In this section, optimal water system management with DR participation is evaluated. Then, water system strategies regarding bids on the spot market are analyzed, according to spot price scenarios. Finally, the benefits for using the flexibility of the water system for power system management are discussed. Optimization Problem 1 described in Section 3 has been resolved for a range of market price scenarios using the branch and bound algorithm (B&B) under the CPLEX optimization solver.
A real drinking water system in France was used as benchmark. This system contains one production plant, 11 pumping stations, and 14 distribution reservoirs. The average daily water demand of the system is about 50000 m3 in winter.
A water demand history of 32 scenarios is available in winter for the system. These scenarios were used to build the forecasted maximum and minimum hourly water demand profiles. Extreme demands (max and min) were constructed by taking upper and lower envelopes over a proportion p of historic scenarios. The choice of the scenarios on which the envelopes were calculated is such that the area between maximum and minimum envelopes is minimal (the mathematical method for extracting these scenarios is not detailed in this article).
As shown in Fig. 3, the hourly water demand profile is similar to that of the electricity load. The forecasted profile was built by taking an arithmetic mean on the 32 historical demands. Extreme demands were built by taking upper and lower bound on a fixed number of 25 scenarios, corresponding to 80% of scenarios. The 80% value was chosen because it corresponds to a safe level of control of uncertainties.
For numerical simulations, we used data for the year 2016 in winter, corresponding to spot and compensation prices between 18:00 to 20:00. Spot prices are available in the French power exchange (Epex Spot) website. The compensation price was 56.10 €/MWh in winter 2016 at peak times.
Resolution of Problem 1 yields optimal schedules for pumps, an optimized management of tank levels covering potential water demand uncertainties, and optimal peak power reduction to be sold on the market via the DR NEBEF mechanism. For an average spot price of 81 €/MWh for the year 2016, some simulation results are presented in Figs. 4 and 5.
As shown in Fig. 4, pumping operations are minimized for the water system during peak hours (06:00 to 20:00) to meet the demand at minimum cost. Meanwhile, tank levels gradually decrease, without reaching the minimum level of security in order to anticipate possible water demand forecasting errors (see Fig. 5). However, a higher activity of pumps is observed at off-peak hours (20:00 to 06:00) to take advantage of the cheapest electricity tariffs. During the DR period, the tanks level drop as pumping operations isminimized, but it does not reach the minimum level of security in anticipation of unexpected water demand hazards. On the other hand, some peak hours experience pumping operations:
1) During the morning water peak period 08:00 when the water demand is very high;
2) Midday at 13:00 to anticipate possible water demand hazards;
3) During the past reference period (16:00 to 18:00) to have a water reserve during the DR event (18:00 to 20:00).
Problem 1 was solved for a range of spot prices. The reported results are optimal DR powers maximizing the profitability of the water system while meeting all constraints. The net benefit was defined as the difference between spot price and compensation. Simulation results as well as net benefit ranges for winter 2016 between 18:00 to 20:00 are presented in Table 1.
Net benefit (€/MWh) <0 1 to 50 51 to 100 >100 Frequency (%) 4.5 74.0 6.5 15.0 DR power (MW) 0.00 2.00 to 2.40 2.40 to 2.50 2.50 to 2.74
Table 1. Net benefit ranges frequency between18:00 and 20:00
As shown in Table 1, the NEBEF mechanism was not financially viable during 4.5% of the time as spot prices were less than the compensation price (negative net benefit). This implicitly implies that the power system did not need any DR because the available generation was sufficient to meet the requested demand at minimum cost.
For the positive net benefit ranges, the function of evolution of optimal DR power reduction is obviously growing with market price (see Fig. 6). This is justified by the objective function, which aims to maximize the economic value of DR. The function is concave and the slope is decreasing with the price. The optimal DR power is:
1) Very sensitive for prices between 0 and 100 €/MWh since the water system still has an enough flexibility to react to the price signal;
2) Minimally sensitive for prices between 100 €/MWh to 400 €/MWh since the water system has only a reduced available flexibility;
3) Constant for prices >400 €/MWh as the water system is using its maximum DR power capacity.
On the other hand, the DR peak load reduction curve is compatible with the needs of the electric power system. The high price periods correspond to the most stressed supply/demand equilibrium periods on the market, when high-cost high-emissions fossil generation units are the most solicited and when DR is the most useful.
For financial analysis and for all market price scenarios considered for winter 2016, we compared:
1) The economic cost of a pump-scheduling day without DR consideration, which corresponds to the classical pump scheduling problem.
2) The economic cost of a pump-scheduling day with DR participation, where the economic cost corresponds to the pumping cost minus the DR economic benefits and depends on the market price scenarios considered.
The aim of this comparative study was to highlight the economic interest that DR through the NEBEF mechanism could bring to water utilities. For this purpose, two Monte-Carlo simulations were used to find the average strategic behavior of the water system regarding bids on the spot market. We considered market prices for winter 2016 on working days, corresponding to a total of 62 scenarios. Two Monte-Carlo simulations were performed:
1) Simulation 1: Removing five scenarios from November 2016 with price spikes above 250 €/MWh (57 scenarios). These scenarios were removed because they corresponded to the extreme and rare situations where the power grid was on the edge of stress. The results of this simulation would constitute a lower bound of the expected results.
2) Simulation 2: Considering all price scenarios from winter 2016 (62 scenarios). The results of this simulation would constitute an upper bound of the expected results.
The average economic gain and the average % gain are, respectively, defined as the difference and the relative difference between the optimal pump scheduling cost without DR and the optimal pump scheduling cost with DR, including DR benefits. Table 2 summarizes the numerical results obtained for the two simulations.
Monte-Carlo simulation Average DR peak load reduction (MW) Average economic gain Average gain (%) Simulation 1 2.23 55 2.9 Simulation 2 2.48 62 3.2
Table 2. Monte-Carlo numerical results
For the winter period studied, economic gains made by the water system would be in the interval [2.9%, 3.2%] of its daily electricity bill. DR can thus be considered as a win-win alternative for both power system operators and water utilities.
A major environmental challenge facing the world today is the risk of global warming. One of the major objectives of the energy transition is the reduction of greenhouse gas footprint, which is due in large part to the use of fossil power plants for electricity production.
France drives more than 72% of its electricity from nuclear energy, while fossil generation units account for only 9% of the country’s total electricity production, as shown in Fig. 7. These fossil power plants, thanks to their great flexibilities that they can be activated very quickly, are considered as peak generation units and are used to respond to rapid changes in the electricity demands and to manage special consumption peaks.
The thermo-sensitive nature of the French electricity demand implies a strong solicitation of peak generation units in winter. Fig. 8 shows the difference between CO2 emissions per kWh produced on a winter and summer day, respectively. We observe that 42% more CO2 is emitted in winter as compared to summer.
Figure 8. CO2 emissions for a normal and peak day (data source: RTE éCO2mix).
Taking into account compensation prices for 2016, a DR bid, if accepted in the market, would replace a peak generation unit bid according to the market’s merit-order principle (bids are accepted in an ascending order according to their operating costs). Renewables have a very low marginal cost and are found at the bottom of the market’s supply curve. Nuclear energy also has a low operating cost and follows the renewables in the ranking. Peak power plants, starting with coal-fired power plants, then combining with cycle gas plants (CCGT), and ending with diesel or gasoline fueled, have the highest running cost. Fig. 9 illustrates the merit-order principle and shows how DR could replace peak generation production.
In the example of Fig. 9, a peak day is considered with a compensation price of 56.1 €/MWh. Two supply curves on the market are considered: One with DR and one without DR consideration. In the situation without DR, block 4, corresponding to a combined cycle gas power generation bid, balanced the market with a marginal price of P*. With DR consideration, the DR block 4’ put for sale with a price of P*’<P*, replaced block 4 according to the merit-order principle and led to a new market price P*’<P*. As shown in Fig. 9, the DR block 4 would be inserted between two peak generation unit blocs, depending on the DR bid price and peak generations unit variable cost. In addition, it could also lower the market price if the DR bid is competitive (large volume).
For environmental analysis, Monte-Carlo simulation results from Table 2 were used to calculate the CO2 savings for the system through peak load reduction. It is assumed that each DR bid sold on the market is a complete substitution to a peak generation production. Table 3 shows the average contributions of the French peak generation technologies to CO2 emissions. Since it is difficult to estimate accurately the peak generation technology replaced by DR blocs, the average grams CO2/kWh (g CO2/kWH) ratio from all French peak generation technologies was used, weighted by their utilization rates during the year 2016.
Peak generation technology Emissions (g CO2/kWh) Coal groups 956 Fuel groups 800 Gas groups 360 Weighted average 2016 486
Table 3. Contribution of French fossil power plants to CO2 emissions in grams CO2 (source RTE éco2mix)
Significant CO2 reductions by the water system through peak load reduction during evening peak are highlighted in Table 4. The water system can reduce for up to 2.4 tons of CO2 by day, which is the equivalent of the emission of 1600 cars during 10 kilometers of driving.
Monte-Carlo simulation Average DR peak load reduction (MW) CO2 saving (tons) Simulation 1 2.23 2.16 Simulation 2 2.48 2.40
Table 4. CO2 savings by the water system through DR participation
To give more significance to the previous results, we propose to estimate the DR NEBEF potential at the French scale. The approach considered consists in extrapolating the results obtained from the system studied to all the French water systems, assuming they all have a comparable flexibility. Indeed, a water system’s flexibility depends on the profile of its water demand, the characteristics of its equipment (storage tanks and pumps), and the nature of its topology. However, because tanks are sized to cover summer water demand peaks, they have an extra reserve margin in winter. This extra reserve margin can be optimized for DR operations, which justifies the assumption of a comparable flexibility of French water systems in winter.
In France, the average daily consumption of a person is around 140 liters, which gives, for the whole country, a daily consumption of around 9100000 m3. Previous results obtained on the system with a demand of 50000 m3 were extrapolated to a water demand of 9100000 m3 as shown in Table 5.
Value per day/system Value per day/France Financial gains (€) 55 to 62 10 k to 12 k Peak power reduction (MW) 2.23 to 2.48 405 to 450 CO2 emissions avoided (tons) 1.08 to 1.20 392 to 436
Table 5. NEBEF potential for water systems in France
Results shown in Table 5 demonstrate that water utilities can trade DR on the French spot market while generating significant economic gains on their electricity bill. In addition, the aggregation of the water systems’ flexibility in France can reduce the power up to 450 MW during winter peaks. This peak power reduction, even if it is small in the French system where the peak load amounts to 90000 MW, can be very important in a period of stress on the power system. Indeed, the example of the crisis in California in June 2000 illustrates this fact: Rolling blackouts had occurred due to a shortage of 300 MW in a system of 50000 MW. Furthermore, many CO2 emissions could also be saved by avoiding the production of additional electricity coming from fossil generation units to balance the supply and demand on the market.
The development of demand side management in the industrial sector could be hampered by two obstacles: Financial viability and risk management. Companies could be reluctant to participate in DR programs if they do not well manage the uncertainties and risks about the operation of their systems. Meanwhile, they must ensure a sufficient financial viability for the DR participation to remain competitive in markets. Mathematical programming could address both of these challenges, as shown in this article for the water industry where the case of a medium size water system was discussed. The mathematical model makes it possible to:
1) Estimate, based on a water demand history, the extreme water demands with a certain degree of robustness;
2) Secure the operation of the system regarding water demand hazards by keeping an extra water volume margin in tanks (optimization of tank level management);
3) Optimize DR load reduction powers by scheduling pumps.
Numerical results were discussed considering French spot prices for the winter 2016. Two Monte-Carlo simulations were performed, corresponding to low and high averages of the expected results. The results were discussed under three criteria:
1) Operational criterion: Operating the water system;
2) Economic criterion: % of gains for the water utility;
3) Ecological criterion: DR load reduction powers by scheduling pumps.
Benefits have been demonstrated considering these three criteria, confirming the relevance of the approach. However, the bold extrapolation made in subsection 4.5 may be questionable. Indeed, the hypothesis of a comparable flexibility for all French systems in winter is based on the fact of a better flexibility of tanks in winter due to a lower water demand. However, other parameters have not been taken into consideration such as the nature of pumps and the topography of the system.
Finally, it would be interesting to aggregate the flexibility of several water systems to propose large volumes of peak load reduction, enabling to improve the power system’s reliability at peak times. The difficulty would be to manage several independent systems through a mathematical optimization model. Information exchange between different water systems and the joint management of uncertainties are two challenges to be tackled.