International Core Journal of Engineering 2020-26 | Page 25
C. Decision Rule of DS Evidence Theory
After using the evidence theory to fuse multiple
evidences, the final BPA on the recognition framework will
be obtained. The corresponding support evidence interval,
trust interval and rejection evidence interval can be obtained
by calculating the corresponding reliability and plausibility
function, shown in Fig. 2.
A. Power Market Settlement Data and Pretreatment
The settlement data includes settlement electricity price
and settlement electricity. The settlement electricity can be
subdivided into market electricity volume, actual electricity
generation/consumption, auxiliary service electricity, etc.
During the settlement process, the price and electricity are
related to settlement interval and settlement entity, so the
settlement data constitute a three-dimensional matrix
X(I×J×K). Which I represents the market entity, J represents
the settlement price and the settlement electricity amount
information, K indicating the settlement interval at which
the data is located.
Trust interval
Bel A
Support evidence interval
Pls A
Since the dimensions of the established three-
dimensional matrix have different meanings and the
settlement of electricity prices and electricity also have
different physical meanings and units, the direct use of the
original data will lead to the theoretical analysis of the
evidence subject to the influence of electricity price and
electricity value, highlighting the role of higher-value
elements. Therefore, it requires data preprocessing of the
matrix to normalize the matrix. The paper adopts the
common Min-Max standardization method, also known as
dispersion standardization, which linearly transforms the
original settlement price and electricity.
Rejection evidence interval
Informed interval
Fig. 2. Description of evidence interval in DS evidence theory
There is often a case where evidence supports multiple
propositions in the case of multiple evidence fusions, and
there is a connection between propositions. The final
reliability of proposition A should be at [Bel(A), Pls(A)], the
specific choice of what value as the final reliability of the
proposition A is the decision rule of the evidence theory. In
general, commonly used decision rules include maximum
Bel(•) method, maximum Pls(•) method, combination rule
method, evidence interval method and Pignistic probability
method.
B. Multiple Evidence Construction
Evidence for identifying data risks in evidence theory
needs to be constructed by appropriate statistical analysis
methods. It is necessary to extract the statistical
characteristics information in the settlement data in the
process of constructing evidence, so that the extracted
evidence can reflect the abnormality of the settlement data
as completely and accurately as possible. The PCA and ICA
in statistical methods have been widely used in many fields
as statistical methods for extracting multivariate features.
Since the settlement data does not exist in isolation, and
there is a certain correlation between the variables, the PCA
can convert these possible related variables into a linear set
of linear unrelated variables, and then calculate statistic that
is used to identify anomalous data. ICA is an extension of
principal component analysis, which can describe the
characteristics of data information more essentially. The
statistics calculated by the two methods can be used as
evidence sources to complement each other and obtain
accurate results.
1) Maximum Bel(•) method: Select Bel(•) as the final
confidence value for the proposition.
2) Maximum Pls(•) method: Select Pls(•) as the final
confidence value for the proposition.
3) Combination rule method: Add one or more of the
following restrictions:
a) The proposition has the maximum confidence limit.
b) The reliability difference between propositions has
a minimum lower limit.
c) Uncertainty reliability allocation (BPA) should
have an upper limit.
4) Evidence interval method: Re-plan the confidence
interval of the proposition.
5) Pignistic probability method: Pignistic probability
method believes that reliability exists on two levels: the
credal layer and the Pignistic layer. The Pignistic probability
transformation method should satisfy Equation (9).
Bel A i d Probability A i d Pls A i
°
®
Probability A i 1
°̄ A ¦
i 4
1) PCA detection statistics and BPA: Since PCA can
only be applied to the processing of two-dimensional data,
and the power market settlement data is a three-dimensional
matrix, it needs to be decomposed in a certain direction to
obtain a two-dimensional matrix. The paper will expand
X(I×J×K) in the K direction to get X(I×KJ), and the two-
dimensional matrix will be obtained. The line represents the
settlement data of a settlement entity in all settlement
intervals. In order to reflect the influence of the principal
subspace and the residual space on the data, the paper
introduces two statistics, Hotelling’s T 2 and Square
Prediction Error (SPE), to identify the data risk of the power
market.
(9)
III. R ISK I DENTIFICATION M ODEL FOR P OWER MARKET
S ETTLEMENT D ATA B ASED ON E VIDENCE T HEORY
The risk identification process of power market
settlement data based on evidence theory consists of four
parts: data preprocessing, multi-evidence construction, multi-
evidence fusion and decision-making.
The PCA operation expression of X(I×KJ) is Equation
(10).
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