Model parameter assignment

After all the model indices are given, the model can be further specified with the assignment of all parameters, which conforms to the real situation of the area analyzed.

A comprehensive list of assigments for most parameters in the Taichung Industrial Park model is shown in Appendix 1. In this case, multiple common or different parameters are assigned to the five scenarios.

Banking interest rate (i.e. Inst) is set up based on the value typically used in the examples of most financial textbooks. The regulated demand charge rate of electricity (i.e. EDchars) is assigned with the value in scenario 1 approximity equal to the price that is currently charged by Taipower Company in Taiwan, and the values in scenario 2 to 5 kept increasing until the value equal to twice the current price. The assumption is that it is unlikely that the electricity price can remain in the current level in the long run, as well as increase to twice the current amount in the near future. It is more likely that the price of electricity will increase to a certain level but not too much based on inflation.

The same reasoning applies to the unit tariff rate for electricity purchase from the national grid (i.e. Epricems), with one difference that Taipower Company currently adopts a different tariff rate level for summer usage, with the electricity charge rate in summer (i.e. June to September) significantly higher than that in other months. This is due to the fact that there is typically much higher power demand in Taiwan during the summer in relation to the high utility rate of air conditioners, which in turn places additional burden to the centralized power supply system. By contrast, the selling price of electricity from various power sources to the national grid (i.e. Spriceis), can be subject to different kinds of condition (e.g. with a uniform price regardless DER source types or different unit prices depending on government policies).

The carbon tax per unit weight of carbon credit (i.e. CTaxs) is set up such that the value in scenario 1 is in accordance with the rate that is currently charged, while it is expected that the rate will be gradually increased in the future (i.e. scenario 2 to 5) with humans’

increasing concern on environmental sustainability. The carbon intensity of electricity supplied by the national grid is referred to an average value represented by coal firing

power generation, which currently accounts for the largest portion of world power generation. By comparison, the carbon intensities of different fuel types are referred to the generic data that can be found in previous research.

Some of the capital letters are designated for use in some logical formula in this model (e.g. A), while others are designed to be used by the model users for controlling the microgrid operating conditions and performance (e.g. B, C, G). The conversion factor of area of PV panels vs. 1kW electricity capacity, D, is assigned based on the calculation from some real PV panel products. Additionally, the weight of expected cost in the dual objective function, L, which also determines the weight of worst-case cost as (1-L), should be given based on the analysts’ judgement and risk consideration.

Due to the lack of trading data with regard to bulk sales of energy-carrying fuels (i.e.

Fpricefs), such as biomass and hydrogen, in Taiwan, unit fuel prices of differet fuel types are given by citing the generic data from other research. Regarding detailed equipment characteristics of all DER power sources, they are assigned to the model with referece to Table 3 (Ren and Gao, 2010)⁵. Related characteristics of different DER technologies include: average efficiency of each DER technology (i.e. effif), unit fixed capital cost of each DER technology per kW (i.e. FCostis), prevalent or average life time period of each technology in years (i.e. LTimeis), fixed operation and maintenance unit cost of each DER technology per kW per year (i.e. OMfis), and variable operation and maintenance unit cost of DER technology per kWh (i.e. OMvis). The representative values assigned to these DER characteristics have been chosen with careful assessment by evaluating the relative relationships among properties of various equipment types/models. It should be noted that the DER technology information listed in Table 3 is reported based on

“equipment concern”, which means that different models or levels of the same kind of DER technology will have different characteristics, depending on the capacities and characteristics of different machine.

By contrast, in the model of this study, DER technologies are evaluated based on

“capacity concern”, which means that within the same kind of DER technology, the equipment characteristics are assumed to vary along a linear relationship in proportion to the capacity of the equipment. This measure helps reduce the problem of selecting particular machine, which must be solved with complicated integer variables, to the

problem of determining the total capacity of each DER technology to be installed, which can significantly enhance the efficiency of problem solving in practice. The output of this model will render reasonable recommendation for total capacity allocation, regardless the specific machine types and the number of machine for each type. There can be a number of possible permutations and combinations for a certain amount of total capacity, the planners can further decide these specific arrangements in the next stage of detailed design, taking into account how many manufacturers they would like to invite for tendering and which kinds/ models of certain DER equipment should be considered, as well as how many sets of each kind of equipment should be installed.

However, in order to prevent the current model from oversimplified, a piece-wise linear relationship is adopted to simulate the effect of economy of scale. It is usually the case that when the capacity of certain equipment increases, the cost of the machine increases along a quadratical or non-linear curve. In this model, different sections of cost-capacity relationships are defined, each section with a linear relationship of a differet slope, to approximate the non-linear cost-capacity relationship.

Although the piece-wise linear relationships can be used to allocate the total capacity of each DER technology through optimization, there should be an upper limit of total power capacity for each DER technology in reality, depending on the budgeting or power generation diversity concern of the planners or government policies. This issue is addressed in this model with the parameter – maximum power capacity of each DER technology (i.e. MaxEqmis). There is also a lower limit of total power capacity for each DER technology (i.e. MinEqmis), because for any certain technology there should be an equipment model/type with minimum possible power capacity in practice.

For the same reason as above, the maximum energy storage level (i.e. ESMaxts), as well as the minimum energy storage level (i.e. ESMints), should be assigned to the model as parameters for each type of storage (i.e. electricity and heat). In the meantime, the initial energy storage level in the beginning (first) time period should also be given according to the residual level of energy storage in the pervious time period or the last time period of previous time span (e.g. December of previous year if the current analysis starts from January this year). By doing so recursively, the model can be capable of planning for a time span of several years.

Furthermore, the values of cut in wind speed of wind turbines (i.e. Vcis), nominal wind speed of wind turbines (i.e. Vnis), and cut off wind speed of wind turbines (i.e. Vfis) are specifically assigned to the wind power sources (i.e. wi) as part of equipment properties.

Table 3: DER equipment information

Source: Ren and Gao, 2010⁵

Some parameters regarding mechanical efficiencies of different DER technologies, as well as operation efficiencies of equipment for direct fuel consumption and energy storage, are represented by Greek letters. Appendix 2 describes the value assignments of these characters, which include: heat recovery efficiency of each DER source (i.e. αi), Energy conversion efficiency of each fuel type for different end uses through direct fuel consumption of boilers (i.e. βfu), utilization efficiency of recovered heat from each power source (i.e. γiu), utilization efficiency of stored energy from each type of storage (i.e. δtu), storage coefficient of each storage type (i.e. εt), and the minimum percentage of electricity purchase from the national grid (i.e. θ), as well as the unit start and stop cost of each DER source in $/time.

The efficiency in terms of heat vs electricity ratio of each DER technology (i.e. αi) is determined by referring to the technical data listed in Table 3. The efficiency for each fuel type to be converted into the heat form to support end use in heating and cooling (i.e. βfu) is derived as explained in the note of Appendix 2. It should be noted that unlike the conversion factors of fuels for DER power generation which are separated from fixed cost of equipment, the conversion factors of fuels for direct consumption have been estimated by incorporating all the fixed and variable costs associated with the process. The other data entered as assigned values are obtained with reference to other research.

Since the power sources of renewable energy, such as PV panels and wind turbines, play a significant role in the microgrid layout and their operation and performance are often subject to uncertainties of weather conditions, it is strongly recommended that the local weather data of Taichung Industrial Park be included in this model for predicting the output of power generation from the sources of solar and wind energy. It is well understood that energy from sunlight and wind changes from place to place and from time to time. In order to make a reasonable prediction on the weather conditions to be input the model, a set of one-year local weather data for Taichung area in 2011 was obtained from Central Weather Bureau of Taiwan, as shown in Appendix 3.

Local irradiation data in different months (i.e. Rms) within a year, together with the energy transforming efficiencies of the solar panels, are of great importance to the prediction of PV generation output. Although the local irradiation data of previous year may not be the same as those of the current year, they can serve as valuable reference points as to making predictions for the near future. Likewise, on-site wind speeds in different months (i.e. Vwms) have direct impact on the power output of wind turbines.

Obtaining the wind speed data of 2011 for Taichung may contribute to a more accurate estimate on future wind speed. With these empirical data serving as benchmark, a reasonable prediction of future weather condition can be made in the following chapter to allow evaluation of the impact of changes in weather on the model performance.

Variations in customer demand is one of the most critical factors that constitute the uncertainties faced by a microgrid. To construct the scenarios with realistic customer loads is especially important as to enhancing the accuracy of the modeling, and this is

normally achieved by referring to the historical data of electricity bills of the studied area. However, real electricity load data of all tenants in Taichung Industrial Park are extremely difficult to obtain, because neither Taichung Industrial Park Service Center nor Taipower Company have the statistics regarding the total sum of monthly electricity bills of all individual organizations in the park, not to mention other detailed data of customer loads in heating and cooling services.

Nevertheless, a reasonable prediction of different kinds of customer loads in Taichung Industrial Park can still be made via a reverse way (i.e. based on the capacity of supply).

It is well known that the four existing transformer stations of Taipower Company are currently supplying power with a total capacity of 146.8MW to the park. A report of factories data obtained from Taichung Industrial Park Service Center indicates that as of March 2012, the total contracted power capacity (i.e. estimated power demand) of all companies in the park amounts to 128.2MW. Together with other generic information such as the nationwide average reserve capacity rate of 20.6% as of August 18, 2011, and that in general the electricity demand in summer is roughly twice that in winter, a set of hypothesized demand schemes of Taichung Industrial Park for five scenarios can be constructed as shown in Table 4.

The five scenarios of monthly average customer loads have been arranged in the logic that scenarios with extremely large or small variations in customer demand should have lower probability of occurrence than those with moderate variations do. Scenarios with the largest demand in July would be likely to have relatively higher probability of occurrence than those with the largest demand in June or August, based on the fact that the highest average air temperature normally occurs in July. However, these principles do not necessarily apply because sometimes their influences can be mixed with those of other factors. Therefore, the overall probability of each scenario should be evaluated with careful consideration.

Regarding the heating and cooling demand of Taichung Industrial Park, it is assumed that the heating demand in winter should be higher than that in summer, while the cooling demand in summer should be higher than that in winter. Although this principle holds true for all five scenarios, the degree of variations in monthly heating and cooling demands is different for each scenario.

Table 4: Model Parameters – Hypothesized Demand Schemes of Taichung Industrial Park

Unit Capacity Electricity Heating Cooling Electricity Heating Cooling Electricity Heating Cooling Scenario 1 Avg Customer Load kW 146,800 82,208 54,805 27,403 88,080 58,720 29,360 93,952 62,635 31,317

Percentage 100% 56% 60% 64%

Scenario 2 Avg Customer Load kW 146,800 68,996 45,997 22,999 80,740 53,827 26,913 99,824 66,549 33,275

Percentage 100% 47% 55% 68%

Scenario 3 Avg Customer Load kW 146,800 74,868 49,912 24,956 82,208 54,805 27,403 91,016 60,677 30,339

Percentage 100% 51% 56% 62%

Scenario 4 Avg Customer Load kW 146,800 64,592 43,061 21,531 67,528 45,019 22,509 70,464 46,976 23,488

Percentage 100% 44% 46% 48%

Scenario 5 Avg Customer Load kW 146,800 58,720 39,147 19,573 73,400 48,933 24,467 85,144 56,763 28,381

Percentage 100% 40% 50% 58%

Unit Capacity Electricity Heating Cooling Electricity Heating Cooling Electricity Heating Cooling Scenario 1 Avg Customer Load kW 146,800 101,292 50,646 50,646 108,632 54,316 54,316 115,972 38,657 77,315

Percentage 100% 69% 74% 79%

Scenario 2 Avg Customer Load kW 146,800 114,504 57,252 57,252 127,716 63,858 63,858 142,396 47,465 94,931

Percentage 100% 78% 87% 97%

Scenario 3 Avg Customer Load kW 146,800 101,292 50,646 50,646 115,972 57,986 57,986 121,844 40,615 81,229

Percentage 100% 69% 79% 83%

Scenario 4 Avg Customer Load kW 146,800 91,016 45,508 45,508 102,760 51,380 51,380 121,844 40,615 81,229

Percentage 100% 62% 70% 83%

Scenario 5 Avg Customer Load kW 146,800 102,760 51,380 51,380 117,440 58,720 58,720 129,184 43,061 86,123

Percentage 100% 70% 80% 88%

Unit Capacity Electricity Heating Cooling Electricity Heating Cooling Electricity Heating Cooling Scenario 1 Avg Customer Load kW 146,800 124,780 41,593 83,187 117,440 39,147 78,293 111,568 37,189 74,379

Percentage 100% 85% 80% 76%

Scenario 2 Avg Customer Load kW 146,800 137,992 45,997 91,995 126,248 42,083 84,165 108,632 36,211 72,421

Percentage 100% 94% 86% 74%

Scenario 3 Avg Customer Load kW 146,800 136,524 45,508 91,016 123,312 41,104 82,208 110,100 36,700 73,400

Percentage 100% 93% 84% 75%

Scenario 4 Avg Customer Load kW 146,800 136,524 45,508 91,016 143,864 47,955 95,909 127,716 42,572 85,144

Percentage 100% 93% 98% 87%

Scenario 5 Avg Customer Load kW 146,800 146,800 48,933 97,867 132,120 44,040 88,080 123,312 41,104 82,208

Percentage 100% 100% 90% 84%

Unit Capacity Electricity Heating Cooling Electricity Heating Cooling Electricity Heating Cooling Scenario 1 Avg Customer Load kW 146,800 104,228 52,114 52,114 96,888 48,444 48,444 89,548 59,699 29,849

Percentage 100% 71% 66% 61%

Scenario 2 Avg Customer Load kW 146,800 93,952 46,976 46,976 73,400 36,700 36,700 60,188 40,125 20,063

Percentage 100% 64% 50% 41%

Scenario 3 Avg Customer Load kW 146,800 101,292 50,646 50,646 91,016 45,508 45,508 85,144 56,763 28,381

Percentage 100% 69% 62% 58%

Scenario 4 Avg Customer Load kW 146,800 118,908 59,454 59,454 105,696 52,848 52,848 83,676 55,784 27,892

Percentage 100% 81% 72% 57%

Scenario 5 Avg Customer Load kW 146,800 105,696 52,848 52,848 89,548 44,774 44,774 70,464 46,976 23,488

Percentage 100% 72% 61% 48%

Source: The demand scheme was developed based on the data of current Taipower supply capacity and the total demand of Taichung Industrial Park as of March, 2012

According to the list of hypothesized demand schemes in Table 4, the load-time curve of each scenario can be drawn as illustrated in Figure 9. It is expected that the diversity and variation among scenarios and within scenarios should be able to account for the

possible uncertainies facing the microgrid model.

Figure 9: Monthly customer demand curves of Taichung Industrial Park for five scenarios