US 2026/0010677 A1 · OPTIMAL LOAD CURTAILMENT CALCULATING METHOD BASED ON LAGRANGE MULTIPLIER AND APPLICATION THEREOF

Abstract

There is provided an optimal load curtailment calculating method based on Lagrange multiplier and an application thereof in power system reliability assessment, wherein the calculating method includes the following steps: inputting all system states to be analyzed for reliability assessment and establishing corresponding optimal load curtailment models; classifying the optimal load curtailment models according to Lagrange multiplier to obtain several sets; and solving the optimal load curtailment models in each set by using Lagrange multipliers to obtain an optimal load curtailment corresponding to the system state. A processor executing the method is integrated as a part of a controller with a power system reliability assessment service, and then the power system uses the controller to control the power system by using data from the power system reliability assessment device maintain grid stability and reduce power consumption.

A method of an optimal load curtailment calculation based on Lagrange multiplier in power system reliability assessment, the method, when executed by a processor, causes the processor to carry out the steps, comprising:

Step 1:
inputting all system states s collected by current transducers. voltage sensors, and power analyzers and energy monitors to be analyzed for reliability assessment, and establishing corresponding optimal load curtailment models, namely:
min
c
T
⁢
x
s
.
t
.
Ax
=
b
,
x
≥
0
(
1
)
where x is a variable vector;
A is a coefficient matrix;
b is a right-hand-side vector;
c is a cost coefficient vector;
wherein the current transducers measure the electrical current flowing through a circuit;
voltage sensors measure the electrical potential difference;
power analyzers provide comprehensive measurements of power;
and energy monitors measure and track energy consumption over time;
Step 2:
classifying the above optimal load curtailment models into several sets by the Lagrange multiplier λs;
and
Step 3:
solving all the optimal load curtailment models in each set by the Lagrange multiplier λs of the set, to obtain optimal load curtailments fLC_s of the system states;
wherein the Step 3 comprises a step as follows:
calculating the optimal load curtailments fLC_s of the system states s by the Lagrange multiplier λs:
f
LC
⁢
_
⁢
s
=
λ
s
⁢
b
(
2
)
where b is determined by the optimal load curtailment model established in the Step 1;
wherein the Step 2 comprises the following steps:
comparing an unclassified optimal load curtailment model with a classified one, and the two models belong to the same set if the Lagrange multipliers of the two models are the same;
determining whether the Lagrange multipliers of the two optimal load curtailment models are the same comprises the following steps:
adopting judgment criteria to determine whether the different vectors A, b, and c of the two models will lead to different Lagrange multipliers As;
wherein the judgment criteria are as follows:
{circle around (1)} If the difference occurs in a cost coefficient vector c, wherein c is a cost coefficient vector it is assumed that the model in the Step 2 is c+Δc, and the model corresponding to the system state to be compared with is the vector c;
if formula (3) is met, the two system states belong to the same COLM-set:
(
c
+
Δ
⁢
c
)
T
-
(
c
B
+
Δ
⁢
c
B
)
T
⁢
B
-
1
⁢
A
≤
0
(
3
)
as the cost coefficient vector c is different, the Lagrange multiplier As of the system state s in the Step 1 is:
λ
s
=
(
c
B
+
Δ
⁢
c
B
)
T
⁢
B
-
1
(
4
)
{circle around (2)} If the difference occurs in the branch power flow limits b, it is assumed that the model in the Step 2 is b+Δb, and the model corresponding to the system state to be compared with is the branch power flow limits b;
if formula (5) is met, the two system states belong to the same COLM-set:
B
-
1
(
b
+
Δ
⁢
b
)
≥
0
(
5
)
the Lagrange multiplier λs of the system state s in the Step 1 is:
λ
s
=
c
B
T
⁢
B
-
1
(
6
)
{circle around (3)} If the difference occurs in a column vector pk in the coefficient matrix A, it is assumed that the model in the Step 2 is pk+Δpk, and the model corresponding to the system state to be compared with is the column vector pk;
if the column vector pk does not belong to an optimal basis B, (i.e., the corresponding variable Xk is not the basic variable), and formula (7) is met, the two system states belong to the same COLM-set:
c
k
-
c
B
T
⁢
B
-
1
(
p
k
+
Δ
⁢
p
k
)
≤
0
(
7
)
where Ck is the cost coefficient of the corresponding variable Xk;
the Lagrange multiplier λs of the system state s in the Step 1 is:
λ
s
=
c
B
T
⁢
B
-
1
(
8
)
{circle around (4)} If the variable x changes, it is assumed that a new variable Xn+1 is added to the model of the system state to be compared in the Step 2;
the cost coefficient Cn+1 and coefficient matrix column vector pn+1 are added accordingly;
if formula (9) is met, the two system states belong to the same COLM-set:
c
n
+
1
-
c
B
T
⁢
B
-
1
⁢
p
n
+
1
≤
0
(
9
)
the Lagrange multiplier λs of the system state s in the Step 1) is:
λ
s
=
c
B
T
⁢
B
-
1
(
10
)
the maximum time of judgment criteria is proposed;
if it is exceeded, an optimal load curtailment model with the same Lagrange multiplier λs is not found, and this optimal load curtailment model is regarded as a single set;
and
comparing and judging the values of A, b, and c of the two models in descending order according to the similarity thereof, wherein
the method based on Lagrange multiplier in power system reliability assessment is implemented in such a way that the processor executing the method is integrated as a controller with the power system reliability assessment service, and then a power system uses the controller to use the data from the power system reliability assessment device to control the power system to reduce power consumption;
the method is applied to establish a power system reliability assessment device resulting in the power system reliability assessment device comprising an input and initialization module, a system state selection module, a state impact analysis module, and a reliability indices calculation module;
the input and initialization module is configured to input power system data, component reliability data, and preset parameters of reliability assessment methods, including topological structure, branch parameters, component parameters, load data, renewable generation locations, renewable generation output data, and reliability parameters of components;
the system state selection module is configured to select the system states to be analyzed for the reliability assessment, including component contingency state, load time sequence state, and renewable generation output time sequence state;
the state impact analysis module analyzes the impact of the system states selected by the system state selection module using the optimal load curtailment calculating method of Lagrange multiplier, and represents the impact by the load curtailments and all reliability indices;
the reliability indices calculation module is configured to compute the reliability indices of the power system based on impact analysis results of the system states;
and
the power system reliability assessment device quantitatively assesses the power system risks with reliability indices is of guiding planning, design, operation, and maintenance of power systems.

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Optimal load curtailment calculating method based on lagrange multiplier and application thereof

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Optimal load curtailment calculating method based on lagrange multiplier and application thereof

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Abstract

Claims3