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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

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Front. Energy    2020, Vol. 14 Issue (4) : 801-816    https://doi.org/10.1007/s11708-020-0687-y
RESEARCH ARTICLE
An operating state estimation model for integrated energy systems based on distributed solution
Dengji ZHOU, Shixi MA, Dawen HUANG, Huisheng ZHANG(), Shilie WENG
Key Laboratory of Power Machinery and Engineering of the Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
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Abstract

In view of the disadvantages of the traditional energy supply systems, such as separate planning, separate design, independent operating mode, and the increasingly prominent nonlinear coupling between various sub-systems, the production, transmission, storage and consumption of multiple energy sources are coordinated and optimized by the integrated energy system, which improves energy and infrastructure utilization, promotes renewable energy consumption, and ensures reliability of energy supply. In this paper, the mathematical model of the electricity-gas interconnected integrated energy system and its state estimation method are studied. First, considering the nonlinearity between measurement equations and state variables, a performance simulation model is proposed. Then, the state consistency equations and constraints of the coupling nodes for multiple energy sub-systems are established, and constraints are relaxed into the objective function to decouple the integrated energy system. Finally, a distributed state estimation framework is formed by combining the synchronous alternating direction multiplier method to achieve an efficient estimation of the state of the integrated energy system. A simulation model of an electricity-gas interconnected integrated energy system verifies the efficiency and accuracy of the state estimation method proposed in this paper. The results show that the average relative errors of voltage amplitude and node pressure estimated by the proposed distributed state estimation method are only 0.0132% and 0.0864%, much lower than the estimation error by using the Lagrangian relaxation method. Besides, compared with the centralized estimation method, the proposed distributed method saves 5.42 s of computation time. The proposed method is more accurate and efficient in energy allocation and utilization.
Keywords integrated energy system      state estimation      electricity-gas coupling energy system      nonlinear coupling      distributed solution     
Corresponding Author(s): Huisheng ZHANG   
Online First Date: 07 September 2020    Issue Date: 21 December 2020
 Cite this article:   
Dengji ZHOU,Shixi MA,Dawen HUANG, et al. An operating state estimation model for integrated energy systems based on distributed solution[J]. Front. Energy, 2020, 14(4): 801-816.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-020-0687-y
https://academic.hep.com.cn/fie/EN/Y2020/V14/I4/801
Fig.1  Electricity-gas integrated energy system and coupling components.
Fig.2  Flowchart of parallel ADMM distributed state estimation.
Fig.3  An object of the analysis of integrated energy system state estimation.
Gas-fired power plants Power grid nodes Natural gas network nodes
1 36 3
2 35 4
3 38 5
4 33 7
5 37 6
6 34 8
7 30 9
8 32 11
9 39 10
10 31 12
Tab.1  Connection nodes of gas-fired power plants
Compressor units Power grid nodes Natural gas network nodes
1 22 5–6
2 26 7–8
3 – 9–10
4 – 11–12
Tab.2  Connection nodes of motor-driven compressor units
Node Source flow/(kg·s–1) Demand/(kg·s–1) For electricity/(kg·s–1) Pressure/kPa ?Pipe Ci j Gas flow/(kg·s–1)
1 36.8100 0 0 8273.8 ?1 0.00878 36.8118
2 47.1900 0 0 8951.5 ?2 0.00880 47.1947
3 0 0 4.9436 7132.0 ?3 0.01046 7.4922
4 0 0 1.2861 7167.8 ?4 0.00882 39.4075
5 0 0 7.4072 5559.3 ?5 0.00847 38.3457
6 0 0 5.2893 10006.4 ?6 0.00822 26.7240
7 0 0 6.8061 5557.9 ?7 0.00517 30.2046
8 0 0 1.3309 10560.1 ?8 0.00533 10.5008
9 0 0 15.8916 9463.1 ?9 0.00505 1.2743
10 0 0 0.3410 9463.1 ?10 0.00403 3.7756
11 0 0 5.1177 8795.0 ?11 0.00578 5.4156
12 0 0 23.8411 9234.2 ?12 0.00530 3.4334
13 0 1.3156 0 9255.6
14 0 1.6164 0 9230.8
15 0 8.8532 0 9208.0
Tab.3  Main parameters of natural gas networks
Sub-systems Measurement parameters Number of measurement points
(Specific description)
Power system Voltage amplitude 1
(V39)
Voltage phase 1
(θ39)
Active power injection 15
(P25 P26 P27 P28 P29 P30 P31 P32 P33 P34 P35 P36 P37 P38 P39)
Reactive power injection 15
(Q25 Q26 Q27 Q28 Q29 Q30 Q31 Q32 Q33 Q34 Q35 Q36 Q37 Q38 Q39)
Branch active power 32
(P1,39 P2,25 P2,30 P4,5 P4,14 P5,6 P6,31 P7,8 P8,9 P9,39 P10,11 P10,13 P10,32 P12,11 P16,17P16,19 P16,21 P16,24 P17,18 P17,27 P19,20 P19,33 P20,34 P22,23 P22,35 P23,36 P25,26 P25,37 P26,28 P28,29 P29,38, P29,39)
Branch reactive power 32
(Q1,39 Q2,25 Q2,30 Q4,5 Q4,14 Q5,6 Q6,31 Q7,8 Q8,9 Q9,39 Q10,11 Q10,13 Q10,32 Q12,11 Q16,17Q16,19 Q16,21 Q16,24 Q17,18 Q17,27 Q19,20 Q19,33 Q20,34 Q22,23 Q22,35 Q23,36 Q25,26 Q25,37 Q26,28 Q28,29 Q29,38, Q29,39)
Natural gas system Pipeline flow rate 7
(q1,3 q2,4 q3,5 q4,7 q6,9 q8,11 q10,13)
Node flow rate 13
(q3 q4 q5 q6 q7 q8 q9 q10 q11 q12 q13 q14 q15)
Node pressure 13
(p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15)
Pipeline friction 12
(C1,3 C2,4 C3,4 C3,5 C4,7 C6,9 C8,11 C10,13 C12,14 C13,14 C13,15 C14,15)
Tab.4  Measurement parameters and number of measurement points in integrated energy system
State estimation methods Error types Power grid Natural gas network
Voltage amplitude Vi/% Voltage phase θij/% Node pressure Pi/% Pipeline flow rate qij/%
Method A Maximum error 1.51×10–2 1.75×10–2 1.53×10–1 3.98×10–2
Average error 1.32×10–2 5.45×10–4 8.64×10–2 2.88×10–2
Method B Maximum error 1.76×10–2 2.96×10–2 1.82×10–1 1.03×10–1
Average error 1.44×10–2 7.83×10–3 1.19×10–1 5.45×10–2
Method C Maximum error 4.52×10–2 2.98×10–2 2.87×10–1 8.9×10–2
Average error 3.43×10–2 1.68×10–2 1.51×10–1 6.22×10–2
Tab.5  Maximum and average errors of state variables obtained by different state estimation methods
State estimation methods Error types Power grid Natural gas network
Active power flow Pij/% Reactive power flow Qij/% Active power Pi/% Reactive power Qi/% Pipeline friction resistance Cij/% Node flow rate qi/%
Method A Maximum error 7.83×10–2 5.88×10–2 6.0×10–2 5.75×10–2 3.16×10–3 7.09×10–1
Average error 2.64×10–2 1.88×10–2 2.10×10–2 2.19×10–2 2.16×10–3 7.08×10–1
Method B Maximum error 9.35×10–2 9.32×10–2 6.33×10–2 7.88×10–2 4.07×10–3 1.47
Average error 2.88×10–2 2.48×10–2 2.86×10–2 2.57×10–2 2.15×10–3 1.77×10–1
Method C Maximum error 2.32×10–1 1..91×10–1 1.83×10–1 1.98×10–2 3.4×10–3 7.43×10–2
Average error 7.06×10–2 5.25×10–2 5.90×10–2 7.93×10–2 9.32×10–4 3.65×10–2
Tab.6  Maximum and average errors of measurement variables obtained by different state estimation methods
Fig.4  Relative error of power grid node voltage amplitude state estimation.
Fig.5  Relative error of power grid node voltage phase state estimation.
Fig.6  Relative error of gas network node pressure state estimation.
Fig.7  Relative error of gas network pipeline flow rate state estimation.
Fig.8  Relative error of gas network node flow rate state estimation.
Fig.9  Relative error of power grid node active power state estimation.
State estimation methods Computing time/s
Method A 1.44
Method B 4.77
Method C 0.35
Tab.7  Time taken by different state estimation methods
Fig.10  Comparison of convergence of different methods.
x* Optimal estimated value
z Actual measured value
zt True value vector of parameters
r Measured error vector
qi Pipeline flow of node i
h(x) System simulation model
Wack Measurement covariance matrices of power grid
W gasm Measurement covariance matrices of gas networks
J(x) Deviations between the measured and estimated
xack Power gird state variable
xgasm Gas network state variable
Pi j Active power flow of branch ij
Qi j Reactive power flow of branch ij
ε Convergence threshold
pi Pressure of node i
v Polytropic coefficient
Pi Active power of node i
Qi Reactive power of node i
Vack, i Voltage of node i
θack, ij Phase of node i
Ci Pipeline friction resistance
Gi Node flow
η Power generation efficiency
Hu pp,i Natural gas calorific value
λ Lagrangian multiplier
ρ Penalty coefficient
v Average value of state variables
S¯M Measurement error
o Number of iterations
t Sampling time
N Number of samples
s Total number of measurement point
ac Alternating current power grid
k kth alternating current power grid sub-system
gc Natural gas compressor
i,j Number of nodes
gas Natural gas network
m mth gas network sub-systems
pp Power plant
cp Coupling point
  
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