# Dispatching of Wind/Battery Energy Storage Hybrid Systems Using Inner Point Method-Based Model Predictive Control

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## Abstract

**:**

## 1. Introduction

## 2. The Wind/Battery Energy Storage Hybrid System Modeling

#### 2.1. System Configuration

_{D}as much as possible. In order to achieve the goal, a wind power forecasting model is applied to predict future p-step wind power at each sampling point, and the dispatch order is based on these predicted values. The reasonable action of the BESS (P

_{B}) is calculated by the control strategy in the PMU to compensate for the difference between the dispatch order P

_{D}and the actual wind power P

_{W}. Under this strategy the power injected to the grid (total output of the wind/battery energy storage hybrid system) P

_{G}would follow the dispatch order from the transmission system operator (TSO), and the effects mainly depends on the capacity of the battery and the control algorithm in the PMU.

#### 2.2. System Modeling

_{G}(k) is the total output of the wind/battery energy storage hybrid system; P

_{B}(k) is the power control signal for the BESS. When P

_{B}(k) > 0, it denotes the BESS discharges power; when P

_{B}(k) < 0, it denotes the BESS charges power. P

_{W}(k) denotes the actual wind power, E

_{B}(k) denotes the remaining energy in the BESS. State of Charge (SOC) of a BESS is the ratio between available energy and its rated capacity, expressed as a percentage. ΔT

_{B}is the transfer coefficient from MW to MWh, for instance when the sampling time is 5 min, ΔT

_{B}= 5 min/60 min = 1/12.

_{B}(k); system output: y(k) = P

_{G}(k); combined with the system:

_{1}, AB

_{1}] is full rank, so the system is controllable.

_{2}(k) denotes the remaining energy at time k; C

_{B}denotes rate capacity of a BESS; S

_{min}denotes lower limit of a BESS, S

_{max}denotes upper limit of a BESS.

_{c}(k) and P

_{d}(k) are the available charging power and discharging power of the BESS, respectively, P

_{max_ch}and P

_{max_f}are the maximum charging power and discharging power separately.

## 3. Dispatching Strategy for Wind/Battery Energy Storage Hybrid System Based on MPC

#### 3.1. Wind Power Predicting and Dispatch Curve

_{G}) could trace the dispatch curve. Therefore, a reasonable dispatch order is significant to achieve the goal.

_{1}, ϕ

_{2}, …, ϕ

_{p}and θ

_{1}, θ

_{2}, …, θ

_{q}are all constants. a

_{t}is white noise time series, therefore time series {z

_{t}} comply with ARMA with the order of (p, q), described as ARMA(p, q). Wind power is a non-stationary time series that needs to be tackled with difference processing. After being processed d times, {${\nabla}^{d}{z}_{t}$} becomes a stationary ARMA series, therefore:

_{1}, ϕ

_{2}, ϕ

_{p}and θ

_{1}, θ

_{2}, θ

_{q}. In the paper, least squares estimation is used to identify the parameters which involves minimizing the residual sum of squares.

^{th}dispatching interval i.e., kT

_{d}< t ≤ (k + 1)T

_{d}, the dispatch power is defined as follows:

_{d}is the dispatching interval and it is assumed to be 30 min in this paper. The control interval of the BESS is 5 min. The sampling time interval of actual wind power is 5 min and the interval of predictive wind power is also 5 min. The method of acquiring the dispatch order is illustrated in Figure 2.

#### 3.2. Design for MPC Contoller for Dispatching

_{p}is the predictive horizon, m

_{c}is the control horizon, $\mathsf{\alpha}\in (0,\text{\hspace{0.17em}}1)$ is the balance coefficient of the tracing performance and the control action. In order to simplify the calculations, in this paper the predictive horizon equals the control horizon, i.e., m

_{p}= m

_{c}= p.

_{ref}is reference trajectory, which in this paper is the dispatch order.

_{i}(k+1) at time k and formulation (2), and it could be described as (15):

#### 3.3. Rolling Optimization Using Inner Point Method

- Step 1: Select the initial condition (x(0), s(0), z(0)) satisfying s(0) > 0, z(0) > 0.
- Step 2: Obtain the Δu and Δz satisfying the following equation:$$\left[\begin{array}{cc}H& {A}_{\text{ineq}}^{\mathrm{T}}\\ {A}_{\text{ineq}}& \Gamma \end{array}\right]\left[\begin{array}{c}\Delta u\\ \Delta z\end{array}\right]=\left[\begin{array}{c}{r}_{1}\\ {r}_{2}\end{array}\right]\text{and}\Delta s=-s+{Z}^{-1}\left(\mathsf{\beta}e-T\Delta Z\right).$$$$\mathsf{\Gamma}=-{Z}^{-1}{S}^{k},\text{}S=\left[\begin{array}{cccc}{s}_{1}& 0& \cdots & 0\\ 0& {s}_{2}& \cdots & 0\\ \vdots & \vdots & \ddots & \vdots \\ 0& 0& \cdots & {s}_{m}\end{array}\right],\text{}Z=\left[\begin{array}{cccc}{z}_{1}& 0& \cdots & 0\\ 0& {z}_{2}& \cdots & 0\\ \vdots & \vdots & \ddots & \vdots \\ 0& 0& \cdots & {z}_{m}\end{array}\right],\text{}e={\left[\begin{array}{c}1\\ 1\\ \vdots \\ 1\end{array}\right]}_{{m}_{c}\times 1}.\phantom{\rule{0ex}{0ex}}{r}_{1}=-Hu-f-{A}_{\text{ineq}}^{-\mathrm{T}}z,\text{}{r}_{2}=-{A}_{\text{ineq}}u+{b}_{\text{ineq}}-\mathsf{\beta}{{\rm Z}}^{-1}e.$$
- Step 3: Update the variable through increment.$$\text{\hspace{0.17em}}\left(x\left(1\right),s\left(1\right),z\left(1\right)\right)=\left(x\left(0\right),s\left(0\right),z\left(0\right)\right)+a\left(\Delta x\left(0\right),\Delta s\left(0\right),\Delta z\left(0\right)\right),\text{}0a1.$$
- Step 4: Judge the convergence. If it converges, the procedure would stop and the optimal control values are obtained, otherwise, the value are treated as initial value and sent into step 2 to solve iteratively.

## 4. Simulation Results

_{max_ch}and max-discharging power P

_{max_f}are both 3 MW; initial SOC is 0.5; the limit of SOC is 0.2–0.8.

_{c}≤ m

_{p}. In this paper wind power is forecasted 30 min in the future according to the wind data during the last 12 h, as a consequence, in order to ensure sound control effects, the predictive horizon and control horizon are both set to be 30 min, i.e., m

_{c}= m

_{p}= 6, (30 min), α is 0.8.

#### 4.1. Capacity of BESS in 4.5 MWh

#### 4.2. Capacity of BESS in 9 MWh

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

Symbol | Description |

P_{G}/x_{1} | Total output of the wind/battery energy storage hybrid system |

P_{B}/u | The action of the BESS/control value |

P_{W}/d | Actual wind power/disturbance |

E_{B}/x_{2} | The remaining energy in a BESS |

SOC | State of Charge of a BESS |

ΔT_{B} | Sampling time |

C_{B} | Rate capacity of a BESS |

S_{min} | Lower limits of a BESS |

S_{max} | Upper limit of a BESS |

P_{max_ch} | Maximum of charging power of a BESS |

P_{max_f} | Maximum of discharging power of a BESS |

P_{c} | Maximum available charging power of a BESS |

P_{d} | Maximum available discharging power of a BESS |

a_{t} | White noise time series |

z_{t} | Time series |

ϕ, θ | Constants in ARMA |

F | Backward difference operator |

T_{d} | Dispathcing interval |

P_{D}/y_{ref} | Dispatching power |

α | Balance coefficient of the tracking performance and control action |

m_{p}/p | Prediction horizon |

m_{c} | Control horizon |

y | Predicted system response |

A/B_{1}/B_{2}/C | Model parameter for expression (2) |

Y | Predicted output in matrix form |

U | Control value in matrix form |

D | Disturbance in matrix form |

G/K/L/Ψ/W | The matrices after being processed |

Q/R | Weight matrices |

H/f | Matrices in standardquadratic programming |

A_{ineq} | Liner inequality matrix |

b_{ineq} | Liner inequality vetor |

β | Interation variable |

σ | Diminish interation variable |

s | Slack variable |

z | Lagrange multipliers corresponding to s |

m | The number of inequality constraints |

r_{1} | Dual residual |

r_{2} | Inequality constraint residual |

a | Iterative coefficient |

## References

- The World Sets New Wind Installations Record: 63,7 GW New Capacity In 2015. Available online: http://www.wwindea.org/the-world-sets-new-wind-installations-record-637-gw-new-capacity-in-2015/ (accessed on 9 August 2016).
- Fox, B. Introduction. In Wind Power Integration: Connection and System Operational Aspects; IET Power and Energy Series: Stevenage, UK, 2007; Volume 50, pp. 77–85. [Google Scholar]
- Bouffard, F.; Galiana, F.D. Stochastic security for operation planning with significant wind power generation. IEEE Trans. Power Syst.
**2007**, 23, 306–316. [Google Scholar] [CrossRef] - Liu, J.Z. Basic issues of utilization of large-scale renewable power with high security and efficiency. Proc. CSEE
**2013**, 33, 1–9. [Google Scholar] - Barton, J.P.; Infield, D.G. Energy storage and its use with intermittent renewable energy. IEEE Trans. Energy Convers.
**2004**, 19, 441–448. [Google Scholar] [CrossRef] - Divya, K.C.; Østergaard, J. Battery energy storage technologies for power system—An overview. Electr. Power Syst. Res.
**2008**, 79, 511–520. [Google Scholar] [CrossRef] - Ru, Y.; Kleissl, J.; Martinez, S. Storage size determination for grid-connected photovoltaic systems. IEEE Trans. Sustain. Energy
**2013**, 4, 68–81. [Google Scholar] [CrossRef] - Bindner, H.; Lundsager, P. Integration of wind power in the power system. In Proceedings of the 28th Annual Conference of the Industrial Electronics Society, Sevilla, Spain, 5–8 November 2002.
- Teleke, S.; Baran, M.E.; Bhattacharya, S. Optimal Control of Battery Energy Storage for Wind Farm Dispatching. IEEE Trans. Energy Convers.
**2010**, 25, 787–794. [Google Scholar] [CrossRef] - Jia, H.X.; Zhang, Y.; Wang, Y.F. Application of Energy storage technology in wind power systems. Renew. Energy
**2009**, 27, 10–15. [Google Scholar] - Nguyen, T.T.; Yoo, H.J.; Kim, H.M. A Flywheel Energy Storage System Based on a Doubly Fed Induction Machine and Battery for Microgrid Control. Energies
**2015**, 8, 5074–5089. [Google Scholar] [CrossRef] - Teleke, S.; Baran, M.E.; Huang, A. Control strategies for battery storage for wind farm dispatching. IEEE Trans. Energy Convers.
**2009**, 24, 725–732. [Google Scholar] [CrossRef] - Wang, X.Y.; Vilathgamuwa, D.M.; Choi, S.S. Determination of battery storage capacity in energy buffer for wind farm. IEEE Trans. Energy Convers.
**2008**, 23, 868–878. [Google Scholar] [CrossRef] - Jiang, Q.; Wang, H. Two-time-scale coordination control for a battery energy storage system to mitigate wind power fluctuations. IEEE Trans. Energy Convers.
**2013**, 28, 52–61. [Google Scholar] [CrossRef] - Nguyen, C.L.; Lee, H.H.; Chun, T.W. Cost-optimized battery capacity and short-term power dispatch control for wind farm. IEEE Trans. Ind. Appl.
**2015**, 51, 595–606. [Google Scholar] [CrossRef] - Arulampalam, A.; Barnes, M.; Jenkins, N. Power quality and stability improvement of a wind farm using STATCOM supported with hybrid battery energy storage. IEE Proc.-Gener. Transm. Distrib.
**2006**, 153, 701–710. [Google Scholar] [CrossRef] - Zeng, J.; Zhang, B.; Mao, C. Use of battery energy storage system to improve the power quality and stability of wind farms. In Proceedings of the 26th International Conference on Power system Technology, Chongqing, China, 22–26 October 2006.
- Trung, T.T.; Ahn, S.J.; Choi, J.H. Real-Time Wavelet-Based Coordinated Control of Hybrid Energy Storage Systems for Denoising and Flattening Wind Power Output. Energies
**2014**, 7, 6620–6644. [Google Scholar] [CrossRef] - Yoshimoto, K.; Nanahara, T.; Koshimizu, G. New control method for regulating state-of-charge of a battery in hybrid wind power/battery energy storage system. In Proceedings of the Power System Conference and Exposition, Atlanta, GA, USA, 29 October–1 November 2006.
- Hong, H.S.; Jiang, Q.Y.; Yan, Y.T. An optimization control method of battery smoothed in real time. Autom. Electr. Power Syst.
**2012**, 37, 103–109. [Google Scholar] - Vahidi, A.; Stefanopoulou, A.; Peng, H. Current management in a hybrid fuel cell power system: A model-predictive control approach. IEEE Trans. Control Syst. Technol.
**2006**, 14, 1047–1057. [Google Scholar] [CrossRef] - Kassem, A.M.; Yousef, A.M. Voltage and frequency control of an autonomous hybrid generation system based on linear model predictive control. Sustain. Energy Technol. Assess.
**2013**, 4, 52–61. [Google Scholar] - Torreglosa, J.P.; García, P.; Fernández, L.M.; Jurado, F. Energy dispatching based on predictive controller of an off-grid wind turbine/photovoltaic/hydrogen/battery hybrid system. Renew. Energy
**2015**, 74, 326–336. [Google Scholar] [CrossRef] - Wu, W.; Xu, J.P.; Hwang, J.J. Multi-loop nonlinear predictive control scheme for a simplistic hybrid energy system. Int. J. Hydrog. Energy,
**2009**, 34, 3953–3964. [Google Scholar] [CrossRef] - Kou, P.; Gao, F.; Guan, X.H. Stochastic predictive control of battery energy storage for wind farm dispatching: Using probabilistic wind power forecasts. Renew. Energy
**2015**, 80, 286–300. [Google Scholar] [CrossRef] - Roy, B.; Bipul, K.; Rajesh, K. Unit Commitment Risk Analysis of Wind Integrated Power Systems. IEEE Trans. Power Syst.
**2009**, 24, 930–939. [Google Scholar] - Sodium Sulfur Battery Catalog; NGK Insulators Ltd.: Tokyo, Japan, 2009.

Method | Max Deviation | Min Deviation (MW) | Mean (MW) | Std. (MW) | |
---|---|---|---|---|---|

Value (MW) | Time | ||||

IN-MPC | 1.478 | 10 | 0 | 0.2047 | 0.1096 |

QP-MPC | 1.537 | 13 | 0 | 0.4139 | 0.1706 |

Method | Max Deviation | Min Deviation (MW) | Mean (MW) | Std. (MW) | |
---|---|---|---|---|---|

Value (MW) | Time | ||||

IN-MPC | 0.524 | 21 | 0 | 0.0689 | 0.0142 |

QP-MPC | 0.537 | 19 | 0 | 0.1529 | 0.0385 |

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**MDPI and ACS Style**

Yang, D.; Wen, J.; Chan, K.-w.; Cai, G.
Dispatching of Wind/Battery Energy Storage Hybrid Systems Using Inner Point Method-Based Model Predictive Control. *Energies* **2016**, *9*, 629.
https://doi.org/10.3390/en9080629

**AMA Style**

Yang D, Wen J, Chan K-w, Cai G.
Dispatching of Wind/Battery Energy Storage Hybrid Systems Using Inner Point Method-Based Model Predictive Control. *Energies*. 2016; 9(8):629.
https://doi.org/10.3390/en9080629

**Chicago/Turabian Style**

Yang, Deyou, Jiaxin Wen, Ka-wing Chan, and Guowei Cai.
2016. "Dispatching of Wind/Battery Energy Storage Hybrid Systems Using Inner Point Method-Based Model Predictive Control" *Energies* 9, no. 8: 629.
https://doi.org/10.3390/en9080629