Model Predictive Control of Induction Machine for Energy Efficient

Model Predictive Control of Induction Machine for Energy Efficient HVAC Operation Hanwen Zhang

Abhisek Ukil, Senior Member, IEEE

School of EEE Nanyang Technological University, Singapore Email: [email protected]

Dept of ECE University of Auckland, New Zealand Email: [email protected]

Abstract—Recently, the energy efficiency i n t he b uilding has attracted significant r esearch a ttention. M any p apers t alk about the optimizations around the Heating Ventilation and AirConditioning (HVAC) system, such as sensors and model predictive control (MPC)-based thermostats in the system. However, most of them do not consider the energy usage on the drive level where the fans and pumps are powered by the Induction Machine (IM) which consumes about 50% to 75% of total energy consumption in the overall HVAC system. The various drive control strategies might render different energy savings by considering the losses in the IM (e.g., switching, current, and torque loss) in the different HVAC operating conditions (e.g., ambient temperature changes, etc.). This paper has analyzed the drive performance under different HVAC operating conditions, including the simulation results for the speed and torque ripples; torque loss and fan power consumption. Index Terms—Building automation, demand response, energy efficiency, H VAC, s mart b uilding, d rive, MPC.

I. I NTRODUCTION Recently, the energy efficiency in the building has attracted much attention by the researchers. Many papers talk about the optimizations around the Heating Ventilation and AirConditioning (HVAC) system, such as sensors and thermostats in the system. The improvement on energy efficient HVAC operation examples are: the improved vapor compression cycle operation in [1], [2]; the HVAC fault detection method in [3]; a smart thermostat in [4]; other HVAC improvements in [5]–[7]. However, most of them do not consider the non-optimal energy usage at the motor-drives level, where the fans and pumps are powered by the Induction Machine (IM), consuming about 50% to 75% of total energy consumption in the overall HVAC system [8]. The various drive control strategies might render different energy savings by considering the losses in the IM (e.g., switching, current, and torque loss) in the different HVAC operating conditions (e.g., ambient temperature changes, etc.). The large stator current ripple in the IM would cause high current harmonics, which is undesirable for the grid and the IM, resulting in significant l osses. T he h igh t orque ripple induces large torque loss and increases wear and tear on the IM that reduces the lifetime of the IM. It also creates large speed ripple, which deteriorates the overall HVAC system energy efficiency. A s a r esult, i t i s i mportant t o i nvestigate about the different control strategies of IM for the HVAC system

Fig. 1. Overview of a multi-zone HVAC model (modified from [17]).

application. In this paper, a gray-box HVAC model has been built up and integrated with a recent (yr. 2016) developed drive control strategy namely, Model Predictive Flux Control (MPFC) [9] for the investigation of drive performance under different HVAC scenarios. The remainder of the paper is organized as follows. Section II describes a construction of the HVAC model in Matlab. Modeling of the drive system is described in details in Section III. Section IV presents the simulation results for the integrated HVAC and drive system model, followed by conclusions in Section V. II. H EATING V ENTILATION AND A IR -C ONDITIONING (HVAC) M ODEL Normally, the HVAC model has been classified into 3 types namely, white-box, black-box, and gray-box model. The white box model-based commercial softwares called ``FloVENT® ´´ [10] and ``Thermolib® ´´ were used in [11]–[15]. The artificial neural network, fuzzy logic, and stochastic model, etc., are the black-box models. In this paper, an RC-network in [16]–[19] (gray-box model) has been used for the investigation of drive performance under different HVAC operation scenarios. A schematic diagram of the typical HVAC system (modified from [17]), is shown in Fig. 1. A fan controller for the function of ancillary services in the original paper [17], has been removed in this case, as only the HVAC portions are considered. In Fig. 1, m(t) is the total supplied mass airflow

rate by the fan in kg/s; md (t) is the total desired mass airflow rate in kg/s; v d (t) is the desired fan speed in percentage (e.g. v d (t)=100 means the fan is running at rated speed, v d (t)=50 means the fan is running at half of the rated speed); v(t) is the supplied fan speed in percentage; mdi is the desired airflow rate in the i-th zone; mi is the supplied airflow rate in the i-th zone; Ti is the i-th zone temperature in °C.

= 1.005 × 103 J/(kg · K)); mi is the supplied airflow rate in the i-th zone; TSAT is the supply air temperature (12.8°C); Qi is the external heat sources from appliance and occupants in the i-th zone; Ci,j is the wall capacitance between the i-th zone and j-th zone; Tj is the j-th zone temperature.

A. Airflow Rate Converter

1) Zone Size: A schematic diagram of a single zone is shown in Fig. 2a. It has a size of 5m×5m×3m, and consists of an HVAC supply, a door, and two windows. The designed door size is 970mm × 2080mm (2.0176 m2 ) and a single window size is 1.35 m2 for the operable glazing windows stated in ASHRAE 2005 Handbook respectively [20]. 2) R & C Parameters: The thermal resistance (R) and capacitance (C) of the wall are 0.18 m2 ·K/W and 149.83×103 J/K/m2 respectively for the ``200 mm concrete block´´ type of concrete wall stated in chapter 30 of the ASHRAE 2005 Handbook [21]. Similarly, the ``opaque spandrel glass´´ type of windows were used in this paper, which have the parameter of R = 0.01 m2 · K/W and C = 14.1 × 103 J/K/m2 . The ``slab doors (wood slab in wood frame)´´ type of door were applied in the model with parameters of R = 0.33 m2 · K/W and C = 50.49 × 103 J/K/m2 .

The airflow rate converter in Fig. 1 is used to convert the speed into supply airflow rate [17]: m(t) = c2 v(t),

(1)

where c2 is a constant coefficient. In this case, the maximum airflow rate at each zone is limited to 0.25 kg/s, which is the same as that in [16]. There are in total of 3 zones in the HVAC system model. c2 at full speed can be calculated as: (0.25 kg/s) × (3 zones) = c2 × (100) ⇒ c2 = 0.0075kg/s. B. Speed Converter The speed converter in Fig. 1 is used to convert the desired mass airflow rate (md (t)) to the desired fan speed (v d (t)). This conversion equation is given as: md (t) dv d (t) + v d (t) = , dt c2 where τ2 is the time constant (τ2 =10s, [17]). τ2

E. Single Zone Model

(2)

C. Thermostat For the energy efficiency of the HVAC system, a smart thermostat in [4] is developed which used the Model Predictive Control (MPC) strategy, considering the demand response at the same time. In order to reduce the complexity of thermostat model, the classic PI controller is used in this paper with the parameter of Kp ≈ −4.194 and Ki ≈ −0.011. D. Thermal Dynamics Model The thermal dynamic model in Fig. 1 is a gray-box model namely ``RC-Network´´ model. It has been proved to be working well in the papers [16]–[19]. The RC-network model is given as: dTi Toa − Ti X Ti,j − Ti Ci = + + cp mi (TSAT − Ti ) + Qi , dt Ri Ri,j jNi (3) dTi,j Ti − Ti,j Tj − Ti,j Ci,j = , (4) dt Ri,j Ri,j where i denotes the i-th zone; j denotes the j-th zone, which is adjacent to the i-th zone; Ci is the i-th zone capacitance in J/K (Ci = 7.8×105 J/K). Toa is the outdoor air temperature (ambient temperature); Ri is the window thermal resistances in the i-th zone; Ti,j is the instantaneous wall temperature calculated by Eq. (4); Ri,j is the wall thermal resistance between the i-th and the j-th zone; Ni is a set of [i , j] defined in the paper [16], which includes all combination of [i , j] sets where i 6= j; j ∈ Ni indicates all adjacent zones of the i-th zone; cp is the specific heat of the air (cp

(a) Single zone model

(b) Three zones model Fig. 2. The schematic diagram of the (a) single and (b) three zones model

F. Three Zones Model The 3-zone model in Fig. 2b, is formed by three identical single zone model in Fig. 2a with parameters in Section II-E2

TABLE I OTHER HVAC PARAMETERS FOR E QS . (3) AND (4)

Symbol mi,max Tceiling Tf loor Thallway Twindows Tdoor

Definition Max airflow rate limit at each zone Zone ceiling temperature Zone floor temperature Hallway temperature Windows outer layer temperature Door outer layer temperature

Parameters 0.25 kg/s Toa 25 °C 25 °C Toa 25 °C Fig. 3. The control diagram of Model Predictive Flux Control (MPFC) [9].

and Table I. The supply airflow rate at each zone can be estimated as:

The discretized IM model can be express as [25], [26]:  k+1 xp = xk + Ts (Axk + Buk ) d d mi (t) = ai m(t) where, ai = & m (t) = mi (t), , (8) Ts i=1 xk+1 = xk+1 + A(xk+1 − xk ) p p (5) 2 where mi (t) is the instantaneously supplied airflow rate in i-th where k is the time instant; xk+1 is the predictor-corrector of p zone; ai is the required airflow rate ratio in the HVAC system; state vector; xk+1 is the predicted state vector for the stator mdi (t) is the instantaneously desired airflow rate in i-th zone; current and flux; and T is the sampling time of the system s In this case, n = 3 for 3 zone model. (or the drive control period). The power consumption of a fan can be expressed by [17], The predicted rotor flux (Ψrk+1 ) and electromagnetic torque [22], [23]: (Tek+1 ) can be express as [9], [25]–[27]: P (t) = c1 [v(t)]3 , (6) Lr k+1 1 k+1 Ψrk+1 = Ψs − i , (9) Lm λLm s where P (t) is the fan power consumption in W ; c1 is a constant coefficient for the fan power estimation in W ; Eq. (6) 3 , (10) Tek+1 = Np Ψsk+1 ⊗ ik+1 s is deduced by the fan law stated in [24]. In this case, a 2.2 kW 2 induction machine is used for the airflow supply in the HVAC where Np is the pole pair of the IM; ``⊗´´ is the symbol for system, c1 can be calculated as: 2.2 × 103 = c1 [100]3 ⇒ c1 = cross product. 0.0022 W . B. Design of MPFC III. M ODEL P REDICTIVE F LUX C ONTROL (MPFC) OF The overall control diagram of MPFC is shown in Fig. 3, I NDUCTION M ACHINE (IM) M ODEL where the state voltage vector (uk ); stator current (iks ); and in Eqs. (8) The fan plant in Fig. 1, is discussed in this Section III. rotor speed (ωr ) at time instant k, are substituted k+1 , Ψrk+1 , and and (9) to obtain the predictive values of Ψ s Most of the prior works consider this fan plant as a first order k+2 k+1 is estimated by the current model [9], [27]: transfer function, e.g. in [17], [22]. However, when this fan is . Then, Ψr mdi (t) md (t)

n X

plant is looked into details, a lot of optimization regarding the drive itself could be found out. In this section, a detailed drive model is built up for investigating the drive performance under different HVAC operating scenarios in Table II. A. Dynamic Equation of IM The dynamic equation can be expressed as a state space model in the stationary reference frame [9]: x˙ = Ax + Bu,

(7)

where x = [is Ψs ]T , is a state vector; is is the stator current; Ψs is the stator flux of the IM; u is the selected stator voltage vector for the 2-level voltT age source inverter in this case; B = [λL   r 1] ; −λ(Rs Lr + Rr Ls ) + jωr λ(Rr − jLr ωr ) A = ; λ = −Rs 0 1/(Ls Lr − L2m ); Rs and Rr are the stator and rotor resistance of IM respectively; Ls and Lr are the stator and rotor inductance respectively; ωr is the rotor speed.

Lm k+1 Rr i −( − jωrk )Ψrk+1 ], (11) Lr s Lr which is used to calculate the angle of the reference stator flux in Eq. (12). With the inputs of reference torque (Teref ) and the magnitude of reference stator flux (|Ψsref | = 0.91W b), the Ψsref can be estimated as: Ψsref = Ψsref 6 Ψsref , where 6 Ψ ref is evaluated by [9], [27]: s   Teref 6 Ψ ref = 6 Ψ k+2 + sin−1 ref k+2 3 s r N λL |Ψ ||Ψ | . (12) Ψrk+2 = Ψrk+1 + Ts [Rr

2

p

m

r

s

Afterwards, the cost function minimization block in Fig. 3, compares Ψsref and Ψrk+2 by the cost function of J1 = ref Ψ − Ψrk+2 , where Ψrk+2 is calculated by the voltage s model: Ψsk+2 = Ψsk+1 + Ts (uk+1 − Rs ik+1 ) [9], [27]. s Finally, an optimal voltage vector (uopt = uk+1 ) corresponding to the minimum cost of J1 , is selected and supplied to the 2-level voltage source inverter. For more detail construction of MPFC, parameters of the IM (e.g. stator resistance and inductance, etc.), and the comparisons between the MPFC with other MPC-based drive control strategies can be found in [9].

TABLE II T HE THREE HVAC SCENARIOS FOR INVESTING THE CHANGES OF

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C. Fan Load & Mechanical IM Model The fan load is expressed as the torque-speed characteristic of the fan or pump type of load [28]: Tm = kωr2 ,

(13)

where ωr ≈ 157.08rad/s (1500 rpm, full speed); Tm ≈ 14N m (2kW of IM at full speed) is the maximum load torque; k is a constant coefficient, which can be estimated by 14 = k(157.08)2 ⇒ k ≈ 5.67 × 10−4 . The mechanical model of IM can be expressed as [29]–[31]: dθr dωr = Te − Bωr − Tm and = ωr , (14) dt dt where J is the coefficient of the motor inertia (J = 0.01 kg · m2 ); ωr is the rotor speed; θr is the rotor angular position; Te is the electromagnetic torque; Tm is the mechanical torque generated by the motor shaft (load torque); B is the viscous friction coefficient (B = 0, ignored). J

IV. S IMULATION AND D ISCUSSION With the fan plant model constructed as the MPFC drive model in Section III, MPFC drive model is integrated into the HVAC system constructed in Section II, as shown in Fig. 4. In order to reduce the calculation time, the simulation time of this integrated MPFC and HVAC model is set as the 2500s (≈ 42mins), with a base sampling frequency of 10 kHz [25]. The simulation was carried out based on the three HVAC cases in Table II, where the initial zone temperature is at 26 °C; the individual zone temperature is set as 25 °C; Q1, Q2, and Q3 represent the heat emitted by the occupants in zone 1, 2, and 3 respectively in Fig. 2b. One person is estimated to generate 80 W of heat in the zone. The examples of motor performance, fan load and power consumption are shown in Figs. 5 and 6, for the HVAC case 1. Their responses, in other two HVAC cases, are similar to that in the HVAC case 1, but with different response time.

Fig. 5. Motor output performance at HVAC case 1.

Therefore, only HVAC case 1 is presented as an example in this paper. The ``Phase 1´´ and ``Phase 2´´ , in Figs. 5 and 6, indicate the full speed performance at the beginning when the zone temperature is at 26 °C, and the steady-state performance at the partial-load condition where the zone temperature has reached the set-point temperature of 25 °C , respectively. The phase 1 at case 1, case 2, and case 3 are defined as the 80s ∼ 739s, 80s ∼ 399s, and 97s ∼ 398s respectively. Phase 2 was measured at the steady-steady period of 1994s ∼ 2500s in all cases. Equation (15) was used in Tables III and IV for calculating the reference tracking performance and the speed and torque ripples: ∗ |βrms − βrms | × 100%; ∗ βrms Rp,ave Rp,% = × 100% ; Rp,+ve = βmax − βrms ; βrms Rp,+ve + |Rp,−ve | Rp,ave = ; Rp,−ve = βmin − βrms ; 2 (15) where β is a symbol that represents the speed (N ) in Table III, and the torque (Te ) in Table IV respectively. ξrms is the approximated RMS error that investigates the error in between the RMS values of the supplied and reference speed, and torque respectively. Rp,% shows the percentage of speed, and torque ripple respectively. Rp,ave is the actual average speed

ξrms =

TABLE IV E LECTROMAGNETIC TORQUE OF THE INDUCTION MACHINE UNDER DIFFERENCE CASES IN TWO STEADY- STATE PERIODS HVAC Cases Case 1 Case 2 Case 3

T erms

Phases Phase Phase Phase Phase Phase Phase

1 2 1 2 1 2

14.3 5.20 14.30 5.32 14.30 5.33

Nm Nm Nm Nm Nm Nm

T e∗rms 14.00 4.95 14.00 1.97 14.00 2.30

ξrms

Nm Nm Nm Nm Nm Nm

2.14 5.01 2.14 170.45 2.14 132.32

Rp,ave % % % % % %

6.81 8.50 6.81 8.59 6.81 8.71

Nm Nm Nm Nm Nm Nm

Rp,% 47.65 163.71 47.65 161.61 47.65 163.34

% % % % % %

TABLE V FAN LOAD (N M ) AND POWER (W)

HVAC Cases Case 1 Case 2 Case 3

Fig. 6. Fan load and power consumption at HVAC case 1. TABLE III M OTOR SPEED UNDER DIFFERENCE CASES IN TWO STEADY- STATE PERIODS

HVAC Cases Case 1 Case 2 Case 3

Phases Phase Phase Phase Phase Phase Phase

1 2 1 2 1 2

Nrms 1495 854.5 1495 459.4 1495 498.5

rpm rpm rpm rpm rpm rpm

∗ Nrms

1500 854.4 1500 459.4 1500 498.5

rpm rpm rpm rpm rpm rpm

ξrms 0.33 0.01 0.33 0.00 0.33 0.00

% % % % % %

Rp,ave 4 14.7 4 6.4 4 6.65

rpm rpm rpm rpm rpm rpm

Rp,% 0.27 1.72 0.27 1.39 0.27 1.33

% % % % % %

and torque ripple. Rp,+ve is the error between the maximum and RMS value of the speed and torque within a specific time period. Rp,−ve is the error between the minimum and RMS value of the speed and torque within a specific time period. A. IM Speed The speed performance, according to the different HVAC cases are recorded in Table III, where Nrms is the RMS value ∗ of the supplied speed; Nrms is the RMS value of the reference speed. In phase 1, the IM was running at the full speed with speed ripple around 0.27% in all three HVAC cases. The reference tracking error (ξrms ) is slightly larger than that in phase 2. In phase 2, the IM was running at the steady-state under different HVAC cases. When the ambient temperature decreased by 5 °C (from case 1 to 2), the speed in steady-state reduced by almost 46%, and the speed ripple is reduced by around 0.33%. Comparing the case 3 to case 2, the occupants increased by 3 in zone 1, which led to an increase of 8.6% of speed requirement and reduced the speed ripple by 0.06%. The speed tracking error (ξrms ) is very low (≈ 0) when the IM runs below full speed. B. IM Torque The torque performances, according to the different HVAC cases, are recorded in Table IV, where T erms is the RMS

Phases Phase Phase Phase Phase Phase Phase

1 2 1 2 1 2

TL,rms 13.91 4.545 13.91 1.314 13.91 1.547

Nm Nm Nm Nm Nm Nm

T erms 14.30 5.20 14.30 5.32 14.30 5.33

Nm Nm Nm Nm Nm Nm

Tloss,% 2.73 12.51 2.73 75.29 2.73 71.00

% % % % % %

Pf an 2177 406.7 2177 63.22 2177 80.77

W W W W W W

value of the supplied torque. T e∗rms is the RMS value of the reference torque. The RMS error and ripples were calculated by the Eq. (15). In phase 1, the RMS error and torque ripple are the same in all cases, with the values of 2.14% and 47.65% respectively. In phase 2, comparing the case 2 to case 1, the ambient temperature decrease caused a large torque tracking error (170.45%), and slightly decrease of 2.09 % torque ripple. Considering the occupancy, the increased occupants in zone 1 led to a decrease of 38.13% RMS error (case 3 vs. case 2), and a small increase of torque ripple of 1.73%. C. Torque Loss and Fan Power The fan load, power consumption of the fan (Pf an ), and the calculated torque loss are recorded in Table V, where the torque loss, Tloss,% = (T erms -TL,rms )/T erms , and TL,rms is the RMS value of the load torque. The fan load torque and the power response corresponding to the time in HVAC cases 1 are shown in Fig. 6. The estimated fan power and the real power were the same in all HVAC cases. The estimated fan power was evaluated by Eq. (6). The real fan power was calculated by the load torque multiplying the motor speed. In phase 1, the fan runs at full speed with the power consumption of 2177 W and torque loss of 2.73% in all cases. The maximum rating of the IM is 2 kW , which is slightly higher than the fan power consumption in this case. This may be caused by a non-optimal tuned PI-controller (speed regulator) in the MPFC model or the characteristic of IM used in the system. In phase 2, the IM reached steady-state in each case, the torque loss increased by 62.77%, and fan power consumption decreased by 84.46% in case 2 comparing to the case 1. Compared to case 2, case 3 had slightly decrease in torque loss of 4.29% and an increase of 27.76% fan power consumption.

V. C ONCLUSION This paper has integrated the HVAC system with one of most recent developed drive control strategy (MPFC) together and analyzed the drive level performance under different HVAC operating scenarios. The simulation results show that the percentage of speed ripple is the lowest at full speed (≈ 0.27%). The ambient temperature and occupancy changes, would not affect the speed ripple too much when the machine operates at the steady-state of phase 2. However, the speed ripple in full speed is slightly lower than that in the partial-load speed. Although there was a huge power savings potential caused by the decreased ambient temperature, it also results in a large increase of torque loss (i.e. energy loss) at the drive level. The change of occupancy is another very important factor for the HVAC engineer to consider, as in this case, there were only 3 occupants more in one zone, which is able to cause an increase of 27.76% total fan power consumption. The one could expect that if there were 3 occupants more in each zone, the power consumption would be even higher. Therefore, the Demand Controlled Ventilation (DCV) is necessary, which has been mentioned in [19], [32]. In order to achieve more energy efficient HVAC operation inside the building, a multi-point sensor concept in [11], [14] should be considered further, as it gives not only the comfort to occupants but also reduced the energy consumption of the system. On the other hand, one technique may not be suitable for all applications, which is shown in [25] where their proposed control method is not good at the high-speed operation in terms of current Total Harmonic Distortion (THD). Therefore, it is recommended to have a hybrid drive control strategy for the HVAC application. R EFERENCES [1] B. P. Rasmussen and A. G. Alleyne, “Gain scheduled control of an air conditioning system using the youla parameterization,” IEEE Tr. Control Systems Tech., vol. 18, no. 5, pp. 1216–1225, 2010. [2] N. Jain, B. Li, M. Keir, B. Hencey, and A. Alleyne, “Decentralized feedback structures of a vapor compression cycle system,” IEEE Tr. Control Systems Tech., vol. 18, no. 1, pp. 185–193, 2010. [3] A. Bashi, V. P. Jilkov, and X. R. Li, “Fault detection for systems with multiple unknown modes and similar units and its application to HVAC,” IEEE Tr. Control Systems Tech., vol. 19, no. 5, pp. 957–968, 2011. [4] X. Qin, S. Lysecky, and J. Sprinkle, “A data-driven linear approximation of HVAC utilization for predictive control and optimization,” IEEE Tr. Control Systems Tech., vol. 23, no. 2, pp. 778–786, 2015. [5] E. Semsar-Kazerooni, M. J. Yazdanpanah, and C. Lucas, “Nonlinear control and disturbance decoupling of HVAC systems using feedback linearization and backstepping with load estimation,” IEEE Tr. Control Systems Tech., vol. 16, no. 5, pp. 918–929, 2008. [6] M. Zaheer-Uddin, R. V. Patel, and S. A. K. Al-Assadi, “Design of decentralized robust controllers for multizone space heating systems,” IEEE Tr. Control Systems Tech., vol. 1, no. 4, pp. 246–261, 1993. [7] B. Arguello-Serrano and M. Velez-Reyes, “Nonlinear control of a heating, ventilating, and air conditioning system with thermal load estimation,” IEEE Tr. Control Systems Tech., vol. 7, no. 1, pp. 56–63, 1999. [8] X. Liu, Y. Jiang, and T. Zhang, Characteristics of Conventional AirConditioning Systems, Springer, Heidelberg, 2013, pp. 1–19. [9] Y. Zhang, H. Yang, and B. Xia, “Model-predictive control of induction motor drives : Torque control versus flux control,” IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. 4050–4060, 2016.

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