Implications of temporal resolution for modeling renewables-based power systems

Renewable Energy 41 (2012) 285e293

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Implications of temporal resolution for modeling renewables-based power systems Eric J. Hoevenaars*, Curran A. Crawford Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada V8W 3P6

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 August 2011 Accepted 8 November 2011 Available online 7 December 2011

It is common in quasi-steady-state models of renewable power systems to use a 1 h time step despite the variability of the load and renewable sources within the hour. The purpose of this study was to examine the efficacy of this level of temporal resolution for a model that includes variable residential loads, wind, solar, diesel generator, and batteries. The component models were analyzed individually and as a complete system to develop an understanding of how each is affected by the temporal resolution. With higher resolution, the wind energy output and the fuel consumption of the genset increased. The PV and battery simulations were unaffected by temporal resolution. Agreement between optimization results was found to greatly depend on system configuration. Systems with only diesel for backup were found to increase in cost with higher temporal resolution. Those with battery backup were much less affected by the time step. For systems with both diesel and battery backup, the optimal system costs were fairly close but the optimal component sizes differed. Because of the many factors that affect the results of these systems, it is not yet possible to determine a general recommendation for choosing a time step prior to a simulation. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: PV Batteries Genset Wind turbine Energy system optimization

1. Introduction In many remote locations where diesel fuel is the typical energy source, renewables-based power systems provide an opportunity to generate cleaner electricity with a lower levelized cost of energy. Proper sizing is important to ensure that the system is reliable and cost-effective but this is made difficult by the variability imposed on the system by unsteady loads, intermittent power sources, and fluctuating storage levels. To be autonomous, a system must not only provide enough total energy to meet the load but also be able to meet the instantaneous power demand at all times. Many power system models use a quasi-steady-state approach, simulating the performance in the time-domain. These include the two commonly used models: HOMER [1] and Hybrid2 [2]. Within each time step of the quasi-steady-state approach, an energy balance ensures that all of the energy being converted into electricity by the power sources is subsequently used to meet the load, used to charge an energy storage system, or passed to a dump load. It is common to use a standard time step of 1 h and a total simulation time of one year.

* Corresponding author. Department of Mechanical Engineering, University of Victoria, Engineering Office Wing, Room 231, 3800 Finnerty Rd., Victoria, BC, Canada V8W 3P6. Tel.: þ1 250 721 8938. E-mail addresses: [email protected] (E.J. Hoevenaars), [email protected] (C.A. Crawford). 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.11.013

The purpose of this work was to determine the efficacy of this standard time step length. The literature associated with the time step issue is fairly limited. Notton et al. [3] examined the influence of the simulation time step for sizing autonomous photovoltaic systems. They found that the use of daily data resulted in significant undersizing but there was a good agreement between the minute and hourly results. However, the load profiles used in this work did vary throughout the day but not within the hour. Ambrosone et al. [4] found that daily time steps could be used when the storage system was sized for at least two days of storage but hourly steps were required otherwise. Hawkes and Leach [5] examined the influence of temporal precision in optimizing a micro-combined heat and power system. They found that a fine temporal precision was required to reduce the averaging effect. The current study aimed to determine the influence of the time step on the sizing of a complete hybrid system. The results were compared using time steps of 1 s, 10 s, 1 min, 10 min, and 1 h. Since a shorter time step is able to more closely represent reality, the “errors” using longer time steps were calculated by comparing with the 1 s results. The system components that were considered were the load, renewable sources (wind and solar), gensets, and battery bank. These components were first analyzed individually in order to pinpoint the possible sources of error and were then combined and

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simulated as complete hybrid systems, including component optimization. The systems in this analysis were designed to meet the load of a single off-grid house. The same model could be used to simulate and optimize larger systems for entire rural communities or grid-connected systems (in which case the diesel generator would be unnecessary). In the larger systems, the short-term load fluctuations would likely be less pronounced due to spatial averaging. Therefore, the effect of temporal resolution would likely be less than for the single house scenario but could be analyzed using the same procedure. 2. Power system model The model used in this work was developed in Matlab and used a general quasi-steady-state time series method to model the electrical flow of power and optimize the sizes of the system components. To ensure that the temporal variability of power output was accurate when using the shorter time steps, a dynamic model was used to calculate the performance of the wind turbine. The physics of the other components did not necessitate additional dynamic models. The model could be used to perform an analysis of a particular system design or as optimization tool using a full factorial search for the component sizes that minimize net present cost. While not the most efficient optimizer, this method makes it possible to ensure a global minimum is found. The speed of the model makes this approach feasible and consistent with HOMER. This approach is similar to other quasi-steady-state models, but offers the flexibility to alter the control strategy of the backup generator, change the objective function, and alter components or include new ones. In this work, two control strategies were considered (load-following and cycle-charging) and the objective function was to minimize the net present cost. 3. Background/methodology The individual component models were first tested in isolation to develop an understanding of how each component is affected by the temporal resolution before integrated sizing simulations. 3.1. Load profile While not a physical component, the load is the most important element of a power system as all components are sized in order to meet this demand. The load profile can take many shapes and sizes. If it contains a high number of sharp fluctuations, averaging them over an hourly time step would artificially smooth out the profile. The presence of very peaky loads in a system under design by the authors was the original motivation for the current work. This would likely result in an undersized system and the simulation would misrepresent the operation of the individual components. The load profile used in this work was synthesized for a typical residence using GridLAB-D [6] for 1 min intervals over the course of a year. The load included a heat pump and various household appliances. The heat pump demand was calculated with a building heat model that accounted for the ambient and internal temperatures as well as the temperature set point. The program used typical weather data from Seattle, WA. The on/off schedules for the appliances were input based on reasonable estimates of a typical residential household. Fig. 1 shows a typical day taken from the load profile used in the “Complete system” section of the analysis. The smoothing effect is evident when the load was averaged over an hourly time step. To create the high frequency data (1 s and 10 s), the load was held constant within each minute.

Fig. 1. Sample of synthetic load data (March 8).

3.2. Wind power The theoretical power available in the wind is proportional to the cube of the hub-height wind speed, resulting in a non-linear power curve. Therefore, by averaging the wind speed values over an extended period, the energy available in the wind will be underestimated. However, it is not the available energy in the wind that is important but rather the energy output from the turbine. Inertial effects of the turbine limit its ability to extract the energy contained in the turbulence. This type of analysis required wind speed data at 1 s intervals. Because data sets with this level of precision were difficult to obtain, the sub-minute data used in this work were synthesized from the Kaimal spectrum. A dynamic model of the turbine was created in Simulink. 3.2.1. Generating wind speed data In this work, low frequency variances in the wind were accounted for by using 1 min wind data, at a height of 12.8 m, for all of 2010 at NREL’s Solar Radiation Research Laboratory (SRRL) [7]. Within each minute, 1 s data was synthesized using the Kaimal spectrum as it has been shown to provide a good empirical description of the observed spectra in the atmosphere [8]. Using each 1 min data point as the mean wind speed, Matlab’s ifft function was used to perform an inverse fast fourier transform based on the method from Branlard [9]. The final values were then blended between the minutes to smooth out the abrupt changes at each minute and scaled by a factor of 2 so that the wind regime was more viable for power production. This created a set of wind speeds at 0.1 s intervals. These values were then aggregated to create separate data sets for the various time steps being considered in this work (1 s, 10 s, 1 min, 10 min, and 1 h). A 20 min sample is shown in Fig. 2 for time steps of 1 s,

Fig. 2. Twenty minute sample of synthetic wind speed data.

E.J. Hoevenaars, C.A. Crawford / Renewable Energy 41 (2012) 285e293 Table 1 Wind turbine parameters.

ld

R

ulim

sgen, lim

I

5

2m

25 rad/s

200 N m

8.2 kg m2

a b

K

ra

hgen

0.6

1.225 kg/m3

90%

PPV ¼ Prated fPV

GT GT;STC

287



1 þ aP Tc  Tc;STC




(1)

where Prated is the PV rated power, GT is the incident solar radiation, and fPV is the derating factor to account for the reduced power output in real world applications. GT;STC and Tc;STC are the incident solar radiation (1 kW/m2) and cell temperature (25  C) at standard test conditions. The temperature coefficient of power, aP, is specific to the solar cell. The cell temperature, Tc, was calculated at each time step using the same method that HOMER uses [1]. Another important consideration for the PV model was ensuring that the method of converting global horizontal radiation to incident radiation on a tilted surface was valid for any time step length. First, the diffuse fraction was estimated using Erbs’ empirical regression [17]. Vijayakumar et al. [18] compared the results of this regression with actual diffuse radiation data. The general trend was followed but there was significant scatter, suggesting the possibility of inaccuracies on short time scales. However, these errors appear to cancel out over the long run. Using Erbs’ regression and the Perez model [19], the difference in monthly average radiation on a tilted surface using hourly data and 1-min data was found to be within 1% for most months and 2% for some winter months [18]. Therefore, the inaccuracies for the tilted surface radiation calculation are likely to be less significant for systems with storage. The model developed by Reindl et al. [20], referred to as the HDKR model [21], is similar to the Perez model as they are both anisotropic sky models that account for circumsolar diffuse radiation and horizon brightening [21]. The authors are unaware of any tilted surface models or diffuse fraction regressions that are better suited for short-term data. The PV input parameters are shown in Table 2. The location and time zone, Z, were chosen to represent NREL’s solar laboratory where the wind, solar, and temperature data were obtained from. The slope, b, was set equal to the latitude and the azimuth angle, g, was set to zero so that the panel faced due south. The ground reflectance, rg, was assumed. The temperature coefficient of power, aP, the nominal operating cell temperature, Tc;NOCT , and the cell efficiency at standard test conditions, hPV, were based on the specifications of the 175 W ‘48MC’ PV model manufactured by Day4 Energy.

b

Assuming the standard atmosphere at sea level . F. M. White, Fluid Mechanics, 6th Edition, McGraw-Hill, 2008.

1 min, and 1 h, illustrating temporal smoothing with longer time steps. 3.2.2. Wind turbine model In many models, the output power of the wind turbine is interpolated from the turbine’s power curve [1,2,10,11]. These curves are typically based on 10 min averages [12] and are not applicable for high frequency wind data. To account for the turbine’s inertia, a dynamic model was created in Simulink along with a proportional feedback controller. The purpose was not to design an optimal controller but only to ensure that the turbine power output in the simulation was realistic in accounting for the response time of the turbine. The feedback controller was based on that of McIntosh [13]. The dynamics were solved using a 1 s time step. The turbine parameters used in this work are shown in Table 1. The assumed Cp -l curve and the rotor inertia, I, were derived by performing a blade optimization procedure in the ExcelBEM model from Crawford [14]. The tip speed ratio demand, ld, was defined as the point at which the turbine operates most efficiently, corresponding to Cp;max . The rotational speed limit, ulim, and generator torque limit, sgen;lim , along with the generator efficiency, hgen resulted in a maximum output of 4.5 kW. For system sizing purposes, this was assumed to be the rated power. 3.3. Solar power A maximum power point tracker (MPPT) ensures that the PV array voltage is always at the maximum power point of the cell’s IeV curve. The result is that the relationship between incident radiation and output power becomes approximately linear [1]. This is supported by Perpiñan et al. [15], who showed that the energy produced by a PV grid-connected system follows a quasielinear relation with irradiation on the generator surface. This means that the estimate of total energy production should be similar regardless of the data resolution used, as shown by Gansler et al. [16] for a PV system with an MPPT. In this work, it was assumed that an MPPT controller was installed with the system and therefore total electricity production was independent of the time step chosen. For this reason, the PV component was not analyzed individually. It was included in the “Complete system” analysis because the sub-hour fluctuations could affect system operation depending on how it matched with the load. One min global horizontal surface radiation was obtained from the SRRL database for 2010 [7]. For sub-minute data, these values were held constant within the minute since it is not common for cloud cover to change multiple times within any minute. The power output from the PV array with MPPT controller was calculated proportional to the incident radiation and with a factor accounting for cell temperature:

3.4. Backup diesel generator In many models, a linear relationship is assumed between the fuel consumption and power output [1,2,10,22,23]. Here, the fuel curve is defined as in HOMER [1]:

F ¼ F0 Ygen þ F1 Pgen

(2)

where F is the fuel consumption (L/h), Ygen is the rated capacity (kW), Pgen is the instantaneous power output (kW), and F0 and F1 are the fuel curve intercept (L/hkWr) and slope (L/hkWr). The intercept represents the fuel consumed while the generator runs idle. The diesel generator parameters used in this work are shown in Table 3. A high number of generator start/stop cycles and significant partial loading can cause long term maintenance problems [2,24]. Therefore, a minimum run time of 10 min and minimum power output of 30% of the rated power was enforced in the simulations.

Table 2 PV parameters. fPV

Lat.

Long.

Z

b

g

rg

aP

Tc,

0.8

39.74 N

105.18 W

MST

39.74

0

0.2

0.44%/ C

46.9  C

NOCT

hPV

Life

14.7

25 yr

288

E.J. Hoevenaars, C.A. Crawford / Renewable Energy 41 (2012) 285e293

Table 3 Diesel generator parameters.

Table 5 Assumed component costs.

F0

F1

r

LHV

Life

0.08 L/h k Wra

0.25 L/h k Woa

832 kg/m3b

43.1 MJ/kgb

20,000 h

a

C. D. Barley, C. B. Winn, Optimal dispatch strategy in remote hybrid power systems, Sol. Energy 58 (4e6) (1996) 165e179. b R. Edwards, J.-F. Lariv’e, V. Mahieu, P. Rouveirolles, Well-to-wheels analysis of future automotive fuels and powertrains in the European context, Tech. Rep. 3, EUCAR, CONCAWE, JRC/IES (2008).

If a system also includes batteries, many different control strategies can be used to command the generator’s operation. Two of the basic strategies were used in this work: load-following and cycle-charging. In both strategies, the generator only runs when the renewables and batteries cannot meet the load. With loadfollowing control, the generator only outputs enough power to meet the instantaneous load (unless it is below the minimum power output). With cycle-charging control, the generator operates at its rated power and excess energy is stored in the batteries. 3.5. Battery bank A battery’s performance is determined by how much energy it can store and the power at which it can charge or discharge. Both the energy and power capabilities are affected by several battery parameters and depend also on the state of charge. To account for these influences, a kinetic battery model [25] was used. The model treats the battery as a set of two tanks storing “available energy” and “bound energy” with conductance between the two. It mimics dynamic processes within deep-cycle lead-acid batteries such as the change in capacity with state of charge and the recovery of charge. In this work, a maximum charging current, Imax is also imposed on the battery model. The equations from the kinetic battery model depend on the length of the time step. This influence was examined in two different scenarios: continuous charge and combined charge/discharge. Table 4 shows the battery parameters used in this study. The capacity, voltage, and kinetic battery parameters, k and c, were chosen to represent East Penn’s ‘8L16P’ battery model. Both k and c were estimated by a least squares fit of the capacity curve, as described by Manwell and McGowan [25]. The charging and discharging efficiencies, hc and hdc were chosen to provide a roundtrip efficiency of 85%. Finally, to reduce wear on the batteries, a minimum allowable state of charge of 30% was applied. 3.6. Complete system Several system configurations were considered in this work in varying combinations of wind, solar, diesel, and battery components, as each combination will have a non-linear effect on the time-domain performance. The analysis of the complete system was divided into two steps. For each configuration, an optimization procedure was run to compare the optimal component sizes and total cost using time steps of 1 h, 10 min, and 1 min. Next, a single simulation was run with the optimal component sizes for each optimal system in order to analyze the results further and determine how the choice of time step (1 h, 10 min, 1 min, 10 s, or 1 s) affects system operation in the model.

Table 4 Battery parameters. Capacity

Voltage

k

c

hc

hdc

Imax

Life

370 Ah

6V

0.6298 h1

0.3474

92.2%

92.2%

75 A

10 yr

Solar (175 W) Wind (4.5 kW) Diesel (1 kW) Battery (370 Ah) Inverter (1 kW)

Capital

Replacement

O&M

Fuel

$1000 $21,750 $500 $375 $500

$785 $20,000 $500 $375 $500

$0 $500/yr $0.10/hr $0 $0

e e $1.50/L e e

The costs used in this work are shown in Table 5. Capital and replacement costs were estimated based on the catalog from a local distributor of renewable energy devices. Annual wind O&M costs were assumed to be 2.3% of the total invested cost [26]. The fuel cost was simply an estimate based on current diesel prices and considering the extra expenses associated with its transport to a remote location. Additionally, an annual real interest rate of 5% was assumed over a 25-year project lifetime. 4. Results The influence of the time step length on the individual components and complete system was analyzed using the methods described above. 4.1. Wind power For the wind turbine analysis, nine data sets were created (each with 6 h worth of data). The mean wind speeds were set to 6, 9, and 12 m/s with three unique data sets generated for each because of the random process of determining the Fourier coefficients. For calculating the friction velocity, the height and surface roughness were assumed to be 15 m and 0.1 m, respectively. These nine data sets were input into the dynamic turbine model to compare the total energy produced over a 6 h period with different temporal resolutions. Table 6 shows the kinetic energy in the wind and Table 7 shows the resulting power output from the turbine. As expected, the amount of kinetic energy in the wind was lower for the longer time steps because of the cubic relationship between wind speed and theoretical power output. The available energy in the wind decreased as the wind speed fluctuations were smoothed out. The smoothing effect caused the total energy output to decrease at the lower mean wind speeds (6 and 9 m/s) but increase at the higher wind speed (12 m/s). At 12 m/s, the turbine was operating at its limits and was not able to take advantage of the extra energy available in the high frequency components of the wind. This is clear in Fig. 3 which shows the generator operating at its torque limit for a significant period of time. By ignoring the turbulence in the lower resolution simulations, the turbine continued to operate at its maximum output. The higher resolution simulations accounted for the drops in power due to turbulence and result in a lower total energy output. The maximum error of 7% with a 12 m/s mean wind speed suggest that the temporal resolution is significant when the wind speed is close to the turbine’s rated wind speed (according to the Cp -l curve).

Table 6 Total wind kinetic energy, in kWh, over a 6 h period (% error from 1 s results). U (m/s)a

1s

10 s

1 min

10 min

1h

6 9 12

10.43 35.04 83.23

10.35 (0.75%) 34.71 (0.94%) 82.34 (1.07%)

10.21 (2.09%) 34.24 (2.27%) 81.15 (2.49%)

10.03 (3.77%) 34.13 (2.61%) 80.09 (3.77%)

9.98 (4.24%) 33.70 (3.82%) 79.86 (4.04%)

a Results are averaged using three synthetic wind speed data sets for each mean speed.

E.J. Hoevenaars, C.A. Crawford / Renewable Energy 41 (2012) 285e293 Table 7 Total wind energy output from turbine, in kWh, over a 6 h period (% error from 1 s results). U (m/s)a

1s

10 s

1 min

10 min

1h

6 9 12

4.20 14.10 25.23

4.17 (0.73%) 13.97 (0.88%) 25.58 (1.38%)

4.11 (2.14%) 13.78 (2.27%) 26.22 (3.92%)

4.04 (3.82%) 13.60 (3.56%) 26.96 (6.85%)

4.02 (4.29%) 13.56 (3.83%) 27.00 (7.02%)

a Results are averaged using three synthetic wind speed data sets for each mean speed.

4.2. Backup diesel generator To isolate the influence of the time step on the diesel generator, a simulation was run with a constant 10 kW load and wind penetration levels of 0%, 30%, and 60% (i.e. mean power outputs of 0, 3, and 6 kW) in order to add variability to the generator’s output power. A 10 kW backup generator was the only component available to meet whatever load was not met by the wind. With 0% wind penetration, the generator constantly operated at its rated power and the fuel consumption was the same regardless of the time step. However, with increasing wind penetration, the variability of the load needing to be met by the generator meant that a longer time step would introduce error due to averaging. As seen in Table 8, there was no noticeable change in fuel consumption until the wind penetration level was set to 60%. With low levels of wind penetration, the load on the generator was consistently above the minimum allowable power output. Therefore, because of the assumed linear relationship between fuel consumption and power output, the total fuel consumed did not depend on the temporal resolution. At 60% wind penetration, the mean load on the generator was reduced to 4 kW which was only slightly higher than the 3 kW minimum allowable output. With the variability from the wind, the instantaneous load frequently dropped below 3 kW [Fig. 4(a)], meaning the generator was not able to continuously follow the load [Fig. 4(b)]. Because the generator was forced to operate at the minimum power output even when the load dropped lower, the total fuel consumption increased for the shorter time steps (Table 8). Therefore, the choice of time step will affect the estimated fuel consumption of the generator if it operates near its minimum allowable output.

289

Table 8 Diesel fuel consumed, in L, over a 6 h period (% error from 1 s results). Wind (%)

1s

10 s

1 min

10 min

1h

0 30 60

19.80 15.30 11.44

19.80 (0%) 15.30 (0.01%) 11.23 (1.85%)

19.80 (0%) 15.30 (0.01%) 10.98 (4.04%)

19.80 (0%) 15.30 (0.01%) 10.80 (5.59%)

19.80 (0%) 15.30 (0.01%) 10.80 (5.59%)

1667 Ah and a nominal voltage of 6 V, resulting in an energy capacity of 10 kWh. The minimum allowable state of charge was 30%. For the “battery charging” scenario, a wind power data set was taken from the “wind power” analysis and normalized to a mean of 1 kW over the 6 h period. The initial battery state of charge was set to 40% and a 6 h simulation was run. Table 9 shows the final state of charge of the battery, the total charge absorbed by the battery, the amount of energy sent to the dump load because the battery could not handle it, and the overall efficiency (defined as the ratio of energy absorbed by the battery to the energy generated by the wind). There is a clear agreement between the results of the simulations using different time steps, confirming that the kinetic battery model can be used for any level of temporal precision. For the combined charge/discharge scenario, a constant load of 2 kW was assumed along with a mean wind power of 2 kW over the 6 h period. Therefore, the battery operation alternated between charging and discharging as the wind power fluctuated above and below the constant load. The initial state of charge was set to 70%. Again, the results showed little difference between the different time steps (Table 10). The final state of charge when using the shorter time steps was lower because of the extra efficiencies associated with charge/discharge cycles within the longer time step.

4.3. Battery bank Battery bank performance was analyzed for two scenarios: continuous charge and combined charge/discharge. For this section of the analysis, the battery bank was assumed to have a capacity of

Fig. 3. Generator torque for 10 min of wind turbine simulation (1 s time step, 12 m/s mean speed).

Fig. 4. Diesel generator (a) load and (b) actual power output for 20 min of simulation (1 s time step).

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Table 9 Battery simulation results, continuous charge, 1 kW average charge.

Final SOC Charge (kWh) Dump (kWh) Efficiency

1s

10 s

1 min

10 min

1h

84.63% 4.463 1.160 74.38%

84.63% 4.463 1.159 74.39%

84.64% 4.464 1.158 74.40%

84.66% 4.466 1.156 74.44%

84.57% 4.457 1.166 74.28%

4.4. Complete system For the analysis of the system sizing procedure, it was assumed that all of the components were modular. The PV array consisted of Day4 Energy’s 175 W ‘48MC’ PV modules. The wind turbine considered was the 4.5 kW model described earlier. The diesel generator rated power was limited to multiples of 1 kW. The battery bank consisted of East Penn’s 370 Ah ‘8L16P’ models and only strings of 8 batteries were considered as they could be connected in series to ensure a 48 V system. The inverter was sized to meet the maximum output from the PV or wind components. For the optimizations, a constraint ensured that the load was met at all time steps throughout the year. 4.4.1. Optimization Based on the criteria stated above and the component costs from Table 5, the optimal sizes for all of the possible configurations were found and are shown in Table 11(a)e(c). For this part of the study, a load-following control strategy was assumed. The optimal configuration consisted of a combination of wind and solar with both a battery bank and a diesel generator for backup. The batteries allowed more of the wind and solar energy to be used to meet the load and the generator ensured that the load could be met during long periods with poor wind and little sunshine. However, it was the relative results using various time steps, not the specific results for this scenario, that were important for this study. As the size of the time step changed, the NPC over the 25-year project lifetime changed as well and this change was more significant for certain configurations. Three main factors were identified earlier that affected the results as the level of temporal resolution varied:  Increase in wind energy using shorter time steps  Artificial smoothing caused by averaging data over longer time steps  Temporal matching between renewable sources and load The increase in wind energy is evident from the results of the wind-battery configuration. It is the only explanation of why the NPC decreased as the temporal resolution increased. The other two factors are related since it is the smoothing of the load over longer time steps that causes the model to ignore the temporal matching between the renewable sources and the load. However, they affect the results separately. Load-smoothing mostly affects the diesel generator and is the reason why its rated power tends to be higher with a shorter time step. While the size of a battery bank represents its energy capacity, the size of a generator represents its power

Table 10 Battery simulation results, combined charge/discharge.

Final SOC Loss of Charge (kWh)

1s

10 s

1 min

10 min

1h

68.69% 0.131

68.89% 0.111

69.27% 0.073

69.76% 0.024

69.92% 0.008

capacity. Since load averaging affects only the power distribution of the load, and not the total energy required, it affects the size of the generator much more than the size of the battery bank. The third factor, temporal matching, is most significant for configurations that do not have a battery bank and was the main reason why the NPC was significantly underestimated when using a 1 h time step. This makes sense since, with a higher degree of temporal resolution, the wind and solar power must line up with the load at the sub-hour level. Without a battery bank, any excess wind and solar energy would be lost, meaning the diesel generator must be used to fill in the gaps. Combined with the fact that the generator is sized much larger than with lower temporal resolution (because of load-smoothing), much more generator fuel and maintenance is required to supplement the wind and solar energy. 4.4.2. Analysis: diesel backup Table 11(a)e(c) clearly show that simulations of systems with only diesel for backup were far more susceptible to error using coarser temporal resolution. The most basic case is the diesel-only configuration. For optimizing such systems, it is obvious that the maximum power output of the generator must be greater than the peak load. When choosing a time step, the user must be sure that load-smoothing does not allow the generator to be undersized. If this requirement is satisfied, the time step will have a negligible impact on the system cost. In this case, the 10 min time step was sufficient and this was confirmed by the similar NPC found using 10 min and 1 min time steps. With a 1 h step, the effect of loadsmoothing was enough to allow the generator to be significantly undersized in the simulation. Therefore, the fuel consumption (and total NPC) was underestimated. The same rule should be applied to more complex systems with only diesel for backup, though the error is smaller since a greater percentage of the load is met by non-diesel power sources. Because solar power on its own is inherently unreliable and will never be available outside of daytime hours, the generator must always be sized to meet the peak load. This is not necessarily true when wind power is added since, in a good wind regime, the non-operational time of a wind turbine is far less than for a PV array. Since it is possible that the optimal generator size is less than the peak load, one cannot simply look at the results and determine if the temporal resolution is sufficient. The optimization results for the wind-diesel system in Table 11(a)e(c) show that time steps longer than 1 min were not able to provide an accurate representation of the system. In fact, the results continued to change fairly significantly all the way down to a 1 s time step. Table 12 shows the total wind production and fuel consumption over a 1-month simulation. Despite the extra energy from the wind with shorter time steps, fuel consumption increased because of the poor temporal matching between the wind and the load caused by the wind turbulence. This mismatch meant that the genset had to turn on for brief periods but also had to stay on for the 10 min minimum run time. As Table 13 shows, the solar-winddiesel configuration is affected by the time step in the same way. The large number of start/stop cycles and partial loading of the generator in a wind-diesel system suggest that a high temporal resolution is required. This also suggests that these systems are not suitable for this application. Unacceptably high numbers of stop/ start cycles and prolonged low-load running of the generator will cause increased wear and reduce its lifetime [24]. Also, without a battery bank and charge controller, short-term fluctuations from wind turbulence will cause variations in the system voltage and frequency [24]. Attempting to meet a highly fluctuating load with unpredictable and fluctuating energy resources without a battery bank for storage will inevitably lead to all of these issues and should be avoided.

E.J. Hoevenaars, C.A. Crawford / Renewable Energy 41 (2012) 285e293

291

Table 11 System optimization results. Config.

D S-D S-B W-D W-B D-B S-W-D S-W-B S-D-B W-D-B S-W-D-B

(a) 1 h,

(b) 10 min

(c) 1 min

S

W

D

B

NPC

S

W

D

B

NPC

S

W

D

B

NPC

e 39 101 e e e 26 46 63 e 27

e e e 2 3 e 1 1 e 2 1

7 7 e 6 e 7 6 e 6 6 5

e e 80 e 120 8 e 96 32 24 16

$324,956 $276,414 $169,056 $200,675 $202,524 $261,997 $190,094 $154,548 $120,932 $121,953 $99,630

e 65 104 e e e 29 45 66 e 26

e e e 2 2 e 2 1 e 2 1

14 14 e 12 e 13 12 e 12 13 12

e e 80 e 160 8 e 88 32 24 24

$629,546 $488,583 $172,438 $297,634 $190,222 $292,847 $265,241 $147,900 $127,946 $121,013 $102,426

e 65 105 e e e 30 44 66 e 25

e e e 2 2 e 2 1 e 2 1

14 14 e 13 e 14 13 e 14 13 11

e e 80 e 152 8 e 88 32 24 40

$631,560 $498,599 $173,565 $340,338 $184,702 $292,271 $301,170 $146,773 $129,996 $118,692 $105,720

S - 175 W solar modules; W - 4.5 kW wind turbines; D - 1 kW diesel gena; B - 370 Ah batteries. a Assuming a load-following control strategy.

Table 12 Results from 1-month simulation (2 wind turbines, 13 kW generator).

Wind (kWh) Fuel (L) Gen Hours

1s

10 s

1 min

10 min

1h

2019.6 993.1 478.9

2017.0 921.3 443.2

2016.3 860.1 412.9

1969.6 799.6 385.8

1858.0 839.4 415.0

Table 13 Results from 1-month simulation (30 PV modules, 2 wind turbines, 13 kW generator).

Wind (kWh) Fuel (L) Gen Hrs

1s

10 s

1 min

10 min

1h

2019.6 778.1 373.1

2017.0 715.0 341.9

2016.3 661.0 315.0

1969.6 603.0 288.7

1858.0 617.4 305.0

4.4.3. Analysis: battery backup Again referring to Table 11(a)e(c), the change in system costs with a change in temporal resolution was much smaller for systems with only a battery bank for backup. The total NPC of the solarbattery configuration was only 2.6% higher with a 1 min step size than with a 1 h step and the PV array was 3.8% larger. This agreement is due to the linear relationship between PV power output and incident radiation and the applicability of the battery model for any time step. Fig. 5 shows the change in the battery’s state of charge (SOC) over the course of a typical day. By the end of the day, they will have all converged apart from the small battery losses that could exist because of temporal matching between the solar resource and the load. It is the temporal matching that caused the PV array size to be slightly larger with a shorter time step. However, it appears that a 1 h time step is sufficient for a solar-battery system, as long as both the PV array size and the NPC are scaled up by 5%. With a wind-battery system, the system cost was slightly overestimated using coarser temporal resolution. This was simply because of the additional energy available in the high frequency components of the wind. Tracking the battery SOC as in Fig. 6 clearly shows the influence of the extra wind energy on the simulation. Fig. 7 demonstrates why the optimal system using a 1 min time step was not feasible when less temporal precision was used, since the SOC dropped below the 30% minimum. Looking at the minimum and final battery SOC of a 1-month simulation shown in Table 14, it is clear that using a time step shorter than 1 min would not affect the results. This analysis suggests that a 1 h step is acceptable and will lead to a slightly oversized system

Fig. 5. Battery SOC on Day 18 (105 PV modules, 80 batteries).

Fig. 6. Battery SOC on Days 19e23 (3 wind turbines, 120 batteries).

Fig. 7. Battery SOC on Days 18e23 (2 wind turbines, 152 batteries).

292

E.J. Hoevenaars, C.A. Crawford / Renewable Energy 41 (2012) 285e293

Table 14 Results from 1-month simulation (3 wind turbines, 120 batteries).

Min SOC (%) Final SOC (%)

1s

10 s

1 min

10 min

1h

62.4 89.3

62.3 89.3

62.3 89.3

61.2 88.8

56.9 87.8

Table 15 Percentage of load met by diesel generator, based on optimal system simulations.

S-D-B W-D-B S-W-D-B

1 min

10 min

1h

12.3 7.6 4.1

11.6 8.7 6.6

11.7 10.3 9.2

design. Better temporal resolution will bring the system costs down and is recommended if possible. Similarly, the system costs of the solar-wind-battery were overestimated with less temporal precision. Again, greater temporal resolution is not strictly necessary but would help design the optimal system. 4.4.4. Analysis: diesel/battery backup A significant reason why optimizations of systems with only diesel backup were more influenced by the temporal resolution was the smoothing of the load as it is averaged over longer time steps. This led to the generator being undersized with longer time steps, meaning the minimum power output was also smaller and it was more able to follow the load without having to dump excess power. With a battery added to the system, the excess generator power could be stored in the batteries. As such, the results between time steps agree significantly better than with only diesel for backup. In the simplest diesel-battery configuration without solar and wind, the same conclusion can be drawn as for the diesel-only case. This was that the diesel generator must be sized to meet the peak load. The role of the battery bank in this system was to store the excess power from the generator when it is required to output more than what is needed to meet the load. Only a small level of storage was required. With the addition of solar and/or wind power, most of the load was met by the renewable sources because of the high cost of fuel. Table 15 lists the percentage of the load met by the diesel generator in the optimal system simulations. Clearly, the battery bank ensured that most of the load was met by the renewable sources. Despite the fact that the same errors affect

the fuel consumption estimations when the generator was undersized, the impact on the total system costs was much smaller because the contribution of the genset was smaller. However, this also makes it more difficult for the user to determine whether the model was accurately simulating the system’s operation. With only diesel for backup, it was shown that the system costs would be quite accurate as long as the temporal resolution was high enough that the genset was sized to meet the peak load. With a renewable source and a battery bank, it is unknown what size the generator must be and it is therefore difficult to determine from the results whether load-smoothing had a significant impact. 4.4.5. Recommendations With so many factors affecting the results, it is difficult to develop a simple recommendation for the choice of time step when sizing a generic renewable power system with both diesel and batteries for backup. Small nuances within the model can be the difference between a feasible and an infeasible system. The most obvious example of this is with the solar-wind-diesel-battery configuration, a typical mix in real-world installations. Despite the fairly similar results for total NPC, the optimal system sizes were found to be significantly different. To determine the reason for this, the three optimal configurations were simulated with each time step in an attempt to compare the component costs. As expected, the “1 h optimal” configuration was infeasible with a 10 min and 1 min time step. This was obviously because the 5 kW generator was unable to meet spikes in the load when it was not smoothed out. The “10 min optimal” was also found infeasible with a 1 min time step. Investigating where the failure occurred, it was clear that load-smoothing was again the reason. An unexpected result was that the “1 min optimal” configuration was infeasible when using a 10 min time step. In this case, it was the extra energy in the high frequency components of the wind that made the system feasible with a 1 min step but infeasible with a 10 min step. There are several factors affecting the results, sometimes competing against each other in determining whether a system is feasible and often depend on the choice of time step. Identifying beforehand which of these factors will affect the results is evidently not a simple task. With both a diesel genset and a battery bank, the control strategy for the generator can be changed. In this study, the results using a cycle-charging strategy were compared with the loadfollowing strategy assumed thus far. The optimal component sizes are shown in Table 16(a)e(c). It is clear that cycle-charging control was preferred in this case, but the results were affected by the level of temporal resolution in much the same way. Hence, the conclusions reached throughout this section remain valid for both charging control strategies.

Table 16 Optimization results, comparing control strategies. Config.

Load-fol. D-B S-D-B W-D-B S-W-D-B Cycle-ch. D-B S-D-B W-D-B S-W-D-B

(a) 1 h

(b) 10 min

(c) 1 min

S

W

D

B

NPC

S

W

D

B

NPC

S

W

D

B

NPC

e 63 e 27

e e 2 1

7 6 6 5

8 32 24 16

$261,997 $120,932 $121,953 $99,630

e 66 e 26

e e 2 1

13 12 12 12

8 32 24 24

$292,847 $127,946 $121,013 $102,426

e 66 e 25

e e 2 1

14 14 13 11

8 32 24 40

$292,271 $129,996 $118,692 $105,720

e 55 e 21

e e 1 1

6 5 6 5

8 32 16 16

$174,195 $112,496 $103,204 $93,251

e 59 e 18

e e 1 1

11 11 11 9

24 32 16 16

$192,778 $117,133 $101,311 $92,413

e 61 e 16

e e 1 1

13 13 13 12

24 32 16 16

$197,064 $119,140 $101,933 $93,381

S - 175 W solar modules; W - 4.5 kW wind turbines; D - 1 kW diesel gen; B - 370 Ah batteries.

E.J. Hoevenaars, C.A. Crawford / Renewable Energy 41 (2012) 285e293

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