information is configured to be a representative value of the data in a predetermined time zone.

According to this, it is possible to predict the electric power demand of the consumer by simple processing based on the meteorological information that can be obtained more easily, and the electric power demand by using the time-dependent meteorological information. It is possible to avoid complication of prediction processing.

Further, in the seventh invention, an event information acquisition unit for acquiring information on past events held in the area where the consumer is located, which is input by the operator, is further provided, and the second item is the event. The power demand calculation unit includes a function based on the influence, and the power demand calculation unit applies the schedule information of the event to be held on the forecast target day to the mathematical model in which the plurality of model parameters are determined, so that the consumer's The configuration is such that the amount of electricity demand is calculated.

According to this, by considering the information of past events, it becomes possible to predict the electric power demand of the consumer more accurately.

Further, the eighth invention is a method of predicting electric energy by an electric energy forecasting device that predicts electric energy of a consumer based on a mathematical model, and acquires information on past electric energy used by the consumer. , Acquire past weather information of the area where the customer is located, determine a plurality of model parameters included in the mathematical model based on the information on the amount of electric energy used and the past weather information, and determine the forecast target date. By applying the forecast information of the weather in the above to the mathematical model in which the plurality of model parameters are determined, the electric energy demand of the consumer is calculated, and the electric energy of the consumer predicted by the mathematical model. The quantity is the first term including a function based on the past power consumption excluding the past weather-dependent power consumption, and the function based on the weather-dependent power consumption on the forecast target day. The configuration includes a second term including and a third term as an error term.

According to this, past consumers do not need to perform complicated processing such as extracting data that is highly correlated with the outside temperature in the past consumer power consumption data and predicting the behavioral state of the consumer. It is possible to predict the electric energy demand of consumers by simple processing using the data related to the electric energy consumption of.

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

(First Embodiment)
FIG. 1 is a functional block diagram of the electric power demand amount prediction device 1 according to the first embodiment of the present invention.

The electric power demand forecasting device 1 predicts the electric power demand of a plurality of consumers 2 at the forecast target date and time (here, a plurality of time zones constituting the forecast target date) based on the forecast model (mathematical model) described later. It is a device. The power demand forecasting device 1 is communicably connected to the aggregator 4 via a communication network 3 such as the Internet or LAN. The prediction result by the power demand prediction device 1 is provided to the aggregator 4. As a result, the aggregator 4 procures electric power that may be used by a plurality of consumers 2 from the electric power trading market 5 on the forecast target date and time based on the electric power demand forecast result.

The plurality of consumers 2 are, for example, persons (residents, facility managers, etc.) who use electric power demand facilities such as houses and office buildings. Each consumer 2 is provided with a smart meter (SM) 6 that measures the amount of electric power used (here, the amount of electric power used for each 30 minutes constituting one day) at predetermined time intervals. The smart meter 6 is communicatively connected to the aggregator 4 and transmits the measured power consumption data to the aggregator 4.

The aggregator 4 is, for example, a small-scale electric power company such as a new electric power company, and includes a management device 10 that performs necessary information processing. In the aggregator 4, by using the management device 10, the operator can perform a process of aggregating the data of the electric power consumption measured by each smart meter 6 and a process of procuring electric power from the electric power trading market 5. .. The management device 10 can be configured by a computer that operates by a predetermined program, similarly to the power demand prediction device 1 described later. However, the processing executed by the management device 10 may be shared by a plurality of computers.

The electric power trading market 5 is, for example, the Japan Electric Power Exchange, which enables the aggregator 4 and the power generation company to buy and sell electric power.

As shown in FIG. 1, the power demand prediction device 1 includes a power consumption acquisition unit 11, a storage unit 12, a weather information acquisition unit 13, an event information acquisition unit 16, a model parameter determination unit 17, and a power demand calculation unit 21. , And a prediction result transmission unit 23.

The power consumption acquisition unit 11 sequentially acquires information on the past power consumption (that is, the actual power consumption) by the consumer 2 from the aggregator 4. The acquired power consumption information is stored in the storage unit 12.

The meteorological information acquisition unit 13 sequentially acquires past meteorological information in the area where the consumer 2 is located (that is, the electric power demand facility of the consumer 2 is installed) from the external meteorological information database (DB) 14. The acquired past weather information is appropriately associated with the above-mentioned information on the amount of power used, and is stored in the storage unit 12. Although not shown, the weather information database 14 can communicate with the electric power demand forecasting device 1 via the network 3.

Such past meteorological information includes data on air temperature (outside air temperature), humidity, weather, precipitation, and the like. Here, the past weather information may be a representative value of data in a predetermined time zone (for example, a daily average value, a median value, a maximum value, a minimum value, etc.). However, the electric power demand forecasting device 1 can also use the past weather information at a predetermined date and time.

The event information acquisition unit 16 acquires information on events that have been held in the past in the area where the power demand facility of the consumer 2 is installed, and information on the schedule of events that will be held on the forecast target date. The acquired information is stored in the storage unit 12. Information on such an event includes information such as the name of the event or event held in the target area, the date and time when the event was held, and the like. Further, the event information acquisition unit 16 acquires information on past events input by the operator from the input device 35 (see FIG. 2) of the power demand forecasting device 1 and scheduled information on the event to be executed on the forecast target date. be able to.

The model parameter determination unit 17 acquires past power consumption information, past weather information, and past event information from the storage unit 12. Further, the model parameter determination unit 17 determines the model parameters of the prediction model, which will be described in detail later, based on the past information. In determining the model parameters, past event information is not essential, and the model parameter determination unit 17 may omit the acquisition of event information.

The electric power demand calculation unit 21 calculates the electric power demand of the consumer by applying the forecast information of the weather on the forecast target date to the forecast model. Further, the electric power demand calculation unit 21 can use the schedule information of the event to be carried out on the forecast target day as necessary for calculating the electric power demand of the consumer. In this prediction model, the model parameters are determined by the model parameter determination unit 17.

Further, the electric power demand calculation unit 21 acquires the weather forecast information from the external weather forecasting organization 22. The weather forecasting agency 22 is, for example, the Japan Meteorological Agency or a private private weather information company. The electric power demand calculation unit 21 can acquire weather forecast information from the server devices operated by them. The electric power demand amount calculated by the electric power demand amount forecasting device 1 is the total amount of the electric power demand amount of the plurality of consumers 2, but it is also possible to individually predict the electric power demand amount of each customer 2.

The prediction result transmission unit 23 transmits the prediction result including the power demand amount (prediction value) of the consumer calculated by the power demand amount calculation unit 21 to the management device 10 of the aggregator 4 via the network 3.

Although FIG. 1 shows an example in which the power demand prediction device 1 and the aggregator management device 10 are individually provided, the power demand prediction device 1 is provided integrally with the management device 10 (that is, the power is provided in the management device 10). It is also possible to add a function as the demand amount forecasting device 1). Alternatively, the aggregator management device 10 may have some functions of the power demand prediction device 1 and may be configured to predict the power demand of the consumer 2 in cooperation with the power demand prediction device 1.

FIG. 2 is a hardware configuration diagram of the power demand forecasting device 1 according to the first embodiment.

The power demand forecasting device 1 is composed of a computer having known hardware. The main body of the power demand prediction device 1 includes a processor 31 including a CPU (Central Processing Unit) that comprehensively executes various information processing and control of peripheral devices based on a predetermined control program, and a work area of the processor 31. A RAM (Random Access Memory) 32 that functions as such as, a ROM (Read Only Memory) 33 that stores control programs and data executed by the processor 31, and a network interface 34 that executes communication processing via the network 3 are provided. Each of these components is connected to each other via a bus 40.

Further, the power demand prediction device 1 is an input device 35 composed of a keyboard, a touch panel, or the like for the operator of the power demand prediction device 1 to input various commands and data as peripheral devices, and the power demand prediction device 1. A storage consisting of a monitor 36 that displays various information related to the power demand prediction process executed by the user, and an HDD (Hard Disk Drive) that stores various data used in the power demand prediction process and the calculation results of those data. 37 is provided. The storage 37 constitutes the above-mentioned storage unit 12.

The functions (at least a part thereof) of each part in the power demand prediction device 1 shown in FIG. 1 described above can be realized by the processor 31 executing a predetermined control program. At least a part of the function of the power demand prediction device 1 may be replaced by processing by other known hardware.

Next, the power demand prediction process by the power demand prediction device 1 will be described. FIG. 3 is a flow chart showing a flow of the power demand amount prediction process by the power demand amount prediction device 1 according to the first embodiment.

In the power demand prediction process, the model parameter determination unit 17 determines the model parameters of the prediction model (here, the first to third model parameters α, γ, σ, which will be described in detail later) (ST101).

Subsequently, the electric power demand calculation unit 21 acquires the weather forecast information of the forecast target day (the day when the electric power is procured from the electric power trading market 5) from the weather forecast organization 22 (ST102). At this time, the electric power demand calculation unit 21 can acquire the schedule information of the event to be carried out on the forecast target day as needed.

After that, the electric power demand calculation unit 21 calculates the electric power demand (predicted value) of the consumer 2 by applying (inputting) the weather forecast information (for example, the predicted value regarding the temperature and the like) to the forecast model (for example). ST103). Here, the calculated electric power demand amount is provided to the aggregator 4 as a prediction result of the electric power demand amount prediction device 1. In this case, the power demand calculation unit 21 can apply the digitized event schedule information to the prediction model as a part of the weather prediction information.

FIG. 4 is a flow chart showing details of the model parameter determination process (step ST101) in FIG.

In the model parameter determination process, first, it is determined whether or not the forecast target is the amount of electric power demand for the previous day forecast used for the procurement of electric power in the one day market by the aggregator 4 (ST201).

When the prediction target is the previous day's forecast in step ST201 (Yes), the power consumption acquisition unit 11 acquires information on the past power consumption up to the previous day (ST202). On the other hand, in step ST201, when the forecast target is not the previous day's forecast (that is, the forecast target is the power demand for the current day forecast used for procuring power in the current market by the aggregator 4) (No), the power consumption acquisition Unit 11 acquires information on the amount of power used in the past up to the previous day (ST203).

Next, the model parameter determination unit 17 acquires information on the past power consumption from the storage unit 12 (ST204). At this time, the model parameter determination unit 17 acquires past event information as needed.

Subsequently, the model parameter determination unit 17 acquires predetermined initial values for the first to third model parameters α, γ, and σ, respectively (ST205).

After that, the model parameter determination unit 17 determines the first to third model parameters α, γ, and σ, respectively, based on the coordinate descent method.

First, the model parameter determination unit 17 fixes the first and third model parameters α and σ, and sets the second model parameter γ that maximizes a predetermined log-likelihood function (see equation (11) described later). Find (ST206). Note that maximizing the log-likelihood function (that is, maximum likelihood method) includes the least squares method.

Similarly, the model parameter determination unit 17 fixes the second and third model parameters γ and σ and obtains the first model parameter α that maximizes the predetermined log-likelihood function (ST207).

Similarly, the model parameter determination unit 17 fixes the first and second model parameters α and γ and obtains a third model parameter σ that maximizes a predetermined log-likelihood function (ST208).

Next, the model parameter determination unit 17 determines whether or not the first to third model parameters α, γ, and σ have converged (ST209). If the first to third model parameters α, γ, and σ have not converged in step ST209 (No), the process returns to step ST206 again, and the same process is executed.

When all the model parameters α, γ, and σ finally converge (ST209: Yes), the model parameter determination process ends.

Next, the details of the prediction model used for predicting the power demand of the plurality of consumers 2 in the power demand prediction device 1 will be described.

<Prediction model>
The forecast model is based on the actual value of the past power consumption by the consumer 2 for a certain period in the past from the forecast target date (here, from the forecast target date to T + 1 day before) and the influence of the weather (temperature, etc.) on the forecast target date. It is built in consideration of. The prediction model is defined as follows.

ただし、
ｙ_ｉｊ：ｉ日目の時間帯ｊの電力需要量（予測値）
μ_ｉｊ：需要家２による過去の使用電力量（過去の気象に依存する分を排除したもの）に基づく項（第１の項）
ｂ_ｉｊ：予測対象日の気象に依存する使用電力量に基づく項（第２の項）
ε_ｉｊ：誤差項（第３の項）

However,
y _ij : Electric power demand (forecast value) in the time zone j on the i-day
μ _ij : A term based on the past power consumption by consumer 2 (excluding the amount that depends on the past weather) (first term)
b _ij : A term based on the amount of power used depending on the weather on the forecast target day (second term)
ε _ij : Error term (third term)

By using this prediction model, the electric power demand forecasting device 1 can perform the previous day forecast used for procuring electric power in the one day before market of the electric power trading market 5 and the same day forecast used for procuring electric power in the same day market. it can.

<About _{ε ij>}
Here, it is assumed that ε _{ij to} N (0, σ _j ² ) and the errors are independent. That is, ε _ij follows a normal distribution with mean 0 and error variance σ _j ² (third model parameter).

<About _bij>
In the present embodiment, as the data such as the temperature included in the meteorological information used for calculating (predicting) the electric power demand of the consumer, the representative value of the data in a predetermined time zone (here, one day) is used. As such a representative value, for example, a maximum temperature, a minimum temperature, an average temperature, an average value of humidity, and the like can be used. Further, by using the representative value of the data in this way, it is possible to suppress an excessive increase in the number of parameters in the prediction model, and it is possible to avoid complication of the prediction processing of the power demand amount. Further, here, the digitized event information can be treated as a part of the meteorological information.

On the other hand, the influence of the weather in the area where the consumer 2 is located on the power demand is expected to change depending on the time zone j. _{Therefore, b ij} is known basis functions _{g m (s i) (m} = 1, ···, M) by linear combination, are to be estimated by the following equation. Here, M can be the number of clusters described later, and can be appropriately set so that the prediction error of the power demand amount becomes small.

ただし、
ｓ_ｉ：気象情報に含まれる気温等のデータ

However,
s _i: data of air temperature and the like included in the weather information

Further, it _{is assumed that φ m} (j) can be base-expanded as follows based on the known basis functions h _q (j) (q = 1, ..., Q). Here, γ _qm (second model parameter) is a model parameter relating to the amount of power used depending on the past weather (temperature, etc.) (that is, included in the function based on the amount of power used depending on the past weather). is there.

Here, when the equation (3) is substituted into the equation (2), it becomes as follows.

_Also, the g m _{(s i),} for example, the following RBF (Radial Basis Function) can be used (also _{h q} (j) similar.).

Here, it relates _{g m (s i),} for example _s 1, if there is data for temperatures · · · · _{s n} may These data are clustered by the k-means method. At this time, the number of clusters M can be determined by using an evaluation method such as cross-validation. When _si is one-dimensional, it is not necessary to use the k-means method, and the data may be classified at predetermined intervals (for example, equal intervals).

The values of the parameters contained in the RBF is a cluster obtained by the k-means method _{(C 1, ····, C M} ) can be estimated as follows using. Here, #Cm is the number of elements of the m-th cluster.

Thus, for g m _{(s i),} it can be determined based on a plurality of clusters generated by the clustering.

On the other hand, for h _q (j), data can be taken at predetermined intervals. For example, when Q = 10, for 24 hours a day (30 minutes x 48 pieces), the time zone of 30 minutes x 4 is divided into two consecutive times, and the time zone of 30 minutes x 5 is divided into eight consecutive times. be able to. _{Then, h q} (j) can be obtained by calculating (estimating) the mean and variance for those time zones and substituting them into the same equation as in equation (5).

<About _{μ ij>}
mu _ij is past power demand _{y (i-t-Lα)} j (L α ≧ 0) influence of temperature from _{b (i-t-Lα)} y which eliminated the _{j (i-t-Lα)} j - Similar to the term for the previous day's forecast as a weighted sum based on b _{(it-Lα) j and the term for this previous day's forecast, the past power demand y i (j-u-Lβ)} (L _β ≧) section on day predictions as a sum of weighted based on 0) effect of temperature from _{b i (j-u-Lβ} ) y i which eliminated the _{(j-u-Lβ) -b} i (j-t-Lβ) and Therefore, it can be assumed as follows. When making the previous day's forecast, the item related to the current day's forecast based on _{y i (j-u-Lβ) -bi (j-t-Lβ) is omitted.}

Here, α _jt and β _ju (first model parameter) relate to the past power consumption by the consumer 2 (excluding the portion depending on the past weather) (that is, the past from the past power consumption). It is a model parameter (included in the function based on the one in which the amount of electricity used depending on the weather is excluded). Further, L _α and L _β are correction parameters for adjusting the influence of a predetermined bid time when the aggregator 4 procures electric power from the electric power trading market 5.

Here, by substituting the equation (4) into the equation (8), μ _ij can be obtained as follows.

As a result, the equation (1) showing the prediction model is expressed as follows.

This equation (10) differs from the normal regression model in that it includes the product of the model parameters α (here, _{corresponding to α jt} and β _{ju) and γ.} Therefore, in estimating the model parameters, it is preferable to use the coordinate descent method in which each model parameter is estimated alternately (see steps ST206-208 in FIG. 4). Each model parameter is determined so that the amount of power used depending on the past weather (temperature, etc.) can be reproduced well.

Next, a method for determining the above-mentioned first to third model parameters (α _{jt (including β ju} if necessary), γ _qm , and σ _j ^{2) will be described.}

<Estimation of model parameters>
Model parameters can be determined using a predetermined log-likelihood function. In this embodiment, the following regularized log-likelihood function is obtained by maximizing it.

Here, l (θ) is a log-likelihood function, and P _λ (α, γ) is a penalty term. They are given as follows.

Therefore, the log-likelihood function l _λ (θ) is given as follows.

Here, μ _ij and b _ij are given by the above equations (4) and (8), respectively, and depend on the model parameters α and γ, respectively.

The model parameter α may be obtained after _{standardizing each j with σ j} ² (so that the variance is 1). That is, the diagonal matrix with diagonal elements the sigma sigma _j, and a unit matrix I _n,

とすると、モデルパラメータαは、以下のように推定することができる。

Then, the model parameter α can be estimated as follows.

とすると、以下のように推定することができる。 Similarly, for the model parameter γ,

Then, it can be estimated as follows.

Further, σ _j ² can be estimated as follows.

By paying attention to the model parameters α and γ and displaying them in a matrix, such a prediction model can be formulated in the same manner as a normal regression model, and an algorithm can be easily constructed.

First, focusing on the model parameter α, when the model parameter γ is given when calculating the _{power demand amount (predicted value) y ij , bi j} is given.

Using vectors and matrices, if we define as follows,

z _i can be expressed as follows.

とおくと、 In addition, it should be noted.

If you say

より、

Than,

となる。このｂ_ｉは予め行列演算で計算できる。

Will be. The b _i can be calculated in advance by matrix operation.

とおくと、 further,

If you say

z is expressed as follows.

Next, we focus on the model parameter γ.

Using vectors and matrices, if we define as follows,

The above equation (10) is expressed as follows.

Further, the equation (10) can be expressed as follows.

とすると、 here,

Then

y _i is expressed as follows.

とすることにより、 Also,

By

γ can be expressed as follows.

This is a normal regression model, but it should be noted that the value of the error variance changes depending on each time zone j.

<Asymptotic dispersion>
In a linear regression model, the asymptotic variance of the ridge estimator is explicitly obtained (see, eg, Hoerl, AE and Kennard, RW (1970) Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12, 55-67.).

However, since the prediction model of the present embodiment includes the product of model parameters, the variance cannot be explicitly obtained. Cessie and Houwelingen show that the asymptotic variance of the parameter θ = (α ^T , γ ^T , σ ^T ) ^T is given as follows (Cessie, SL and Houwelingen, JCV (1992) Ridge Estimators in Logistic. -See Regression. Journal of the Royal Statistical Society Series C (Applied Statistics), 41, 191-201.).

However, this asymptotic dispersion is not appropriate because the limit is ambiguous. In addition, Cessie and Houwelingen point out that confidence intervals cannot be constructed because this asymptotic variance does not take into account the bias of the estimator (Cessie, SL and Houwelingen, JCV (1992) Ridge Estimators in Logistic. -See Regression. Journal of the Royal Statistical Society Series C (Applied Statistics), 41, 191-201.).

Therefore, refer to Takagi, Y. and Inagaki, N. (1993) Estimating Function with Asymptotic Bias and Its Estimator. Annals of the Institute of Statistical Mathematics, 45, 499-510. ). In the ridge estimation, the asymptotic distribution of θ is as follows according to Theorem 4.3 (or Theorem 4.2, Knight and Fu, 2000, etc.) by Takagi and Inagaki (1993).

However, I (θ) is a Fisher information matrix. Using this property, the following holds.

とおくと、 here,

If you say

The above equation (62) can be expressed as follows.
here,

Next, the derivation of the Fisher information matrix (derivative of the log-likelihood function) will be described.

<Derivation of Fisher information matrix>
In essence, finding the asymptotic variance is finding the second derivative of the regularized log-likelihood function. Therefore, the second derivative is actually calculated. The log-likelihood function is given by the following equation.

Now consider calculating the second derivative of || r-Lγ || ^2. First, the first derivative is expressed as follows.

The second derivative for the same variable is expressed as follows.

Subsequently, equation (67) is differentiated with respect to α.

First,

となる。ただし，Ｅ_ｉｊは、(ｉ,ｊ)成分のみ０となる行列である。よって、例えば、以下の式を用いて計算可能である。 Because it is

Will be. However, E _ij is a matrix in which only the (i, j) component is 0. Therefore, for example, it can be calculated using the following formula.

とおくと、 here,

If you say

となり、

Next,

となるため、以下の式が得られる。 further,

Therefore, the following equation is obtained.

とおくことにより、以下の式が得られる。 further,

By setting, the following equation can be obtained.

Moreover, the following equation is obtained.

The second derivative is given by the following equation, including the estimator.

Furthermore, the following can be calculated in combination with the above equations (66) and (67).

<Forecast of electricity demand>
As described above, when the estimated values of the model parameters α and γ are obtained _{, the power demand amount y n + 1 is calculated by applying the weather forecast information sn + 1} (predicted value data such as temperature) to the above equation (44). ) Is calculated from the following formula.

<Prediction interval>
Next, the prediction interval will be described.

Regarding the prediction model in this embodiment, the prediction interval can be obtained by the delta method. Here, it is assumed that the asymptotic variance of the parameter θ is given (it can be calculated by including the coincident estimator derived from the equation (60)).

とし、このｇ_ｊ(θ)をテイラー展開すると、以下のように表される。 here,

Then, when this g _j (θ) is Taylor-expanded, it is expressed as follows.

より、以下のようになる。 here,

Therefore, it becomes as follows.

より、

となり、以下のようになる。 Also,

Than,

And it becomes as follows.

Therefore, the confidence interval of 100 (1-α)% of _{g j} (θ _{0) is as follows.} Here, z _α is the upper 100 α percent point of the standard normal distribution.

ただし、

However,

Actually, the following prediction intervals can be used.

Therefore, the confidence interval can be obtained by substituting the matching estimator into _{θ 0.}

_{The derivative of gi} (θ) can be easily calculated. For example, _{the derivative at α j} is given by the following equation.

<Bayesian inference of γ>
Next, Bayesian estimation of the second model parameter γ will be described.

The value of γ is based on the influence of meteorological information, but it is difficult to estimate it accurately unless data on meteorology (here, temperature) for a relatively long period (for example, one year) is obtained. However, if such long-term data are not available, Bayesian inference can be used as an alternative.

_{Here, it is assumed that γ 0} is obtained using a certain data set regarding the weather. However, if the magnitude of the power demand to be estimated is different from that of another power demand, it may not be possible to estimate it well. Therefore, it is necessary to prepare _{γ 0 in which the power demand is scaled in advance.} In this case, for example, it is conceivable to replace it _{with kγ 0} by using the ratio k of the average value of each power demand.

Here, it is considered that Bayesian estimation of γ is performed by minimizing the following function based on the linear regression model of the equation (59) with the design matrix L and the regression coefficient vector γ. Here, n means the number of days of past data used for learning.

When this is differentiated, it becomes as follows,

Further, the following equation is obtained.

となる。この場合、事前情報の強さρは、例えば、クロスバリデーションなどの評価方法を用いて選択することができる。 Here, if the strength of the prior information is ρ → ∞,

Will be. In this case, the strength ρ of the prior information can be selected using, for example, an evaluation method such as cross-validation.

(Second Embodiment)
Next, the electric power demand forecasting device 1 according to the second embodiment of the present invention will be described. Hereinafter, the details of the prediction model used for predicting the power demand of a plurality of consumers 2 in the power demand prediction device 1 according to the second embodiment will be described. Regarding the electric power demand forecasting device 1 and its processing according to the second embodiment, matters not particularly mentioned below are the same as in the case of the first embodiment described above.

In the first embodiment, the vector γ was estimated using the above equation (59). At this time, the loss function in the least squares estimation is minimized as shown in the following equation.

However, empirically, the element γ of the least squares estimation can be negative. In such a case, in the above equation (4), basis functions _{h q} (j) and _g m _{(s i)} is generally to a positive _value, the value of _{b ij} is negative. The value of b _ij, since illustrates the effect of weather on the power consumption, b _ij is sensuously easier to understand when to take a non-negative value. Interpretation of the effects of weather is useful from the perspective of the power supplier (eg, J. Moral-Carcedo and J. Vicens-Otero. Modeling the non-linear response of Spanish electricity demand to temperature variations. Energy Economics, 27 ( 3): See 477-494, May 2005.).

In the second embodiment, γ is constrained to a non-negative value so that _{the second term (bij} ) based on the amount of electricity used depending on the weather on the forecast target day in the above equation (1) becomes non-negative. The non-negative value of b _ij is realized when at least all the elements of γ are non-negative. For the estimation of the non-negative regression coefficient, the non-negative least squares (NNLS) estimation is useful as in the following equation. Here, all elements of γ are non-negative.

The optimization problem for equation (113) is a non-negative constraint (eg, V. Franc, V. Hlavac, and M. Navara. Sequential coordinate-wise algorithm for the non-negative least squares problem. Computer Analysis of Images and Patterns, Proceedings, 3691: 407-414, 2005.) This is a special case of quadratic programming. As a result, the NNLS estimation becomes a convex optimization problem. Several efficient algorithms for obtaining solutions in equation (113) are available in the literature (eg CL Lawson and RJ Hanson. Solving Least Squares Problems. Society for Industrial and Applied Mathematics, 1995. doi: 10.1137 / 1.9781611971217. URL https: // epubs. See siam.org/doi/abs/10.1137/1.9781611971217.). Here, the NNLS loss function is given a ridge penalty (see AE Hoerl and RW Kennard. Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12 (1): 55-67, Feb. 1970.) as follows: to add.

ここで、λ＞0は正則化パラメータである。発明者らの経験では、リッジペナルティは安定した推定量をもたらし、また予測精度が改善される。

Here, λ> 0 is a regularization parameter. In our experience, the ridge penalty provides a stable estimator and improves prediction accuracy.

It is generally difficult to find a confidence interval when the parameter γ is estimated under a non-negative (0 or more) constraint. Therefore, consider a two-step estimation. First, the non-zero element is extracted by the equation (114). Then apply the least squares method based on its non-zero elements. At this time, a prediction interval is required under the condition that non-zero elements are extracted. For the derivation of the prediction interval, refer to Lee, J.D., & Taylor, J.E. (2014). Exact Post Model Selection Inference for Marginal Screening. ArXiv preprint arXiv: 1402.5596. Lee et al. (2014).

Although the present invention has been described above based on specific embodiments, these embodiments are merely examples, and the present invention is not limited to these embodiments. It should be noted that all the components of the power demand prediction device and the power demand prediction method according to the present invention shown in the above embodiment are not necessarily all indispensable, and are appropriately selected as long as they do not deviate from the scope of the present invention. It is possible.

1: Electric power demand forecasting device 2: Consumer 3: Network 4: Aggregator 5: Electric power trading market 6: Smart meter 10: Management device 11: Electric energy consumption acquisition unit 12: Storage unit 13: Meteorological information acquisition unit 14: Meteorological Information database 16: Event information acquisition unit 17: Model parameter determination unit 21: Electric power demand calculation unit 22: Weather forecast organization 23: Forecast result transmission unit 31: Processor

Claims (8)

It is a power demand forecasting device that predicts the power demand of consumers based on a mathematical model.
The power consumption acquisition unit that acquires information on the past power consumption by the consumer,
The meteorological information acquisition department that acquires the past meteorological information of the area where the customer is located,
A model parameter determination unit that determines a plurality of model parameters included in the mathematical model based on the power consumption information and the past weather information.
It is provided with a power demand calculation unit that calculates the power demand of the consumer by applying the forecast information of the weather on the prediction target date to the mathematical model in which the plurality of model parameters are determined.
In the mathematical model, the predicted power demand of the consumer includes a function based on the past power consumption excluding the power consumption depending on the past weather, the first term, the prediction. A power demand forecasting device including a second term including a function based on the amount of power used depending on the weather of the target day, and a third term as an error term. The plurality of model parameters include the first to third model parameters included in the first to third terms, respectively.
The power demand forecasting device according to claim 1, wherein the second model parameter is constrained to a non-negative value so that the second term becomes positive. The plurality of model parameters include the first to third model parameters included in the first to third terms, respectively.
The model parameter determination unit fixes any two of the first to third model parameters so as to maximize a predetermined log-likelihood function including the first to third model parameters. The power demand prediction device according to claim 1, wherein the first to third model parameters are sequentially determined by determining the remaining one model parameter. The model parameter determination unit clusters the data constituting the past weather information.
The power demand forecast according to any one of claims 1 to 3, wherein a function based on the power consumption depending on the past weather is determined based on the plurality of clusters generated by the clustering. apparatus. The power demand forecasting device according to any one of claims 1 to 4, wherein the past weather information includes at least one data of temperature, humidity, weather, and precipitation. The power demand forecasting device according to claim 5, wherein the past weather information is a representative value of the data in a predetermined time zone. It also has an event information acquisition unit that acquires information on past events held in the area where the customer is located, which is input by the operator.
The function included in the second term is based on the amount of power used depending on the past event.
The electric power demand calculation unit calculates the electric power demand of the consumer by applying the scheduled information of the event to be held on the forecast target day to the mathematical model in which the plurality of model parameters are determined. The electric power demand forecasting device according to any one of claims 1 to 6, wherein the electric power demand forecasting device is characterized. It is a power demand prediction method using a power demand forecaster that predicts the power demand of consumers based on a mathematical model.
Obtaining information on the amount of electricity used in the past by the consumer,
Acquire past weather information of the area where the customer is located,
Based on the power consumption information and the past weather information, a plurality of model parameters included in the mathematical model are determined, respectively.
By applying the forecast information of the weather on the forecast target date to the mathematical model in which the plurality of model parameters are determined, the electric power demand amount of the consumer is calculated.
In the mathematical model, the predicted power demand of the consumer includes a function based on the past power consumption excluding the power consumption depending on the past weather, the first term, the prediction. A method for predicting electric power demand, which comprises a second term including a function based on the amount of electric power used depending on the weather of the target day, and a third term as an error term.

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