MPC-based Power Management in the Shipboard Power System S. Paran, T. V. Vu, T. El Mezyani, C. S. Edrington Electrical and Computer Engineering, Florida State University Tallahassee, USA
[email protected] The optimal operation of all subsystems onboard can lead to improved fuel consumption (FC) reduction and further increases overall ship efficiency [1]. Therefore, the implementation of innovative technologies, that reduce FC, are becoming a pressing need [1], [2]. In this paper, we mainly focus on the power management for the ship system efficiency. The ship power system (SPS) controls rely on power management control (PMC) strategies to coordinate the power sources and loads to achieve efficient and robust operation and to meet the various dynamic requirements. PMC must be simple to tune in order to be able to trade off and rebalance performance attributes. Several approaches have been proposed for the shipboard PMC. In [6], an automated selfhealing strategy is investigated by solving an optimization problem with constraints, utilizing a linear programming algorithm. A decentralized control approach utilizing an intelligent multi-agent system for the ship board power system is proposed in [15]. One of the promising methods which has been gaining more attention in many fields is model predictive control (MPC). MPC is an effective control methodology that exploits the solution of a receding horizon optimal control problem to enforce constraints [16]-[18]. The problem under consideration has been treated as a real time optimization problem for obtaining optimal energy/power management, where different optimization based methods have been explored (see a detailed survey in [19]). These methods include dynamic programming (DP) [20], stochastic dynamic programming (SDP) [21], equivalent consumption minimization strategy (ECMS) [22], and particle swarm optimization (PSO) [23], [24]. We have chosen PSO method since it is not dependent on a set of initial points, implying that the convergence algorithm is robust. In addition, PSO can generate higher quality solutions within a shorter calculation time and stable convergence characteristics in comparison to other evolutionary methods [17]. In this paper, we develop a power management methodology within the all-electric-ship and formulate it as an optimal dispatch problem. MPC is utilized to achieve the optimal power dispatch. It is assumed that ship load forecasting is available. Thus, the target of the proposed method is the optimization of power generation within a specific time horizon. The system under study, which is adopted from the notional MVDC system, includes two generators and one propulsion load. The rest of the paper is organized as follows: Section II illustrates the concept of MPC and PSO; Section III introduces
Abstract — This paper represents the development of an intelligent control by applying model predictive control to the power management of a DC-based ship system. In a shipboard power system, the control approach should ensure optimal load sharing among generators while maintaining the DC bus voltage stability. Model predictive control is a promising optimal control which has been proven to be efficient and robust for dynamic systems. Model predictive control is applied in order to meet the load centric energy/power demand. It will provide a predictive and adaptive approach to energy/power management routines. The algorithm and method are presented and validated through simulation in MATLAB/Simulink and PLECS. Keywords— Microgrid; power management; model predictive control; particle swarm optimization
I.
INTRODUCTION
Ship system control is challenging as it is composed of distributed subsystems such as electrical power, electric drive propulsion, distributed chiller systems, and various auxiliary systems. In the electric ship system, there are multiple DC sources including the main DC sources (powered by gas turbine generators) and energy storage as shown in Fig. 1. For a given load demand, while maintaining DC bus voltage, an appropriate intelligent distributed control algorithm enables: 1. Accomplishing the mission independent of load types, i.e. pulsed load, propulsion, etc. 2.
Improvement of system efficiency by coordinating different sources.
The primary objective of the intelligent distributed control is to meet the energy and power constraints to complete and expand mission operations, such as: adhering to generator ramp rate, available energy storage, charge/discharge rates, reducing/shedding non-critical loads as needed, and operating multiple systems (sensors and propulsion). Several measures are available in order to improve ship energy efficiency, such as: power and energy management and vessel performance [1]-[3]; route optimization; demand-side management [4]; ship cruising speed reduction; cold ironing [5], [6]; electric energy saving devices; energy storage systems (ESS) [7]-[9]; power system reconfiguration [10] and design [11]; and power factor correction [12]. Moreover, design and operation of the ships should comply with ship energy efficiency indicators imposed by new ship energy directives [13].
This project is funded by Office of Naval Research under award number N00014-10-1-0973 and additionally facilities provided for the Florida State University – Center for Advanced Power Systems.
978-1-4799-1857-7/15/$31.00 ©2015 IEEE
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the system under study with the simulation results in Matlab/Simulink/PLECS; and Section IV concludes the paper.
Subject to : ∑ 0
CONTROL METHODOLOGY
≤
,
(3)
,
(4)
,
MPC Controller
A. Model Predictive Control MPC is broadly utilized in industry with wide applications differing in time scale and model complexity [25]-[27]. MPC operates by generating a future sequence of control inputs and the corresponding output trajectory that optimizes a cost function, which is tied to the system’s interest. In large-scale applications such as power systems, and manufacturing systems, it is advantageous to have distributed or decentralized control schemes, where local control inputs are computed using local measurements and reduced-order models of the local dynamics [28], [29]. The MPC method is based on the receding horizon technique. The prediction model predicts the plant response over a specified time horizon. The block diagram (Fig. 2) illustrates the MPC process. The controller consists of the prediction model and the optimization block. A numerical optimization program utilizes the predictions to determine the control signal that minimizes the performance criterion over a specified horizon. The input information for the MPC control is the power demand. The control outputs of the MPC are the power references. In the MPC, control decisions are made at discrete time instants k (k = 0, 1, 2,...), which usually represents equally spaced time intervals. The general form of the cost function on the generation side for one generator is a quadratic convex cost function (1) [30] which is a part of the total cost function indicated in (2), where represents the prediction horizon and n is the number of generators in the system. Cost coefficients are represented by , , and . To achieve the optimal power (control action) over a predicted horizon, the optimization problem (2) needs to be solved subject to the equality and inequality constraints (3) and (4): )
,
In the preceding formulation, the cost function (operating cost) J is minimized under the power balance constraints. Predictions are based on the power model of the system. The physical limits of the system are represented by the constraints. The optimization generates an open-loop optimal control sequence. In the sequence, the first control value is applied to the system. Then, the controller waits for the next control instant and repeats this process to find the next control action.
Fig 1. Diagram of multiple DC sources system.
II.
(2)
,
PSO Optimization
Reference Power P*
Demand Power Prediction Model
Ship Power System
Output Power Pi
Fig. 2. Model predictive control process.
B. Particle Swarm Optimization In order to solve the optimization problem (2), PSO is utilized. PSO is a recently developed evolutionary computation technique which was introduced in 1995 [23]. PSO has been applied in various fields of power system optimization [24]. PSO is one of the modern heuristic algorithms which have been found to be robust for continuous linear/non-linear optimization problems. The optimization process can be defined by equations (5) and (6) for the particle where is the position and is the velocity of particle. The PSO flowchart is shown in Fig. 3 in detail. .
.
). .
) ).
)
(5)
(6)
(1)
15
j
iteration
C1, C2
cognitive and social constants
w
weighting factor
rand1,2
random number in the range [0 1]
the current velocity of particle i at iteration j In order to test the optimization algorithm, we take one of the general objectives in power system optimization which is the economic dispatch [30] . In the available laboratory environment there exists a 400V DC microgrid testing system which includes two AC generators (Genset1,2) with active neutral point clamp (NPC) rectifiers and an AC load connected to the DC bus, where a subsystem is shown in Fig. 4. The generators’ power rates are presented in TABLE II. The MPC control algorithm is simulated in MATLAB/Simulink with the generation models implemented in PLECS. The coefficients of the cost function ( , , , , , ) are shown in TABLE I [30]. The generator cost function can be sufficiently approximated by second order polynomials.
the personal best position of particle i the global best position of the swarm the current position of particle i at iteration j the modified position of particle i
In the velocity equation (5), the second part indicates the particle’s own experience which makes the particles move toward its personal best position. The third part represents the global experience which makes the particles move toward the global best position. Thus, the optimization process will avoid the local maxima and thus achieve the global maxima. The authors in [31] have concluded the advantages of the PSO technique over other optimization techniques as follows: • It is easy to implement and program with basic mathematical and logic operations, • It can handle objective functions with a stochastic nature, such as in the case of representing one of the optimization variables as a random process, and • It does not require a good initial solution to start its iteration process. However, the drawbacks of the PSO technique still exist in that [31]: • More tuning of parameters is required, and • Programming skills are required to develop and modify the competing algorithm to suit different optimization problems.
(7)
)
(8)
(9)
TABLE I. COST COEFFICIENTS Cost coefficients ($/h)
0.000008
0.007
0.2
0.000005
0.004
0.4
Power sharing and DC voltage stability are the criteria of the microgrid control and management. In the scenario, the power or current share for generators are controlled to achieve the optimal share relative to their power capability. The terminal voltage of the DC bus is maintained in 400V. Figure 5 shows the load profile that varies from 2.4 kW to 5 kW in a periodic manner. Based on this load and the optimization algorithm, two generators are shared in an optimal manner. The outputs of the MPC are power references of the Genset1 and Genset2 as shown in Fig. 5. The power references are fed back to the power controllers and are compared with the actual output power of the generators which are shown in Fig. 6. The output power of the generators, are the optimal powers which are obtained from optimization and minimization of the objective function. Figure 7 and 8 depict the output current and voltage of the generators. The output voltage remains stable at 400 (V) DC. Figure 9 shows the optimized cost for the entire time.
- Initialize Np Particles Pi =[Pi1, Pi2] - Initialize the number of iterations Niter
Cost Function Update personal best
No
Yes Evaluate global best position Update velocity If iteration=Niter
)
,
Start
If i=Np
SIMULATION RESULTS
III.
the modified velocity of particle i
No
Yes End
Fig. 3. PSO flowchart.
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Output Current (A)
6 4 2 Genset1 0
0
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50 Time (s)
60
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Output Current (A)
10
5 Genset2 0
Fig. 4. Test system configuration.
90
100
Fig. 7. Output current of the generators.
TABLE II. SPECIFICATIONS OF THE SYSTEM AND PSO PARAMETERS Parameter Symbol Quantity
400
1s
Power rate of generator1
4 kW
Power rate of generator2
4 kW
Prediction horizon
20
Iteration
50
Swarm size
Ns
25
Weighting factor
W
0.9
Cognitive and social constant
C1, C2
2
output voltage of Genset 1 output voltage of Genset 2
350
DC bus voltage (V)
Sample time
300 250 200 150
Demand Power (W)
2000
0
4000 2000 0
5
10
15
20
25
30
35
40
Time (s) Fig. 8. DC output voltage of the generators. Load 0
10
20
30
40
50
60
70
80
90
2
100
1.5 1000
Cost Function
Reference Power (W)
Reference Power (W)
100 6000
Genset1 0
0
10
20
30
40
50
60
70
80
90
100
3000
1
0.5
2000 1000 0
Genset2 0
10
20
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40
50 Time (s)
60
70
80
90
0 100
0
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40
60
80
100
Time (s)
Fig. 9. Optimal cost profile.
Fig. 5. Generated power references by MPC. Output Power (W)
2000
IV.
1500
500 0
Genset1 0
10
20
30
40
50
60
70
80
90
100
4000 Output Power (W)
CONCLUSION
This paper studies the incorporation of the MPC for optimal power management in the SPS. Prediction and optimization are included in the MPC algorithm. PSO is utilized for the optimization methodology. The simulation results prove that the MPC is capable of managing power between different generators based on the load demand.
1000
3000 2000 1000 0
REFERENCES
Genset2 0
10
20
30
40
50 Time (s)
60
70
80
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[1]
100
Fig. 6. Actual output power of the generators.
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