4. Chapter Four: Optimal Operation of Microgrids
4.3 Optimisation Model of Microsources
Energy management of the microgrid sets the active and reactive power output of each of the microsources. It was developed and tailored for the microgrid with the high penetration of distributed generators, including renewable energy sources. The energy management problem amounts to minimising the microgrid social net cost. It affects operation cost, minimises the network losses, reduces greenhouse gas emissions and particulates, and adjusts the value of voltage and frequency in microgrid operation. The economic optimisation of the microgrid regarding costs, losses and greenhouse gases, is implemented using the economic dispatch. The main impact of the economic dispatch is balancing the generation and demand in microgrid operation to maintain the voltage and frequency range. This section focuses on the economic dispatch problem to produce an output power of microsources in a multiobjective function, in both grid connected mode and islanded mode. The objective function introduces multiobjective functions, which are lowest operation cost, lowest pollutants treatment cost and lowest carbon dioxide treatment cost. The output of the optimisation model is the optimal operation of the microgrid when considering all parameters, which include the following:
Technical performance of available energy sources. Sun irradiation.
Fuel cost. Daily sell-buy power tariff.
Startup cost. Losses of the microgrid operation.
Wind speed. Pollutants treatment costs.
Several different kinds of literature have detailed the modelling of various microsources of the microgrid, such as [106], [287]–[291]:
4.3.1 Wind turbines model
Two important factors are considered in the design of the wind turbine model: the wind speed at the specific location and the power curve of the wind turbine. The optimisation wind turbine model, which is used to calculate the output power supplied by the wind turbine generator as a function of wind velocity, density of air, capture area or swept area, and capacity factor, can be calculated by 𝑃𝑊= { 0 𝜈 < 𝜈𝑐𝑖 0.5. 𝑠𝑎. 𝑣3 . 𝑟ℎ𝑜. 𝑐𝑓 𝜈𝑐𝑖 ≤ 𝜈 ≤ 𝜈𝑐𝑜 𝑃𝑊𝑟 𝜈𝑐𝑜 ≤ 𝜈 < 𝜈𝑐𝑐𝑜 0 𝜈𝑐𝑐𝑜 < 𝜈 4-1 𝑆𝑤𝑒𝑝𝑡𝑎𝑟𝑒𝑎(𝑠𝑎) = 𝜋 (𝑟𝑜𝑡𝑜𝑟𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 2 ) 2 4-2 where Cut on speed 𝜈𝑐𝑖 = 3 𝑚/𝑠 Corner Speed 𝜈𝑐𝑜 = 14 𝑚/𝑠 Cut out speed 𝜈𝑐𝑐𝑜 = 25 𝑚/𝑠 Rotor Diameter = 10 𝑚 The density air 𝜌 = 0.1 𝑘𝑔/𝑚3
Capacity Factor (cf): it is actual output to potential output ratio.
The wind speed data for the rated power of 50kW from the wind generator output is obtained from [292] for 24 hours on 26 July 2015, as shown in Figure 4-6.
Figure 4-6: Wind turbine power generation (simulated results)
4.3.2 Photovoltaic arrays model
The photovoltaic system is a set of solar cells electrically connected and supported in a mechanical structure. The simple equivalent model of a solar cell is shown in Figure 4-7; it is represented by a diode in parallel with the constant current source and shunt resistance, all of which are connected in series with resistance. The series resistance represents the internal resistance of the current flow, whereas the shunt resistance relates inversely to the leakage current to the ground. Ideally, there is no series loss. Thus, the series resistance is equal to zero, and there is no leakage to the ground where shunt resistance is equal to infinity. The photovoltaic model is very sensitive to any variation in series resistance, whereas it is not sensitive to the variation of shunt resistance. Therefore, any change in series resistance could affect the photovoltaic model output significantly. The output current of a solar cell is proportional to the light falling on the cell. It is necessary to take weather data (irradiance and temperature) as an input variable to draw current, voltage, and power as an output value. The net current of the solar cell, which represents the difference between photocurrent and diode current [293], [294], is explained in the following:
𝐼 = 𝐼𝐿− 𝐼𝑜𝑠(𝑒𝑞(𝑉+𝐼𝑅𝑠)𝑛𝑘𝑇 − 1) −𝑉 + 𝐼𝑅𝑠 𝑅𝑠ℎ 4-3 𝐼𝐿 = 𝐺 100[𝐼𝑆𝐶𝑅 + 𝐾𝐼(𝑇 − 25)] 4-4
𝐼𝑜𝑠= 𝐼𝑜𝑟(𝑇 𝑇𝑟) 3 𝑛 𝑒 𝑞𝐸𝐺𝑂 𝑛𝑘(1 𝑇− 1 𝑇1) 4-5 𝐼𝑜𝑟 = 𝐼𝑠𝑐(𝑇) (𝑒𝑞(𝑉𝑜𝑐(𝑇))𝑛𝑘𝑇1 − 1) 4-6
The series resistance of each cell can be written as: 𝑅𝑠 = − 𝑑𝑉 𝑑𝐼𝑉𝑜𝑐− 1 𝑋𝑉 4-7 𝑋𝑉 = 𝐼0(𝑇) 𝑞 𝑛𝑘𝑇1 𝑒𝑞(𝑉𝑜𝑐(𝑇))𝑛𝑘𝑇1 4-8
. The net output power of a photovoltaic cell depends mainly on the number of solar cells connected to the model. A photovoltaic system output is typically connected to microgrid via an inverter to convert the output DC power of the photovoltaic system side to AC power at the grid side. D + - Rsh Rs Ipv Load
Figure 4-7: Photovoltaic model
The standard output power and maximum output power tracking of the cell are shown in the following:
𝑃𝑐𝑒𝑙𝑙 = 𝑉𝑔𝐼 4-9
𝑃𝑚 = 𝑉𝑚𝐼𝑚 4-10
The solar generation data for photovoltaic generation output are obtained from [292] for 24 hours on 26 July 2015, as shown in Figure 4-8. The rated power of the photovoltaic cell is 50 kW and the total surface to combine them can be described by.
Figure 4-8: Photovoltaic power generation (simulated results)
4.3.3 Microturbines model
The microturbine is a small combustion distributed generator with a power output of 25 kW to 500 kW. The microturbine creates high-speed rotation by burning gaseous and liquid fuel to generate electricity. Typically, the microturbine can ramp up within a short time, estimated to be between 10 seconds and several minutes, to generate electricity based on the size range [289]. Microturbine efficiency increases with the increase of supplied power [295]. The microturbine has the environmental advantage of low emissions as well as fuel cells [296]; fuel cells are quieter than microturbines.
4.3.4 Fuel cells model
A fuel cell is a small electrochemical process distributed generator with a power output of a few kilowatts. The fuel cell produces energy using an electrochemical reaction between oxygen and hydrogen. The fuel cell has a higher efficiency and lower emissions than diesel engines; however, it is too expensive for many applications.
4.3.5 Diesel generators model
A diesel generator is a small combustion distributed generator with various power outputs from small units of 1 kW to large units of several tens of MW. The diesel generator is used in many applications because of its high efficiency and reliability. The diesel generator also has a fast dynamic response for disturbance rejection to cover any sudden changes in demand. However, the power cost and carbon dioxide emissions of a diesel generator are relatively higher than other distributed generators. The fuel cost of diesel generator power can be modelled as a quadratic polynomial according to
𝐶𝑑𝑔,𝑖 = ∑ 𝛼𝑖 + 𝛽𝑖𝑃𝑑𝑔,𝑖+ 𝛾𝑖𝑃𝑑𝑔,𝑖2 𝑁
𝑖=1
4-12
The comparison between distributed generators is shown in Table 4-1.
Table 4-1: Distributed generators compression [297]–[300]
Criterion Fuel cell Gas turbine Diesel
Efficiency over a wide range of loads
Relatively flat Best at > 80%, very poor at partial load
Best at > 75%, poor at partial load
Response to load changes
Slow at start-up Fast Good
Life 5 years (goal) 20+ years 20+ years
Noise vibration Low Medium High
Power range 20-2500 kW modular Up to 50 MW Up to 68 MW
NOx, CO, HC
emissions, CO2
Very low, reduced CO2
Medium, no CO2
benefit
Medium
Life time in operation hours
>2,000 >20,000 ~13,000
Moving parts number of units
Blower/pump Rotor only >50
Thermal management
Water cooled Exhaust emission Water cooled
Onboard fluid storage
Water antifreeze None Water antifreeze and lubricating oil
Electrical generation Yes Yes Yes
Emission control treatment
No Yes Yes
Freeze tolerant No Yes Yes
>60oCambient operation
Not proven Not proven yes
Heat to power ratio 1.4 2.6 1.6