Adaptive model predictive control with propulsion load estimationand prediction for all-electric ship energy management
Jun Hou a, *, Jing Sun a, b, Heath Hofmann a
a Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USAb Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
a r t i c l e i n f o
Article history:Received 23 June 2017Received in revised form25 January 2018Accepted 3 March 2018Available online 6 March 2018
Keywords:Propulsion-load torque estimation andpredictionAdaptive model predictive controlAll-electric shipHybrid energy storageEnergy management strategy
Electric ships experience large propulsion-load fluctuations on their drive shaft due to encounteredwaves and the rotational motion of the propeller, affecting the reliability of the shipboard power networkand causing wear and tear. To address the load fluctuations, model predictive control has been exploredas an effective solution. However, the load torque of the propulsion system, knowledge of which isessential for model predictive control, is difficult to measure and includes multi-frequency fluctuations.To deal with this issue, an adaptive model predictive control is developed so that the load torque esti-mation and prediction can be incorporated into model predictive control. In order to evaluate theeffectiveness of the proposed adaptive model predictive control, an input observer with linear predictionis developed as an alternative approach to obtain the load estimation and prediction. Comparativestudies are performed to illustrate the importance of the load torque estimation and prediction, anddemonstrate the effectiveness of the proposed adaptive model predictive control in terms of improvedefficiency, enhanced reliability and reduced wear and tear.
Integrated power system (IPS), which is the key enabling tech-nology of All-Electric Ship (AES) [1], provides the electrical powerfor both ship service and electric propulsion loads by integratingpower generation, distribution, storage, and conversion [2].Although IPS offers considerable benefits to modern ships, tech-nical challenges exist in order to fully realize those benefits. Forexample, the propulsion load fluctuations experienced by thepropeller, which also exist in traditional mechanical drive systems,have very different implication because of the inter-connectivitybrought in by the IPS, as these fluctuations can affect the elec-trical shipboard network through the electric motors and theirdrives. This problem calls for new solutions that could effectivelyaddress the load fluctuations to assure reliability and integrity ofthe overall electrical network.
Three different propulsion load fluctuations have been studiedin the literature:
� fluctuations resulting from the impact of the first-order wave atthe encounter-wave frequency,
� fluctuations arising from the in-and-out-of-water effect,� fluctuations caused by propeller rotation at the propeller-bladefrequency (i.e., number of blades times shaft speed in rps).
These fluctuations, especially when the propeller is in-and-out-of-water, will cause unpredictable power consumption, reduceelectrical efficiency, and affect power quality on the shipboardpower network. The fluctuations caused by the in-and-out-of-water effect can be as high as 100% of the rated load. The loadfluctuations caused by the encountered wave and the in-and-out-of-water effect are defined as low-frequency fluctuations in thispaper. The fluctuations caused by the propeller rotation at thepropeller-blade frequency are defined as high-frequency fluctua-tions. The impact of propeller-load fluctuations has been reportedin the literature. In Ref. [3], the power combined with torque con-trol was developed to deal with the low-frequency load fluctua-tions. The importance of torque balance is discussed in Ref. [4]. Thetorque unbalance is responsible for the propeller wear and tear. Thein-an-out-of-water effect has been studied in Ref. [5]. These high-frequency fluctuations are reported as one of the main causes forsevere mechanical wear and tear of the propulsion unit [5]. In
Ae=Ao Expanded blade-area ratioCUC Capacitance of ultra-capacitorCBus Capacitance of DC busD Propeller diameterGPG DC gain of generator set modelH Total inertiaIB; IUC Current of battery and ultra-capacitorJA;KT ;KQ Advance, thrust, and torque coefficientsNB;NUC ;NGen Number of battery modules, ultra-capacitor
modules and generator setsN Predictive horizonNT Performance investigation windown;Pitch=D Propeller rotational speed and pitch ratioPB;PUC Output power of battery and ultra-capacitor
PrefGen;PrefM Reference power of generator and motor
QB Capacity of batteryRn Propeller Reynolds numberRB;RUC Internal resistance of battery and ultra-capacitorSOCB;SOCUC SOC of battery and ultra-capacitorTload Propeller-load torqueTs Sampling timeVmax Maximum voltage of ultra-capacitor
VOC Battery open circuit voltageVd Desired DC bus voltagew Wake fieldZ Number of propeller bladesb Loss factorbM Viscous damping coefficient of the motor and
propellerbLP Linear prediction coefficientr Water densityhM Efficiency of the motor and its inverterl Weighting factorxL Measurement noisetPG Time constant of generator set modelud desired motor rotational speedAES All-electric shipAMPC Adaptive model predictive controlEMS Energy management strategyHESS Hybrid energy storage systemIO Input observerIPS Integrated power systemLP Linear predictionPM Prime moverUC Ultra-capacitor
J. Hou et al. / Energy 150 (2018) 877e889878
Ref. [6], the high-frequency load fluctuations caused by wake fieldare studied. The experimental results of both low and high fre-quency fluctuations in Ref. [7] showed the significant negative ef-fect of load fluctuations.
In order to address the impact of propulsion-load fluctuations,hybrid energy storage system (HESS) can be a potential solution.HESS has been exploited for considerable applications, such ashybrid electric vehicle [8], micro-grid [9] and all-electric ship [10],in order to provide complementary characteristics and achievedesired performance. In this paper, HESS serves as a buffer toabsorb power when the propulsion motor is under-loaded andsupply power when it is overloaded, thereby isolating the electricshipboard network from propulsion load fluctuations. The effec-tiveness of the proposal HESS solution highly depends on the sys-tem energy management strategy (EMS). In order to achieve robustand efficient operation and to meet various dynamic operationalrequirements, optimization-based EMS has been suggested in theNaval Power Systems Technology Development Roadmap [11].More specifically, an effective EMS should provide improved fuelefficiency, enhanced response speed, superior reliability, andreducedmechanical wear and tear. Given the unique characteristicsof IPS in AESs, as highlighted in Ref. [12] that include: nonlinear andmulti-input-multi-output plant characteristics, multi-scale timedynamics, and multiple operating constraints, model predictivecontrol (MPC) emerges as the natural choice for optimization-basedEMS [13e15].
In Ref. [13], battery modules are controlled by MPC to assist theturbine and fuel cell in tracking the power command. In Ref. [14],the MPC is developed to reduce the pulse power effect. In order toreduce wear and tear on the generator sets, batteries are used inRef. [15] to “smooth” the generator power by using MPC. Theliterature mentioned above do not require the propulsion-loadtorque information, since the control objectives and applicationsare different. In this manuscript, the propulsion-load torque isimportant to reduce the mechanical wear and tear and enhance thesystem reliability. In most marine applications, however, the
propulsion-load torque is difficult to measure and includes multi-frequency fluctuations. Given the importance of the propulsion-load torque for the proposed EMS using MPC, this paper focuseson its estimation and prediction.
Load-torque estimation has been explored in a number ofstudies [16e18]. In Refs. [16,17], the load torque is assumed to beconstant or slowly time-varying. The literature [16] focuses on thelow-frequency load torque estimation, and the constant distur-bance torque estimation is addressed in Ref. [17] for permanentmagnet synchronous motor. For our problem, however, the loadtorque investigated here consists of multi-frequency fluctuationcomponents. The input observer (IO) approach presented inRef. [18], on the other hand, is not based on the assumption that theload torque is constant or slowly time-varying. Note that the inputobserver is also referred to as a disturbance observer in the litera-ture, since an unknown input can be considered as a disturbance[19]. Despite the contributions of these works, the aforementionedapproaches do not take advantage of the physical characteristics ofthe propulsion-load dynamics, especially the fast dynamics.Furthermore, these approaches cannot be directly used to predictthe future load torque, which is required for implementing MPC.Additional load predictive capabilities are therefore required. Inthis paper, linear prediction (LP) is used to predict future load in-formation. On the other hand, a model-based approach can beeasily integrated with the MPC to formulate an Adaptive MPC(AMPC) to estimate and predict propulsion-load torque. However,the complexity of the propulsion-load model is the main challengefor real-time applications.
In this paper, a system-level energy management strategy isdeveloped using model predictive control. The motivation of thispaper is to mitigate the negative effect of both low and high fre-quency load fluctuations on the shipboard network. This proposedstrategy encompasses the controls of the primary power sourcesand propulsion motor, in addition to the HESS, and allows judiciouscoordination to achieve desired performance in terms of increasedsystem efficiency, enhanced reliability, reduced mechanical wear
J. Hou et al. / Energy 150 (2018) 877e889 879
and tear, and improved load-following capability. This paper fo-cuses on the propulsion-torque estimation and prediction forimplementing the proposed MPC-based EMS. The main contribu-tions of this research are summarized in the following:
� An integrated EMS is developed to fully coordinate generatorsets, HESS, and motor drive. The integrated approach takesadvantage of the predictive nature of MPC and allows the de-signers to judiciously coordinate the different entities of theshipboard network under constraints, thereby providing bene-fits to system performance.
� The proposed MPC formulation is able to achieve comprehen-sive performance in terms of improved efficiency, enhancedreliability, and reduced mechanical wear and tear. Differentcontrol strategies, such as power, speed and torque control, areintegrated into one MPC-based EMS.
� Two different approaches, namely adaptive model predictivecontrol and input observer with linear prediction, are developedto estimate and predict propulsion-load torque. The effective-ness and limitations of these two approaches are evaluated.
� A simplified propulsion-load torque model is developed for theproposed adaptiveMPC to reduce the computational complexityand facilitate the real-time capability.
The paper is organized as follows. In Section 2, the shipboardelectrical propulsion system is described and the integrated EMSusing MPC is presented. The proposed AMPC approach and thealternative approach (i.e., IO with LP) are developed in Section 3.The comparison study is performed in Section 4, and results arepresented to illustrate the effectiveness of the proposed AMPC.Section 5 concludes this paper with a discussion of the results.
2. System description and adaptive model predictive controlformulation
The schematic of the electric propulsion system under investi-gation is shown in Fig. 1. In this propulsion system, electric power isgenerated by prime mover and generator (PM/G) sets, and thepropulsion thrust is generated by electric motor(s). The motor ismechanically connected with the propeller, so that the propulsiontorque generated by the propeller becomes the load torque of themotor, as shown in Fig. 2 [10]. Due to the encountered waves andthe rotational motion of the propeller, this propulsion-load torquecontains multi-frequency fluctuations which affect the systemreliability and efficiency. The HESS is used to isolate the powerfluctuations from the DC bus in order tomitigate the effects of thesefluctuations. The inverter and DC/DC converters are used to control
Fig. 1. Schematic of the electric p
the motor and HESS, respectively. Medium voltage DC (MVDC)power generation is used as the architecture of the shipboardnetwork in this paper. MVDC is able to decouple prime moverspeed from the frequency of the bus, leading to optimization of thegenerator for each type of prime mover without having to incor-porate gears and without being restricted to rotational speed or agiven number of poles. The benefits of MVDC include: reducedpower conversion, increased power density, the elimination oftransformers, and advanced reconfigurability [20].
In order to achieve complementary characteristics, two differentHESS configurations, namely batteries with ultra-capacitors (UC)and batteries with flywheels, are taken into consideration. Batterieshave high energy density, while UCs have high power density.Compared to batteries and UC, flywheels offer an intermediatechoice with respect to energy and power density. Both of UC andflywheel have long cycle life, which can be used to extend thebattery cycle life by a well-developed control strategy. As discussedin Ref. [21], the battery/flywheel configuration outperformsbattery/ultra-capacitor at high sea states. At nominal or low seastates, such as sea states 4 and 2, the battery/ultra-capacitor hasbetter performance than battery/flywheel. Note that, the proposedalgorithm does not depend on the HESS configuration, so that bothof those two configurations can be used in this paper. Because ofthe full coordination of the proposed AMPC, motor and generatorscan help HESS mitigate the negative effect of load fluctuations,especially at high sea states, where battery/flywheel configurationhas better performance. Therefore, the battery/ultra-capacitorconfiguration is used in this paper.
2.1. Optimization-oriented dynamic model and operationalconstraints
The electric power generation system includes diesel-generatorsets and their associated rectifiers. The diesel engine is used as theprime mover (PM), and is connected to the synchronous field-winding generator to provide AC power. The rectifier converts ACpower into DC power. A speed regulator is used to control the dieselengine so as to keep the generator at the reference speed. In orderto develop a control-oriented model, a linearized model of theelectric power generation system is developed in this section. Thefield-winding voltage of the generator is defined as the controlvariable uG, and the DC output current of the diode rectifier isdefined as the state variable xG. The DC bus voltage is assumed asthe reference value when linearizing the power generation system.The dynamic models described in this paper are discretized usingthe Euler method with sampling time Ts. Therefore, the electricpower generation system can be described as:
ropulsion system with HESS.
Fig. 2. Propeller and ship dynamics model structure [10].
Table 1State variables and control inputs in the optimization-oriented design model.
Variable Symbol Description
State variables xG Generator DC output current ðAÞxM Motor rotational speed ðrad=sÞxB Battery SOC ð%ÞxUC Ultra-capacitor SOC ð%ÞxDC DC bus voltage ðVÞ
Control inputs uG Generator field-winding voltage ðVÞuM Motor torque ðNmÞuB Battery output current ðAÞuUC Ultra-capacitor output current ðAÞ
J. Hou et al. / Energy 150 (2018) 877e889880
xGðkþ 1Þ ¼ xGðkÞ þTstPG
ð � xGðkÞ þ GPGuGðkÞÞ; (1)
where tPG and GPG are the time constant and DC gain of the line-arized generator set model, respectively.
For the propulsion motor, the control variable uM is the torquecommand, and the state variable xM is the shaft rotational speed.The motor shaft dynamic system can be described in the following:
where bM is the viscous damping coefficient of the motor andpropeller, H is the total inertia, and TLoad is the load torque.
The state of charge (SOC) of the battery pack and UC modulesused in the HESS configurations are defined as the state variables xBand xUC , respectively, and the battery and UC currents as the controlinputs uB and uUC , respectively. The HESS dynamic model istherefore described as follows:
xBðkþ 1Þ ¼ xBðkÞ �Ts
3600QBuBðkÞ;
xUCðkþ 1Þ ¼ xUCðkÞ �Ts
VmaxCUCuUCðkÞ;
(3)
where QB is the capacity of the battery, and CUC and Vmax are thecapacitance and the maximum voltage of the UC, respectively. Notethat the HESS discharge is defined as the positive direction in thispaper.
The total power output of battery and UC are obtained asfollows:
PB ¼ NB ��VOCuB � RBu
2B
�;
PUC ¼ NUC ��VmaxxUCuUC � RUCu
2UC
�;
(4)
where NB and NUC are the number of modules, and RB and RUC arethe internal resistance of the battery and UC modules, respectively.
The DC bus voltage dynamics are based on current flow into thebus capacitor, and the voltage of the DC bus is defined as the statevariable xDC . The DC bus dynamic model is expressed as follows:
xDCðkþ1Þ¼ xDCðkÞþTs
CBusxDCðkÞðPBðuBðkÞÞþPUCðxUCðkÞ;uUCðkÞÞÞ
þ TsCBusxDCðkÞ
ðNGenxGðkÞxDCðkÞ�xMðkÞuMðkÞ=hMÞ;
(5)
where CBus is the DC bus capacitance, NGen is the number ofgenerator sets, and hM is the efficiency of the motor and its inverter.
The state variables and control inputs of the optimization-
oriented model are summarized in Table 1. The system hasseveral constraints, including state constraints and control inputconstraints, that represent hardware limitations and operationalrequirements. These constraints are mathematically expressed inthe following:
0 � xG � 1000A;
0 � xM � 160RPM;
20% � xB � 90%;
75% � xUC � 99%;
�10V � uG � 10V ;
�1:25� 106Nm � uM � 1:25� 106Nm
�200A � uB � 200A;
�240A � uUC � 240A:
(6)
2.2. Control objectives
For the electric propulsion system, one of the main objectives isto generate the required thrust to move the ship forward at thedesired speed. This is accomplished by controlling the motor speed,torque, or power to follow the references. Motor speed control isthe most commonly used solution [5]. Besides thrust production,system reliability is also an important objective [14]. Due to theload fluctuations, especially when the propeller is in-and-out ofwater, the shipboard power network can experience large voltagevariations which could significantly affect system operation.Therefore, voltage regulation is necessary. Other objectives,including system efficiency improvement and wear-and-tearreduction, are also taken into consideration. In order to improvesystem efficiency, the generator set and motor should operate attheir most efficient operating points [14]. Furthermore, the HESSlosses should be minimized. For the motor and propeller, the me-chanical wear and tear is mainly caused by transients and oscilla-tions in the shaft torque [5]. For the generator set, the mitigation ofpower oscillations can contribute to a reduction ofmechanical wearand tear [15]. Since the DC bus voltage is close to its reference, the
Table 2Control objectives, descriptions and their mathematical expression for the electric propulsion system with HESS.
Control objectives Mathematical expression Descriptions
System reliability minðVd � xDC ðkÞÞ2 Minimize bus voltage variation to maintain the system reliability.
Thrust production minðud � xMðkÞÞ2 Follow desired motor rotational speed to achieve the desired thrust.
System efficiency minðPrefGen � xGðkÞxDC ðkÞÞ2 Follow the reference to operate the generator at the high-efficiency point.
minðPrefM � xMðkÞuMðkÞÞ2 Follow the reference to operate the motor at the high-efficiency point.
minðRBu2BðkÞþ RUCu2UCðkÞÞ Minimize HESS losses.
Wear-and-tear mitigation minðxGðkþ 1Þ � xGðkÞÞ2 Minimize generator oscillations to reduce wear and tear on the generator set.
minðuMðkÞ � uMðk� 1ÞÞ2 Minimize motor torque oscillations to reduce wear and tear on the motor and propeller.
minðxMðkþ 1Þ � xMðkÞÞ2 Minimize speed oscillations to balance the motor torque and the load torque.
J. Hou et al. / Energy 150 (2018) 877e889 881
oscillation of the generator DC output current (i.e., xG) is minimizedin the optimization. The control objectives and their mathematicalexpression are summarized in Table 2, where Vd is the desired busvoltage, ud is the desired reference speed of the propulsion motor,
and PrefGen and PrefM are the reference powers of the generator sets andmotor, respectively.
2.3. Adaptive model predictive control problem formulation
Given the nature of the electric propulsion system, as well as theoperational constraints involved, MPC becomes a natural formu-lation. Since the propulsion-load torque TLoad in (2) is difficult tomeasure for marine applications, estimation of TLoad is required.Furthermore, in order to implement MPC, prediction of TLoad in theMPC predictionwindows is also required. To address the estimationand prediction of the propulsion-load torque, an adaptive MPC isdeveloped which minimizes a cost function subject to constraintswithin the prediction horizon. This can be mathematicallyexpressed as follows:
Pðx0Þ : minx:½t;tþN�/R5u:½t;tþN�1�/R4
J�x;u; bTLoad
�(7)
where:
J�x;u; bTLoad
�¼ Fðxðt þ NÞÞ þ
XtþN�1
k¼t
L�xðkÞ;uðkÞ; bTLoadðkjtÞ
�;
(8)
subject to:
xðkþ 1Þ ¼ f�xðkÞ;uðkÞ; bTLoadðkjtÞ
�; xðtÞ ¼ x0; (9)
CðxðkÞ;uðkÞÞ � 0; (10)
where FðxðNÞÞ and LðxðkÞ;uðkÞ; bTLoadðkjtÞÞ are the terminal andinstantaneous cost functions, N is the time window over which thecost will be evaluated, CðxðkÞ;uðkÞÞ represents the inequality con-straints, t represents the current time, and xðkÞ, uðkÞ are theinstantaneous values of the states and controls at time k, respec-
tively. bTLoadðtjtÞ is the estimation of the propulsion-load torque, andbT LoadðkjtÞ for k ¼ t þ 1;…; t þ N � 1 are the predictions of the loadtorque at time t.
According to the aforementioned dynamic models and controlobjectives, the AMPC formulation takes the following form:
for all k2½t; tþ N� 1�, subject to (1)e(3) and (5)e(6), where lVDC ,lu, lPGen , lPM , lHESS, lDIPG , lDTM and lDu are the weighting factors forthe penalties of DC bus voltage variation, tracking performance ofmotor speed, generator andmotor power, HESS losses, variations ofgenerator output DC current, motor torque and motor speed,respectively. The estimation and prediction of propulsion loadtorque is addressed in the following section.
Remark 2.1. (Motor control): Motor speed control has the bestperformance on the thrust production, but can cause more me-chanical wear and tear and introduce power fluctuations on theshipboard network. Motor power control can significantly mitigatepower fluctuations on the shipboard network, but can cause sig-nificant mechanical wear and tear, especially when the propeller isin-and-out of water. Motor torque control can reduce the me-chanical wear and tear if the propulsion-load torque is known, buthas worse performance on thrust production and generate morepower fluctuations. As shown in Equation (12), the proposed AMPCintegrates all of these three control strategies: motor speed control
term “luðud � xMðkÞÞ2”, motor power control term
“lPM ðPrefM � xMðkÞuMðkÞÞ2” and motor torque control term
“lDTM ðuMðkÞ � uMðk� 1ÞÞ2”. Therefore, the comprehensive perfor-mance can be achieved.
Remark 2.2. (Generator control): Similar to motor control, the
generator power control lPGen ðPrefGen � xGðkÞxDCðkÞÞ2and bus voltage
regulation lVDCðVd � xDCðkÞÞ2 are integrated into AMPC. The bene-fits of power control and voltage regulation can be achieved.
Remark 2.3. (Full-coordinated control): The proposed AMPC alsoprovide a full-coordinated control for the shipboard system. Themotor, generators and HESS are all connected into the DC bus. TheDC bus voltage can be used to identify the stability of DC ship powersystems [22]. In order to maintain the bus voltage stable (mini-
mizing lVDCðVd � xDCðkÞÞ2), the motor and generators can assistHESS to mitigate load fluctuations, especially at high sea states
J. Hou et al. / Energy 150 (2018) 877e889882
where the HESS cannot fully address the load fluctuations.Furthermore, undesirable interactions among motor, generatorsand HESS can be avoided.
Fig. 3. Schematic diagram of the first approach (IO-LP).
3. Propulsion-load torque estimation and prediction
In order to take advantage of the physical characteristics of thepropulsion-load dynamics, a model-based approach is developedto estimate the propulsion-load torque for all-electric ships. Due tothe complexity of the propulsion-load torque model, a simplifiedmodel is developed first, which is able to capture the key dynamics.Because of uncertainties in the model parameters, adaptiveparameter identification is used, leading to improved robustness ofthe control system. This model-based approach can be easily in-tegrated with the MPC to formulate an AMPC. In order to evaluatethe proposed AMPC approach, the IO presented in Ref. [18] is usedas an alternative approach to estimate the propeller-load torque. Inthis alternative approach, linear prediction [23] is combined withIO to predict the future propulsion-load torque. A comparativestudy is performed to evaluate the effectiveness of the proposedAMPC, in terms of minimizing bus voltage variation, regulatingrotational speed, and reducing high-frequency motor torque vari-ation. The implications of accurate estimation and prediction arealso illustrated and analyzed in this study.
3.1. First approach: input observer with linear prediction
In order to estimate the propulsion load torque, the inputobserver (IO) presented in Ref. [18] is used. The general propeller-motor dynamic is described by the following equation:
_u ¼ TMðtÞ � bMu� TLoadðtÞH
: (13)
Define
uLðtÞ ¼ TLoadðtÞ=H;
zLðtÞ ¼TMðtÞ � bMuðtÞ
H;
yLðtÞ ¼ uðtÞ þ xLðtÞ;
(14)
where xLðtÞ is the measurement noise.The unknown input uLðtÞ can be then estimated by the following
where aL >0 is the observer gain and the states of the observer arefL and εL.
Since the input observer cannot predict future load torque,linear prediction is used. Linear prediction incorporates theknowledge of the signal frequency spectrum and autocorrelation todetermine the linear prediction coefficients (LPCs) [24]. Only pastdata, which can be obtained from IO estimation results, is requiredfor LP. To predict the load torque at time tþ1, linear prediction isformulated as follows:
bT Loadðt þ 1jtÞ ¼Xi¼1
NLP
bLPibTLoadðt � iþ 1jtÞ; (16)
where NLP is the prediction order, and bLPi (i ¼ 1;…;NLP) are the
linear prediction coefficients. The coefficients can be calculatedusing theMatlab function “lpc”. The inputs of “lpc” are the past dataand the desired prediction order. The next step is to combine IOwith LP. The algorithm can be easily implemented, as shown inFig. 3. However, there are several limitations of this approach,summarized in the following:
Remark 3.1. The gain aL in (15) is the only parameter used to tuneIO. Since the high-frequency fluctuation is at the propeller-bladefrequency, i.e., around 8Hz, the minimum cut-off frequency isdesigned at 8Hz, leading to a minimum observer gain aL ¼ 50. Asshown in Fig. 4, the phase shift at the cut-off frequency is about 45�,which could significantly affect the estimation performance. Inorder to reduce the estimation error, the high-gain input observer isa reasonable choice if the noise can be ignored. However, noise is anissue under many conditions; the estimation performance of ahigh-gain observer, e.g. aL ¼ 400, might be even worse than oneusing the minimum gain. The optimum observer gain is difficult todetermine when the noise is random and unknown.
Remark 3.2. The predictive performance of LP highly depends onpast data. The performance of IO directly affects LP. Furthermore,the predictive error is accumulated as the predictive horizon ex-
tends. For example, predicting bTLoadðt þ 2jtÞ requires the predictionvalue bT Loadðtþ 1jtÞ, which means the predictive error ofbTLoadðt þ 1jtÞ affects the prediction bTLoadðtþ 2jtÞ.
Since only the general propeller-motormodel (13) is used in thisapproach, the dynamics of the propeller load torque is not taken
J. Hou et al. / Energy 150 (2018) 877e889 883
into consideration. In order to address the limitations discussed inRemarks 3.1 and 3.2, a model-based approach is required, leadingto the adaptive model predictive control discussed in the nextsection. The major challenge of this approach is the complexity ofthe load torque model (17). The focus of the next section is todevelop a simplified model of (17), which is able to capture the keydynamics of the propeller-load torque.
3.2. Second approach: adaptive model predictive control
Instead of the general propeller-motor model (13), thepropeller-load torque model presented in (17) can provide addi-tional useful information to estimate the load torque. Thispropulsion-load torque model is expressed in the following:
ci (i¼ 0,1,2,3), M0 and M1 are unknown parameters; b is the lossfactor; r is the density of water; D is the diameter of the propeller;fKQ
is the torque coefficient function; and q is the angular position ofone blade (this angular position is assumed to be measurable). InfKQ
, JA is the advance coefficient; Pitch=D is the pitch ratio; Ae=Ao isthe expanded blade-area ratio, with Ae being the expanded bladearea and Ao being the swept area; Z is the number of propellerblades; and Rn is the Reynolds number.
The parameters in (17) are usually fitted off-line. For example,parameters c0;1;2;3 in the function fKQ
are based on the fitted KQ
Fig. 5. Outputs of the detailed and simplified propeller-load to
curves for the Wageningen B-Series Propellers [25] and the KQ
correction multiplier [26]. The multiplier in Ref. [26] is chosen tominimize the error in the range of maximum efficiency. If thepropeller is not operating in the maximum efficiency range, theerror could be enlarged significantly. Furthermore, the coefficientsin fKQ
can vary with the wear and tear of the propeller. As theoperating environment changes, the parameters in the propeller-load model (17) can also change. Therefore, to use (17) for loadtorque estimation, online parameter identification is necessary.
In this detailed load model (17), six parameters c0; c1; c2; c3;M0;
M1 are used in the nonlinear parametric model, making parameterestimation difficult. To facilitate online parameter estimation, thefollowing simplified model (18) is proposed, whose derivation isgiven in the Appendix.
TLoadzC1 þ C2cosð4qÞ þ C3
�n� nref
�: (18)
The output of the detailed propeller-load torque model and thesimplified model (18) at sea state 4 and 6 are shown in Fig. 5.
With the combination of (13) and (18), the new propeller-motormodel is developed in the following:
_u ¼TMðtÞ � bMu�
�C1 þ C2cosð4qÞ þ C3Du=2p
�H
: (19)
For parameter estimation, the parametric model is defined inthe following:
zpar ¼ C�Tparfpar; (20)
where,
zpar ¼�
lparsþ lpar
��_u� 1
HðTM � bMuÞ
�;
C�par ¼
hC1 C2 C3
iT;
fpar ¼� �lparsþ lpar
�½1 cosð4qÞ Du=2p�T ;
rque models at sea state 4 (top) and sea state 6 (bottom).
Fig. 6. Schematic diagram of the AMPC controller.
Table 4Parameters for simulation in two sea states [21].
Description Parameter Value
Wave period Twave 12 secWave height hwave 2m (SS4)/4m (SS6)Wave length Lwave 40:29%LshipShip speed command Ud 12.4 knot
Table 5Performance metrics.
Performance Mathematical expression
Voltage RegulationffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNT
lpar is the filter gain, and f,g represents the dynamic operator ofthe filter, whose transfer function is ð,Þ. The filter is introduced toavoid taking numerical derivatives in estimation.
The normalized gradient algorithm is chosen as the adaptivelaw, and presented in the following [27]:
and G ¼ GT is a positive-definite matrix, satisfying the real part ofthe eigen-values of G is between ð0;2=TsÞ, which affects how fastCpar updates.
The speed variation within the predictive horizon is assumed tobe very small, i.e., xMðtþ N� 1ÞzxMðtþ N� 2Þz…zxMðtÞ. Thisresults in an estimation of the future propeller-blade position attime k as follows:
qðkÞ ¼ qðtÞ þ ðk� tÞTsxMðtÞ: ðt � k � t þ N � 1ÞTherefore, the schematic diagram of the proposed AMPC is
shown in Fig. 6, and the new propeller-motor dynamic is expressedin the following:
xMðkþ 1Þ ¼ xMðkÞ � TsC3
2pHðxMðkÞ � udÞ
þTsH
�uMðkÞ � bMxMðkÞ � C1
��TsHC2cosð4ðqðtÞ þ ðk� tÞTsxMðtÞÞÞ:
(21)
Table 3Ship parameters [21].
Description Parameter Value
Ship length Lship 190mShip breadth Bship 28.4mDraft H 15.8mMass m 20000 tonAdded-mass mx 28755 tonThrust deduction coefficient td 0.2Propeller diameter D 5.6mWetted area S 12297m2
To quantitatively compare and analyze the performance of theproposed algorithm, two sea states (SS4 and SS6), corresponding tomoderate and severe operating conditions, respectively, are used inthe performance evaluation. Ship parameters as well as waves in-formation are shown in Tables 3 and 4 [21]. Because the negativeeffects of load fluctuations at high sea states are much more sig-nificant than those at low sea states and HESS can fully address theload fluctuations at low sea states (such as sea state 2), the low seastates (such as sea state 2) are not reported in this paper.
According to the control objectives, the performancemetrics arepresented in Table 5, where NT equals ½ðtT � t0Þ=Ts�, with ½,� beingthe integer rounding of, and t0 and tT are the initial and final valuesof the time period being investigated. In this paper, the samplingtime Ts is 0.02 s and the investigation time is 60 s (about 5 waveperiods). In order to evaluate the proposed approaches to loadtorque estimation and prediction, results obtained from six caseshave been studied and analyzed in this section. These six cases aredescribed in the following:
� Case 1, “Ideal”: In this case, the actual propulsion-load torque(17), without any uncertainty, is used. Nonlinear MPC usesperfect knowledge to predict the future load torque in its opti-mization. Because there is no uncertainty in this case, it isreferred to as “Ideal”.
� Case 2, “Frozen prediction”: In this case, the current load torqueis obtained from the load torque model (17) without any un-certainty. Compared to Case 1, the future load torque used in theMPC is assumed to be same as the current load torque, i.e.,TLoadðtþ N� 1jtÞ ¼ TLoadðtþ N� 2jtÞ ¼ … ¼ TLoadðtjtÞ.
� Case 3, “LP-Only”: Different from Case 2, the future load torquein this case is predicted using linear prediction. The true value isused for the current load torque.
Speed Regulation NTk¼0
ðud�xM ðkÞÞ2NTþ1
Gen Power TrackingffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNT
Fig. 7. Estimation error of the adaptive parameter identification and input observer.
SS4 SS6
Deg
rade
d P
erfo
rman
ce (%
)
0
10
20
30
40
50Total Cost
Case 2Case 3
Fig. 8. Cases 2 and 3 degraded “Total Cost” performance compared to Case 1.
J. Hou et al. / Energy 150 (2018) 877e889 885
� Case 4, “IO-Only”: In this case, the input observer is used, insteadof the true load torque. The future load torque is assumed to bethe same as the current IO estimation.
� Case 5, “IO-LP”: The first approach, i.e., IO combined with LP, isused in this case.
� Case 6, “AMPC”: This case is the proposed AMPC.
The estimation performance is evaluate first. Among these sixcases, Cases 4, 5, and 6 require estimation of the load torque. Asshown in Fig. 7, adaptive parameter identification has better esti-mation performance than the input observer. The reason is thatmore propeller-load information is taken into consideration in thisadaptive approach.
The key performance metrics and results are presented inTable 6. The performance results of each case are normalized byCase 1. Smaller values represent better performance. Note that theperformance of Cases 2e6 from best to worst are colored in thefollowing sequence: blue, green, yellow, brown and red.
Table 6Performance comparison.
As can be seen in Table 6, the performance of Case 6 (“AMPC”) isthe closest to Case 1 (“Ideal”). Case 1 (“Ideal”) uses the accuratedetailed propeller-load model and takes its dynamics into consid-eration, leading to the best performance among all of the investi-gated cases. The “Total Cost” in the performance metrics representsthe overall performance, which takes all of the other metrics alongwith their priorities (i.e., their weighting factors) into consider-ation. The mathematical expression of “total cost” is shown inTable 5. According to “Total Cost”, the performance from the best tothe worst are Case 1 (“Ideal”), Case 6 (“AMPC”), Case 3 (“LP-Only”),Case 2 (“Frozen prediction”), Case 5 (“IO-LP”), and Case 4 (“IO-Only”) at both sea states 4 and 6. Based on the performance com-parison, key observations are presented in the following remarks.
Remark 4.1. (Effects of load prediction): Cases 1 (“Ideal”), 2(“Frozen prediction”) and 3 (“LP-Only”) all assume perfect loadestimation at time t, but use different load predictions. Case 1(“Ideal”) takes the load dynamics into consideration, and Case 3(“LP-Only”) uses the signal spectrum and correlation information to
SS4 SS6
Deg
rade
d P
erfo
rman
ce (%
)
0
10
20
30
40
50Total Cost
Case 4Case 5
Fig. 9. Cases 4 and 5 degraded “Total Cost” performance compared to Case 1.
SS4 SS6
Deg
rade
d P
erfo
rman
ce (%
)
0
10
20
30
40
50Total Cost
Case 3Case 5
Fig. 11. Cases 3 and 5 degraded “Total Cost” performance compared to Case 1.
J. Hou et al. / Energy 150 (2018) 877e889886
predict future torque, while Case 2 (“Frozen prediction”) uses noneof these, leading to the worst performance of the three cases. The“Total Cost” performance degradation of Cases 2 (“Frozen predic-tion”) and 3 (“LP-Only”) compared to Case 1 (“Ideal”) is shown inFig. 8. Because all the performance values of Case 1 (“Ideal”) areone, performance degradation (%) can be expressed that the per-formance values of Case 2e5 minus one and then time 100%.Another comparative result can be shown between Cases 4 (“IO-Only”) and 5 (“IO-LP”). Both Cases 4 (“IO-Only”) and 5 (“IO-LP”) use
the input observer to estimate bT loadðtjtÞ, but differ in the predictionscheme. The “Total Cost” degradation of Cases 4 (“IO-Only”) and 5(“IO-LP”) compared to Case 1 (“Ideal”) is shown Fig. 9. Note that thedifference between Cases 4 (“IO-Only”) and 5 (“IO-LP”) is smallerthan that between Cases 2 (“Frozen prediction”) and 3 (“LP-Only”),because the estimation error in Case 5 (“IO-LP”) influences theprediction performance.
Remark 4.2. (Effects of load estimation): The difference betweenCase 2 (“Frozen prediction”) and Case 4 (“IO-Only”) is in the loadtorque estimation, where the former uses the actual load torque butthe latter employs an IO to estimate the load torque. Case 2 (“Frozenprediction”) outperforms Case 4 (“IO-Only”) in terms of most of the
SS4 SS6
Deg
rade
d P
erfo
rman
ce (%
)
0
10
20
30
40
50Total Cost
Case 2Case 4
Fig. 10. Cases 2 and 4 degraded “Total Cost” performance compared to Case 1.
performance metrics. Their “Total Cost” performance is shown inFig. 10. Similarly, Case 3 (“LP-Only”) and Case 5 (“IO-LP”) use thesame prediction method, but have different load estimation. Asshown in Fig. 11, the difference between Cases 3 (“LP-Only”) and 5(“IO-LP”) is larger than that between Cases 2 (“Frozen prediction”)and 4 (“IO-Only”). This is because the estimation affects not onlythe instantaneous information, but also the prediction in Cases 3(“LP-Only”) and 5 (“IO-LP”). Case 1 (“Ideal”) has better performancethan Case 6 (“AMPC”) as expected, due to the uncertainties in thedynamic model used for Case 6 (“AMPC”). These comparisonsdemonstrate that load torque estimation plays a key role inachieving good performance.
Remark 4.3. (Effects of data-based LP): Except for Cases 1 (“Ideal”)and 6 (“AMPC”), Case 3 (“LP-Only”) has the best performanceamong the remaining 4 cases. Even though Case 3 (“LP-Only”) onlyuses a data-based load predictor, the prediction still contributessome benefits, especially with regard to reducing wear and tear. Asshown in Fig. 12, metric “Torque Oscillation Reduction” demon-strates that Case 3 (“LP-Only”) can achieve almost the same smallmotor torque variations as Case 6 (“AMPC”). Moreover, Case 3 (“LP-Only”) outperforms Cases 2 (“Frozen prediction”), 4 (“IO-Only”) and5 (“IO-LP”) in terms of metrics “Gen Oscillation Reduction” and“Speed Oscillation Reduction”, as shown in Table 6, further
Table 7Performance comparison: Case 6 vs. Case 1 with 2% modeling error.
J. Hou et al. / Energy 150 (2018) 877e889 887
demonstrating the benefits of LP in performance metrics ofreducing the wear and tear of the motor and generator sets.Compared to Case 3 (“LP-Only”), Case 5 (“IO-LP”) also uses LP topredict future torque. However, the estimation error of the inputobserver affects the prediction performance, as discussed in Remark4.2. As can be seen, only at sea state 4 can Case 5 (“IO-LP”) achieveperformance similar to Case 2 (“Frozen prediction”). At sea state 6,the performance of Case 5 (“IO-LP”) is worse than Case 2 (“Frozenprediction”). This comparison illustrates that the load torque esti-mation is essential for improving the performance of data-based LP.
Remark 4.4. (Effects of adaptation): Case 6 (“AMPC”) is the onlycase that achieves competitive performance to Case 1 (“Ideal”). Thisis because only in these two cases the load dynamics are trulycaptured by using the propulsion-load torque model, therebymaintaining the motor and generator sets working around thereference points through subsystem coordination. Without theability to capture the load torque dynamics, however, other casesneed the assistance of the motor and generator sets to mitigate thebus voltage variations, leading to degraded system efficiency andincreased wear and tear. In order to evaluate the effects of adap-tation, a comparative study is performed between Case 6 (“AMPC”)and Case 1 (“Ideal”) with 2%modeling errors (2%Err are added on c0and M0). As shown in Table 7, most performance indices are verysensitive to modeling error. These 2% modeling errors (without
adaptation) can cause “Total Cost” 100% and 40% higher than Case 6(with adaptation) at sea state 4 and 6, respectively. Moreover, theperformance is even much worse than Case 4 (“IO-Only”). The keyfactors that renders favorable performance of AMPC are summa-rized in the following:
� The foundation of AMPC is a well-developed simplified modelthat captures the essential dynamics of the load torque. Withaccurate parameter identification, AMPC can predict the futureload torque much better than LP.
� When the load torque dynamicmodel is integrated into theMPCcontroller, AMPC truly takes the load torque dynamic intoconsideration, resulting in the unique advantage of AMPCcompared to the other 4 cases (Case 2 (“Frozen prediction”), 3(“LP-Only”), 4 (“IO-Only”) and 5 (“IO-LP”)).
Remark 4.5. (Effects of weighting factors): The weighting factorscan undoubtedly influence the performance of the proposed AMPC.In this paper, each weighting factor l assigns a relative priority to aperformance attribute. Given the main objectives, the system reli-ability and thrust production have the highest priority. Theweighting factor can be tuned to reflect different design emphasis.One performance metric can be improved by tuning its weightingfactor, but this could result in other metrics being negatively
Fig. 13. Torque comparison (sea state 4): Case 6 vs. Test 1.
Fig. 14. Torque comparison (sea state 6): Case 6 vs. Test 1.
J. Hou et al. / Energy 150 (2018) 877e889888
affected. Two tests are studied to demonstrate how the weightingfactors affect the performance. These two tests are described in thefollowing:
� Test 1: 10lDTM is used in this test to further reduce the motortorque oscillations.
� Test 2: 10lHESS is used with an emphasis on improving the en-ergy efficiency of HESS.
As shown in Table 8, the motor torque oscillation has beensignificantly reduced by increasing the weighting factor lDTM in Test1 (10lDTM ). As shown in Figs. 13 and 14, there is almost no motortorque oscillation in Test 1 (10lDTM ). Similarly, the losses of HESS aresignificantly reduced in Test 2 (10lHESS). However, the highweighting factor lHESS forces the HESS to limit its operation at verylow currents, leading to the loss of ability in isolating the loadfluctuations from the DC bus. This causes negative effects on mostof other performance metrics. Test 2 (10lHESS) also provides theinsights into the importance of HESS in mitigating the effect of theload fluctuations.
5. Conclusion
This paper proposes a new energy management strategy, AMPC,to integrate power generation, electric motor, and hybrid energystorage control for electric ship propulsion systems in order toaddress the effects of propulsion-load fluctuations in the shipboardnetwork. This approach addresses the estimation and prediction ofthe propulsion load torque. In order to evaluate the proposed
AMPC, an alternative control is developed by integrating the inputobserver with linear prediction into the MPC strategy. Compared tothe alternative approach, the proposed AMPC achieves much betterperformance in terms of improved system efficiency, enhancedreliability, improved thrust production, and reduced mechanicalwear and tear. In addition to the alternative control, other cases arestudied in this paper to illustrate the importance of the load esti-mation and prediction. In future work, computationally-efficientoptimization algorithms for implementing the proposed EMS willbe investigated.
Acknowledgment
This work was sponsored by the U.S. Office of Naval Research(ONR) under Grants No. 00014-15-1-2668. The authors would liketo thank the editor and reviewers for their valuable feedback.
Appendix
Considering the propeller load torque model of (17) with
ci ¼ sgnðnÞbrD5ci
�UD
�i
; ði ¼ 0;1;2;3Þ and 1� w ¼ M0 � M1cosð4qÞ,The derivation of the simplified model (18) is presented in thefollowing:
The first step of simplification is to ignore the high-frequency
J. Hou et al. / Energy 150 (2018) 877e889 889
terms, i.e.,�0:5c2M2
1þ 1:5c3M0M211n
�cosð8qÞ� c3M3
1cosð4qÞ3, which
are greater than the propeller blade frequency. This is because theamplitudes of these high-frequency terms are much smaller thanother terms, and they can be filtered significantly by the inertia ofthe propeller. The second step is to linearize the load torque modelaround the reference speed.
In this linearized model, the component C4Dncosð4qÞ onlycontains the variation terms, such as M1, Dn, cosð4qÞ, and can beconsidered as a high order component. Because C4Dncosð4qÞ ismuch smaller than the other components, it can also be ignored.Finally, the linearized model C1 þ C2cosð4qÞ þ C3Dn has only threeunknown parameters. According to the time-scale separationapproach, these three parameters are assumed to be slowly time-varying.
References
[1] McCoy TJ. Electric ships past, present, and future [technology leaders]. IEEEElectr Mag 2015;3(2):4e11.
[2] Doerry N. Naval power systems: integrated power systems for the continuityof the electrical power supply. IEEE Electr Mag 2015;3(2):12e21.
[3] Sørensen AJ, Smogeli ØN. Torque and power control of electrically drivenmarine propellers. Control Eng Pract 2009;17(9):1053e64.
[4] Radan D. Integrated control of marine electrical power systems. Ph.D.dissertation. Norwegian University of Science and Technology; 2008.
[5] Smogeli ØN, Sørensen AJ. Antispin thruster control for ships. IEEE TransControl Syst Technol 2009;17(6):1362e75.
[6] McCarthy J. On the calculation of thrust and torque fluctuations of propellersin non-uniform wake flow. Research and Development Report. Hydrome-chanics Laboratory; October 1961.
[7] Koushan K. Dynamics of propeller blade and duct loading on ventilatedthrusters in dynamic positioning mode. In: DP conference, Houston; 2007.p. 1e13. October 9-10.
[8] Song Z, et al. Sliding-mode and Lyapunov function-based control for battery/supercapacitor hybrid energy storage system used in electric vehicles. Energy2017;122:601e12.
[9] Sarrias-Mena R, et al. Fuzzy logic based power management strategy of amulti-MW doubly-fed induction generator wind turbine with battery and
ultracapacitor. Energy 2014;70:561e76.[10] Hou J, Sun J, Hofmann HF. Mitigating power fluctuations in electric ship
propulsion with hybrid energy storage system: design and analysis. IEEE JOcean Eng 2017;43(1).
[11] Kuseian J. Naval power systems technology development roadmap, ElectricShips Office. PMS 2013;320.
[12] Sun J. Optimisation-based control for electrified vehicles: challenges andopportunities. J Control Decis 2015;2(1):46e63.
[13] Seenumani G, Sun J, Peng H. Real-time power management of integratedpower systems in all electric ships leveraging multi time scale property. IEEETrans Control Syst Technol 2012;20(1):232e40.
[14] Park H, et al. Real-time model predictive control for shipboard power man-agement using the ipa-sqp approach. IEEE Trans Control Syst Technol2015;23(6):2129e43.
[15] Bø TI, Johansen TA. Battery power smoothing control in a marine electricpower plant using nonlinear model predictive control. IEEE Trans Control SystTechnol 2016;25(4).
[16] Smogeli ØN. Control of marine propellers: from normal to extreme conditions.Ph.D. dissertation. Norwegian University of Science and Technology; 2006.
[17] Solsona J, Valla MI, Muravchik C. Nonlinear control of a permanent magnetsynchronous motor with disturbance torque estimation. IEEE Trans EnergyConvers 2000;15(2):163e8.
[18] Kolmanovsky I, Sivergina I, Sun J. Simultaneous input and parameter esti-mation with input observers and set-membership parameter bounding:theory and an automotive application. Int J Adapt Control Signal Process2006;20(5):225e46.
[19] Chen W-H, Yang J, Guo L, Li S. Disturbance-observer-based control and relatedmethods - an overview. IEEE Trans Ind Electron 2016;63(2):1083e95.
[20] Doerry N. Naval power system technology development Roadmap. ElectricShips Office, SEA 05; 2007.
[21] Hou J, Sun J, Hofmann H. Battery/flywheel hybrid energy storage to mitigateload fluctuations in electric ship propulsion systems. In: American controlconference; 2017. p. 1296e301.
[22] Cupelli M, et al. Power flow control and network stability in an all-electricship. Proc IEEE 2015;103(12):2355e80.
[23] Vaidyanathan P. The theory of linear prediction. Synth Lect Signal Process2007;2(1):1e184.
[24] So HC, Chan KW, Chan YT, Ho KC. Linear prediction approach for efficientfrequency estimation of multiple real sinusoids: algorithms and analyses. IEEETrans Signal Process 2005;53(7):2290e305.
[25] Barnitsas M, Ray D, Kinley P. Kt, kq and efficiency curves for the wageningenb-series propellers. 1981.
[26] HydroComp. Kt, kq and efficiency curves for the wageningen b-series pro-pellers. 2003.
[27] Ioannou PA, Sun J. Robust adaptive control. 2012.
