Research on Investment Measurement Model of Grid Infrastructure Projects Based on Improved Discrete Gray Forecasting

Grid project investment occupies an important position for power grid companies. It is not only related to the development of regional economy, the normal production and life of the residents, but also will have a far-reaching impact on the sustainable, healthy and rapid development of the whole society [1-3]. Generally, power grid projects involve huge investment. Due to the limitations of the investment budget, a large number of planned projects to be built often only a small portion of the investment can be invested in construction, at this time there is a need for a project investment evaluation and decision optimization methods and tools suitable for the requirements of the actual grid construction projects, to provide certain decision support for the grid company [4-6].

With the gradual deepening of power marketization and grid enterprise system reform, the economic efficiency factor of the grid company accounts for an increasing proportion of the investment decision, and at the same time, the uncertainty of the decision-making factors, the complexity of the decision-making elements and the diversification of the decision-making body, all of which put forward a new challenge to the grid company’s project investment decision-making problems. Therefore, it is necessary to comprehensively consider all aspects of the factors in the investment planning of the grid project, adopt a scientific method to objectively assess the grid project, and then make a scientific project investment budget [7-9].

In recent years, power grid companies have carried out a lot of work in comprehensively strengthening budget management, and have obtained some positive results. However, how to improve the accuracy of investment forecasting and how to make the grid investment strategy more scientific has not yet been well solved [10-11]. Investment measurement is not only an important practical application project, but also a complex academic theoretical problem. In the long-term research on investment measurement, a more mature theory and method system has been gradually formed [12-13].

Grid project investment measurement has the following characteristics, first of all, the grid company’s investment measurement involves social, economic and other factors, these factors itself there are a large number of random perturbations, and at the same time, the grid company’s policy changes increase the uncertainty of investment decision-making, followed by the existence of a number of factors simultaneously affecting the size of the capital to be measured for the grid construction investment project, and then with the grid Project investment measurement related to the lack of historical data, and finally the uncertainty between the investment scale of each grid project to be measured and the factors affecting the investment measurement of the grid company [14-16]. Therefore, it is necessary to carry out research on the grid company project investment measurement, from which to seek a comprehensive, objective, scientific method for the enterprise’s project investment decision-making to provide a certain basis [17].

Grid infrastructure projects to take effective measures for cost management, that is, the project cost reasonable control, to avoid the cost is too high to affect the economic benefits of enterprises, in order to ensure the smooth realization of the management objectives, should be the first to design a reasonable management program, the application of suitable management tools, and ultimately be able to achieve the effect of cost control management. Grid infrastructure projects to implement the process of cost management, should have a general understanding of the project management object, and then be able to have a direction to control the project cost, give full play to the construction investment utilization [18-20].

The article firstly analyzes the three grid infrastructure demands of socio-economic level, grid scale and load power consumption, discusses the relationship between grid infrastructure related indicators and investment projects, and thus proposes the grid infrastructure investment measurement index system. Then, it studies the investment measurement model of grid infrastructure projects, discusses the basic principle of gray prediction model, and further improves it on the basis of gray prediction model, so as to put forward the gray metabolic discrete MDGM(1, 1) prediction model. In the experimental part, the article examines the performance of the gray prediction model proposed in this paper through performance measurement and analyzes it with the empirical research on the grid infrastructure investment in region A.

2

Method

2.1

Indicator System for Measuring Investment in Power Grid Infrastructure

Grid infrastructure is affected by a variety of factors, including the regional economic level, population, area, grid size, social electricity consumption level, and other aspects of various indicators. The demand for grid infrastructure can basically be reflected by three aspects: socio-economic level, grid size, and load electricity consumption level.

2.1.1

Socio-economic level

The development and changes in society have a great impact on the scale of grid construction, while the number of people supplied with electricity reflects the development of society. When the value of the indicator of the population supplied with electricity grows, it indicates that the demand for electricity in the region has increased, and the investment in the construction of the grid should be increased.

The development and change of the economy will also have a great impact on the construction scale of the power grid, while the gross regional product (GDP) mainly reflects the development of the economy. When the value of the gross regional product (GDP) indicator grows, it means that the region’s economy is developing well, the income increases, the level of demand increases, and the consumption capacity also increases, which can increase the investment to meet the growing demand for electricity [21].

Therefore, the power supply population indicator and the gross regional product (GDP) indicator can reflect the development of the society from the social and economic aspects respectively, which affects the investment in the construction of power grids from different perspectives.

2.1.2

Grid size

The “transformer capacity” of a power grid refers to the capacity of the main transformer of the substation of the grid, which mainly reflects the ability of the transformer to deliver electricity. Reasonable allocation of substation capacity is one of the important elements of power grid planning and design, affecting the safety and reliability of power supply and the economy of power grid operation. Transformer capacity is too large, resulting in a waste of funds. Transformer capacity is too small, the flexibility and adaptability of the grid is poor, poor safety and reliability. China mainly uses 110kV and 220kV voltage grids as its backbone network. Therefore, the index system selects 110kV and 220kV grid substation capacity to reflect the scale of the grid.

2.1.3

Level of electricity consumption of loads

Whole society’s electricity consumption refers to the total amount of electric energy consumed in all areas of electricity consumption in primary, secondary and tertiary industries, including industrial electricity consumption, agricultural electricity consumption, commercial electricity consumption, residential electricity consumption, electricity consumption by public facilities and other electricity consumption. Regional maximum load reflects the annual peak load of a region. When the electricity consumption of the whole society and the maximum load of the region increase, the corresponding investment in the power grid should be increased: while the electricity consumption of the whole society and the maximum load is flat or reduced, the investment can be slowed down or reduced accordingly to adapt to different electricity demand. Therefore, the indicator system selects the whole society’s electricity consumption and the maximum load to reflect the regional grid load electricity consumption level [22].

By analyzing the meaning of the following indicators and their relationship with grid infrastructure investment, the grid infrastructure investment measurement indicator system is shown in Figure 1.

2.2

Discrete gray prediction model for metabolism

2.2.1

Fundamentals of Gray Prediction Models

Gray predictive modeling is a prediction method based on gray systems theory, the basic principle of which is to use known data to make predictions about unknown data. Gray systems theory holds that man-made systems are often described by an accurate mathematical model, while natural systems often have only some scattered observational data. Therefore, the goal of gray system theory is to study how to obtain the dynamic laws of natural systems with only a small amount of observational data [23].

The gray prediction model divides data into two categories according to the correlation between data: white data and gray data. Among them, white data refers to known data and gray data refers to unknown data. A common method used in the modeling process is the hourglass function. The hourglass function is a special type of differential equation that describes the phenomenon of consumption in a physical system. In gray prediction models, the hourglass function is then used to describe the process by which data lose information.

The basic idea is to decompose the original data series into four parts: trend, period, cycle and noise. Using the information from these four parts, a three-step process of modeling, prediction, and validation is used to achieve a prediction of future data. In the gray prediction model, researchers can use simple mathematical models and empirical formulas to achieve fast prediction of future data. This method helps to analyze and make decisions on some complex problems.

2.2.2

Gray model construction

Let X(0) = (X⁽⁰⁾(1)X⁽⁰⁾(2),...(n)) be the initial non-negative data column, which is accumulated once to get the new generated data column x⁽¹⁾: (1) $X^{(1)} = (x^{(1)} (1), x^{(1)} (2), ... x^{(1)} (n))$ (2) $x^{(1)} (m) = \sum_{i = 1}^{m} x^{(0)} (i), m - 1, 2, ... n$

where,

Let Y⁽¹⁾ be the immediately neighboring mean generating series of the series x⁽¹⁾, i.e: (3) $Z^{(1)} = (z^{(1)} (2), z^{(1)} (3), ... z^{(1)} (n))$

where, Z⁽¹⁾(m)=δx⁽¹⁾(m)+1(–δ)x⁽¹⁾(m–1),m = 2,3,...n and δ = 0.5.

Equation x⁽⁰⁾(k)+aZ⁽¹⁾(k)=b(k = 2,3,...n) is the basic form of the GM(1, 1) model, where b denotes the gray role quantity and –a denotes the development coefficient.

The matrix form is introduced: (4) $u = {(\begin{matrix} a, b \end{matrix})}^{T}, Y = [\begin{matrix} x^{(0)} (2) \\ x^{(0)} (3) \\ ⋮ \\ x^{(0)} (n) \end{matrix}], B = [\begin{matrix} - z^{(1)} (2) & 1 \\ - z^{(1)} (3) & 1 \\ ⋮ & ⋮ \\ - z^{(1)} (n) & 1 \end{matrix}]$

Thus, the GM(1, 1) model x⁽⁰⁾(k)+aZ⁽¹⁾(k)=b(k = 2,3,...n) can be expressed as: (5) $Y = B u$

The estimate of parameter a,b is obtained using the least squares method as: (6) $\hat{u} = (\begin{matrix} \hat{a} \\ \hat{b} \end{matrix}) = {(B^{T} B)}^{- 1} B^{T} Y$

Furthermore, if the moments of x⁽⁰⁾(m) are considered as continuous variables t, then x⁽⁰⁾(t) is considered as a function of time t, denoted as x⁽⁰⁾(t), and x⁽⁰⁾(k) corresponds to the derivative $\frac{d x^{(1)} (t)}{d t}$ and z⁽¹⁾(k) to x⁽¹⁾(t), the white differential equation with respect to the gray equation GM(1, 1) can be established: (7) $\frac{d x^{(1)} (t)}{d t} = - \hat{a} x^{(1)} (t) + \hat{b}$

Find its corresponding solution as: (8) ${\hat{x}}^{(1)} (t) = (x^{(0)} (1) - \frac{\hat{b}}{\hat{a}}) e^{- \hat{a} (t - 1)} + \hat{b}$

Further the solution of the GM(1, 1) model can be obtained as: (9) ${\hat{x}}^{(1)} (m + 1) = (x^{(0)} (1) - \frac{\hat{b}}{λ}) e^{- \hat{a} m} + \frac{\hat{b}}{λ}, m = 1, 2, ... n - 1$

Due to $x^{(1)} (m) = \sum_{i = 1}^{m} x^{(0)} (i), m = 1, 2, \dots, n$ , it can be obtained: (10) ${\hat{x}}^{(0)} (m + 1) = {\hat{x}}^{(1)} (m + 1) - {\hat{x}}^{(1)} (m) = (1 - e^{\hat{a}}) (x^{(0)} (1) - \frac{\hat{b}}{\hat{a}}) e^{- \hat{a} m}, m = 1, 2, ..., n - 1$

To make a prediction on the raw data, simply take m ≥ n in the above equation.

2.2.3

Modeling of discrete GM(1, 1) measures of gray metabolism

After a prediction, the oldest information X⁽⁰⁾(1) in the original dataset is deleted, the obtained latest information X⁽⁰⁾(n + 1) is added, and the process is repeated to obtain information data at the most recent time to construct a new discrete GM(1, 1) model. This is repeated until the prediction target appears, i.e., the discrete GM(1, 1) prediction model for gray metabolism [24].

2.2.4

Gray model testing

In order to make the constructed metabolic discrete gray prediction MDGM(1, 1) model with high accuracy and credibility, it is also necessary to test it from three aspects, namely, residual difference test, a posteriori difference test and correlation test.

1)

Residual test

The residuals are defined as follows:

Absolute residuals: (11) $ε (k) = x^{(0)} (k) - {\hat{x}}^{(0)} (k), k = 2, 3, ... n$

Relative residuals: (12) $ε_{r} (k) = \frac{| x^{(0)} (k) - {\hat{x}}^{(0)} (k) |}{| x^{(0)} (k) |} \times 100 %, k = 2, 3, ... n$

Average relative residuals: (13) $\bar{ε_{r}} = \frac{1}{n - 1} \sum_{k = 2}^{n} | ε_{r} (k) |$

If $\bar{ε_{r}} < 0.2$ , then GM(1, 1) is considered to have fair correlation with the original data.

If ε_r < 0.1, then GM(1, 1) is considered to have strong correlation with the original data.

2)

Rank-ratio deviation test

The rank ratio σ^(k) of the original data is first calculated from X⁽⁰⁾(k–1) and X⁽⁰⁾(k): (14) $σ (k) = \frac{x^{(0)} (k)}{x^{(0)} (k - 1)}, k = 2, 3, ..., n$

The corresponding grade deviation and average grade deviation are then calculated from the predicted development factor $(- \hat{a})$ : (15) $η (k) = | 1 - \frac{1 - 0.5 \overset{\land}{a}}{(1 + 0.5 \overset{\land}{a}) σ (k)} |, \bar{η} = \sum_{k = 2}^{n} η (k) / (n - 1)$

If $\bar{η} < 0.2$ , then GM(1, 1) is considered to have fair correlation with the original data. If $\bar{η} < 0.1$ , then GM(1, 1) is considered to have strong correlation with the original data.

3)

Posterior residual test

Test the statistical properties of the residual distribution.

First, calculate the standard deviations S₁ and S₂

Let $φ (k) = | ε (k) |$ : (16) $S_{1} = \sqrt{\frac{\sum (x^{(0)} (k) - \bar{x^{(0)}})^{2}}{k - 1}}$ (17) $S_{2} = \sqrt{\frac{\sum {(φ (k) - \bar{φ (k)})}^{2}}{k - 1}}$

Second, the calculated residual ratio C: (18) $C = \frac{S_{2}}{S_{1}}$

Calculate the small error probability P: (19) $P = | (φ (k) - \bar{φ (k)} | < 0.6754 S_{1}$

2.3

Investment Measurement Model for Grid Infrastructure Projects

If we want to realize the accurate calculation of the planned annual grid infrastructure investment scale, so that the determined investment scale can meet the needs of regional economic, social and grid development, we need to be able to accurately predict the development trend of the indicators in the grid infrastructure investment measurement index system, and guide the scale of grid infrastructure investment according to the development trend of the indicators. At the same time, the relationship between grid investment and indicators is complex, and it is difficult to directly determine the quantitative relationship between changes in indicators and investment scale. Therefore, accurately predicting the development trend of each index in the measurement index system and determining the quantitative relationship between the investment and the changes in the index is the key to establishing the grid infrastructure investment measurement model.

The grid infrastructure investment measurement model studied in this paper uses the metabolic discrete gray prediction model to predict the development trend of the indicators, and obtains the target value of the indicators at the end of the plan: the hierarchical analysis method is used to analyze the relationship between the indicators and the investment, and obtains the indicator impact coefficients: on the basis of the combination of the two, the grid infrastructure investment measurement model is established, and the grid infrastructure investment scale value is obtained to satisfy the demand for the development of the grid in the plan year. Infrastructure investment scale value. Measurement model for:

(20)

z = \sum_{i = 1}^{n} u_{i} \cdot (y_{i} (k + 1) - y_{i} (k))

Where z is the measured value of the grid infrastructure investment at the end of the program. u_i is the impact coefficient of the i rd indicator, i.e., the amount of change in investment corresponding to the change in the unit of the indicator. y_i(k + 1) is the target value of indicator i for year k + 1 (planning year). (k + 1) is the actual value of indicator i for year k.

3

Results and discussion

3.1

Performance Measurements

In this section, the performance of the gray metabolism discrete model MDGM(1, 1) proposed in this paper is measured, and the gray metabolism discrete model MDGM(1, 1) proposed in this paper is compared and analyzed with the DGM(1,2) model and DGM(1,N). The results of the simulated and MAPE values are compared comprehensively so as to verify the validity and scientificity of the gray metabolic discrete model MDGM(1,1) model proposed in this paper. The model simulation and measurement results are shown in Table 1. The relative error fluctuations of the simulation and measurement of the three models are shown in Figure 2. It can be concluded through the table that although the DGM(1,2) model avoids the jumping error between the difference equation to the differential equation, it is to use the information of the role of the driving factors, and it is only applicable to the modeling and measurement of the system of the near-exponential law with constant growth rate, and the performance of the modeling of the sequences with the characteristics of volatility and hysteresis is poorer, so that the average simulation and measurement errors are 6.02% and 13.65%, respectively. The DGM(1,N) model, although using the same driver variables as in this paper, does not further analyze the effects between grid input projects and grid infrastructure projects, not to mention discussing the past period drivers, so the model has a large simulation and measurement error of 3.91% and 25.16%, respectively, and has lost its modeling significance. In contrast, the model proposed in this paper not only has a much lower modeling error than the DGM(1,2) and DGM(1,N) models, but also has a much lower measurement error than the latter two types of models, avoiding the phenomenon of the measurement error jumps that occur in the latter two types of models between 2018-2023, with the two errors being 4.76% and 4.93%, respectively.

Table 1.

Model simulation and prediction results

Year	Original Value	Ours		DGM (1,2)		DGM (1,N)
Year	Original Value	Analog Value	Mape/%	Analog Value	Mape/%	Analog Value	Mape/%
2018	3.36	3.36	0	3.36	0	3.36	0
2019	4.4	4.36	0.98	4.25	13.58	4.42	3.45
2020	4.91	4.44	9.58	5.24	11.34	2.81	41.45
2021	5.3	4.86	4.56	6.55	14.58	3.47	38.1
2022	6.27	5.04	2.46	7.57	25.85	4.14	33.57
2023	7.29	6.49	12.01	9.15	16.57	5.23	34.38
Mape/%		0.45		7.82		37.51
Correlation degree		0.9436		0.8755		0.6635

In addition, from the perspective of the validity test of the gray correlation method, the absolute correlation between this paper’s model MDGM(1, 1) and the original sequence is 0.9436, while the absolute correlation between the fitted sequence obtained by the traditional gray DGM(1,2), model, and the DGM(1,N) model and the original sequence is 0.8755 and 0.6635, respectively, which shows that this paper’s model MDGM (1,1) pairs are more accurate in describing the characteristics of the series relative to the other two models, and are more feasible to be used for measurement. Comprehensively using two test methods to compare the modeling effect of various models, this paper’s gray metabolism discrete model MDGM (1, 1) can continue to reduce the modeling and measurement errors, applicable to the grid infrastructure project investment measurement.

3.2

Calculation of return on investment benefits based on grid infrastructure in region A

The grid infrastructure investment data of Region A from 2018 to 2023 are selected, and each grid development indicator with strong correlation with grid infrastructure investment is used as the input of the gray model to measure the corresponding annual investment amount. If the original gray model fails in the precision test, the residual correction model can be established by using each grid development indicator again to improve the accuracy of the gray model.

The transmission power is closely related to the social development and economic factors of the corresponding region.The monthly transmission power (billion kWh) from 2018 to 2023 in region A is shown in Figure 3. The data of delivered power in the corresponding period of different years show a certain seasonal cycle, i.e., the delivered power is not only related to the social and economic development, but also affected by seasonal factors such as the temperature and the month in which the large-scale holidays are held. The correlation between the growth trend component of the transmission power and the corresponding growth and decline trend of the social factors is even closer. When utilizing socio-economic factors for transmission power measurement, the trend part and seasonal part of the corresponding data can be decomposed, measured through the trend part of the data, and then the trend data can be reduced to get the final result.

In the gray correlation analysis of the factors affecting transmission volume, quarterly data is used. However, there are only 32 sets of quarterly data from 2018 to 2023, and when measuring the seasonal component, which is highly cyclical, the smaller amount of data affects the effectiveness of the model’s fitting measurement of the seasonal component. Therefore, monthly data on socio-economic components are used to measure the monthly delivered power, increasing the amount of data inputted into the model before constructing the quarterly return on investment model for grid infrastructure investment. The correlation results of the quarterly indicators show that the regional gross domestic product (GDP) and the value added of industries above large scale all exhibit a certain correlation with the delivered electricity, and considering the difference between quarterly and monthly data and the serious lack of some monthly data, the industrial indicator that occupies a greater proportion of the electricity consumption, i.e., the value added of industries, is finally adopted to replace the regional gross domestic product, and is combined with the sequence of the regional fixed asset investment data to construct a model of the delivered electricity. The investment measurement model for grid infrastructure projects includes a trend component for electricity consumption.

The original gray model is more suitable for data that are more linear in terms of overall growth and decrease in trend, or data that are not too volatile when measured. When there is a complex nonlinear relationship between the sequence of related factors and the sequence of behaviors, the GM(1, N) model selects the first numerical point of the sequence as the initial condition, but in fact the cumulative sequence does not necessarily pass through the first numerical point of the initial sequence, and at the same time, the GM(1, N) model involves simulation of differential equations for measurement, and it is inevitable that errors will be generated in this process. According to the construction method of the MDGM(1, 1) model described in the previous chapter, the trend component of the delivered electricity is simulated and measured using the relevant socio-economic indicators. A comparison of the gray model measurement results is shown in Figure 4. The model proposed in this paper corresponds to a residual ratio C of 0.118 and a small error probability P of 0.984, and the trend of the measured data basically matches the trend of the real-value data, and the model is of excellent quality, which can be used in the grid infrastructure project investment measurement model.

Taking the two models as a comparison, from the measured and real values of the model MDGM(1, 1) proposed in this paper, its average absolute error MAPE is 0.92%, and the multiple linear regression model can be calculated from the measured and real values to get the corresponding MAPE of 2.18%. When using regional economic indicators to measure the trend component of electricity data, it can be better measured by constructing the MDGM(1,1) model. The relative error of the measurement model is shown in Table 2.

Table 2.

Measuring relative error of model

Time	Relative Error
Time	Multivariate Linear Regression	Ours
2023.1	1.95%	0.55%
2023.2	2.03%	0.68%
2023.3	2.14%	0.79%
2023.4	2.18%	0.88%
2023.5	2.24%	0.93%
2023.6	2.24%	0.96%
2023.7	2.25%	0.99%
2023.8	2.25%	1.02%
2023.9	2.23%	1.03%
2023.10	2.24%	1.04%
2023.11	2.22%	1.06%
2023.12	2.2%	1.05%

Combining the above quantities, we obtain a model of the degree of return on grid infrastructure investment measured by grid infrastructure-related indicators, so as to introduce the corresponding regional socio-economic indicators into the model of return on grid infrastructure investment. By introducing the corresponding regional socio-economic factors into the model of grid infrastructure investment return, the connection between the macro socio-economic development status and the grid infrastructure investment return can be reflected to a certain extent.

4

Conclusion

The study focuses on using the metabolic discrete gray prediction model to invest in power grid infrastructure projects. The research in this paper draws the following conclusions: first, in the performance measurement experiments on the model, the modeling error of the model proposed in this paper is much lower than that of the DGM(1,1) and DGM(1,N) models, and the two errors are 4.76% and 4.93%, respectively. Secondly, in the empirical analysis, the average absolute error MAPE of the measured and real values of the trend component of the power data of region A of the model proposed in this paper is 0.92%, which can be obtained that the model proposed in this paper can better solve the problem of investment measurement of the available grid infrastructure projects.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Research on Investment Measurement Model of Grid Infrastructure Projects Based on Improved Discrete Gray Forecasting

Zhiyong Chen

Liangdong Qin

Pengfei Sun

Zihao Zhao

Wei Guo

Published Online: Mar 17, 2025

Received: Oct 30, 2024

Accepted: Feb 09, 2025

DOI: https://doi.org/10.2478/amns-2025-0340

KeywordsDiscrete gray prediction, Investment measurement, Grid infrastructure, Measurement model

© 2025 Zhiyong Chen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Discrete gray prediction, Investment measurement, Grid infrastructure, Measurement model