Improving Solar Power PV Plants Using. Multivariate Design Optimization. Seyed Ali Arefifar, Member, IEEE, Francisco Paz, Student Member, IEEE, and Martin ...
Improving Solar Power PV Plants Using Multivariate Design Optimization Seyed Ali Arefifar, Member, IEEE, Francisco Paz, Student Member, IEEE, and Martin Ordonez, Member, IEEE Abstract— The proliferation of PV installations across the globe has accelerated dramatically in the past decade covering home, rural, mobile, industrial, and utility scale applications. In all these cases, improving payback time and energy production for PV installations is a very complex design tradeoff that involves multiple variables such as irradiance fluctuations, inverter efficiency, operating temperature variation, and PV panel type. In this paper, a detailed multivariate study of PV plant design is presented, resulting in an improved technique to increase the potential benefits of solar plants with lower capital costs. This new approach includes detailed consideration of the probabilistic hourly temperature and solar irradiation profile of the installation site, the efficiencies and operating areas of different grid-tie inverters, and detailed models of different PV modules in the optimal design process. The harvested energy, total costs and payback time are the objective functions in this approach, while the number of series and parallel panels, the tilt angle, and inverter topology and PV module type are determined from a list of possible candidates. The optimization process is implemented for a sample system and the results are compared to both a traditional and design-software approach. It is seen that by applying the proposed approach with lower capital costs, the harvested energy, financial benefits and the payback time can be improved by 9.3%, 1%, and 6.95% respectively. Several case studies are then presented to investigate the sensitivity and robustness of the design with regard to the ambient temperature variation, solar irradiation fluctuation, and available surface area for PV module installation. Index Terms— Solar plant design, inverter, PV module, optimal design, Tabu search.
I. INTRODUCTION
A
DVANCEMENTS in the cost and performance of solar cells and power inverters have accelerated the adoption of solar power, now the third highest installed capacity renewable energy technology after hydro and wind [1]-[4]. Moreover, other factors such as emerging standards, decreasing costs of installations, and incentives such as feed-in-tariffs provided by governments [5]– [6] have increased the installed capacity of solar plants in modern distribution systems. In order to design and deploy solar power plants, a wide variety of PV modules, inverters, and power interconnection architectures can be selected for a given geographical location. These types of multivariate systems with many components present formidable design challenges. The architecture configuration can severely affect the PV power plant performance in terms of financial benefits, efficiency, investment cost, and reliability [7]–[9]. Interesting approaches to power PV plants design, analysis and operation have been published considering novel architectures [1]-[3], [7]-[19]. For instance, the work in [3] presented an algorithm for the economical design of a utility-scale PV plant, compromising between the cost of energy and the availability of the plant. Their algorithm provided optimum inverter ratings and the interconnection topology of PV panels by obtaining the plant’s peak power and the price of inverters. A methodology for optimal design of transformer-less
photovoltaic (PV) inverters designing cost-effective gridconnected PV systems was presented [10]. The optimal switching frequency as well as the optimal values and types of the PV inverter components was calculated to minimize the PV inverter levelized cost of the generated electricity (LCOE) for the PV system lifetime period. The work reported in [11] presented a methodology for designing PV plants with the objective of maximizing economic profits during the plant’s lifetime period. Their approach is suitable to be executed using high timeresolution (i.e., 1-min-average) values of the meteorological input data. Among several solar plant topologies, the solar plants based on single-stage conversion photovoltaic inverters, without the dc-dc boost stage, have become more popular due to their simplicity, high efficiency, and cost-effectiveness [12]. As an example, a method for optimal design of large PV plants, such that LCOE is minimized is presented in [13], where the type of inverter and PV panels are pre-selected for the design. In [13], the PV plant is designed by considering the impact of solar module arrangement for optimizing the lifetime cost and energy production of the plant. The published literature on solar PV plant design considers the series/parallel configuration [3], [7]-[8], [11]-[13]; tilt angle [11][13]; detailed PV module characteristic [12]; brief inverter characteristics, solar irradiance and ambient temperature [11][13]; as well as power rating of inverters ([3]) in their optimal design process. However, there are still issues remaining for solar power plant designers to reflect on for improvements. These issues include selecting the most appropriate PV modules and inverters by considering their detailed specifications (e.g. optimum operating area, efficiency, etc.), and considering the probabilistic nature of solar irradiance and ambient temperature, which can significantly affect the PV plant design in terms of harvested energy, financial benefits and payback time. The robustness of design with variation of system parameters is also imperative and is investigated during design process. This work addresses such technical challenges by proposing a new multivariate optimization approach to determine the optimal design and configuration of single-stage converter solar power PV plants. The process takes into account detailed characteristics of candidate PV modules and the efficiency curves and operating areas of candidate grid-tie inverters and selects the optimum device and system configuration for a selected location. The probabilistic nature of the solar and ambient temperature of the plant’s location and available installation area is considered in the optimal design. Tabu Search (TS) is used as the optimization approach for three different objectives including: maximizing annual harvested energy, maximizing total financial benefits and minimizing the payback time. Several case studies are also presented to investigate the robustness of the design in case of variation of ambient temperature, solar irradiance and available area. The contributions of the paper to the research field can be summarized as follows.
Fig. 1. Proposed versus traditional approach for designing PV solar plants. The harvested energy (MWH/year), financial benefits (K$) and payback days can be improved with the proposed approach, by considering detailed design characteristics and different options for selecting inverter and PV modules.
Accounting for detailed characteristics of various grid-tie inverters in PV plant design including efficiency curves and operating area, Including detailed characteristics of PV panels at different operating points (not limited to MPP) for designing PV plants, Factoring the probabilistic nature of solar irradiance and ambient temperature in designing PV plants, Considering lists of commercially available PV panels and gridtie inverters as candidates for designing PV plant, Performing several sensitivity studies to investigate the sensitivity and robustness of the design in case of variation of ambient temperature, solar irradiation and available area for installation of PV modules. Fig.1 shows the advantages of the proposed design approach over the traditional methods, for a sample case study presented in the paper. As shown in this figure, by considering different objectives for designing the PV plants, the financial benefits of the solar PV plant can be increased by one percent (from $102k to $103k), the payback period can be shortened by 6.95% (from 2503 days to 2329 days), and the harvested energy can increase by 9.30% (from 51.6MWh per year to 56.4MWh per year). These values are related to the sample study presented in this paper and could be different but similar for other systems. The paper is organized as follows. The system components and design considerations are presented in Section II. The formulation of the problem is explained in Section III and the solution algorithms are presented in Section IV. The optimal design procedure is implemented for a sample system in Section V and the results are compared with the results of traditional approaches. The robustness of the design in terms of ambient temperature, solar irradiation and available area is investigated by performing sensitivity studies in Section VI and finally, the paper is concluded in Section VII. II. SYSTEM COMPONENTS AND DESIGN CONSIDERATIONS The PV module characteristics, grid-tie inverter characteristics and the need for having an optimization procedure for the design are explained in this section. A. PV Module Characteristics A PV module consists of a number of interconnected solar cells forming a single unit. To model current-voltage (I-V) or power voltage (P-V) characteristics of PV module, the I-V or PV characteristics of a single solar cell should be determined and
I + Irr ID
VD -
Rs Rp
+ V -
Fig. 2. General model of a solar cell including parallel and serial resistors.
then expanded to obtain the behavior of a PV array or module [20]. A solar cell is traditionally represented by an equivalent circuit composed of a current source, an anti-parallel diode, a series resistance Rs and a shunt resistance Rp, [21], as shown in Fig. 2. The current Irr in Fig.2 is the irradiance current which is generated when the cell is exposed by sunlight and is dependent on the solar irradiance and temperature, shown in (1). G (1) 1 T (T Tref ) I irr I irr _ ref Gref where G and T are the solar irradiation (kW/m2) and cell temperature. The subscript ref represents the standard reference conditions and T represents the rate of change of the shortcircuit current with respect to temperature and is usually provided by the manufacturers. The cell temperature is a function of changes in the ambient temperature and changes in the insolation as shown in (2) [21]. NOCT 20o C (2) T Tamb G 0.8 where Tamb is the ambient temperature and NOCT represents the nominal operating cell temperature provided by the manufacturer. G represents the solar irradiation at the ambient temperature, Tamb. In Fig. 2, ID is the current of the anti-parallel diode, which characterize the nonlinearity of the solar cell, and is a function of diode’s voltage and temperature, calculated as shown in (3).
qVD (3) I D I 0 e nkT 1 where q is the electronic charge (q =1.602 × 10−19 C), k is the Boltzmann constant (k =1.3806503 × 10−23 J/K), n is the ideality factor or the ideal constant of the diode and T is the temperature of the cell. The ideality factor (n) represents the different mechanisms of moving carriers across the junction.
Fig. 3. Variation of voltage-power characteristics of PV array with variation of (a) solar irradiance and (b) temperature.
If the transport process is purely diffusion, n will be 1 and if it is primarily recombination in the depletion region, n will be 2. As an example, for silicon, n will be 1.3 [22]. I0 is the diode saturation current or cell reverse saturation current and is calculated as shown in (4). 3
qEg _ ref
qEg
T nkTref nkT (4) I 0 I 0 _ ref e Tref where Eg is the bandgap energy (eV) and depends on the materials used for manufacturing the cell. As an example, for silicon, this value is calculated as shown in (5) [23].
T2 (5) Eg 1.16 7.02 104 T 1108 I0_ref is the reference diode saturation current and can be approximately obtained using the PV cell’s open circuit voltage (Voc) and short circuit current (Isc) as shown in (6). qVoc (6) I o _ ref I sc e nkNOCT 1 Therefore, the relation between the voltage and current of the PV cell can be. q (V IRs ) V IRs (7) I I irr I 0 e nkT 1 Rp And for a PV panel with Ns number of series cells and Np number of parallel cells we can rewrite (7) as (8). q (V IRs Ns N p ) V IRs N s N p nkT (8) I N p I irr N p I 0 e 1 R N N p s p In this equation Ns represents the total number of series cells, which is the number of series cells in each module/array multiplied by the number of series modules/arrays, and Np represents the total number of parallel cells which is the number of parallel cells in each module/array multiplied by the number of parallel modules/arrays. The V-I relationship of a PV panel shown in (8) can be used to obtain the voltage-power relationship of a PV plant in different ambient temperature and solar irradiance and determine the maximum power point of the PV plant. In cases that the resistive parameters, Rs and Rp, are not provided by the manufacturer of the PV panels, the equations can
be simplified by setting them as zero and infinity, respectively. As an example, the voltage-power characteristics of a PV array consisting of 72 PV cells connected in series is shown in Fig. 3. The voltage-power curves change significantly with variation of solar irradiance and PV panel temperature. B. Grid-Tie Inverter Characteristics The optimal selection of the PV plant is influenced by the characteristics of the grid-tie inverter, which determine the usability of the array through the complete period of time. Namely, these characteristics are: 1) the operating region of the inverter; 2) the efficiency of the inverter; and 3) the relative availability of each operating point through the year. In Fig. 4, the operating region of the converter is illustrated as a function of the load and the PV array voltage (input voltage to the inverter). The minimum input voltage is given by the modulation strategy implemented. For a SPWM with third harmonic injection, the maximum modulation index (ma) is given by
ma
Vˆo 1.1547 V pv
where Vˆo is the peak output voltage and
(9)
V pv is the voltage at the
output of the PV panel (DC input of the inverter). Equation (9) yields a minimum V pv which allows the inverter to operate, and which is given by
V pv,min Vˆo / 1.1547
(10)
The maximum open circuit voltage is the maximum voltage that the PV array can have without damaging the inverter. This is given by the rating of the semiconductors selected. The maximum rated voltage (Vrated) determines the maximum voltage at which the inverter can output the full rated power. The inverter will need to work at any operating point that is within or in the boundary of the operating region. The efficiency of the inverter at different operating regions is shown by the isolines. As can be seen, the same input power can be transferred more efficiently if the operating point lands in a region of higher efficiency. As can be seen, the same input power can be transferred more efficiently if the operating point lands in a region of higher efficiency. For example, in Fig. 4, points A and B yield the same input power but point A is in an area of higher efficiency, resulting in higher
Fig. 4. Operating region of the PV inverter as a function of the input voltage; the efficiency at every operating point is indicated.
Fig. 5. Efficiency as a function of the load, for different operating voltages.
output power. Considering the effort that has been invested in increasing the accuracy of MPPT algorithms, selecting the optimal operating region in terms of efficiency is a key result. The efficiency curves outlined in Fig. 4 are characteristics of each inverter, especially regarding the selected topology and power components. When the inverter is selected from a pool of commercially available devices, these curves will be provided by the manufacturer. If the inverter under consideration is being designed in house, the curves have to be calculated. In any case, the equations that define the power losses and efficiency provide useful design insights into the causes of the reduced efficiency under different operating conditions. For a topology that has several power semiconductors, the losses in the i-th device are given by Pt ,i Pcond,i Psw,i (11) Where
Pcond ,i is the conduction losses in the i-th device and Psw,i
are the switching losses in the i-th device. The Pcond ,i is given by 2 Pcond,i Von,i I ave,i Ron I rms ,i
(12)
While the switching losses are given by [24]
Psw
f sw Ts k i idt 2 0
(13)
Where fsw is the switching frequency, Ts is the fundamental period, ki is the switching energy divided by the current and i is the current through the device. The efficiency is given by
( Pin Ploss ) Pin
(14)
The capture in Fig. 5 shows the typical efficiency curves of a grid tie inverter for constant input voltage (a vertical cut through Fig. 4). Depending on the operating region, the efficiency of the curve is dominated by a source of losses: in Region I (light load condition) the losses are dominated by switching, while in Region II the losses are governed by the conduction losses. The higher efficiency is achieved in the region in the middle. For higher voltage, the efficiency is lower due to the increment in the switching losses caused by the dependency of the Total Switching Energy (Etotal) on the voltage.
Fig. 6. Variation of maximum, average and minimum of ambient temperature for a one year period
Considering the operating region and the efficiency of the inverter in each region will lead to a more efficient use of the PV installation. In cases that the detailed parameters of the inverter is not available for calculation of inverter’s efficiency, the efficiency table provided by the manufacturer could be used and interpolated to generate the efficiency curves for all operating voltages and powers of the device. C. Design Considerations Several factors should be considered in designing solar plants. As mentioned in the previous sub-sections, the PV panel has different voltage-power characteristics at different temperatures and solar irradiance levels. For a sample location for this research, the variation in temperature and irradiance over a oneyear period is plotted in figures 6 and 7. Moreover, the grid-tie inverters have an operating area and, within the operating area, they have different efficiency curves. In order to achieve the maximum benefits from a solar power plant, the inverter, the PV modules and the number of series/parallel PV modules should be appropriately selected.
Fig. 7. Maximum and average solar irradiance for a one year period.
An example of the variation of the voltage-power characteristics of a PV array as a function of the number of series (Ns) and parallel (Np) modules, and the inverter’s operating area are plotted in Fig. 8. It is seen that by changing the number of series/parallel PV modules for a selected type of PV module and inverter, the possible operating points will change significantly. In general, the operating point for each selected inverter, PV module, Ns and Np, should be on the power-voltage curves of the PV module and simultaneously inside the inverter’s operating boundaries. The operating voltage will determine the operating point for the inverter and the PV module; therefore, it should be selected so that the operating point falls within the operating boundaries of the inverter, on the maximum efficiency curve and on the power-voltage curve of the PV module. A simple search algorithm is implemented in this research for this purpose, as follows: for V = 0 to VPV_max if Vinv_min < V < Vinv_max Pout(V) = ηinv(V) × PPV(V) end end Pmax = max(Pout) Voperation = V(Pmax) where VPV_max, Vinv_min, Vinv_max, Pout, ηinv PPV(V) are the maximum open circuit voltage of PV modules, the minimum and maximum operating voltages of the inverter, the output power of the solar plant, the efficiency of the inverter and the output power of the PV module, respectively. Pmax is the maximum output power of the PV plant and Voperation is the operating voltage of the inverter and the PV panel. The mathematical formulations used to calculate the parameters mentioned in the search algorithm are explained in Section III. The search algorithm will determine the operating point, and it is clear that the selection of the number of series and parallel panels, as well as the selection of the inverter’s operating area, will significantly affect the operating point and the total energy that can be captured from a solar plant. Moreover, the variation of the PV modules voltage-power characteristics, combined with variation in temperature and irradiance for the design period and the variation of operating boundaries and
Fig. 8. Variation of voltage-power characteristics of PV panel array with the variation of number of series (Ns) and parallel (Np) modules.
Fig. 9. The probabilistic approach to calculating the total captured energy.
efficiency curves of different inverters, further manifests the need to incorporate such details into modeling, as well as the need for an optimization procedure to maximize the benefits obtained from a solar plant. III. FORMULATION OF THE PROBLEM The design problem defined in Section II is formulated in this section as an optimization problem with different objectives. The optimization constraints and control variables are also explained here. A. Optimization Objective Function Considering different types of solar cells, grid-tie inverters and different temperature and solar irradiance profiles, three different objectives can be considered in designing a solar power plant. The first objective function (F1) is set as the total energy that can be captured from the solar plant during the lifetime period of the solar modules. The probabilistic approach to calculating the total captured energy is shown in Fig. 9. Starting from left to right, we have 25 years of the solar panel’s lifetime, and each year has 365 days and each day has 24 hours. For each hour of the day, the historic data can be used to create a probabilistic function for temperature and irradiance. The probabilistic functions will show the probability that the temperature or solar irradiance will be a specific value. Then, such functions, if not already discrete, can be digitized into different states, where each state has its own probability of occurrence. Irrj is the probability of solar
irradiance to be in state “j” and
T
i
is the probability of
temperature to be in state “i”. In this research, the probabilistic functions are divided into 12 sections in order to create probability states of solar irradiance and temperature. Increasing the number of states will increase the calculation time, while decreasing the number will reduce the accuracy of the results. With selection of 12 states, for each hour we will have 12*12 probabilistic states, where the probability of occurrence of each state will be the product of the two probabilistic states of solar irradiance and temperature. The total harvested energy, then, can be calculated by calculating the energy for each state and accumulating it by using the probability of each state. Therefore, the first objective function (F1) can be calculated using the following steps. The output power of PV plant consisting of Ns×Np number of PV modules of type NPV at a specific time of year (Y), day (D) and time (T) can be calculated as shown in (15).
PPV [1 Y r (Y )][1 df ] N Irr NT
P Ns, Np, , Y , D, T , I j 1 i 1
PVr
rr
, T , N PV Irrj Ti
(15)
where r(Y) is the annual reduction coefficient of the PV module in % per year; df is the PV module output power derating factor due to the dirt that is deposited on its surface (derating up to 6.9% has been reported for large-scale PV plants in [25]); PPVr is the rated power of PV module, β is the tilt angle of modules, Irr and T are irradiance and temperature at the probabilistic state i,j, and ρIrr and ρT are the probability of irradiance and temperature of state i, j in day D and time T. Finally, NPV represents the PV module number that is selected from a list of candidates. Since the PV plants are assumed to be connected to the grid through a grid-tie inverter, the energy that is transferred to the grid at that specific time period (Δt) will be: (16) E Plant PPV Inv PPV ,VPV , N Inv t where ηInv is the efficiency of inverter at the operating point of PPV and VPV and NInv represent the inverter number that is selected from a list of candidates. Since hourly time steps of solar irradiance and temperature is used in this research, Δt will be 1. Therefore, the first objective function (F1) which is the total energy captured from the solar plant during the lifetime of the PV modules can be calculated as shown in (17) F1
NY 365 24
E Y 1 D 1 T 1
NY 365 24
P Y 1 D 1 T 1
PV
Plant
(17)
( Ns, Np, , Y , D, T , N PV ) Inv PPV ,VPV , N Inv
F1 is a function of PPV and ηInv and NY represents the lifetime of the solar modules. PPV is a function of number of series/parallel PV modules, tilt angle, day of year and time of day and the PV module’s characteristics. Also, the efficiency of the inverter is a function of output voltage and power of PV module and the inverter’s characteristics. The second objective function (F2) can be defined as the costs or the total benefits obtained during the lifetime of the solar plant. For formulating this objective function, the information on the installation and operation and maintenance costs of solar plants and inverters and the price of energy is required. The total costs
of the solar plant for the lifetime of the solar modules can be written as (18), which includes the installation costs (ICst) as well as NY years’ operation and maintenance costs (CO&M).
Costs I Cst YN CO&M (18)
CInv N s N p Pr CPV YN CO&M _ Inv N s N p Pr CO&M _ PV
where CInv CPV, Pr, CO&M_Inv and CO&M_PV are the inverter installation costs, PV module installation costs, the rated power of each PV module, and the annual operation and maintenance costs of the inverter and PV panels, respectively. Having the total installation and operational costs of the solar plant, the second objective function which is the total financial benefits obtained from the solar plants can be formulated as (19),
F2
YN 365 24
E Y 1 D 1 T 1
Plant
CE (Y , D, T ) Costs
(19)
where CE is the cost of energy at time T day D and year Y and EPlant is calculated in a similar way as in (17). And finally the third objective function (F3) can be set as minimizing the payback time period required for installation of a PV plant. The payback period is the length of time required to recover the cost of the plant. Therefore, it ends when the financial benefits achieved by the PV plant are equal to the total costs of the plant. In other words, it ends when F2, which is initially negative, equals zero and starts to increase to a positive value. This objective function can be formulated as shown in (20). (20) F3 Y 365 D s.t. F2 0 Depending on the requirements of the plant designer, each of the three objectives, or a combination of them, can be used to produce an optimal design for the solar plant. Since the dimensions of the objective functions are not the same, their normalized values can be combined to form a single objective function by using weighting coefficients as shown in (21).
F K1
F1 F1Opt F1Opt
K2
F2 F2Opt F2Opt
K3
F3 F3Opt F3Opt
(21)
The optimum values are calculated by using each objective functions individually. In other words, to get the F1Opt, K2 and K3 should be set as zero and the objective function will be F1Opt. The same should be done to get F2Opt and F3Opt. The selection of K1, K2 and K3 will determine whether the target of the objective function is to maximize harvested energy, financial benefits or the payback period. B. Optimization Decision Variables In order to achieve the optimum design, some decision variables should be determined; these variables are listed as follows: 1) The first variable is the type of PV module chosen from a list of candidates. Besides its cost, each PV module has its specific characteristics in terms of physical size, open circuit voltage and short circuit. Therefore, the optimum module should be selected in terms of current, etc. Its selection will affect the objective functions,
2) The second decision variable is the inverter. Like the PV module, each inverter has an affect on the defined objective, 3) The next set of parameters to be selected is the number of series and parallel PV modules that should be put in a specific area, 4) Finally, the tilt angle of the module should be determined to enable the optimum performance of the PV plant. To summarize, the decision variables can be written as the following vector. (22) Z N s N p N PV N Inv where NPV and NInv represent the PV module number and inverter number that are selected from a list of candidates. For instance, if we have 10 types of PV modules to select from, NPV could be a number between 1 and 10. Since the characteristics of each PV module and inverter are pre-determined by the manufacturer, only their selection from a look up table is considered as the decision variable and the detailed properties (e.g. power rating, cost, etc.) are determined based on the selected device. C. Optimization Constraints Several constraints can be considered in the design process. These constraints can vary from the initial installation costs of the whole system or each part to the limitations of available installation area, shown in the following. (23) ICst Budget
Ns N p SPV Available Area
(24)
(25) N PV Number of PV Candidates (26) N Inv Number of Inverter Candidates where ICst and Budget represent the installation costs and the related budget limit, respectively and SPV is the required area for installing one module of PV. NPV and NInv are the candidate numbers of the selected PV module and inverter from the candidate list, respectively. Such values should be less than the maximum number of available PV module and inverter types. As will be explained in the next section, at each iteration stage all these conditions should be satisfied. IV. SOLUTION ALGORITHMS The problem defined in Section III is a mixed integer nonlinear problem demanding intelligent solution algorithms. In this paper the Tabu Search (TS) is used for finding the optimum solution and is explained in details in this section. TS is a heuristic search algorithm that uses different memory structures to find the optimum solution [26]-[27]. It is an iterative-based algorithm in which the optimization process starts with a feasible solution and continues searching in the neighborhood until a certain criterion, which is usually the maximum number of iterations, is reached. The flowchart of the algorithm is shown in Fig 10. The first step in TS is to select the starting point. The starting point can be selected as a decision variable with arbitrary but feasible values. In order to implement the TS and explain it in a more clear way, the decision variables explained in (22) are represented as binary digits shown in the following vector: Ns
Np
N Inv
N PV
Z [1 ...1 1 ...1 1 ...1 1 ...1 1 ...1]
(27)
Set Z = [0 1 0 1 ….1 0] as the starting point
Create a neighbour for Z by ITM that satisfies constraints (23)-(26)
# of neighbou rs Reached? Extract the parameters Ns,…NInv from vector Z of each neighbor
Select the best vector Z as the local optima, if not in the TL and save the local optima in TL
Calculate the objective function for the neighbours using (15)-(21)
Yes Maximum Iterations?
The best Local Optimum is the Global Optimum
Similar Recent Local Optimums
Jump to a new region using LTM
Set the recent local optimum as the new starting point and update ITM Fig. 10. The flowchart of the proposed Tabu Search based algorithm for designing PV solar plants
In this vector, the set of digits represents Ns, the second set represents Np and the last set represents NPV. The size of each set depends on the maximum value that each parameter can have. For instance, if the number of candidate PV modules is three, then we need two digits to represent all the candidates. The second step is to define moves and create a set of neighbors for the starting point. A. Definition of Moves and Neighborhood The search process from one vector of a trial solution to another is called a move. The set of all possible moves out of a current solution is called the neighborhood or candidate list. Defining the vector Z as a vector of binary digits will make defining the set of neighbors straightforward. For each new neighbor a few number (e.g. 1 to 5) of components of the Z vector are set from 0 to 1 or vice versa. By performing this for a number of times (depending on the desired number of neighborhood) a list of candidates will be generated and the objective function should be calculated for all of them. It should be noted that only the moves or trial vectors of Z are acceptable that satisfy the optimization constraints explained in Section III-C. Moreover, the moves that will lead to the solutions in Tabu List, explained in the next section, are also prohibited.
B. Tabu List (TL) and Aspiration In order to prevent a return to the local optimum just visited and to avoid cycling, the reverse move that is detrimental to achieve a better solution must be forbidden. Tabu restrictions are enforced by a Short-Term Memory (STM) called Tabu List, i.e. a list containing forbidden moves, which allows the search to go beyond the local optimal points while still making the best possible move in each iteration. In this work, the forbidden moves are introduced to the TL by recording numbers that correspond exclusively to each forbidden move. In this research, the TL is constructed from the best recently visited solutions. In order to save memory and accelerate the search process, instead of saving the vectors, a quantity which is unique for each vector Z could be calculated as shown in (28) and saved in TL. LZ
Z (i) 2
i
(28)
i 1
where LZ represents the length of vector Z. Each TL is initially empty, constructed in the first LTL iterations (LTL is Tabu length) and updated in later iterations. The Tabu length plays an important role in finding a good solution. If the Tabu length is too small, cycling may occur in the search process; and if it is too large, higher-quality solutions cannot be explored. In general, the Tabu length should grow with the size of the given problem and is usually determined experimentally. In some cases, a Tabu move can be allowed to have better results. An aspiration criterion is used in such cases to allow Tabu moves to be released. In this work, the aspiration criterion is defined as: if a Tabu move produces a better solution than the best solution so far obtained, the Tabu move will be released and the solution produced by it is viewed as the next trial solution. Briefly, the next solution is chosen from the neighborhood set which is either an aspirant or not Tabu and for which the objective function is optimal. C. Intensification and Diversification To prevent the search becoming an iterated random sampling, Intermediate-Term Memory (ITM) is employed to intensify the search in the neighborhood of the suboptimal solution. Intermediate-term memory records features of a selected number of best trial solutions generated during a particular period of search. Common features of these solutions are taken to be a regional attribute of good solutions. The method then seeks new solutions that exhibit these features by restricting moves during a subsequent period of regional search. In this work, intermediateterm memory is implemented by recording the number of times each component of vector Z has been changed in the past previous best solutions. A more frequently repeated value corresponds to a common feature of the previous solutions. Then, the subsequent moves are restricted to increase the probability of this common feature appearing in the next solutions. For instance, if the third component of vector Z in the past previous best ten solutions has been 8 times one and two times zero, in the next move, the third component of Z should have an 80% chance of being one and a 20% chance of being zero. This can be easily implemented by modifying the rand function in MATLAB that generates random values between zero and one. For this specific example, if rand generates values greater than 0.2, we can assign one as output and, if less than 0.2, we can assign zero as output. When the objective function does not improve during a number of successive iterations, the Long-Term Memory (LTM)
TABLE I. SAMPLE COMMERCIAL PV INVERTER CHARACTERISTICS Inverter Parameter I1 I2 I3 I4 I5 Prated (kW) 12.6 15.6 17.6 20 25 Vmin (V) 380 360 400 320 390 Vrated (V) 800 800 800 800 800 Vmax (V) 1000 1000 1000 1000 1000 Cost ($) 2888 3334 3575 3576 4022 TABLE II. SAMPLE COMMERCIAL PV PANEL CHARACTERISTICS PV Module Parameter PV1 PV2 PV3 PV4 PV5 SPV (m2) 1.63 1.92 1.67 1.67 1.64 Power (W) 250 305 260 255 245 Vmpp (V) 30.72 36.3 30.7 30.77 30.7 Impp (A) 8.15 8.41 8.56 8.37 7.98 Voc (V) 37.59 44.8 38.9 37.83 37.3 Isc (A) 8.65 8.97 9.18 8.9 7.98 TCIsc (%/C) 0.073 0.065 0.04 0.04 0.05 TCVoc (%/C) -0.31 -0.34 -0.3 -0.3 -0.35 TCPmax (%/C) -0.431 -0.43 -0.41 -0.42 -0.45 Ns 60 72 60 60 60 Type Mono Poly Mono Poly Poly Cost ($) 300 300 271 265 280
is employed to escape the local optimum and to diversify the search to unexplored regions of the solution space. To achieve diversification, the algorithm uses the same data used in implementation of the intensification function. In this case, in contrast to the intensification case, the next move is restricted to produce a new trial solution (as a start point in a new search region) that includes different features from those found in the previous solutions. This long-term memory has been implemented in this research in an approach similar to the approach used for intermediate-term memory. The goal is to avoid similar starting points; therefore, the subsequent starting points are restricted to decrease the probability of the common features appeared in the previous starting points. For the specific example mentioned for intermediate-term memory, if rand generates values greater than 0.2, we can assign zero as output and, if less than 0.2, we can assign one as output. The TS algorithm stops after reaching the maximum number of iterations, which depends on the size of the problem and is usually set through experimentation. More information about the characteristics of TS and its implementation can be found in [26] and [27]. V. SOLAR PLANT DESIGN Three different objectives are explained and formulated in Section III. At this stage, considering different options for inverters and solar panels, the solar plant is designed for each objective function individually and the final design is compared with the results of traditional approaches suggested by inverter manufacturers [28] as well as commercially available PVsyst software [29]. A. System Components The PV system is composed of a group of PV panels connected in parallel and series along with one or more inverters. For this research it is assumed that the inverter and PV panel are to be selected from a list of candidates. Table I shows a summary of characteristics of five commercially available inverters, including operating ranges. The characteristics of five commercially available PV panels are also included in Table II. The different operating areas of the PV inverters combined with
TABLE III. PV PLANT DESIGN RESULTS Design for Energy Benefits Payback
Area Limit No Yes No Yes No Yes
Ns
Np
Inv
PV
17 13 19 19 23 19
12 4 6 3 4 3
I5 I5 I5 I4 I5 I2
PV2 PV2 PV3 PV3 PV3 PV3
A (m2) 390 100 191 96 154 96
ICst (K$) 69.2 24.4 39.1 22.6 33.2 22.1
F1 (MWh/y) 56.4 29.6 51.9 29.2 46.7 29.0
F2 (K$) 69 57.5 103 58.1 96 57.8
F3 (Days) 4558 2664 2481 2557 2329 2494
the different characteristics of the PV modules gives an additional degree of freedom to the configuration of the PV system. It should be noted that both inverter and PV candidate lists could include more options and the same approach could be used to find the optimum design. B. Optimal Plant Design In order to design the solar plant, the information about the location of the panels should be available in terms of temperature and solar irradiance. For the case studies presented in this paper, the data recorded by The National Renewable Energy Laboratory (NREL) at Solar Radiation Research Lab (SRRL) with the GPS information of 39.742N and 105.18W is used [30]. The installation cost, yearly operation and maintenance costs of the solar PV plant and the cost of energy are considered to be 1200$/kW, 19$/kW and 0.12$/kW, respectively. Two different set of cases are investigated. In the first set, it is assumed that there is no limit on the available area and in the second set, it is assumed that the available area is limited to 100 square meters. Different objective functions are considered and their effect on the final design are investigated. The Tabu Search algorithm explained in Section IV is applied and the optimum design results, with and without limitations on the available area, are presented in Table III. In all the case studies in this paper, the optimum value for β was selected as 40-south; therefore, it has not been reported in the tables. It can be seen that, depending on the objective function selected, the PV plant orientation and the selected PV panel and inverter are different. With the objective of maximizing the amount of harvested energy per year (F1), without an area limit, 390 m2 is required and inverter 5 and PV module 2 should be selected to have 56.4 MWh/y. In this case, the payback time is the longest and the financial benefits over the 25-year lifetime of the plants will be lowest ($69000). With an area limit of 100 m2, the same inverter and PV module should be selected, but with a different number of series/parallel modules. In this case, we have 29.6 MWh/y harvested energy, $57500 in financial benefits and 2664 days as a payback period. Similarly, when the objective is to maximize financial benefits without an area limit, 166 m2 is required; this produces a lower amount of harvested energy compared to the first case, but the financial benefits will be $103000 and the payback time is significantly shorter. For the same case with an area limit of 100 m2, the amount of harvested energy will be 29.2 MWh/y, which is less than in the first case. The financial benefits and payback time will be $58100 and 2557 days, respectively. Finally, with the objective of minimizing the payback time period, without an area limit, the area will be 134 m2, and by minimizing the payback time to 2329 days, the amount of harvested energy and the total financial benefits will be less than in the second case. The results of a similar case considering the area limit are also presented in Table III, which shows different designs with minimal value for the payback period. This table is provided to show how the
Fig. 11. Variation of voltage-power characteristics of PV array and inverter for a one year period.
optimal design will vary according to variations in the objective function and area limit constraints. In practice, there are usually limitations on the available area for installing the solar plants; therefore, for the rest of the paper, the available area has been limited to 100 m2. The PV panel voltage-power curves for 12 days (one day for each month) and the inverter’s operating area for the case that the objective is to maximize the harvested energy (F1) and the available area is 100m2 are plotted in Fig. 11. It is seen that in some cases the maximum power of the inverter is lower than the maximum power that can be generated by the solar plant. In such cases, the operating point will stay on the operating area of the inverter. Also, it is seen that the maximum open circuit voltage of the plant is less than the maximum voltage of the inverter. This is due to the consideration of the inverter efficiency curves and the derating of the inverter output power after the rated voltage. C. Comparison with Traditional Approaches The results of two traditional approaches to designing PV plants are presented in Table IV, along with the results of the proposed approach. The traditional methods are the design approach suggested by solar inverter manufacturers and the design approach used with PVsyst software. The approach used in PVsyst software is not accessible; however, the approach proposed by the SMA solar inverter manufacturing company is explained briefly in this section and a full description of their approach could be found in [28]. The traditional approach is to not provide the optimum inverter and PV module types. When using a predefined inverter and PV module type, the following steps can be followed to determine the number of series and parallel PV modules in a PV power plant. 1- Determining the Maximum Open-Circuit Voltage of a PV Plant - by using the lowest temperature open-circuit voltage and the temperature coefficient, 2- Determining the Minimum MPP (maximum power point) voltage – by using the highest temperature open-circuit voltage and the temperature coefficient,
TABLE IV. COMPARISON OF PV PLANT DESIGN RESULTS Design Approach Proposed-1 Proposed-2 Proposed-3 Traditional PVSYST
Ns
Np
Inv
PV
17 19 23 23 17
12 6 4 5 3
I5 I5 I5 I5 I5
PV2 PV3 PV3 PV3 PV3
A (m2) 390 191 154 193 97
ICst (K$) 69.2 39.1 33.2 39.2 21.7
F1 (MWh/y) 56.4 51.9 46.7 51.6 26.0
F2 (K$) 69 103 96 102 49
TABLE V. PV PLANT DESIGN FOR VARIOUS AVERAGE TEMPERATURES F3 (Days) 4558 2481 2329 2503 2720
3- Determining the Maximum PV Module Current - the maximum PV module current can be calculated by using the high temperature short-circuit current and the temperature coefficient, 4- Determining the Number of Series PV Modules – the maximum and minimum number of series PV modules can be calculated from the maximum open circuit voltage and minimum MPP voltage of a panel. As a rule of thumb in traditional approaches: the more series PV modules, the more viable the planning of the PV plant, 5- Determining the number of parallel panels – the number of parallel panels is determined from the ratio of the total solar PV plant power (predefined and equal to the inverter’s input power) and the power of all the series PV modules (by using the Maximum PV Module Current). The main difference between the proposed and traditional approaches is in the selection of optimum PVs and inverters, as well as in the detailed consideration given to the operating conditions of the PV modules and inverter, rather than just using the nominal, maximum and minimum values. Additionally, another main difference is in the consideration of detailed design parameters, such as the probabilistic nature of solar irradiance and temperature rather than using maximum and minimum temperature and solar irradiance. Although the results for the traditional and proposed approach are compared in Table IV and may look similar in some respects, this comparison is not made on the same basis. The reason for this, as explained before, is that the traditional methods do not provide the optimum inverter and optimum PV module. One may select other (non-optimum) PV modules and inverters for designing a solar plant, and will get different results. In fact, the PV and inverter used for the traditional approach in the table are copied from the results of the proposed algorithm. Therefore, there is no common base for comparing the proposed approach with traditional ones; however, in order to show how taking detailed models and probabilistic data into account will affect the design even when using the same devices, such comparisons have been presented. It is seen that the suggested values for Ns and Np are 23 and 5 with the inverter manufacturer’s guideline and 17 and 3 with PVsyst, respectively which are different than the results of the proposed algorithm. Comparing the results in terms of the objective functions defined in this paper, shows that by using the proposed approach, other than optimally using the available area and selecting the optimum inverter and optimum PV panels automatically, the annual harvested energy will be increased, the total financial benefits will increase and the payback time, will be improved by lower initial costs. It can be seen that the proposed design procedure by considering detailed properties of the inverter, PV module and the wide range of irradiance and temperature, provides more efficient results.
Temp. Ave. (%) -30 -20 -15 -10 -5 -3 +3 +5 +10 +15 +20 +30
Ns
Np
Inv
PV
13 13 13 13 19 13 13 19 19 19 13 13
4 4 4 4 3 4 4 3 3 3 4 4
I4 I4 I4 I4 I3 I4 I4 I2 I2 I2 I3 I4
PV2 PV2 PV2 PV2 PV3 PV2 PV2 PV3 PV3 PV3 PV2 PV2
A (m2) 100 100 100 100 96 100 100 96 96 96 100 100
ICst (K$) 22.8 22.8 22.8 22.8 22.6 22.8 22.8 22.1 22.1 22.1 22.8 22.8
F1 (MWh/y) 34.15 32.63 31.87 31.07 29.88 29.99 29.07 28.45 27.75 27.03 26.19 24.84
F2 (K$) 72.18 67.61 65.32 62.93 60.00 59.69 56.91 56.19 54.09 51.94 48.28 44.25
F3 (Days) 2184 2301 2341 2388 2455 2484 2623 2592 2655 2708 2925 3078
VI. ROBUSTNESS OF THE DESIGN In this section the robustness of the design is evaluated for different design conditions. Three different scenarios are investigated independently and the optimum results in each case are presented to demonstrate the effect of such variations on the optimum design and assess the robustness of the design. The design objective in all case studies presented in this section is to achieve financial benefits (F2), and the bolded values in the tables indicate that the values remain unchanged and that the design has been robust in that specific case. A. Ambient Temperatures Impact The ambient temperature will affect the optimum design parameters. In order to better illustrate such impacts, the temperature data for the data related to the base case (Section V) have been altered and the problem is solved. For this purpose, the temperature has been changed in terms of the daily average with fixed variations as well as in terms of variance with fixed average values. The formulations used to update the temperature series to give them the same average but different variance is presented in the following. 1 n (29) Var1 ( X 1i X )2 n 1 i 1 Var2 a Var1
a n 1 n ( X 1i X )2 ( X 2i X )2 (30) n 1 i 1 n 1 i 1
Where X1 and X2 are the original and updated temperature series, respectively, and X is the fixed average temperature value for the original and updated temperature series. By solving (30) for each X2i, we will have: (31) X 2i X a X X 1i Equation (31) generates two results for X2i; in order to obtain more meaningful results, the X2i that is closer to X1i is selected to update the temperature series. Therefore, (31) has been modified as shown in (32). (32) X 2i X a X X 1i The average of ambient temperature as well as the variance of daily temperature is changed from -30% to 30% and results are presented in Table V and Table VI. As can be seen the optimum design will be valid with the variation of temperature average for certain values and will be robust for variation of temperature variance (bolded values). This means that the variation in average temperature will more significantly affect the optimum design. For different locations with different average temperatures, the optimum designs are similar; however, the plant could be re-
TABLE VI. PV PLANT DESIGN FOR VARIOUS TEMPERATURE Temp. Var. (%) -30 -20 -15 -10 -5 -3 +3 +5 +10 +15 +20 +30
Ns
Np
Inv
PV
19 19 19 19 19 19 19 19 19 19 19 19
3 3 3 3 3 3 3 3 3 3 3 3
I4 I4 I4 I4 I4 I4 I4 I4 I4 I4 I4 I4
PV3 PV3 PV3 PV3 PV3 PV3 PV3 PV3 PV3 PV3 PV3 PV3
A (m2) 96 96 96 96 96 96 96 96 96 96 96 96
ICst (K$) 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6
F1 (MWh/y) 29.42 29.36 29.33 29.30 29.27 29.26 29.22 29.21 29.18 29.14 29.11 29.05
F2 (K$) 58.62 58.44 58.35 58.26 58.17 58.13 58.02 5798 57.89 57.8 57.7 57.5
TABLE VIII. PV PLANT DESIGN FOR VARIOUS AVAILABLE AREAS F3 (Days) 2522 2533 2539 2545 2552 2554 2561 2563 2568 2573 2579 2589
TABLE VII. PV PLANT DESIGN FOR VARIOUS IRRADIATIONS Irradiance (%) -20 -15 -10 -5 -3 +3 +5 +1 0 +15 +20
Ns
Np
Inv
PV
19 13 19 17 19 13 13 13 19 13
3 4 3 3 3 4 4 4 3 4
I1 I2 I2 I4 I2 I4 I4 I4 I4 I4
PV3 PV2 PV3 PV2 PV3 PV2 PV2 PV2 PV3 PV2
A (m2) 95 100 96 98 96 100 100 100 96 100
ICst (K$) 21.2 22.3 22.1 22.5 22.1 22.8 22.8 22.8 22.6 22.8
F1 (MWh/y) 23.00 24.81 26.12 27.61 28.26 30.46 31.08 32.66 33.76 35.77
F2 (K$) 40.73 44.62 49.22 53.00 55.62 61.10 62.96 67.70 71.96 77.02
F3 (Days) 3097 3039 2787 2701 2615 2434 2387 2299 2171 2042
designed to achieve maximum benefits. Moreover, locations that have similar irradiation profiles and similar average temperatures, but different variance in temperature, will have the same optimum solar plant design. It is clear that the ambient temperature will affect the objective functions, as has been shown in the tables. This study shows that variations in ambient temperature average and variance may affect the optimal solar plant. In other words, the solar plant designed for one location may not be optimum for another location with the same average but different variance of temperature, and vice versa. B. Solar Irradiation Impact The solar irradiation level will also affect the optimum design. Table VII presents the optimal design values for irradiation level from -20% to 20% of the base case (Section V). It is seen that the designed system will be optimal up to some extent and for further decrease and increase in the solar irradiation level, the system should be re-designed. The number of series and parallel and the type of panels are almost the same for some cases; however, the inverter and PV type should be modified from I1 to I4 and from PV2 to PV3, respectively, to maximize the total financial benefits of the design. This study further manifests the need to re-design solar plants for different locations with different solar irradiation profiles. C. Available Areas Impact The impact of the available area for installing PV modules on the optimal design is investigated in this section. The purpose is to show if for any reason after the installations, the available area is reduced or increased, whether the designed system is still optimum or near optimum. The results of this study is shown in Table VIII. It is seen that, with variation of the available area for installing the solar modules, the optimum design will change significantly in terms of Ns, Np, NInv and NPV, and the system will require a complete re-design in this case.
Area (%) -20 -10 -5 -3 +3 +5 +1 0 +2 0
Ns
Np
Inv
PV
23 17 14 19 20 20 13 14
2 3 4 3 3 3 5 5
I1 I2 I2 I4 I4 I4 I4 I4
PV3 PV3 PV3 PV3 PV3 PV3 PV3 PV3
A (m2) 77 86 95 96 101 101 109 117
ICst (K$) 18.2 20.5 21.8 22.6 23.4 23.4 24.8 26.1
F1 (MWh/y) 23.36 26.06 28.38 29.42 30.75 30.75 33.01 35.58
F2 (K$) 46.16 51.39 56.37 58.08 61.42 61.42 66.24 71.98
F3 (Days) 2601 2619 2542 2557 2484 2484 2441 2393
This study shows that knowing the exact available area in a design could significantly affect the solar plant’s design and, consequently, the benefits obtained from the plant. The sensitivity studies presented in this section emphasizes that for having an optimum solar plant design and maximizing the benefits obtained from solar energy, all the design parameters should be considered properly. In other words, an optimal design for a certain temperature and irradiance will not necessarily be optimum for a different location with even slightly different solar irradiance and ambient temperature. VII. CONCLUSIONS The paper proposes an optimization procedure for designing solar power plants. The process takes into account detailed characteristics of the different PV modules and efficiency curves and operating area of the grid-tie inverters. The probabilistic nature of the solar irradiance and ambient temperature is also considered in the optimal design. The optimization process is implemented for designing a solar plant, five commercially available solar modules and five commercially available grid-tie inverters with different characteristics are selected as candidates for the design. The solar plant is designed with three different objectives including, maximizing annual harvested energy, maximizing total financial benefits and minimizing the payback time. Two different cases, by considering and neglecting available area limitations are investigated and the results are compared with the design provided by PVsyst software. It is seen that, other than optimally selecting the PV module and the inverter, by considering detailed characteristics of the PV panels and inverters, the proposed approach provides more efficient results. Several sensitivity studies are also presented to investigate the robustness of the design in case of variation of design parameters. The design parameters include variation of ambient temperature’s average and variance, variation of solar irradiance and variation of available installation area. It is seen that the optimal design is robust to variation of temperature variance variation and is sensitive to temperature’s average variations and variation of solar irradiance as well as variation of available area. In such cases, the solar plant should be re-designed to obtain the maximum financial benefits from the solar plant. The proposed approach and the sensitivity studies presented in this paper provides guidelines for utility engineers and solar plant designers to optimally design their PV plants depending on the special goals requirements and constraints of their project. REFERENCES [1]
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Seyed Ali Arefifar (S’06, M’10) was born in Isfahan, Iran. He received the B.Sc. and M.Sc. degrees with honors in electrical engineering, power systems, from Isfahan University of Technology, Iran, in 2001 and 2004, respectively, and the Ph.D. degree in energy systems, from University of Alberta, Canada, in 2010. He was an NSERC Visiting Fellow at CanmetENERGY, Natural Resources Canada (NRCan) from 2011 to 2014. From 2014 to 2016 he was Post Doctoral Research/Teaching Fellow at Electrical and Computer Engineering Department of the University of British Columbia, Vancouver. Since August 2016, he has been with ECE Department, Oakland University, MI, USA, as Assistant Professor. His research interests include optimizations in planning and operation of energy systems, smart grids and microgrids. Francisco Paz (S’08) is a Ph.D. Student at the University of British Columbia (UBC) in Vancouver, Canada. He was born in La Plata, Argentina. He received the Ing. degree in Electronics Engineering from the National University of Comahue, Argentina, in 2012. He began research activities that same year at the University of British Columbia (UBC) in Vancouver, Canada, where he received the M.A.Sc. degree in Electrical Engineering in 2014; he is currently working towards a Ph.D. degree. His current interests include renewable energy conversion, maximum power point tracking and renewable energy system topologies for solar, wind and marine power. Mr. Paz was recognized with several awards and scholarships, including one from the Argentinian Ministry of Education, Science, Technology and Productive Innovation (2008), the ICICS Graduate Scholarship (2014), the Faculty of Applied Science Graduate Award (The University of British Columbia, 2014, 2015, and 2016), and the Four Year Fellowship for Ph.D. students (2014) from UBC. He was recognized with a “best paper” award in PEDG 2016. Martin Ordonez (S’02–M’09) was born in Neuquen, Argentina. He received the Ing. degree in electronics engineering from the National Technological University, Cordoba, Argentina, in 2003, and the M.Eng. and Ph.D. degrees in electrical engineering from the Memorial University of Newfoundland (MUN), St. John’s, NL, Canada, in 2006 and 2009, respectively. He is currently the Canada Research Chair in Power Converters for Renewable Energy Systems and Associate Professor with the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada. He is also the holder of the Fred Kaiser Professorship on Power Conversion and Sustainability at UBC. He was an adjunct Professor with Simon Fraser University, Burnaby, BC, Canada, and MUN. His industrial experience in power conversion includes research and development at Xantrex Technology Inc./Elgar Electronics Corp. (now AMETEK Programmable Power in San Diego, California), Deep-Ing Electronica de Potencia (Rosario, Argentina), and TRV Dispositivos (Cordoba, Argentina). With the support of industrial funds and the Natural Sciences and Engineering Research Council, he has contributed to more than 100 publications and R&D reports.
Dr. Ordonez is an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS, a Guest Editor for IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, an Editor for IEEE TRANSACTIONS ON SUSTAINABLE ENERGY serves on several IEEE committees, and reviews widely for IEEE/IET journals and international conferences. He was awarded the David Dunsiger Award for Excellence in the Faculty of Engineering and Applied Science (2009) and the Chancellors Graduate Award/Birks Graduate Medal (2006), and became a Fellow of the School of Graduate Studies, MUN.
