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Power hardware-in-the-loop simulation (PHILS) of photovoltaic power generation using real-time simulation techniques and power interfaces
Journal of Power Sources 285 (2015) 137e145
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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Power hardware-in-the-loop simulation (PHILS) of photovoltaic power generation using real-time simulation techniques and power interfaces Jee-Hoon Jung School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 689-798, Republic of Korea
h i g h l i g h t s Single crystalline PV panel is electrically modeled for PHILS applications. Fast and parallel computations methods are proposed for real-time simulation. Model optimization methods are suggested to reduce computation burden. Practical digital signal interface is proposed to control power hardware. Practical analog power interface is considered for implementing PHILS system.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 November 2014 Received in revised form 19 February 2015 Accepted 8 March 2015 Available online 10 March 2015
Power hardware-in-the-loop simulation (PHILS) has been introduced to its rapid prototyping and accurate testing under various load and interface conditions for power electronics applications. Real-time simulation with advancements in computing technologies can effectively support the PHILS to improve the computation speed of complex target systems converted to electrical and mathematical models. In this paper, advancements of optimized model constructions for a single crystalline photovoltaic (PV) panel are built up for the PHILS with a real-time simulator in the view points of improving dynamic model accuracy and boosting the computation speed. The dynamic model accuracy is one of significant performance factors of the PHILS which should show the dynamic performance of the simulation model during elaborate emulations of the power hardware. In addition, several considerations for the PHILS system such as system configuration and communication are provided to electrically emulate the PV panel with power hardware interfaces. The effectiveness of the proposed PHILS developed on Opal RT's RT-Lab real-time engineering simulator based on Matlab/Simulink is experimentally verified using a prototype PHILS system. © 2015 Elsevier B.V. All rights reserved.
Keywords: Power hardware-in-the-loop simulation PHILS Photovoltaic panel Real-time simulation Fast computation Dynamic model
1. Introduction Real-time simulation and rapid prototyping of power electronics, critical loads, and control systems have prompted recent interest in accurate electrical models of photovoltaic (PV) panels and array systems [1e3]. In addition, advancement in computing technologies, such as parallel computing and digital signal processing techniques for real-time simulations have allowed the prototyping of novel apparatus to be investigated in a virtual system under a wide range of realistic conditions repeatedly, safely,
E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.jpowsour.2015.03.052 0378-7753/© 2015 Elsevier B.V. All rights reserved.
and economically [4,5]. Elaborate models have been required to emulate the electrical behaviors of the PV panel accurately. A fiveparameter model of the PV panel is widely used in literature for the power generation of PV systems [6e8]. However, the solution of the PV model is transcendental in nature; hence it is not possible to solve it for voltage in terms of current explicitly and vice versa [9]. To solve the five-parameter model of the PV panel, numerical methods are required since the terminal voltage or current equation has no exact analytical solution [10]. This numerical iteration in model computations requires high computing power and enough computation time. Using a Lambert W-function, the solution of the PV model can be expressed as an exact solution [11,12]. In addition, parameter mismatching and model error were investigated [13]
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and optimum load conditions of PV panels are determined using this function [14]. Replacement of the PV panel with accurate dynamic models and hardware simulators would have lots of benefits for the development and test of the PV panel in a laboratory environment. This hardware simulator can provide useful testing and prototyping environments under various operating conditions without any side-effects of degradations and malfunctions in practical PV power generation during their physical operations [15,16]. Therefore, power hardware-in-the-loop simulation (PHILS) is proposed to emulate the electrical behaviors of the single crystalline PV panel to simulate its power generation in an electrical manner [17,18]. Realtime simulation-based PHILS systems can provide a rapid, safe, and inexpensive way to accurately design and evaluate power converters and power interface for the PV power generation as well as other electrical system applications [19e21]. In this work, models for the PV panel, real-time simulation techniques, and programmable power interfaces are used to develop a PV PHILS platform based on Opal-RT's RT-LAB real-time simulator. The simulator is used to emulate the power generation by the PV panel in this case, as well as to control the power conversion stages associated with the system. For hardware implementation, proper parallel computing methods for the target realtime simulator, RT-LAB, and its software interface, MATLAB Simulink, will be considered for designing the PHILS system [22,23]. In addition, the static characteristics and computation speed improvements of the proposed simulation model will be verified using real-time simulation and experimental data from a target PV panel. The proposed PHILS system is implemented using the RT-LAB real-time engineering simulator and PQA III programmable power supply. Optimal numerical iteration methods will be proposed for this PHILS application. Model considerations for fast calculations, parallel structures, and parallel computing methods supported by MATLAB and RT-LAB will be suggested to boost the computation speed in the real-time simulator. In addition, effective communication protocol and interface between the real-time simulator and the power hardware will be discussed with the prototype PHILS system. Consequently, the performance of the proposed PHILS system will be enhanced with the advanced fast computation methods in the real-time simulation model and the effective signal and power interface between the simulator and the power hardware. All the proposed fast computation methods such as optimized numerical iterations and parallel computing techniques will be verified by testing the speed improvement of a simulation timestep using experimental results of the prototype PHILS system. Additionally, the performance of the proposed PHILS structure will be discussed. 2. Dynamic model of PV panel A dynamic model of the PV panel can be composed of an electrical model for terminal voltage and a thermal model for layer temperature. In this section, the dynamic model of the single crystalline PV panel will be briefly derived using a five-parameter model and a heat-balance equation.
operating conditions. In Fig. 1, the five-parameter model is composed of a series resistance and a diode in parallel with a shunt resistor, and the model represents for an individual panel. The five parameters are the photo light current IL, the diode reverse saturation current Ir, the lumped series resistance Rs, the lumped shunt resistance Rp, and the ideality factor of the diode nI. The IeV relationship at specific panel temperature and solar irradiance can be expressed as follows:
Vo þ Io Rs Vo ¼ Rp ðIL þ Ir Þ Rs þ Rp Io Rp Ir exp nI VT VT ¼
kNs Tp q
(2)
where VT is the thermal voltage, k is the Boltzmann's constant, Ns is the number of panel cells in series, Tp is the operating temperature of the PV panel, and q is the electron charge, respectively. The electrical power generated by the PV panel can be calculated by the product of the panel output voltage, Vo and the panel output current, Io. The PV panel operates at a specific point on the IeV curve described in (1). 2.2. Thermal model for layer temperature The calculations of temperature and heat distribution of the PV panel are required to accurately estimate the electrical power generation from PV systems. Heat exchange between the PV panel layers can be calculated using a general energy balance equation for a specific layer x as follows:
rlx Alx dlx Cp;lx
dTlx ¼ Qlðx1Þ þ Qlðxþ1Þ dt
(3)
where rlx is the density of the layer x, Alx is the area of the layer x, dlx is the depth of the layer x, Cp,lx is the specific heat capacity of the layer x, Tlx is the borderline temperature of the layer x, and Qlx is the heat flow from the layer x, respectively. Assuming that the temperature is uniformly distributed in the layer, each heat flow can be expressed as follows:
h i Qlðx±1Þ ¼ Ulðx±1Þ Alðx±1Þ Tlðx±1Þ Tlx "
Ulðx±1Þ
tlðx±1Þ
t ¼ þ lx klðx±1Þ klx
(4)
#1 (5)
where Ulx is the overall heat transfer coefficient for the layer x, tlx is the thickness of the layer x, and klx is the thermal conductivity of the layer x, respectively. The single crystalline PV panel is composed of four different layers. The governing equation of the first layer, tempered glass face, can be expressed with considering natural and forced
2.1. Electrical model for terminal voltage Electrical model for emulating the terminal voltage of a single crystalline silicon PV panel can be developed using operating data provided by manufacturers. Those data are not sufficient to predict the currentevoltage (IeV) curve of the target panel, therefore, it is significant that how the parameters of the PV panel model can be determined and predicted with experimental data under various
(1)
Fig. 1. Electrically equivalent circuit representing five-parameter model.
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convection effects as follows:
dT Cl1 l1 ¼ Qconv þ Ql2 dt Qconv ¼ hc;for þ hc;fre Al1 ðTamb Tl1 Þ
(6)
f Vo;n Vo;ðnþ1Þ ¼ Vo;n f 0 Vo;n
(7)
where the function of f(Vo,n) and its derivative f0 (Vo,n) can be calculated as shown in (15) and (16).
where Qconv is the heat flow generated by convection, hc,for is the forced convection coefficient, hc,fre is the free convection coefficient, and Tamb is the ambient temperature of PV panel, respectively. The second layer, top trilaminate, is described using the following governing equation:
dT Cl2 l2 ¼ Ql1 þ Ql3 dt
(8)
The third layer, PV cell, should consider radiations and electric loss effects as follows:
Cl3
dTl3 ¼ Qsw þ Qlw þ Ql2 þ Ql4 þ Qele dt
(9)
Qsw ¼ aab $S$Al3 Qlw ¼ sAl3
1 þ cosb 1 cosb εs Ts4 þ εg Tg4 εp Tp4 2 2
f 0ðVo Þ ¼
dTl4 ¼ Ql3 þ Qconv dt
Ir Vo þ Io Rs 1 þ exp Rp nI VT nI VT
(15)
(16)
The exact explicit analytical solutions for the IeV relation of the PV panel have been researched [26]. The solutions based on the Lambert W-function are exact, explicit, and easily differentiable [11]. This function is defined by the solution of equation WeW ¼ x. Using the Lambert W-function, the output voltage of the PV panel, Vo, can be reorganized by (17):
(10)
Vo ¼ Rp ðIL þ Ir Io Þ Rs Io nI VT WðaÞ
(11)
a¼
(12)
where W(,) denotes the Lambert W-function. However, the Lambert W-function also requires numerical iterations to obtain its solution. Generally, the convergence of the NR method is quadratic in a neighborhood of zero [25]. It means that the error is essentially squared at each iteration step. However, the tangent hyperbolas method called Halley's method can show faster convergence speed than the NR method. The update rule of the Halley's method can be expressed as follows:
where Qsw is the heat flow generated by short wave radiation, Qlw is the heat flow generated by long wave radiation, Qele is the heat generated by electric loss, aab is the absorbability of cell surface, S is the total incident irradiance, s is the StefaneBoltzmann constant, b is the tilted surface angle from the horizontal, εs is the emissivity of the sky dome (0.95), εg is the emissivity of ground surface (0.95), and εp is the emissivity of the PV panel (0.9), respectively. Finally, the last layer, bottom trilaminate, is with the convection effects as follows:
Cl4
(14)
Vo þ Io Rs Vo þ Io Rs þ f ðVo Þ ¼ Ir exp þ Io IL Ir nI VT Rp
Qele ¼ Rp Ip2 þ Rs Io2 Vo Io
139
(13)
3. Fast computation methods for PV panel model To improve the computation speed in the real-time simulation, the computation burden of the simulator should be reduced during each simulation time-step. In this section, two approaches of fast computation methods for the PV panel model are introduced: a numerical iteration and a model optimization.
3.1. Numerical iterations Since the implicit transcendental equation of (1) includes the output voltage and current variables inside of an exponential term, the solution of the five-parameter model's IeV relation requires numerical iterations or analytical approximations [24]. The NewtoneRaphson (NR) method is popular in iterative computational applications because of its simplicity and fast convergence characteristics [25]. Using the NR method, the update rule of the numerical iteration for the output voltage of PV panel can be derived by modifying the IeV relation of the five-parameter model of (1) as follows:
Rp Ir Rp ðIL þ Ir Io Þ exp nI VT nI VT
xnþ1 ¼ xn
(17)
(18)
2f ðxn Þf 0ðxn Þ 2½f 0ðxn Þ2 f ðxn Þf 〞ðxn Þ
(19)
where f〞(x) is the double derivative of the function f(x). Using (19), the update rule of the Lambert W-function using the Halley's method can be described in (20).
Wnþ1 ¼ Wn
Wn eWn a aÞðWn þ2Þ ðWn þ 1ÞeWn ðWn e2ðW n þ1Þ Wn
(20)
Fig. 2 shows the comparison of the numerical computations: the NR method and the Halley's method. Fig. 2 (a) shows the geometric interpretation of the NR method. In the NR method, the next iterate zkþ1 ¼ Nf(zk) is the closest to zk in the intersection of the xy-plane and the tangent plane of jf j at the point (zk, jf ðzk Þj). The direction of the Newton step Nf(zk) zk is therefore against the gradient of jf j at zk. However, in Fig. 2 (b) of the Helley's method, the direction of the Newton step Nf(zk) zk is along Vjf jðzk Þ, i.e., the Newton step is on the line connecting zk and the center of the osculating circle of the level set of jf j at zk. To determine the direction of the Halley step, the Halley method for a function f(z) is the same as the Newton method applied to the function g(z) ¼ f(z)[f0 (z)]½ for all z. The Halley step is along Vjgjðxk ; yk Þ, so the direction of the Halley step is generally different from the direction of the Newton step. It means that the convergence speed of the Halley's method can be faster than the NR method. The comparison of convergence speeds discussed in this section will be verified using the results of numerical iterations and real-time simulations in Section 5.
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Fig. 2. Comparison of numerical computations: (a) NewtoneRaphson method, (b) Halley's method.
3.2. Model construction and optimization The IeV characteristics of the PV panel shows the significant correlation between the output current and the PV panel temperature. Fig. 3 (a) shows the PV panel dynamic model constructed using the MATLAB Simulink. In Fig. 3 (a), the panel voltage is a function of the output current, the irradiance, and the panel temperature. Fig. 3 (b) shows the thermal dynamic model of the PV panel layers. The panel temperature depends on the thermal dynamics and the heat exchange of the PV panel layers as well as the ambient temperature. In Fig. 3 (a), the IeV model block calculates the output voltage and the electrical power generated from the PV panel under various operating conditions using the numerical solver. In Fig. 3 (b), the block is composed of the heat generations of each panel layer and interconnections between adjacent layers, which has the thermal exchange achieved by conduction, convection, and radiation. The real-time simulation environment has the limitations of simulator performance and computation time. The real-time simulation system has fixed and limited processing power. The computation time for each simulation time-step is more critical
Fig. 3. PV panel dynamic model constructed using MATLAB Simulink: (a) Structure of PV panel dynamic model, (b) Thermal dynamic model of PV panel layers.
because all computations should be complete within a limited simulation time-step fixed in the simulation set-up. If not, overruns will cause errors by incomplete calculation in the simulation, which can propagate to the entire simulation process. Precalculation of fixed values (PFV) is a method to improve the simulation speed. The PFV is based on extracting fixed parameters and coefficients from the model equations. Since the computational
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results of the fixed values are constant, they can be calculated before the simulation process. For example, the general energy balance equations from (3) to (5) can be divided into fixed values and time-varying variables as follows:
system.
dTlx ¼ g1 Tlðx1Þ þ g2 Tlðxþ1Þ ðg1 þ g2 ÞTlx dt
The RT-LAB real-time simulator used in this work has multiple CPUs and core units. A model computation speed can be improved by using these multiple processor cores, which can be achieved by proper model separation (MS) to assign each model to the processor cores. Simulation models should be divided into several small models, which exchange priority signals (states or statederived signals) between computation subsystems. In this case, algebraic loops can be present in the simulation model, which contains dynamics of subsystems. Fig. 5 shows a simple example of the algebraic loop in a simulation model. Output states are directly dependent on previous outputs due to feedback-based control loops. Simulation blocks have input ports with direct feed-through; it means that the output of these simulation blocks cannot be computed without knowing the values of the signals entering the blocks at these input ports. This forces the simulator to solve each simulation time-step iteratively, therefore it makes the simulation slow down. This algebraic loop generally occurs when an input port with the direct feed-through is driven by the output of the same simulation block. Moreover, in the real-time simulation, the algebraic loop can be occurred among simulation blocks computed in parallel. In order to maximize parallel computation without the algebraic loop, the master and slave subsystems have to compute and send their outputs before they read their inputs within the same simulation time-step when computation nodes exchange only priority signals. The outputs are computed by migrating upstream until a dynamic state is found. If there is nothing, the simulation gives errors. Therefore, the states or state-derived signals have to be identified to enable the parallel computation of subsystems. Fig. 6 (a) shows the best structure for a parallel execution in the realtime simulator. A state can be defined as the output computed only from preceding inputs or outputs. It means that output blocks of the master and slave subsystems have to be delayed. In Fig. 3 (b), fortunately, the output state of the thermal dynamic model is naturally connected to an integrator block. Therefore, the thermal dynamic model is suitable as a slave subsystem. However, in some cases, a simple model separation will not provide the parallel execution needed in the real-time simulation. For example, a gain block does not produce a state because its output at an arbitrary time step depends on its input at the same time step. By using the delay block, the feed-through signals can be converted to the priority signals. Fig. 6 (b) shows a modified PV panel dynamic model for the parallel computing. All output signals are connected to memory or delay blocks to generate the states or the state-derived signals. However, simulation results should be compared before and after to make sure that the impact of the delay block is acceptable. In the case of the proposed thermal dynamic model, the time constant of the thermal dynamics is a few
(21)
i. h g1 ¼ Ulðx1Þ Alðx1Þ Clx
(22)
i. h g2 ¼ Ulðxþ1Þ Alðxþ1Þ Clx
(23)
where g1 and g2 are the precalculated coefficients. Leveraging the power of vector and matrix operation is one of the key methods to improve computation speed in the simulation. For the vector calculation, the preallocation of vector size can boost the computation speed by optimizing memory usage in the simulation. Fig. 4 shows an example of memory storage process with and without the preallocation of vectors. Without the preallocation, all arrays should be resized in the memory, which spends lots of memory space and access time. This balance vectorization and preallocation can reduce the size of arrays to smaller blocks for block processing in the simulation. In addition, a sparse matrix can reduce memory usage in the simulator which can make the computation faster because it stores only nonzero elements and its indices, and eliminate operations on zero elements.
4. Real-time and PHIL simulation methods In this section, there are practical considerations in the implementation of the PHILS system such as a parallel computing in the real-time simulator and a construction of the PHILS system with the power hardware. Since all computations of the PV panel model are achieved in the real-time simulator, parallel computing methods are useful to improve the computation speed using the simulator's multi-cores. In addition, analog and digital interfaces such as data communication and power interface should be properly designed in the PHILS system. Especially, the communication time as a delay factor should be considered to estimate side effects in emulating the dynamics of the PV power generation using the proposed PHILS
Fig. 4. Preallocating process for an effective memory usage.
4.1. Parallel computing methods in real-time simulation
Fig. 5. Simple example of an algebraic loop.
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Fig. 6. Simulation model structures for parallel computing: (a) Parallel computing structure of the simulation model, (b) Modified PV panel dynamic model for parallel computing.
minutes, thus, the impact of the delay is not significant. The MATLAB simulation software supports a parallel computing toolbox for providing the parallel computation in Simulink. In the case of this PHILS research, the designed simulation model for the PV power generation could use parfor-loop instead of for-loop for repetitive calculations. Fig. 7 shows the mechanism of parfor-loops in the repetitive computations and the loop iterations executed by MATLAB. In Fig. 7, there are parallel executions of for-loop iterations according the time domain. Using the parfor-loop, those parallel
Fig. 7. Mechanics of parfor-loops executed by MATLAB.
executions for the for-loop iteration are automatically arranged and achieved by MATLAB real-time workspace. Therefore, using the parfor-loop instead of the conventional for-loop, the computation time of the simulation model can be reduced by the parallel computing provided by MATLAB environment. 4.2. Construction of PV PHILS system Fig. 8 shows the digital interface of the real-time simulation model of the PV panel. The real-time simulator is connected to the programmable power supply, and two signals are communicated between the simulator and the power supply: a command signal and a load current feedback signal. The communication is achieved using the RS232 serial communication under the speed of 19200 bit per second. The RS232 serial communication can transmit and receive only the ASCII data format, however, all parameters and variables are defined to the floating number in the real-time simulator for computing the simulation models mathematically. Therefore, in Fig. 8, the voltage command block converts the number data to the ASCII data and the asynchronous receiving block extracts the current feedback data from the received ASCII data. Fig. 9 shows the block diagram of the interface configuration of the proposed PHILS system. A real power interface is only used between the programmable power supply and the electronic load. The programmable power supply is an electric power emulator as the PV power generation, and the electronic load is an electrically
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Fig. 8. Digital interface of the real-time simulation model of the PV panel.
In the serial communication, a ASCII character has a byte (8 bit) length. Therefore, the data bit length of a pair of the transmitting and receiving signals, Lsp, can be calculated as follows:
Lsp ¼ LTx þ LRx ¼ ð22 þ 6Þ 8 ¼ 224bit
(24)
where LTx is the data bit length of the transmitting signal and LRx is the data bit length of the receiving signal, respectively. Then, the transmission time of the signal pair in the serial communication, tsp, can be calculated as shown in (25).
tsp ¼
Fig. 9. Digital and analog interface configurations of the proposed PHILS system.
virtual load to emulate the load patterns of the PV applications. An ethernet digital interface is used for fast communication between the console PC and the real-time simulator. All other interfaces between the real-time simulator and the programmable power supply, and the monitoring PC and the electronic load are designed by serial communication lines to transfer and receive digital data such as measurements, status, and commands. According to the load current variation, the panel voltage simulated by the real-time simulator is generated through the programmable power supply. Fig. 10 shows a communication protocol between the real-time simulator and the programmable power supply. The command (transmitting) signal is composed of a voltage command and a current measurement command. After transmitting the command signals, the real-time simulator can receive the load current data from the programmable power supply. In the voltage command, the reference voltage data are generated by the dynamic model of the PV panel. All data and commands should be changed to the ASCII code to be transmitted through the serial communication. After receiving the load current data, it should also be changed to the floating number for the real-time simulator.
Lsp 224 bit x12 msec ¼ Baud Rate 19200 bit=sec
(25)
From (25), the transmission time in the serial communication is one of delay factors of the PHILS system, which include the computation time of the real-time simulator, the data process time of the serial communication, and the control dynamics of the programmable power supply. All the delay factors will affect the dynamics of the electrical emulation achieved by the PHILS system. 5. Experimental results In this section, all the proposed methods to enhance the speed and the performance of the real-time simulation and the PHILS will be verified using the prototype PHILS system for emulating the power generation of the single crystalline PV panel. The verifications will include the validation of the real-time simulation model and the enhancement of the computation and simulation speeds. The performance of the proposed PHILS system will also be discussed using experimental data.
Fig. 10. Protocol of serial communication between the real-time simulator and the programmable power supply.
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J.-H. Jung / Journal of Power Sources 285 (2015) 137e145 Table 1 Computation time consumed by the real-time simulator using the proposed methods (Unit:ms). Model
NR
NR/wLW
H/wLW
PFV/Vec
MS/PC
Final
Serial P. Master P. Slave
24 e e
22.4 e e
21.1 e e
15.3 e e
e 2.13 9.1
e 1.57 9.0
curve of the PV terminal voltage model at four operating points. In addition, the dynamic model accuracy of the proposed model is investigated in Fig. 11 (b). Dynamic conditions illustrated in Fig. 11 (b) were an irradiance decrease from 1000 Wm2 to 700 Wm2
Fig. 11. Validations of the proposed PV simulation model using experimental data: (a) Polarization curves according to output current, temperature, and irradiance variation, (b) Dynamic voltage curve according to load and irradiance variation.
5.1. Validation of simulation model The validation of the proposed PV panel model is achieved using experimental data recorded in Refs. [27,28]. In Fig. 11 (a), the data were obtained on a building integrated photovoltaic facility at the National Institute of Standards and Technology (NIST) for four different operating points of temperature and irradiance, which shows the consistency between the experimental data and the IeV
Fig. 12. Convergence speed of the proposed numerical methods.
Fig. 13. Experimental waveforms of the prototype PHILS system: (a) Load current and panel voltage waveforms, (b) Step response when the load current falls, (c) Step response when the load current rises.
J.-H. Jung / Journal of Power Sources 285 (2015) 137e145
(30%) at the operating time of 0.1 s and a load current increase from 1.25 A to 1.75 A (20%) at 0.2 s. For obtaining the sudden change of the effective irradiance, a lamp controlled by a constant voltage source was used in the experiment referred in [28]. Using a graphical inference in Fig. 11, the proposed PV panel model looks suitable for simulating the power generation of the target PV panel. 5.2. Improvement of computation and simulation speeds Fig. 12 shows the convergence speeds of the proposed numerical methods. Iteration numbers are limited to sixteen for the real-time simulation application. The average numbers of the numerical iterations for the NR method without and with the Lambert Wfunction, and the Halley's method with the Lambert W-function are 7.46, 5.73, and 4.54, respectively. Consequently, the Halley's method with the Lambert W-function could reduce the number of numerical iterations around 39% comparing with the conventional NR method. Table 1 shows the time consumptions for the model calculations of all proposed methods in the real-time simulator. In the real-time simulator, the computation speed is improved from 24 m s to 21.1 m s by the Halley's method with the Lambert W-function. In addition, using the PFV method and the preallocation of the vectored variables, the computation speed of the real-time simulation model is enhanced from 21.1 m s to 15.3 m s, which is around 28% improvement. Using the MS method with the parallel computing in the real-time simulator, the computation time of the proposed model is drastically reduced from 15.3 m s to 9.1 m s, which is around 41% improvement. In conclusion, the improvement of the computation speed caused by the proposed model development, the fast computation method, and the parallel computing is in the order of 62.5%. 5.3. Experimental result of PHILS Fig. 13 (a) shows the dynamic waveforms of the load current and the panel voltage in the PHILS system. According to the load current variation, the panel voltage simulated by the real-time simulator is generated through the programmable power supply. This electrical behavior is achieved by the proposed PHILS system to emulate the power generation from the target PV panel. Fig. 13 (b) shows the step response of the PHILS system when the load current falls. The step response consists of the response time delay, td, and the system transient time, tdyn. The response time delay includes the computation time in the real-time simulator, the transmission time in the serial communication, tsp shown in (25), and other data process time in the real-time simulator, the serial communicator, and the programmable power supply. The system transient time includes the dynamics of the real-time simulator and the programmable power supply. Amount of time td and tdyn are around 500 ms and 250 ms, respectively. Fig. 13 (c) shows the step response when the load current rises, and the values of td and tdyn are similar to the case of Fig. 13 (b). To reduce td and tdyn for proper PHILS, high speed data communication and data processing are required. 6. Conclusions The PHILS of the PV power generation was achieved using the distributed real-time simulation model and the fast computation methods such as the numerical iteration and the parallel computing. Using the Halley's numerical iteration method with the
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Lambert W-function, the convergence speed of the solution of the five-parameter PV model was improved. The PFV, the preallocation of the vectorization in variables, the MS, and the parallel computing methods were introduced for efficient computing in the real-time simulator and the PHILS system. As a result, the computation speed of the proposed PHILS system was improved in the order of 62.5% using the proposed methods, and the PHILS system properly emulated the electrical behaviors of the power generation of the target PV panel. Reducing significant delays in the PHILS system architecture will help the exact emulation of electrical behaviors of many electrical system applications under various operating conditions, which is a next goal of the proposed PHILS system.
Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF2013R1A1A1009632). I would like to thank Prof. Katherine A. Kim to provide language help and valuable advice for revision.
References [1] H. Beltran, E. Bilbao, E. Belenguer, I. Etxeberria-Otadui, P. Rodriguez, IEEE Trans. Ind. Electron. 60 (3) (2013) 1225e1234. [2] A. Ahadi, N. Ghadimi, D. Mirabbasi, J. Power Sources 264 (2014) 211e219. [3] P. Garcia, J.P. Torreglosa, L.M. Fernndez, F. Jurado, J. Power Sources 265 (2014) 149e159. [4] J.-H. Jung, S. Ahmed, P. Enjeti, IEEE Trans. Ind. Electron. 58 (9) (2011) 4217e4231. [5] H.F. Blanchette, T. Ould-Bachir, J.P. David, IEEE Trans. Ind. Electron. 59 (12) (2012) 4555e4567. [6] Y. Mahmoud, W. Xiao, H.H. Zeineldin, IEEE Trans. Ind. Electron. 60 (12) (2013) 5708e5716. [7] J. Cubas, S. Pindado, M. Victoria, J. Power Sources 247 (2014) 467e474. [8] L. Peng, Y. Sun, Z. Meng, J. Power Sources 248 (2014) 621e631. [9] R.W. Hornbeck. New Jersey: Prentice-Hall. 1975. Chap. 5. [10] H. Can, D. Ickilli, K.S. Parlak, in: IEEE Power and Energy Engineering Conference (APPEEC), vol. 1, 2012, pp. 1e4. [11] A. Jain, S. Sharma, A. Kapoor, Sol. Energy Mater. Sol. Cells 90 (1) (2006) 25e31. [12] E. Batzelis, I.A. Routsolias, S.A. Papathanassiou, IEEE Trans. Sustain. Energy 5 (1) (2014) 301e312. [13] G. Petrone, G. Spagnuolo, M. Vitelli, Sol. Energy Mater. Sol. Cells 91 (18) (2007) 1652e1657. [14] J. Ding, R. Radhakrishnan, Sol. Energy Mater. Sol. Cells 92 (12) (2008) 1566e1569. [15] M.A.G. de Brito, L. Galotto, L.P. Sampaio, G. de Azevedo e Melo, C.A. Canesin, IEEE Trans. Ind. Electron. 60 (3) (2013) 1156e1167. [16] A. Koran, T. LaBella, J. Lai, IEEE Trans. Power Electron. 29 (3) (2014) 1285e1297. [17] B.A. Mather, M.A. Kromer, L. Casey, in: IEEE PES Innovative Smart Grid Technologies (ISGT), vol. 1, 2013, pp. 1e6. [18] O. Konig, C. Hametner, G. Prochart, S. Jakubek, IEEE Trans. Ind. Electron. 61 (2) (2014) 943e955. [19] M. Steurer, C.S. Edrington, M. Sloderbeck, W. Ren, J. Langston, IEEE Trans. Ind. Electron. 57 (4) (2010) 1254e1260. [20] W.C. Lee, D. Drury, IEEE Trans. Power Electron. 28 (12) (2013) 5949e5959. [21] A. Hasanzadeh, C.S. Edrington, N. Stroupe, T. Bevis, IEEE Trans. Ind. Electron. 61 (6) (2014) 3109e3118. [22] S. Zaranek, E. Johnson, A. Chakravarti, MATHWORKS, 2012. [23] RT-LAB Version 10.5 User Guide (RTLAB-UG-105e00), Opal-RT, 2013. [24] Y. Sukamongkol, S. Chungpaibulpatana, W. Ongsakul, Renew. Energy 27 (2) (2002) 237e258. [25] T.J. Ypma, SIAM 37 (4) (1995) 531e551. [26] A. Jain, A. Kapoor, Sol. Energy Mater. Sol. Cells 81 (2) (2004) 269e277. [27] M.W. Davis, A.H. Fanney, B.P. Dougherty, in: Proc. IEEE Photovoltaic Specialists Conference, vol. 1, 2002, pp. 1642e1645. [28] O. Gil-Arias, E.I. Ortiz-Rivera, in: 11th Workshop on Control and Modeling for Power Electronics, vol. 1, 2008, pp. 1e5.
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Power hardware-in-the-loop simulation (PHILS) of photovoltaic power generation using real-time simulation techniques and power interfaces Jee-Hoon Jung School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 689-798, Republic of Korea
h i g h l i g h t s Single crystalline PV panel is electrically modeled for PHILS applications. Fast and parallel computations methods are proposed for real-time simulation. Model optimization methods are suggested to reduce computation burden. Practical digital signal interface is proposed to control power hardware. Practical analog power interface is considered for implementing PHILS system.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 November 2014 Received in revised form 19 February 2015 Accepted 8 March 2015 Available online 10 March 2015
Power hardware-in-the-loop simulation (PHILS) has been introduced to its rapid prototyping and accurate testing under various load and interface conditions for power electronics applications. Real-time simulation with advancements in computing technologies can effectively support the PHILS to improve the computation speed of complex target systems converted to electrical and mathematical models. In this paper, advancements of optimized model constructions for a single crystalline photovoltaic (PV) panel are built up for the PHILS with a real-time simulator in the view points of improving dynamic model accuracy and boosting the computation speed. The dynamic model accuracy is one of significant performance factors of the PHILS which should show the dynamic performance of the simulation model during elaborate emulations of the power hardware. In addition, several considerations for the PHILS system such as system configuration and communication are provided to electrically emulate the PV panel with power hardware interfaces. The effectiveness of the proposed PHILS developed on Opal RT's RT-Lab real-time engineering simulator based on Matlab/Simulink is experimentally verified using a prototype PHILS system. © 2015 Elsevier B.V. All rights reserved.
Keywords: Power hardware-in-the-loop simulation PHILS Photovoltaic panel Real-time simulation Fast computation Dynamic model
1. Introduction Real-time simulation and rapid prototyping of power electronics, critical loads, and control systems have prompted recent interest in accurate electrical models of photovoltaic (PV) panels and array systems [1e3]. In addition, advancement in computing technologies, such as parallel computing and digital signal processing techniques for real-time simulations have allowed the prototyping of novel apparatus to be investigated in a virtual system under a wide range of realistic conditions repeatedly, safely,
E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.jpowsour.2015.03.052 0378-7753/© 2015 Elsevier B.V. All rights reserved.
and economically [4,5]. Elaborate models have been required to emulate the electrical behaviors of the PV panel accurately. A fiveparameter model of the PV panel is widely used in literature for the power generation of PV systems [6e8]. However, the solution of the PV model is transcendental in nature; hence it is not possible to solve it for voltage in terms of current explicitly and vice versa [9]. To solve the five-parameter model of the PV panel, numerical methods are required since the terminal voltage or current equation has no exact analytical solution [10]. This numerical iteration in model computations requires high computing power and enough computation time. Using a Lambert W-function, the solution of the PV model can be expressed as an exact solution [11,12]. In addition, parameter mismatching and model error were investigated [13]
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and optimum load conditions of PV panels are determined using this function [14]. Replacement of the PV panel with accurate dynamic models and hardware simulators would have lots of benefits for the development and test of the PV panel in a laboratory environment. This hardware simulator can provide useful testing and prototyping environments under various operating conditions without any side-effects of degradations and malfunctions in practical PV power generation during their physical operations [15,16]. Therefore, power hardware-in-the-loop simulation (PHILS) is proposed to emulate the electrical behaviors of the single crystalline PV panel to simulate its power generation in an electrical manner [17,18]. Realtime simulation-based PHILS systems can provide a rapid, safe, and inexpensive way to accurately design and evaluate power converters and power interface for the PV power generation as well as other electrical system applications [19e21]. In this work, models for the PV panel, real-time simulation techniques, and programmable power interfaces are used to develop a PV PHILS platform based on Opal-RT's RT-LAB real-time simulator. The simulator is used to emulate the power generation by the PV panel in this case, as well as to control the power conversion stages associated with the system. For hardware implementation, proper parallel computing methods for the target realtime simulator, RT-LAB, and its software interface, MATLAB Simulink, will be considered for designing the PHILS system [22,23]. In addition, the static characteristics and computation speed improvements of the proposed simulation model will be verified using real-time simulation and experimental data from a target PV panel. The proposed PHILS system is implemented using the RT-LAB real-time engineering simulator and PQA III programmable power supply. Optimal numerical iteration methods will be proposed for this PHILS application. Model considerations for fast calculations, parallel structures, and parallel computing methods supported by MATLAB and RT-LAB will be suggested to boost the computation speed in the real-time simulator. In addition, effective communication protocol and interface between the real-time simulator and the power hardware will be discussed with the prototype PHILS system. Consequently, the performance of the proposed PHILS system will be enhanced with the advanced fast computation methods in the real-time simulation model and the effective signal and power interface between the simulator and the power hardware. All the proposed fast computation methods such as optimized numerical iterations and parallel computing techniques will be verified by testing the speed improvement of a simulation timestep using experimental results of the prototype PHILS system. Additionally, the performance of the proposed PHILS structure will be discussed. 2. Dynamic model of PV panel A dynamic model of the PV panel can be composed of an electrical model for terminal voltage and a thermal model for layer temperature. In this section, the dynamic model of the single crystalline PV panel will be briefly derived using a five-parameter model and a heat-balance equation.
operating conditions. In Fig. 1, the five-parameter model is composed of a series resistance and a diode in parallel with a shunt resistor, and the model represents for an individual panel. The five parameters are the photo light current IL, the diode reverse saturation current Ir, the lumped series resistance Rs, the lumped shunt resistance Rp, and the ideality factor of the diode nI. The IeV relationship at specific panel temperature and solar irradiance can be expressed as follows:
Vo þ Io Rs Vo ¼ Rp ðIL þ Ir Þ Rs þ Rp Io Rp Ir exp nI VT VT ¼
kNs Tp q
(2)
where VT is the thermal voltage, k is the Boltzmann's constant, Ns is the number of panel cells in series, Tp is the operating temperature of the PV panel, and q is the electron charge, respectively. The electrical power generated by the PV panel can be calculated by the product of the panel output voltage, Vo and the panel output current, Io. The PV panel operates at a specific point on the IeV curve described in (1). 2.2. Thermal model for layer temperature The calculations of temperature and heat distribution of the PV panel are required to accurately estimate the electrical power generation from PV systems. Heat exchange between the PV panel layers can be calculated using a general energy balance equation for a specific layer x as follows:
rlx Alx dlx Cp;lx
dTlx ¼ Qlðx1Þ þ Qlðxþ1Þ dt
(3)
where rlx is the density of the layer x, Alx is the area of the layer x, dlx is the depth of the layer x, Cp,lx is the specific heat capacity of the layer x, Tlx is the borderline temperature of the layer x, and Qlx is the heat flow from the layer x, respectively. Assuming that the temperature is uniformly distributed in the layer, each heat flow can be expressed as follows:
h i Qlðx±1Þ ¼ Ulðx±1Þ Alðx±1Þ Tlðx±1Þ Tlx "
Ulðx±1Þ
tlðx±1Þ
t ¼ þ lx klðx±1Þ klx
(4)
#1 (5)
where Ulx is the overall heat transfer coefficient for the layer x, tlx is the thickness of the layer x, and klx is the thermal conductivity of the layer x, respectively. The single crystalline PV panel is composed of four different layers. The governing equation of the first layer, tempered glass face, can be expressed with considering natural and forced
2.1. Electrical model for terminal voltage Electrical model for emulating the terminal voltage of a single crystalline silicon PV panel can be developed using operating data provided by manufacturers. Those data are not sufficient to predict the currentevoltage (IeV) curve of the target panel, therefore, it is significant that how the parameters of the PV panel model can be determined and predicted with experimental data under various
(1)
Fig. 1. Electrically equivalent circuit representing five-parameter model.
J.-H. Jung / Journal of Power Sources 285 (2015) 137e145
convection effects as follows:
dT Cl1 l1 ¼ Qconv þ Ql2 dt Qconv ¼ hc;for þ hc;fre Al1 ðTamb Tl1 Þ
(6)
f Vo;n Vo;ðnþ1Þ ¼ Vo;n f 0 Vo;n
(7)
where the function of f(Vo,n) and its derivative f0 (Vo,n) can be calculated as shown in (15) and (16).
where Qconv is the heat flow generated by convection, hc,for is the forced convection coefficient, hc,fre is the free convection coefficient, and Tamb is the ambient temperature of PV panel, respectively. The second layer, top trilaminate, is described using the following governing equation:
dT Cl2 l2 ¼ Ql1 þ Ql3 dt
(8)
The third layer, PV cell, should consider radiations and electric loss effects as follows:
Cl3
dTl3 ¼ Qsw þ Qlw þ Ql2 þ Ql4 þ Qele dt
(9)
Qsw ¼ aab $S$Al3 Qlw ¼ sAl3
1 þ cosb 1 cosb εs Ts4 þ εg Tg4 εp Tp4 2 2
f 0ðVo Þ ¼
dTl4 ¼ Ql3 þ Qconv dt
Ir Vo þ Io Rs 1 þ exp Rp nI VT nI VT
(15)
(16)
The exact explicit analytical solutions for the IeV relation of the PV panel have been researched [26]. The solutions based on the Lambert W-function are exact, explicit, and easily differentiable [11]. This function is defined by the solution of equation WeW ¼ x. Using the Lambert W-function, the output voltage of the PV panel, Vo, can be reorganized by (17):
(10)
Vo ¼ Rp ðIL þ Ir Io Þ Rs Io nI VT WðaÞ
(11)
a¼
(12)
where W(,) denotes the Lambert W-function. However, the Lambert W-function also requires numerical iterations to obtain its solution. Generally, the convergence of the NR method is quadratic in a neighborhood of zero [25]. It means that the error is essentially squared at each iteration step. However, the tangent hyperbolas method called Halley's method can show faster convergence speed than the NR method. The update rule of the Halley's method can be expressed as follows:
where Qsw is the heat flow generated by short wave radiation, Qlw is the heat flow generated by long wave radiation, Qele is the heat generated by electric loss, aab is the absorbability of cell surface, S is the total incident irradiance, s is the StefaneBoltzmann constant, b is the tilted surface angle from the horizontal, εs is the emissivity of the sky dome (0.95), εg is the emissivity of ground surface (0.95), and εp is the emissivity of the PV panel (0.9), respectively. Finally, the last layer, bottom trilaminate, is with the convection effects as follows:
Cl4
(14)
Vo þ Io Rs Vo þ Io Rs þ f ðVo Þ ¼ Ir exp þ Io IL Ir nI VT Rp
Qele ¼ Rp Ip2 þ Rs Io2 Vo Io
139
(13)
3. Fast computation methods for PV panel model To improve the computation speed in the real-time simulation, the computation burden of the simulator should be reduced during each simulation time-step. In this section, two approaches of fast computation methods for the PV panel model are introduced: a numerical iteration and a model optimization.
3.1. Numerical iterations Since the implicit transcendental equation of (1) includes the output voltage and current variables inside of an exponential term, the solution of the five-parameter model's IeV relation requires numerical iterations or analytical approximations [24]. The NewtoneRaphson (NR) method is popular in iterative computational applications because of its simplicity and fast convergence characteristics [25]. Using the NR method, the update rule of the numerical iteration for the output voltage of PV panel can be derived by modifying the IeV relation of the five-parameter model of (1) as follows:
Rp Ir Rp ðIL þ Ir Io Þ exp nI VT nI VT
xnþ1 ¼ xn
(17)
(18)
2f ðxn Þf 0ðxn Þ 2½f 0ðxn Þ2 f ðxn Þf 〞ðxn Þ
(19)
where f〞(x) is the double derivative of the function f(x). Using (19), the update rule of the Lambert W-function using the Halley's method can be described in (20).
Wnþ1 ¼ Wn
Wn eWn a aÞðWn þ2Þ ðWn þ 1ÞeWn ðWn e2ðW n þ1Þ Wn
(20)
Fig. 2 shows the comparison of the numerical computations: the NR method and the Halley's method. Fig. 2 (a) shows the geometric interpretation of the NR method. In the NR method, the next iterate zkþ1 ¼ Nf(zk) is the closest to zk in the intersection of the xy-plane and the tangent plane of jf j at the point (zk, jf ðzk Þj). The direction of the Newton step Nf(zk) zk is therefore against the gradient of jf j at zk. However, in Fig. 2 (b) of the Helley's method, the direction of the Newton step Nf(zk) zk is along Vjf jðzk Þ, i.e., the Newton step is on the line connecting zk and the center of the osculating circle of the level set of jf j at zk. To determine the direction of the Halley step, the Halley method for a function f(z) is the same as the Newton method applied to the function g(z) ¼ f(z)[f0 (z)]½ for all z. The Halley step is along Vjgjðxk ; yk Þ, so the direction of the Halley step is generally different from the direction of the Newton step. It means that the convergence speed of the Halley's method can be faster than the NR method. The comparison of convergence speeds discussed in this section will be verified using the results of numerical iterations and real-time simulations in Section 5.
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Fig. 2. Comparison of numerical computations: (a) NewtoneRaphson method, (b) Halley's method.
3.2. Model construction and optimization The IeV characteristics of the PV panel shows the significant correlation between the output current and the PV panel temperature. Fig. 3 (a) shows the PV panel dynamic model constructed using the MATLAB Simulink. In Fig. 3 (a), the panel voltage is a function of the output current, the irradiance, and the panel temperature. Fig. 3 (b) shows the thermal dynamic model of the PV panel layers. The panel temperature depends on the thermal dynamics and the heat exchange of the PV panel layers as well as the ambient temperature. In Fig. 3 (a), the IeV model block calculates the output voltage and the electrical power generated from the PV panel under various operating conditions using the numerical solver. In Fig. 3 (b), the block is composed of the heat generations of each panel layer and interconnections between adjacent layers, which has the thermal exchange achieved by conduction, convection, and radiation. The real-time simulation environment has the limitations of simulator performance and computation time. The real-time simulation system has fixed and limited processing power. The computation time for each simulation time-step is more critical
Fig. 3. PV panel dynamic model constructed using MATLAB Simulink: (a) Structure of PV panel dynamic model, (b) Thermal dynamic model of PV panel layers.
because all computations should be complete within a limited simulation time-step fixed in the simulation set-up. If not, overruns will cause errors by incomplete calculation in the simulation, which can propagate to the entire simulation process. Precalculation of fixed values (PFV) is a method to improve the simulation speed. The PFV is based on extracting fixed parameters and coefficients from the model equations. Since the computational
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141
results of the fixed values are constant, they can be calculated before the simulation process. For example, the general energy balance equations from (3) to (5) can be divided into fixed values and time-varying variables as follows:
system.
dTlx ¼ g1 Tlðx1Þ þ g2 Tlðxþ1Þ ðg1 þ g2 ÞTlx dt
The RT-LAB real-time simulator used in this work has multiple CPUs and core units. A model computation speed can be improved by using these multiple processor cores, which can be achieved by proper model separation (MS) to assign each model to the processor cores. Simulation models should be divided into several small models, which exchange priority signals (states or statederived signals) between computation subsystems. In this case, algebraic loops can be present in the simulation model, which contains dynamics of subsystems. Fig. 5 shows a simple example of the algebraic loop in a simulation model. Output states are directly dependent on previous outputs due to feedback-based control loops. Simulation blocks have input ports with direct feed-through; it means that the output of these simulation blocks cannot be computed without knowing the values of the signals entering the blocks at these input ports. This forces the simulator to solve each simulation time-step iteratively, therefore it makes the simulation slow down. This algebraic loop generally occurs when an input port with the direct feed-through is driven by the output of the same simulation block. Moreover, in the real-time simulation, the algebraic loop can be occurred among simulation blocks computed in parallel. In order to maximize parallel computation without the algebraic loop, the master and slave subsystems have to compute and send their outputs before they read their inputs within the same simulation time-step when computation nodes exchange only priority signals. The outputs are computed by migrating upstream until a dynamic state is found. If there is nothing, the simulation gives errors. Therefore, the states or state-derived signals have to be identified to enable the parallel computation of subsystems. Fig. 6 (a) shows the best structure for a parallel execution in the realtime simulator. A state can be defined as the output computed only from preceding inputs or outputs. It means that output blocks of the master and slave subsystems have to be delayed. In Fig. 3 (b), fortunately, the output state of the thermal dynamic model is naturally connected to an integrator block. Therefore, the thermal dynamic model is suitable as a slave subsystem. However, in some cases, a simple model separation will not provide the parallel execution needed in the real-time simulation. For example, a gain block does not produce a state because its output at an arbitrary time step depends on its input at the same time step. By using the delay block, the feed-through signals can be converted to the priority signals. Fig. 6 (b) shows a modified PV panel dynamic model for the parallel computing. All output signals are connected to memory or delay blocks to generate the states or the state-derived signals. However, simulation results should be compared before and after to make sure that the impact of the delay block is acceptable. In the case of the proposed thermal dynamic model, the time constant of the thermal dynamics is a few
(21)
i. h g1 ¼ Ulðx1Þ Alðx1Þ Clx
(22)
i. h g2 ¼ Ulðxþ1Þ Alðxþ1Þ Clx
(23)
where g1 and g2 are the precalculated coefficients. Leveraging the power of vector and matrix operation is one of the key methods to improve computation speed in the simulation. For the vector calculation, the preallocation of vector size can boost the computation speed by optimizing memory usage in the simulation. Fig. 4 shows an example of memory storage process with and without the preallocation of vectors. Without the preallocation, all arrays should be resized in the memory, which spends lots of memory space and access time. This balance vectorization and preallocation can reduce the size of arrays to smaller blocks for block processing in the simulation. In addition, a sparse matrix can reduce memory usage in the simulator which can make the computation faster because it stores only nonzero elements and its indices, and eliminate operations on zero elements.
4. Real-time and PHIL simulation methods In this section, there are practical considerations in the implementation of the PHILS system such as a parallel computing in the real-time simulator and a construction of the PHILS system with the power hardware. Since all computations of the PV panel model are achieved in the real-time simulator, parallel computing methods are useful to improve the computation speed using the simulator's multi-cores. In addition, analog and digital interfaces such as data communication and power interface should be properly designed in the PHILS system. Especially, the communication time as a delay factor should be considered to estimate side effects in emulating the dynamics of the PV power generation using the proposed PHILS
Fig. 4. Preallocating process for an effective memory usage.
4.1. Parallel computing methods in real-time simulation
Fig. 5. Simple example of an algebraic loop.
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Fig. 6. Simulation model structures for parallel computing: (a) Parallel computing structure of the simulation model, (b) Modified PV panel dynamic model for parallel computing.
minutes, thus, the impact of the delay is not significant. The MATLAB simulation software supports a parallel computing toolbox for providing the parallel computation in Simulink. In the case of this PHILS research, the designed simulation model for the PV power generation could use parfor-loop instead of for-loop for repetitive calculations. Fig. 7 shows the mechanism of parfor-loops in the repetitive computations and the loop iterations executed by MATLAB. In Fig. 7, there are parallel executions of for-loop iterations according the time domain. Using the parfor-loop, those parallel
Fig. 7. Mechanics of parfor-loops executed by MATLAB.
executions for the for-loop iteration are automatically arranged and achieved by MATLAB real-time workspace. Therefore, using the parfor-loop instead of the conventional for-loop, the computation time of the simulation model can be reduced by the parallel computing provided by MATLAB environment. 4.2. Construction of PV PHILS system Fig. 8 shows the digital interface of the real-time simulation model of the PV panel. The real-time simulator is connected to the programmable power supply, and two signals are communicated between the simulator and the power supply: a command signal and a load current feedback signal. The communication is achieved using the RS232 serial communication under the speed of 19200 bit per second. The RS232 serial communication can transmit and receive only the ASCII data format, however, all parameters and variables are defined to the floating number in the real-time simulator for computing the simulation models mathematically. Therefore, in Fig. 8, the voltage command block converts the number data to the ASCII data and the asynchronous receiving block extracts the current feedback data from the received ASCII data. Fig. 9 shows the block diagram of the interface configuration of the proposed PHILS system. A real power interface is only used between the programmable power supply and the electronic load. The programmable power supply is an electric power emulator as the PV power generation, and the electronic load is an electrically
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Fig. 8. Digital interface of the real-time simulation model of the PV panel.
In the serial communication, a ASCII character has a byte (8 bit) length. Therefore, the data bit length of a pair of the transmitting and receiving signals, Lsp, can be calculated as follows:
Lsp ¼ LTx þ LRx ¼ ð22 þ 6Þ 8 ¼ 224bit
(24)
where LTx is the data bit length of the transmitting signal and LRx is the data bit length of the receiving signal, respectively. Then, the transmission time of the signal pair in the serial communication, tsp, can be calculated as shown in (25).
tsp ¼
Fig. 9. Digital and analog interface configurations of the proposed PHILS system.
virtual load to emulate the load patterns of the PV applications. An ethernet digital interface is used for fast communication between the console PC and the real-time simulator. All other interfaces between the real-time simulator and the programmable power supply, and the monitoring PC and the electronic load are designed by serial communication lines to transfer and receive digital data such as measurements, status, and commands. According to the load current variation, the panel voltage simulated by the real-time simulator is generated through the programmable power supply. Fig. 10 shows a communication protocol between the real-time simulator and the programmable power supply. The command (transmitting) signal is composed of a voltage command and a current measurement command. After transmitting the command signals, the real-time simulator can receive the load current data from the programmable power supply. In the voltage command, the reference voltage data are generated by the dynamic model of the PV panel. All data and commands should be changed to the ASCII code to be transmitted through the serial communication. After receiving the load current data, it should also be changed to the floating number for the real-time simulator.
Lsp 224 bit x12 msec ¼ Baud Rate 19200 bit=sec
(25)
From (25), the transmission time in the serial communication is one of delay factors of the PHILS system, which include the computation time of the real-time simulator, the data process time of the serial communication, and the control dynamics of the programmable power supply. All the delay factors will affect the dynamics of the electrical emulation achieved by the PHILS system. 5. Experimental results In this section, all the proposed methods to enhance the speed and the performance of the real-time simulation and the PHILS will be verified using the prototype PHILS system for emulating the power generation of the single crystalline PV panel. The verifications will include the validation of the real-time simulation model and the enhancement of the computation and simulation speeds. The performance of the proposed PHILS system will also be discussed using experimental data.
Fig. 10. Protocol of serial communication between the real-time simulator and the programmable power supply.
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J.-H. Jung / Journal of Power Sources 285 (2015) 137e145 Table 1 Computation time consumed by the real-time simulator using the proposed methods (Unit:ms). Model
NR
NR/wLW
H/wLW
PFV/Vec
MS/PC
Final
Serial P. Master P. Slave
24 e e
22.4 e e
21.1 e e
15.3 e e
e 2.13 9.1
e 1.57 9.0
curve of the PV terminal voltage model at four operating points. In addition, the dynamic model accuracy of the proposed model is investigated in Fig. 11 (b). Dynamic conditions illustrated in Fig. 11 (b) were an irradiance decrease from 1000 Wm2 to 700 Wm2
Fig. 11. Validations of the proposed PV simulation model using experimental data: (a) Polarization curves according to output current, temperature, and irradiance variation, (b) Dynamic voltage curve according to load and irradiance variation.
5.1. Validation of simulation model The validation of the proposed PV panel model is achieved using experimental data recorded in Refs. [27,28]. In Fig. 11 (a), the data were obtained on a building integrated photovoltaic facility at the National Institute of Standards and Technology (NIST) for four different operating points of temperature and irradiance, which shows the consistency between the experimental data and the IeV
Fig. 12. Convergence speed of the proposed numerical methods.
Fig. 13. Experimental waveforms of the prototype PHILS system: (a) Load current and panel voltage waveforms, (b) Step response when the load current falls, (c) Step response when the load current rises.
J.-H. Jung / Journal of Power Sources 285 (2015) 137e145
(30%) at the operating time of 0.1 s and a load current increase from 1.25 A to 1.75 A (20%) at 0.2 s. For obtaining the sudden change of the effective irradiance, a lamp controlled by a constant voltage source was used in the experiment referred in [28]. Using a graphical inference in Fig. 11, the proposed PV panel model looks suitable for simulating the power generation of the target PV panel. 5.2. Improvement of computation and simulation speeds Fig. 12 shows the convergence speeds of the proposed numerical methods. Iteration numbers are limited to sixteen for the real-time simulation application. The average numbers of the numerical iterations for the NR method without and with the Lambert Wfunction, and the Halley's method with the Lambert W-function are 7.46, 5.73, and 4.54, respectively. Consequently, the Halley's method with the Lambert W-function could reduce the number of numerical iterations around 39% comparing with the conventional NR method. Table 1 shows the time consumptions for the model calculations of all proposed methods in the real-time simulator. In the real-time simulator, the computation speed is improved from 24 m s to 21.1 m s by the Halley's method with the Lambert W-function. In addition, using the PFV method and the preallocation of the vectored variables, the computation speed of the real-time simulation model is enhanced from 21.1 m s to 15.3 m s, which is around 28% improvement. Using the MS method with the parallel computing in the real-time simulator, the computation time of the proposed model is drastically reduced from 15.3 m s to 9.1 m s, which is around 41% improvement. In conclusion, the improvement of the computation speed caused by the proposed model development, the fast computation method, and the parallel computing is in the order of 62.5%. 5.3. Experimental result of PHILS Fig. 13 (a) shows the dynamic waveforms of the load current and the panel voltage in the PHILS system. According to the load current variation, the panel voltage simulated by the real-time simulator is generated through the programmable power supply. This electrical behavior is achieved by the proposed PHILS system to emulate the power generation from the target PV panel. Fig. 13 (b) shows the step response of the PHILS system when the load current falls. The step response consists of the response time delay, td, and the system transient time, tdyn. The response time delay includes the computation time in the real-time simulator, the transmission time in the serial communication, tsp shown in (25), and other data process time in the real-time simulator, the serial communicator, and the programmable power supply. The system transient time includes the dynamics of the real-time simulator and the programmable power supply. Amount of time td and tdyn are around 500 ms and 250 ms, respectively. Fig. 13 (c) shows the step response when the load current rises, and the values of td and tdyn are similar to the case of Fig. 13 (b). To reduce td and tdyn for proper PHILS, high speed data communication and data processing are required. 6. Conclusions The PHILS of the PV power generation was achieved using the distributed real-time simulation model and the fast computation methods such as the numerical iteration and the parallel computing. Using the Halley's numerical iteration method with the
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Lambert W-function, the convergence speed of the solution of the five-parameter PV model was improved. The PFV, the preallocation of the vectorization in variables, the MS, and the parallel computing methods were introduced for efficient computing in the real-time simulator and the PHILS system. As a result, the computation speed of the proposed PHILS system was improved in the order of 62.5% using the proposed methods, and the PHILS system properly emulated the electrical behaviors of the power generation of the target PV panel. Reducing significant delays in the PHILS system architecture will help the exact emulation of electrical behaviors of many electrical system applications under various operating conditions, which is a next goal of the proposed PHILS system.
Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF2013R1A1A1009632). I would like to thank Prof. Katherine A. Kim to provide language help and valuable advice for revision.
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