Research on Development Level Measurement and Spatial
Differentiation of Small Hydropower in Southern Shaanxi
Haojun Wu
1,2,*
, Jiwei Zhu
1,2
, Shutian Li
1,2
and Liu Yang
1,2
1
State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China, Xi’an University of Technology, Xi’an, China
2
Research Center of Eco-hydraulics and Sustainable Development, The New Style Think Tank of Shaanxi Universities,
Xi’an, China
Keywords: Small hydropower, Development level measurement, Spatial differentiation, Southern Shaanxi
Abstract: To understand the development level of small hydropower (SHP) and its spatial differences in Southern
Shaanxi, this study takes the cities of Southern Shaanxi as the research object, constructs the measurement
index system of the development level of SHP in Southern Shaanxi, establishes a comprehensive
measurement model based on the projection pursuit model, and analyzes the spatial differences of the
development level of SHP in Southern Shaanxi from two aspects of comprehensive evaluation and sub-
dimensional evaluation by means of the visual measurement results of ArcGIS software. The results show
that the spatial differentiation of the development level of SHP in Southern Shaanxi is obvious, among which
Ankang City is higher than Hanzhong city than Shangluo city. Based on the research results, the paper puts
forward some policy suggestions for the development characteristics of SHP in Southern Shaanxi. The
research results have certain value for understanding the development status and spatial distribution difference
of SHP in Southern Shaanxi, and provide important reference for the future development of SHP in Southern
Shaanxi.
1 INTRODUCTION
Under the current standards of China, small
hydropower (SHP) refers to hydropower stations with
an installed capacity of 50 MW and below, also
known as rural hydropower stations, which are
renewable energy with significant benefits. China has
a large number and wide distribution of SHP, with a
development capacity of 128 million KW (Wang et
al., 2016). Southern Shaanxi is rich in hydropower
resources, and the SHP market is large. As an
important water source of the Middle Route Project
of South-to-North Water Diversion, Southern
Shaanxi attaches great importance to ecological
environmental protection, adheres to the positive and
orderly development of SHP, and promotes the green
development of SHP.
At present, domestic and foreign scholars'
research on SHP measurement evaluation and spatial
differentiation mainly focus on the relationship
between hydropower stations and the external
environment and its influence on the external
environment. In terms of the measurement and
evaluation of SHP, scholars have conducted in-depth
research on the impact of SHP on the economy,
society, and ecological environment (Prakasam et al.,
2021; Zali et al., 2019; Liu et al., 2015; Xia et al.,
2019), the evaluation of sustainable development of
SHP (Nautiyal and Goel, 2020; Zhang et al., 2019),
the benefit evaluation of energy conservation and
emission reduction (Ding et al., 2016), and the
evaluation of green SHP (Wang et al., 2016; Li et al.,
2018). Using the AHP method, fuzzy comprehensive
evaluation method, whitening weight function, semi-
structured interview survey method, GIS analysis,
and other methods, relevant conclusions are obtained,
and policy suggestions are put forward based on the
research. In terms of spatial differentiation, Qiao H J,
Huang Z, and other people take Chinese provincial as
the object, using entropy TOPSIS method and
coupling coordination model to evaluate the
development level of SHP in each province and
analyze its spatial pattern evolution (Qiao et al.,
2019a; Qiao et al., 2019b), but the relevant research
is still less.
Overall, the research on the evaluation of SHP has
made some achievements, which lays a good
foundation for further deepening the research of SHP.
304
Wu, H., Zhu, J., Li, S. and Yang, L.
Research on Development Level Measurement and Spatial Differentiation of Small Hydropower in Southern Shaanxi.
In Proceedings of the 7th International Conference on Water Resource and Environment (WRE 2021), pages 304-311
ISBN: 978-989-758-560-9; ISSN: 1755-1315
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

However, the research on the measurement of SHP
development level and the difference of spatial
pattern is relatively less, and the research on the
analysis from the perspective of the city is scarcer,
and the evaluation method is subjective, which needs
to be introduced into the new objective evaluation
method. In view of this, on the basis of existing
research, this paper takes the cities in Southern
Shaanxi as the research object, constructs a
comprehensive evaluation index system combined
with the actual situation of SHP development in
Southern Shaanxi, and introduces the projection
pursuit model evaluation method suitable for multi-
sample and multi-index evaluation. Through GA
algorithm and GIS tools, the development level of
SHP in Southern Shaanxi is measured, the current
development pattern of SHP in Southern Shaanxi is
recognized, and the differences in urban space are
studied, the causes of differences are analyzed and
targeted policy suggestions are put forward, in order
to provide important reference for the follow-up work
of SHP in Southern Shaanxi and promote the green
development of SHP industry, and provide reference
for the development of SHP in other regions.
2 OVERVIEW OF THE STUDY
AREA
Southern Shaanxi refers to the southern region of
Shaanxi, including Hanzhong City, Ankang City and
Shangluo City from west to east. Southern Shaanxi is
mostly mountainous, north by Qinling, south by
Bashan, Han River from west to east through. Except
that Luonan County of Shangluo City is located in the
Yellow River Basin, the rest of southern Shaanxi is
located in the Yangtze River Basin, accounting for
35.4% of the total area of Shaanxi Province. The
average annual rainfall in southern Shaanxi is 894.7
mm, the total water resources is 262.2 billion m
3
, and
the river network density is generally more than 0.5
km/km
2
. The regional situation is shown in Figure 1.
Figure 1: Regional overview of Southern Shaanxi.
The development capacity of SHP resources in
Shaanxi Province exceeds 3110 MW, of which 74.3%
is in Southern Shaanxi, which is the key development
area. By the end of 2019, there are 479 SHP stations
operating in Southern Shaanxi. The total installed
capacity of 1164.02 MW is shown in Figure 2 and
Figure 3. It can be seen from the figure that the
number of SHP installations with installed capacity
below 0.1 million kilowatts accounts for 60.33% of
the total number of SHP in Southern Shaanxi, but
power generation and installed capacity account for
only 7.28% and 7.49% respectively, which brings
great pressure to the standardized management of
SHP industry.
Figure 2: Distribution of SHP generation by installed
capacity in Southern Shaanxi, 2019.
Figure 3: Installation of SHP stations in Southern Shaanxi
at the end of 2019.
3 RESEARCH METHODS AND
DATA SOURCES
3.1 Research Method
3.1.1 Construction of Index System
The development level of SHP in Southern Shaanxi
is essentially a measure of the development status of
Research on Development Level Measurement and Spatial Differentiation of Small Hydropower in Southern Shaanxi
305

SHP in Southern Shaanxi. Its measurement index
system should reflect the connotation and description
of the development of SHP. Therefore, before
selecting the index, it is necessary to analyze and
define the elements of the measurement of the
development level of SHP. The development level of
SHP in Southern Shaanxi represents the development
quality of the SHP industry in Southern Shaanxi and
is a quantitative judgment of the current development
status of SHP in various cities in Southern Shaanxi.
This requires that the development of SHP to a higher
level must meet the requirements of relatively
advanced economy and technology of SHP, a certain
scale of development and utilization of SHP, and
green and sustainable development. Therefore, this
paper believes that the measurement of the
development level of SHP should focus on three
aspects: technological advancement, development
and utilization degree, and green level.
Based on the above considerations, this paper
follows the principles of representativeness,
comparability, sustainability, and data availability,
and combines the actual needs of SHP development,
it innovatively measures the development level of
SHP in Southern Shaanxi from the three dimensions
of technological advancement, development and
utilization degree, and green level. Each dimension is
divided into three indicators, a total of nine indicators.
The indicators are benefit indicators, and the indicator
system is shown in table 1.
3.1.2 Construction of Evaluation Model
The projection pursuit model is a high-dimensional
data modeling method proposed by Friedman in 1974
(Friedman and Tukey,1974), which can be used for
nonlinear and non-normal distribution. Its basic idea
is to project high-dimensional data along a certain
direction to low-dimensional space, explore the
inherent law of data, and have certain advantages in
evaluation (Xiong and Luo,2016). It is widely used in
water quality evaluation, bearing capacity evaluation,
performance evaluation, and other research. Common
algorithms include the GA algorithm and PSO
algorithm (Zhao et al., 2020). In this paper, the
projection pursuit model is introduced into the
measurement of the development level of SHP to
make the evaluation results more objective and
reasonable.
Step 1-Standardization of index data. To
eliminate the influence of dimension and order of
magnitude on the evaluation results, the min-max
standardized processing method is used to
dimensionless the index data. The indexes in this
paper are all benefit indexes, and the calculation
formula is:
'min{}
max{ } min{ }
ij j
ij
j
j
XX
X
XX



(1
)
In this formula: X'
ij
is the original data for the i
region, the j index, min{X
j
} and max{X
j
} represent
the minimum and maximum original values of the j
data, respectively. X
ij
is the value of the i region and
the j index standardized.
Step 2-Determine the projection value. Set
direction vector a={a
(1)
, a
(2)
, …, a
(j)
}, a
j
is the weight
of index j, project X
ij
to a vector, get the projection
value:
() ( )
1
n
ijij
j
Z
aX



(2
)
In this formula: Z
(i)
is the projection value for the
i region, a
(j)
The weight value for indicator j of the
direction vector.
Step 3-Construct projection objective function:
()azzQSD


(3
)
1/2
2
()
1
()
1
m
i
i
z
ZZ
S
m









(4
)

11
(, )) ( (, ))
mm
z
ip
D
Rrip fRrip



(5
)
In this formula: S
z
is the standard deviation of the
projection value Z
(i)
. D
z
is the local density of Z
(i)
. 𝑍

is
the average projection value. r
(i,p)
is the distance
between samples, r
(i,p)
=|Z
(i)
-Z
(p)
|. R is the radius of the
local density window, which is generally 0.1S
z
, f
(R-r(i,
p))
is a unit order function, when R≥r
(i,p)
takes 1,
otherwise, take 0.
Step 4-Construction of fitness function. Optimize
the projection index function, construct the fitness
function maxQ
(a)
, the formula is:
() z zmax S DaQ


(6
)
2
()
1
.. 1
n
j
j
st a



(7
)
Step 5-Function solution. The traditional method
is difficult to solve such complex nonlinear
optimization problems. Therefore, this paper uses the
GA algorithm to obtain the optimal projection vector
a
*
, which is substituted into Equation (2) to obtain
z
*
(i)
. The larger the value is, the higher the
development level of SHP in the region is.
Step 6-Classification of evaluations. In this paper,
the Mean-Standard Deviation Method is used to
divide the evaluation level (Cui et al., 2016; Wang,
2017). The specific classification standard is shown
in table 2.
WRE 2021 - The International Conference on Water Resource and Environment
306

Table 1: Measurement Index System of SHP Development Level in Southern Shaanxi.
Goal layer Criterion layer Indicator layer Unit Content Implication Maximum Minimum
Weight
a
(j)
Development
Level of SHP in
Southern
Shaanxi
Technical
advancement
Annual utilization
hours (X
1
)
hour
The quotient of annual generating capacity and average installed capacity of SHP in the region is an important index to measure the utilization degree of SHP equipment
Reflecting the efficiency
of SHP utilization
3146 1910 0.2803
The proportion of
technical
personnel (X
2
)
%
The ratio of persons with the technical post or above (including engineering, economic) or technical secondary school or above to the total number of employees in the SHP industry in the region
Reflecting the
Specialization Degree of
SHP Operation
Management
45.22% 25.51% 0.4435
Industry per
capita value
creation (X
3
)
CNY
10000/
person
Revenue per capita generated by SHP industry in the region
Reflecting the advanced
level of SHP technology
and economy
31.50 6.98 0.2783
Developmental
and utilization
degree
Installed capacity
(X
4
)
kw
The total capacity of all SHP units in the area
Reflecting the scale of
SHP development
539517 102391 0.2916
Exploitation rate
(X
5
)
%
The ratio of developed to exploitable SHP in the region
Reflecting the degree of
SHP development
61.89% 28.62% 0.1399
Investment
completed this
year (X
6
)
million
yuan
Amount of investment actually completed in the year of SHP projects in the region
Reflecting the strength
of SHP development
21654 4630 0.4688
Green level
Green SHP
creation number
(X
7
)
seat
Total number of SHP in the region that received green SHP titles by the end of 2019
Reflecting the Green
Development Level of
SHP
31 0 0.4678
Substitution
effect (X
8
)
t/kw
Energy Saving and Emission Reduction Capability of SHP Replacing Thermal Power in the Area
Reflecting the
Contribution Ability of
SHP to Ecological
Environment
96.57 58.64 0.1973
Social
contribution (X
9
)
%
The ratio of total annual taxes paid by SHP industry to total annual revenue from electricity generation and sale
Reflecting the
contribution of SHP to
economic society
5.87% 4.30% 0.2553
Research on Development Level Measurement and Spatial Differentiation of Small Hydropower in Southern Shaanxi
307

Table 2: The standard for Classification of SHP Development Levels.
Comprehensive evaluation index
[𝑍
̅
+S
z
, ∞) [𝑍
̅
,𝑍
̅
+S
z
) [𝑍
̅
-S
z
, 𝑍
̅
) [0, 𝑍
̅
-S
z
)
Level Ⅰ Ⅱ Ⅲ Ⅳ
3.2 Data Sources
In this paper, the research data are mainly derived
from the annual statistical data of rural hydropower
of Shaanxi Province in 2019, some of which are from
the series and reports of "
Annual Development Report
of Small Hydropower Industry in Shaanxi Province
2019
" and "Design and Construction of Small
Hydropower Station in Shaanxi Province".
4 RESULTS AND ANALYSIS
4.1 Evaluation of SHP Development
Level
4.1.1 Model Solving
The index data of the cities in Southern Shaanxi were
collected and sorted. The index data were standardized
by formula (1). MATLAB2020a software was used to
solve the fitness function by GA algorithm. The initial
population was set to 400, the maximum iteration
number was set to 100, and the crossover and
mutation probability was 0.5. The weight value of
each index a
(j)
(see table 1) and the scores of each
region in three dimensions were obtained, and then
the projection value Z
(i)
was determined. The specific
results are shown in figure 4.
4.1.2 Classification of Evaluations
According to the grading standards listed in Table 2,
the grading of development level is determined. At
the same time, the levels of technological
advancement, development and utilization degree,
and green level are divided according to the
proportion of weight. The specific grading standards
are shown in Table 3. According to the grading
standards, the development level of SHP in the cities
of Southern Shaanxi is determined, and the results are
shown in Figure 5.
Figure 4: Measurement results of SHP development level
in Southern Shaanxi.
4.2 Spatial Variation Analysis
According to the results shown in Table 3, Figure 4,
and Figure 5, the differences in the development level
of SHP in different cities of Southern Shaanxi are
analyzed from the perspectives of comprehensive
evaluation and sub-dimensional evaluation.
Table 3: Classification standard of SHP development level measurement in Southern Shaanxi.
Level
Value ranges
General developing
level
Technical advancement
Developmental and utilization
de
g
ree
Green level
Ⅰ [2.5482,∞) [0.9046,∞) [0.8126,∞) [0.8310,∞)
Ⅱ [1.5843,2.5482) [0.5624,0.9046) [0.5052,0.8126) [0.5166,0.8310)
Ⅲ [0.6204,1.5843) [0.2202,0.5624) [0.1978,0.5052) [0.2023,0.5166)
Ⅳ [0,0.6204) [0,0.2202) [0,0.1978) [0,0.2023)
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308

(a) General developing level. (b) Technical advancement.
(c) Developmental and utilization degree. (d) Green level.
Figure 5: Evaluation grade results of SHP development level measurement in Southern Shaanxi.
4.2.1 Comprehensive Evaluation Result
There are obvious differences in the development
level of SHP in Southern Shaanxi. The maximum
difference of projection values in each city is nearly 5
times. Ankang City is higher than Hanzhong City and
Shangluo City. Among them:
The projection value of Ankang City is 2.4742,
ranking first among the three. The overall
development level of SHP is in level II, but it is very
close to the level I threshold. On the one hand,
Ankang City reasonably plans the development and
utilization of SHP and attaches great importance to
the comprehensive development of SHP, which is
ahead of Hanzhong City and Shangluo City in all
aspects. On the other hand, due to the advanced
technology and green level remains to be improved,
so the overall development level of SHP failed to
enter the I level.
The projection value of Hanzhong City is 1.7184,
ranking the second among the three. The overall
development level of SHP is at level II, but it is close
to the level III threshold. On the one hand, Hanzhong
City is rich in hydropower resources, has a large
amount of development, and has a high degree of
development and utilization and green level, which
promotes the development of SHP. On the other
hand, the technical level of SHP in Hanzhong City is
relatively backward, which limits the development of
SHP to some extent.
The projection value of Shangluo City is 0.5604,
ranking the last among the three. The overall
development level of SHP is at level IV, but it is very
close to the level III threshold. This is mainly because
Shangluo City is relatively poor in water resources,
low in development, and relatively small in SHP
market, which is difficult to achieve comprehensive
development, leading to a low overall development
level.
4.2.2 Sub-Dimensional Evaluation Results
This part will analyze the measurement results of
SHP development level in Southern Shaanxi from
three dimensions of technological advancement,
development and utilization degree, and green level.
From the perspective of technological
advancement, the projection value of Ankang City is
0.8075, which is at level II and close to level I,
indicating that the level of SHP technology
management in Ankang City is high, and the
technological advantages are obvious. It is mainly
manifested in the good operation and management of
SHP, high utilization rate, high degree of
specialization, considerable economic benefits, and
the formation of a virtuous circle, which continuously
Research on Development Level Measurement and Spatial Differentiation of Small Hydropower in Southern Shaanxi
309

promotes the progress of SHP technology. The
projection values of Hanzhong City and Shangluo
City are 0.4699 and 0.2491, respectively, which are
in grade III, indicating that the technical level of SHP
is relatively backward, the operation efficiency is
low, and the operation benefit is low. It is urgent to
improve the technical progress and pay more
attention to the operation and management of SHP.
From the perspective of the developmental and
utilization degree, the projection value of Ankang
City is 0.8513, which is in level I. The scale of SHP
installations is large, and the development rate is
high. In recent years, SHP has been actively
developed, and the investment completed in 2019 is
also high, which can be located at the level of level I.
The projection value of Hanzhong City is 0.7236,
which is in level II. Although the capacity of SHP and
SHP installations in Hanzhong City is in the first
place and the annual investment is also high, the
overall development rate is relatively low, so the
overall development and utilization degree still has
great room for improvement. The projection value of
Shangluo City is 0.1899, which is at level IV.
Shangluo City is limited by natural conditions,
geographical location, market society and other
factors, resulting in a relatively low degree of
development and utilization of SHP. Whether from
SHP scale, development rate or annual investment, it
is relatively backward.
From the perspective of green level, the projection
values of Ankang City and Hanzhong City are 0.8153
and 0.5250, respectively, which are in level II.
Although both of them are at the same level, there is
still a big gap. The projection value of Ankang City is
very close to level I, while the projection value of
Hanzhong City is very close to level III. This is
mainly due to the positive response of Ankang City
to the policy call. By the end of 2019, the number of
green SHP creation ranks first in the province, and the
scale of SHP development is large, the benefit of
energy conservation and emission reduction is huge,
which has an important contribution to regional
economic and social development. The number of
green SHP creation and social contribution rate in
Hanzhong City are second only to Ankang City, but
the substitution effect is not high. The projection
value of Shangluo City is 0.1214, which is at level IV.
The green development degree of SHP is low, and
there is still great room for improvement in the
substitution effect and social contribution rate. It is
urgent to improve the green level of SHP and realize
the transformation and upgrading development.
5 CONCLUSIONS
Taking Southern Shaanxi as the research object, this
paper selects nine indicators to construct the
development index system of SHP from three
dimensions of technological advancement,
development and utilization degree and green level.
The projection pursuit model is used to measure the
development level of SHP in Southern Shaanxi, and
ArcGIS10.6 software is used to analyze its spatial
differentiation. The main conclusions are as follows:
From the perspective of comprehensive
evaluation results, the spatial differentiation of SHP
development level in southern Shaanxi is obvious,
and Ankang City is higher than Hanzhong City and
Shangluo City. The projection values of Ankang City
and Shangluo City are 2.4742 and 1.7184,
respectively, and the overall development level of
SHP is at level II. The projection value of Shangluo
City is 0.5604, and the overall development level of
SHP is at level IV.
From the results of sub-dimensional evaluation,
the spatial differentiation of cities is still obvious. In
terms of technological advancement, the projection
value of Ankang City is 0.8075, which is at level II.
The projection values of Hanzhong City and
Shangluo City are 0.4699 and 0.2491, respectively,
which is at level III. In terms of the degree of
development and utilization, the projection value of
Ankang City is 0.8513, which is at level I, the
projection value of Hanzhong City is 0.7236, which
is at level II, and the projection value of Shangluo
City is 0.1899, which is at level IV. In terms of green
level, the projection values of Ankang City and
Hanzhong City were 0.8153 and 05250, respectively,
which were in level II, and the projection value of
Shangluo City was 0.1214, which was in level IV.
According to the analysis results, policy
suggestions are put forward, one is to strengthen
operation management, improve utilization
efficiency, and enhance the modernization level of
SHP in Southern Shaanxi. The second is to improve
the development plan, make rational use of
hydropower resources, and properly handle the
relationship between SHP stock and increment. The
third is to strengthen supervision, accelerate
transformation and upgrading, and establish a long-
term mechanism for the green development of SHP.
Four is to adjust measures to local conditions,
positioning, promote the coordinated development of
SHP areas.
WRE 2021 - The International Conference on Water Resource and Environment
310

ACKNOWLEDGEMENTS
This research was funded by Project of National
Natural Science Foundation of China (71774132),
Shaanxi Water Conservancy Science and Technology
Project (2020SLKJ-22), Shaanxi Provincial
Department of Education Key Scientific Research
Project (20JT056).
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