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Coordinated Optimal Allocation of Distributed Generations in Smart Distribution Grids Considering Active Management and Contingencies

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Abstract

This study presents a multi-objective bi-level optimization model for distributed generation (DG) allocation in smart distribution grids integrating energy storage devices. As part of smart distribution grids, four active management schemes, coordinated on-load tap-changer voltage control, DG power factor control, DG curtailment and demand side management, are embedded in the proposed model. Uncertainties related to DGs, loads and contingencies and the capability of energy storage devices for peak shaving and renewable energy compensation are also inherent. The allocation model simulates the network transfer process to postpone the DG investment. The trade-off between the defined annual total cost and N-1 security margin index is achieved in the optimal allocation methodology considering operation thresholds and security improvements. The DG allocation solutions are solved by a hybrid algorithm. The correlated input parameters of the optimization problem, such as wind speed, illumination intensity and load, are generated using quasi Monte Carlo simulation and singular value decomposition and then simplified by fuzzy C-means clustering to improve the computation efficiency of optimal power flow. A modified 104-bus distribution case is used to demonstrate the effectiveness and flexibility of the proposed model.

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Abbreviations

AM:

Active management

DN:

Distribution network

DG:

Distributed generation

DSM:

Demand side management

DSSR:

Distribution system security region

DNDEA:

Dynamic niche differential evolution algorithm

ESD:

Energy storage device

FCM:

Fuzzy C-means

NBI:

Normal boundary intersection

OLTC:

On-load tap-changer

PVG:

Photovoltaic generation

PDIPM:

Primal–dual interior point method

QMCS:

Quasi Monte Carlo simulation

SDG:

Smart distribution grid

SSD:

Steady-state security distance

SVD:

Singular value decomposition

WTG:

Wind turbine generation

\(a_{i}\), \(b_{i}\) :

Number of WTGs and PVGs at bus \(i\)

\(C_{I}\) :

Annual DG investment cost

\(C_{OM,s}\) :

DG operation and maintenance cost

\(C_{AM,s}\) :

DG AM cost

\(C_{P,s}\) :

Cost of energy injected from substations

\(C_{CE,s}\) :

Carbon emission cost

\(C_{DSM,s}\) :

DSM cost

\(c_{i,WTG}^{I}\), \(c_{i,PVG}^{I}\) :

Unit investment cost of WTGs and PVGs at bus \(i\)

\(c_{i,WTG}^{OM}\), \(c_{i,PVG}^{OM}\) :

Unit operation and maintenance cost of WTGs and PVGs at bus \(i\)

\(c_{i,WTG}^{AM}\), \(c_{i,PVG}^{AM}\) :

Unit AM cost of WTGs and PVGs at bus \(i\)

\(d\) :

Annual interest rate

\(E_{i}^{ESD}\) :

Energy reservoir of ESDs at bus \(i\)

\(E_{i,s,ini}^{ESD}\) :

Initial energy storage of ESDs at bus \(i\)

\(E_{i,s,t}^{ESD}\) :

Energy storage of ESDs connected to bus \(i\) at time \(t\)

\(F_{k}\) :

\(k\)Th feeder section

\(G_{ij}\), \(B_{ij}\) :

Conductance and admittance of branch \(ij\)

\(I\) :

Illumination intensity

\(I_{r}\) :

Rated illumination intensity

\(N_{s}\) :

Number of scenarios

\(N_{DG}\) :

Number of DG installation buses

\(N_{bus}\) :

Number of buses

\(N_{DSM}\) :

Number of DSM participation buses

\(P_{Gi,s}\), \(Q_{Gi,s}\) :

Active and reactive power supply at bus \(i\)

\(P_{Li,s}\), \(Q_{Li,s}\) :

Active and reactive power demand at bus \(i\)

\(P_{i,s,t}^{ESD}\) :

Power production of ESDs connected to bus \(i\) at time \(t\)

\(p_{s}\) :

Occurrence probability

\(RU_{i}^{ESD}\), \(RD_{i}^{ESD}\) :

Ramp-up and ramp-down rate of ESDs at bus \(i\)

\(r\), \(c\) :

Shape and scale parameter of WTGs

\(S_{L}\) :

Random variable of loads

\(S_{F}^{k}\) :

Load of \(F_{k}\)

\(S_{T}^{m}\) :

Load of \(T_{m}\)

\(S_{WTG}^{r}\)(\(S_{i,WTG}^{r}\)):

Rated capacity of WTGs (at bus \(i\))

\(S_{PVG}^{r}\)(\(S_{i,PVG}^{r}\)):

Rated capacity of PVGs (at bus \(i\))

\(S_{i,WTG,0}^{r}\) :

Unit capacity of WTGs at bus \(i\)

\(S_{i,PVG,0}^{r}\) :

Unit capacity of PVGs at bus \(i\)

\(S_{i,s,WTG}\) :

Output power of WTGs at bus \(i\)

\(S_{i,s,PVG}\) :

Output power of PVGs at bus \(i\)

\(S_{i,s,DG}\) :

Output power of DGs at bus \(i\)

\(S_{i}^{ESD}\) :

Power rating of ESDs at bus \(i\)

\(S_{grid,s,P}\) :

Power injected from substations

\(S_{j,s,DSM}\) :

Load that participates in DSM at bus \(j\)

\(S_{i}^{\max }\) :

Maximum DG installation capacity at bus \(i\)

\(S_{F,\max }^{l}\) :

Capacity of \(F_{l}\)

\(S_{T,\max }^{n}\) :

Capacity of \(T_{n}\)

\(S_{f,tr}^{k,l}\) :

Load transferred from \(F_{k}\) to \(F_{l}\) when \(F_{k}\) faults

\(S_{T,tr}^{m,n}\) :

Load transferred from \(T_{m}\) to \(T_{n}\) when \(T_{m}\) faults

\(T_{m}\) :

\(m\)Th substation transformer

\(U_{i,s}\) :

Voltage of bus \(i\)

\(U_{OLTCm,s}\) :

Secondary voltage of OLTC \(m\)

\(V\) :

Wind speed at the height of WTGs’ hub

\(V_{ci}\), \(V_{r}\), \(V_{co}\) :

Cut-in, rated and cut-out wind speed

\(W_{f}\) :

Any operating point vector

\(W_{f0}\) :

Operating point vector on \(B_{k}\)

\(y\) :

Service life

\(\alpha\), \(\beta\) :

Parameter of Beta distribution

\(\mu_{p}\), \(\sigma_{p}\) :

Mean and standard deviation of loads

\(\rho_{s}\) :

Electricity price

\(\eta\) :

Unit carbon emission price

\(\lambda\) :

Carbon emission intensity of the external grid

\(\xi\) :

DSM incentive price

\(\theta_{ij,s}\) :

Phase difference between voltages at buses \(i\) and \(j\)

\(\omega_{cur,s}\) :

DG curtailment rate

\(\varphi_{i,s}\) :

Power factor angle of DGs at bus \(i\)

\(\delta\) :

Power injection and extraction efficiency of ESDs

\(\Delta t\) :

Time duration between two adjacent hours

\(\Omega_{DSSR}\) :

Security region for distribution networks

\(\Phi^{(m)}\) :

Set of feeder sections derived from \(T_{m}\)

\(\Gamma ({\kern 1pt} \cdot {\kern 1pt})\) :

Gamma function

\(\left( \cdot \right)_{s}\) :

Value of the corresponding scenario

\(\left( \cdot \right)^{\max }\), \(\left( \cdot \right)^{\min }\) :

Maximum and minimum value of variables

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Acknowledgements

This work was supported by the National Key R&D Program of China (2018YFE0208400) and National Natural Science Foundation of China (U1766201). The authors are grateful to the editor and the anonymous reviewers for their insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Automation, Hangzhou Dianzi University, Hangzhou, China

    Jia Liu, Pingliang Zeng & Hao Xing

  2. Department of Electrical Engineering, Zhejiang University, Hangzhou, China

    Jia Liu

  3. Hangzhou Kelin Electric Company, Hangzhou, China

    Jia Liu

  4. China Electric Power Research Institute, Beijing, China

    Yalou Li

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  1. Jia Liu
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  2. Pingliang Zeng
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Correspondence to Pingliang Zeng.

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Liu, J., Zeng, P., Li, Y. et al. Coordinated Optimal Allocation of Distributed Generations in Smart Distribution Grids Considering Active Management and Contingencies. J. Electr. Eng. Technol. 15, 1969–1983 (2020). https://doi.org/10.1007/s42835-020-00462-1

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