Reference no: EM133120673

ELEC9715 Electricity Industry Operation and Control - University of New South Wales

Question 1

Calculate the optimal unit commitment program using forward dynamic programming for the power system described below over a day's operation. The power system has PV, Wind, Nuclear, Coal, CCGT, Gas Engines and OCGT generation, with operating characteristics as shown in the table below. It also has 16GWh of battery utility energy storage (BESS) with a maximum discharge / charge of 2GW. For simplicity, assume that there are no round trip losses in operating the storage (typically around 95% round trip efficiency for li-ion). Assume that all generators can operate at any level between 0MW and their installed capacity, except the nuclear plant which always runs at its 2GW of rated output. You can ignore network losses and constraints. Note that there is a $50/tCO2 carbon price on the electricity industry.

For convenience the day is divided into 6 four time blocks. Over the day demand varies from 6 to 15GW, while the wind and solar also vary between 1-5GW and 0-7GW respectively as shown in the table below. You'll note the daily capacity factors of around 44% and 30% respectively for wind and solar. You can assume that the day- ahead forecasts for these renewables are very accurate. The residual demand after subtracting renewables that must be met from the thermal generation (Nuclear, Coal, CCGT, Gas Engines and OCGT) is also shown.

To solve optimal battery storage operation and mimimise industry operating costs over the day, first calculate the operating cost for supplying this residual demand over 4 hours in 1GW increments from 2GW (the nuclear power generation which cannot be turned down) to 9GW (the maximum available thermal plant capacity). Now you can solve optimal battery storage operation using dynamic programming. For convenience, you can assume that the BESS is at 50% state-of-charge (8GWh of electricity) just before the first four hour block (0-4 hours). Also, the battery can only operate at 0, 1GW or 2GW charging or discharging, and stays at the chosen rate for the entirety of any four hour period. Also the BESS, and must be returned to 50% state-of-charge at the end of the last time block (20-24 hours) - otherwise, the lowest cost option would always be to empty the storage at the end of the day. You may find the table in the assignment spreadsheet of assistance in solving the dynamic programming, including the way it lays out the state space. Note that not all states at all time periods are feasible (due to 2GW maximum charge/discharge limits on the BESS or the minimum 2GW of nuclear) or acceptable (you can assume that residual demand must always be met).

What is the optimal charging / discharging trajectory for the battery storage over the day, and the lowest possible operating cost for the power system over the day? To assist, I have solved the State transition costs for the first time step (0-4 hours) and there is space for you to calculate the total cost of getting to each State from every other feasible or acceptable State, making it easy to then identify the least cost path to each State, and use these when calculating the least cost for the next time step.

Note that when determining the cost of meeting residual demand you need to consider reduced thermal generation (hence lower system operating costs over the four hours) if you discharge the storage, and increased thermal generation (hence higher system operating costs) if charging over that time. Also, given the maximum charging rate of 2GW the storage state-of-charge can only change by a maximum 50% (8GWh) from one time period to the next.

Discuss your findings and their implications for energy storage in a power system with lots of PV, wind that mainly blows in the early morning and late evening, and demand that is relatively low overnight with a morning peak and then larger early evening peak.

Question 2: Note that an Excel workbook with 30 minute NEM pricing for 2020 is on the Moodle.

You are one of the trading team for a NEM generation participant with a 1000MW coal fired unit in NSW. The operating cost of the plant is $35/MWh and it has a minimum operating level of 400MW.

In December 2019 you were asked to hedge this plant's operation for the following year so you sold a 1000MW CFD for Calendar year at a strike price of $80/MWh (the market expectation for the average NSW spot price over 2020 as reflected in ASX pricing in that month - see below). Now, in January 2021 your manager asks you to assess the success of your hedging strategy for 2020 given that market outcomes are now known. Using the NSW 30 minute pricing data for 2020 provided in the spreadsheet, assess the total operating profit/loss from the plant under different CFD contracting and operating strategies in the spot market:
- No CFD and the plant operates at 1000MW for every 30 minute period in the NEM
- No CFD and the plant the plant operates at 1000MW when the price is above $35/MWh, and at its minimum operating level of 400MW when the price is below $35/MWh
- The 1000MW CFD you sold in December 2019, and the plant operating at 1000MW for every 30 minute period in the NEM
- The 1000MW CFD you sold in December 2019 and the plant operates at 1000MW when the price is above $35/MWh, and at its minimum operating level of 400MW when the price is below $35/MWh.
- Instead of selling a 1000MW CFD you sold a 400MW CFD on the basis that you wanted to have some spot market exposure. The plant again operates at 1000MW for prices above its operating cost, and at minimum operating level when the price is below it.

You can assume that your coal plant offer strategy doesn't impact pricing (although it almost certainly would in practice). Be sure to present your results in a table showing separate CFD and spot market operating profits, as well as total operating profits for each of these 5 scenarios. Discuss your findings. Do you believe that your manager should be providing you with a bonus, or firing you? You might want to consider some reasons why 2020 might have been a rather surprising year for all NEM market participants.

Question 3

A power system has a mix of old thermal, CCGT OCGT gas fired generation as well as considerable wind and PV generation with overall capacity and operating costs as shown below (you may note some similarities with South Australia). The steam turbine gas generation is old and becoming unreliable with an estimated forced outage rate of 0.05 at any given hour. The 2000MW of wind generation has the following overall probability distribution - 1400MW for 35% of hours, and 500MW for the other 65% of hours (yes - rather simplified). The 1000MW of PV can be modelled as operating at 600MW for 50% of hours and 0MW for the rest (yes...)

All of this serves a load with the inverted load duration curve shown below. Note that the value of any Unserved Energy (USE) is estimated to be $15000/MWh while any excess renewable generation is curtailed. Assume that the wind farm output, PV generation and load, as well as the thermal gas plant forced outages are all independent (ie. not correlated in any way) - yes, extremely simplified. Ignore minimum operating levels, network losses and constraints etc (yes, extremely simplified).

The simulation period is one year ahead. Using a table to present your results, enumerate all possible scenarios of generation, wind farm and PV generation and load demand in terms of their probabilities for any given hour, ability of this available generation to meet demand, and associated power system production costs ($/hr). Use this table to calculate over a typical year:
(a) Loss of load probability (total hours/year)
(b) Expected unserved energy (USE) (% of load) over a year
(c) Expected production cost over the year ($000) noting again that USE costs $15000/MWh
(d) Average price for electricity required to cover this expected production cost ($/MWh)

Question 4
Consider a power system with demand varying between around 3-10GW, and a generation mix of 3GW of brown coal, 4.5GW of gas, 4.5GW of wind and 3.5GW of utility PV. You may note some similarities to a potential future Victorian generation mix given their State renewables target, although note there is no Hydro (for simplicity). The 30 minute demand, wind and PV profiles for 2024 are provided in an Excel file on Moodle.

Solve economic dispatch for this power system for each 30 minute period over the year. Hence estimate the:
(a) Loss of load probability (total hours/year)
(b) Expected unserved energy (USE) (% of load)
(c) Production cost over the year ($million) noting that any USE over the year costs $15000/MWh
(d) Proportion of variable renewable generation that is spilled (% of spilled renewables compared with potential renewable generation).
(e) Expected generation mix (ie. the % proportion of generation over the year from each technology adjusting for spilt generation and assuming that solar is curtailed before wind)

You can assume that the coal and gas plant have operating costs of $30 and $100/MWh respectively, with no minimum operating levels or ramp rates, and are always available. The wind and PV have $0/MWh operating costs. Likewise, there are no network interconnections, constraints or losses that you need to consider. For economic dispatch, you need to stack the available generation from lowest to highest operating cost up to the MW of demand for each 30 minute period. Note that Excel has a very useful function - MIN(x, y) that returns the lesser of two numbers, which just might be remaining demand vs available plant capacity for the next least cost generation technology. NORM.INV is another very useful function for this assignment, as you'll see below.

Now consider the case where 1.5GW of the coal-fired generation is increasingly unreliable, and suffers from random failures which require repairs. The time between failures for this 1.5GW of coal generation has an approximate normal distribution with a mean of 700 hours and standard deviation of 190 hours (but noting of course that there can be no negative times between failures, although it is possible the plant fails again almost immediately after repair - it does happen). The time to repair this coal generation after failure (i.e. the time for which it is out of service) also has an approximate normal distribution with a mean of 50 hours and standard deviation of 20 hours (again, there can be no negative repair times but there may well be a number of ‘0' hour repairs where the unit can be bought back into service almost immediately)

At the beginning of the period, you can assume that this 1.5GW of unreliable coal generation has just been repaired and become available. Use Monte-Carlo simulation of the operation of this power system to estimate Loss of Load Probability, Unserved Energy, expected industry production cost, expected generation mix over a year and proportion of spilled renewables using the following technique.
(1) Using the Excel random number generator function to determine time (hrs) to failure (remember that NORM.INV function I flagged earlier), and then to repair for a year of operation of this unreliable coal-fired generation.
(2) Matching these times to failure and repair to the nearest half hour period, solve economic dispatch over the year. The dispatch will be unchanged from the case above when this unreliable coal-fired generation is available, but may change markedly for those time periods that 1.5GW of generation is unavailable.
(3) Assess power system operation using the five metrics noted above.

You are strongly advised to do a number of Monte-Carlo simulations of a year of power system operation to see how much variation you see in annual power system performance due to the particular sequence of random numbers that you use. You can use averaging over multiple years to get a better ‘average' estimate of power system performance. When doing this be sure to ensure that you don't just get the same string of random numbers from the Excel random number generator each time (random number generators often aren't actually random unless you force them - be sure to test if the Excel function does actually provide a new string of random numbers each time you use it. In the past one of the tricks to get truly random numbers was to seed the function with the clock time before using it.)

Discuss your findings, and their potential implications for electricity industries with growing proportions of wind and solar, yet also increasingly unreliable old coal-fired generation.