Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, December 16-18, 2009
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Model Predictive Control for Wind Power Generation Smoothing with Controlled Battery Storage Muhammad Khalid and Andrey V. Savkin Abstract— The aim of this study is to design a controller based on model predictive control (MPC) theory to smooth wind power generation along with the controlled storage of the wind energy in batteries in presence of variety of constraints. In this study, a proposed wind power prediction system is utilized to optimize the performance of the controller. The proposed controller is capable of smoothing wind power by utilizing the inputs from our prediction system which in turn optimizes the maximum ramp rate requirement. At the same time this controller optimizes the state of charge of battery under practical constraints. The prediction model involved is capable of predicting wind power multi-step ahead which are used in the optimization part of the controller. The proposed system is tested for different scenarios and under variety of hard constraints. The effectiveness of our proposed model is shown by simulation results. Index Terms— Model predictive control, battery energy storage, wind power prediction, smoothing.
I. INTRODUCTION Wind energy is becoming the fastest growing energy technology in the world. Wind power provides a clean and cheap opportunity for future power generation and many countries have started harnessing it [1], [2]. As wind power technology has matured, it can now be considered as a valuable supplement to conventional energy sources. However, the drawback is that wind is a highly fluctuating resource. The maximum penetration of wind power in electricity networks is limited by the intermittency of wind energy. Due to this intermittent nature of the wind and built-in uncertainty, efficient and cost effective integration of wind power into electricity grid has become the greatest challenge. Variations in wind energy generation can cause significant problems of frequency control, the voltage support, excessive peak loads on transmission lines, and increasing demand for high ramp rate backup systems. Therefore energy storage is used to smooth the variations in wind power production in order to follow the scheduling plan. Energy storage devices, such as batteries, ultracapacitors, super inductors, flywheels, and fuel cell systems are utilized for this purpose [3]. The storage and prediction system can be combined together to improve the effectiveness of smoothing. Hence This work was supported by the Australian Research Council. M. Khalid is with School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW 2052, Australia
[email protected] A. V. Savkin is with School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW 2052, Australia
[email protected] Corresponding author: Muhammad (
[email protected]), Phone:+61-2-93854918, 93855993
978-1-4244-3872-3/09/$25.00 ©2009 IEEE
Fax:
Khalid +61-2-
an accurate and reliable wind power prediction system is required which can improve the efficiency of power system operation. Prediction can contribute to the economic and secure large-scale wind integration in a power system, and make it possible for efficient management of wind production even in challenging conditions. The proposed method based on model predictive control (MPC) theory is combined with wind power prediction system and battery storage system. Our system for the prediction of power generation is based on measurements from multiple observation points. These measurements are transmitted over communication channels to our designed predictor. In fact, our system is an example of a networked state estimation system. Such systems have attracted a lot of attention in recent years [4], [5], [6], [7], [8]. MPC has also gained popularity in industry since 90s and there is a steadily increasing attention from control practitioners and theoreticians [9], [10]. The practical interest of MPC is mainly due to the fact that today’s processes need to be operated under tight performance specifications and more and more constraints need to be satisfied. These demands can only be met when process constraints are explicitly taken into account in the controller design. MPC is the possible solution for that due to its constraints handling capability. Therefore, we are using MPC theory to smooth wind power and to regulate the wind energy storage in batteries in presence of the practical constraints. As mentioned earlier, to overcome the significant problems due to wind short-term intermittency, the storage system is attached with wind power generation. The solution is valid for both large-scale grid connected and remote area applications. There are certain requirements and limitations for battery storage system i.e. battery life, battery capacity, power smoothing and maximum ramp rate requirement, refer to [11] for CSIRO’s UltraBattery demonstration. An efficient management system is required to increase the effectiveness of energy storage system, therefore, our proposed controller aims to optimize the state of charge of battery, smooth the wind power and to meet the maximum ramp rate requirement by utilizing the inputs from our proposed wind prediction system. As a case study, we tested our controller with real wind farm data of 10 minute resolution from Woolnorth wind farm site in Tasmania, Australia. The wind farm is situated at a coastal site on a cliff which gives the site a very high wind resource with extreme variations [12]. It has been proved that our proposed controller was always stable. The reminder of the paper is organized as follows. Section
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FrB15.3 II describes the problem statement and associated requirements. The proposed model is described in Section III. The controller setup is shown in Section III-A whereas wind power prediction system is presented in Section III-B. The information about data under study is given in Section IV. Section V presents the simulation results. Finally, Section VI concludes the paper with the future works.
with the following cost function, J :=
M−1 X
(r(k) − u(k))2 + α(x2 (k) − L)2 → min
subject to following constraints, 0 ≤ u(k) ≤ c1 ; k = 0, 1, · · ·, M − 1
II. PROBLEM STATEMENT
−c2 ≤ u(k + 1) − u(k) ≤ c2 ; k = 0, 1, · · ·, M − 1
The output power fluctuation of wind turbines is due to wind speed variations. This power fluctuation can cause many problems to the grid, for example, frequency deviations and the power outage. Fluctuations in wind power production also makes it difficult for owners of wind power plants to compete in electricity markets. Therefore, in order to mitigate the power fluctuations, wind power smoothing is required. This efficient smoothing is achieved by combining the storage system with the management and control system. Fig. 1 shows the schematic diagram of the complete system, the primary objective of the problem is to smooth wind power generation along with the controlled energy storage in batteries. Secondly, optimization of the charge/discharge of the battery is required which is affected by the rate of change of wind power.
(3)
k=0
0 ≤ x2 (k) ≤ c3 ; k = 0, 1, · · ·, M − 1
(4) (5) (6)
where r(k) is the real wind power (Pw ), u(k) is the smoothed power (Ps ), x1 (k) is the error between real and smoothed power, x2 (k) is the battery load, L is the desired storage state of the battery, M is the control horizon, c1 , c2 and c3 are the constraints imposed by the system. The constraint (4) keeps the smoothed power between 0 and rated value of the turbine. The constraint (5) is the difference between two consecutive values of the smoothed power, it controls the degree of smoothing which in turn controls the ramp rate, therefore, the constraint (5) is chosen so as to meet the maximum ramp rate requirements. The constraint (6) keeps the storage under battery capacity and prevents the negative load on the battery. The integer k represents the time instant. The parameter α is the weighting factor associated with the storage state control. A. MPC Setup MPC is based on the solution of an on-line optimal control problem where a receding horizon approach is utilized in such a way that for any current state x(k) at time k, an open loop optimal control problem is solved over some future interval taking into account the current and future constraints. The MPC algorithm calculates an open loop sequence of the manipulated variables in such a way that the future behaviour of the plant is optimized. The first value from this optimal sequence is injected into the plant. The procedure is repeated at time (k + 1) using the current state x(k + 1). In our study, we are standardizing our proposed model so as to apply techniques in [13], where the optimal solution of the form,
Fig. 1: Schematic diagram III. THE PROPOSED MODEL In this study, the objective is to regulate the battery storage state at some desired level along with the possible reduction of ramp rate by controlling the smoothing level of wind power. Therefore, variety of constraints are imposed on the system, for example, battery limitation and safety issues, ramp rate requirement, and smoothing level control. In order to satisfy these hard constraints, model predictive control is the most appropriate choice due to its capability of dealing with constraints. Therefore, a linear dynamic model is proposed based on MPC to handle this problem. Consider the following model for wind power smoothing and efficient energy storage system,
U Opt = [¯ uOP T (0), u¯OP T (1), ..., u¯OP T (M − 1)]T
(7)
can be numerically solved as static-optimization problem of the form, U OP T = arg min U T W U + 2U T V U
(8)
LU ≤K
with constraints expressed in the form, LU ≤ K
(9)
x1 (k + 1) = r(k) − u(k) x2 (k + 1) = x1 (k) + x2 (k)
(1)
by using standard Quadratic Programming algorithms. In our case, linear constraints and quadratic cost function associated with the model as in Section III are converted to the standard form and following matrices are formulated,
y(k) = x2 (k)
(2)
¯ T Cψ ¯ +I W = α(Cψ)
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(10)
FrB15.3 and the matrix Vi ∈ ℜn×ni is vi (t)T vi (t − 1)T Vi = .. .
N Wind Velocity
vi (t − N )T
Wind Direction
(16)
with E
vi (t) =
Fig. 2: Wind vector representation. ¯ T (Cψ)] ¯ T − α(Cψ) ¯ TL − R V = α[(Cφ)
vi (t) vi (t − 1) · · ·
vi (t − ni )
T
.
(17)
and the first element of the vector Y is Y (t + 1) =
(11)
The optimization problem at each step is solved using MATLAB. Remark: It is clear that the system (1), (2) with our model predictive controller is stable. Indeed, stability means that for any bounded input r(k) of the system (1), (2), x1 (k), x2 (k), and u(k) are bounded. The constraint (4) obviously implies that u(k) is bounded, and the constraint (6) implies that x2 (k) is bounded. Furthermore, the first equation in our proposed model (1) implies that x1 (k) is bounded for bounded r(k) and u(k).
Y = MX
(12)
Y = [Y(t + 1) · · · Y(t − N + 1) ]T
(13)
X = [c1 · · · cK ]T
(14)
M = [V1 · · · VK ]
(15)
where
cTi vi (t)
(18)
i=1
with ci = [αi,1 · · · αi,ni ]T ∈ ℜni
(19)
where K is the number of the turbines and N is the number of the historical data points taken. ni is the order of the autoregressive (AR) models of the i-th turbine, vi (ξ) is the wind speed recorded at the i-th turbine at time ξ. The vector ci contains the coefficients of the AR model of the i-th turbine. The vector X containing the coefficients of the model for K turbines is estimated using the method of adaptive least squares at each time step. The coefficients are computed using the following relation,
B. Proposed Prediction Model As mentioned earlier, wind power prediction system is attached with battery storage system to improve the overall performance of the controller. In our study, wind power prediction is accomplished in two stages, i.e. the wind speed prediction stage and speed to power conversion stage. In the first stage, our proposed model is based on prediction of wind vectors at the given point using the wind speed and direction measurements from multiple observation points. Based on the predicted direction, the predicted wind speed is converted to predicted wind power using the direction dependent power curves [14]. 1) Wind Speed and Direction Predictions: In the first stage, the proposed model demonstrates that wind speed predictions at a given turbine can be improved by using the wind speed observations from nearby turbines. As there is strong coupling between wind speed and direction, accurate prediction of wind speed as well as the direction can make the operation of wind turbines intelligent and efficient. Therefore, the wind speed and the direction are predicted simultaneously using the proposed model. To achieve the goal, wind data is converted to wind vectors as shown in Fig. 2. Generally this model can be represented as
K X
X = (M T M )−1 M T Y
(20)
The idea is to convert wind data into wind vectors i.e. vx and vy . vx (t) = v(t) cos θ(t) (21) vy (t) = v(t) sin θ(t) where θ(t) is the direction of the wind in degrees measured at time t. The proposed model in (12) is utilized to predict the individual wind vectors vˆx and vˆy . Finally, the wind speed and the direction predictions at each time step are obtained using the following relation. q (22) vˆ(t + 1) = vˆx (t + 1)2 + vˆy (t + 1)2 and
ˆ + 1) = tan−1 ( vˆy (t + 1) ) θ(t vˆx (t + 1)
(23)
ˆ + 1) are the speed and direction where vˆ(t + 1) and θ(t prediction for t+1 made at t respectively. In this way both wind speed and direction are predicted simultaneously. 2) Wind Power Predictions: Wind power prediction is achieved by feeding the predicted wind speed to the input of power curve. The power curve of a wind turbine is a graph that indicates how large the electrical power output will be for the turbine at different wind speeds. The wind power of a wind turbine depends on the wind speed; which depends on regional weather patterns, seasonal variations, and terrain types. It is well known that the theoretical relation between the energy (per unit time) of wind that flows at speed v (m/s) through an intercepting area A (m2 ) is 1 (24) p = ρAv 3 2
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1 0.9 0.8 Normalized power
where ρ is the air density (kg/m3 ), which depends on the air temperature and pressure. The deterministic relation of wind speed and power is different from the empirical relation obtained in the real operation at a wind farm [15]. That’s why the power curve is derived from measured wind speed and power. In our case, the power curve models are sub sector direction dependent empirical power curves based on the historical wind speed and power measurements for a given turbine. As a case study, we consider 4 power curve models for 4 direction sectors based on the direction distribution for the year 2006. Based on predicted wind direction as in Section III-B.1, the appropriate power curve is selected to determine predicted power output. Our controller utilizes this predicted power to smooth the actual wind power. This procedure is repeated at each time step.
0.7 0.6 0.5 0.4 0.3 0.2
Actual power Predicted power 0
20
40 60 10 min periods
80
100
Fig. 3: Actual and predicted wind power.
IV. DATA BASES The wind farm observation data used in this paper is measured at hub height at each of the 37 turbines in the Roaring 40s Woolnorth wind farm in Tasmania, Australia. The data has a 10 min resolution for wind speed, wind direction and wind power and covers the calendar year 2006 and January 2007.
1
Smoothed Original
0.9 0.8
V. RESULTS AND DISCUSSION
VI. CONCLUSIONS AND FUTURE WORK A generic MPC based controller has been developed to smooth wind power generation with controlled energy storage in batteries by combining it with the wind prediction system. This controller is capable of achieving the required maximum ramp rate requirement by properly adjusting the smoothing of wind power along with the optimization of state of charge of battery. The controller performs well under tight practical constraints ensuring the stability of the system.
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Normalized power
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
20
40 60 10 min periods
80
100
Fig. 4: Normalized actual and smoothed power.
1
New rate of change) Old rate of change
0.8 0.6 Normalized power per 10 min
As regards the prediction model, Fig. 3 shows the prediction performance of our proposed model, where predicted power is based on improved wind speed predictions utilizing the optimal number of the turbines involved in the prediction with the best auto regression order. On the controller side, all constraints are chosen based on physical limitations of the system and finally normalized results are presented. Few experiments have been performed for different prediction and control horizon and by varying the constraints to check the validity of the model. The controller optimization is achieved by utilizing the results from our power prediction model for 1-, 2-, 3- and 4-step ahead predictions. Optimized results are presented for 2-step ahead predictions based on the accuracy of the prediction model for our particular case. In practice high sampling data is used in the real operation of the wind farm power system. In our study, due to commercial confidentiality issues, we presented the results with real data of 10 minute resolution from the wind farm. The data is coming from real operation of the wind farm, therefore, all presented results are normalized to avoid any confidentiality conflicts.
0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1
0
20
40 60 10 min periods
Fig. 5: Ramp rate.
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[12] N. Cutler, M. Kay, H. Outhred, and I. MacGill, “High-risk scenarios for wind power forecasting in Australia,” in Proceedings of the European Wind Energy Conference & Exhibition, Italy, May 2007. [13] G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control System Design. New Jersey: Prentice Hall, 2001. [14] M. Khalid and A. V. Savkin, “Development of short-term prediction system for wind power generation based on multiple observation points,” in Proceedings of the International Conference on Sustainability in Energy and Buildings. UK: Springer Verlag, Apr 2009. [15] I. Sanchez, “Short-term prediction of wind energy production,” International Journal of Forecasting, vol. 22, pp. 43–56, 2006. [16] A. V. Savkin and I. R. Petersen, “Robust H ∞ control of uncertain linear systems with structured uncertainty,” Journal of Mathematical Systems, Estimation and Control, vol. 6, no. 3, pp. 349–342, 1996. [17] A. V. Savkin, I. R. Petersen, and S. O. R. Moheimani, “Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data,” Computers and Electrical Engineering, vol. 25, no. 1, pp. 29–43, 1999. [18] A. V. Savkin and I. R. Petersen, “Model validation for uncertain systems with an integral quadratic constraint,” Automatica, vol. 32, no. 4, pp. 603–606, 1996.
Desired storage state Controlled storage state
Normalized storage state
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Fig. 6: Storage state.
The detailed study of the robustness, uncertainty, and noise effects will be the focus of future study. We will apply methods and ideas of the modern robust state estimation theory; see e.g. [16], [17], [18]. VII. ACKNOWLEDGMENT We would like to thank Hugh Outhred, Iain MacGill, Merlinde Kay, and Nicholas Cutler at the Centre of Energy and Environmental Markets (CEEM), UNSW for their assistance in getting the required data. We are also grateful to Roaring 40s for their co operation in terms of providing the required time series data to carry out this research. R EFERENCES [1] S. Breton and G. Moe, “Status, plans and technologies for offshore wind turbines in Europe and North America,” Renewable Energy, vol. 34, no. 3, pp. 646–654, 2009. [2] R. Benoit and W. Yu, “Developing and testing of wind power forecasting techniques for Canada,” in Proceedings of the First Joint Action Symposium on Wind Forecasting Techniques. Norrk¨oping: International Energy Agency (IEA), 2002. [3] J. Baker and A. Collinson, “Electrical energy storage at the turn of the millennium,” Power Engineering Journal, vol. 13, no. 3, pp. 107–112, Jun 1999. [4] A. S. Matveev and A. V. Savkin, “The problem of state estimation via asynchronous communication channels with irregular transmission times,” IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 670–676, 2003. [5] A. S. Matveev and A. V. Savkin, “The problem of LQG optimal control via a limited capacity communication channel,” Systems and Control Letters, vol. 53, no. 1, pp. 51–64, 2004. [6] A. S. Matveev and A. V. Savkin, “An analogue of Shannon information theory for networked control systems. Stabilization via a noisy discrete channel,” in Proceedings of the 43th IEEE Conference on Decision and Control, vol. 4, Paradise Island, The Bahamas, 2004, pp. 4491–4496. [7] A. V. Savkin, “Analysis and synthesis of networked control systems: topological entropy, observability, robustness, and optimal control,” Automatica, vol. 42, no. 1, pp. 51–62, January 2006. [8] A. S. Matveev and A. V. Savkin, Estimation and Control over Communication Networks. Boston: Birkhauser, 2009. [9] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, 2000. [10] S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Engineering Practice, vol. 11, no. 7, pp. 733–764, 2003. [11] P. Coppen. (2008, Nov) Using intelligent storage to smooth wind energy generation. [Online]. Available: http://www.feast.org/roundtable2008/presentations/
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