Numerical Evaluation

2.7.2.1 Using the Generic Price Profile

The RTOS algorithm formulated in Section2.3 (considering the price modulation mech- anism as stated by (2.9)) has been executed in a simulation environment. Three different

price profiles each with different modulation factors are used for evaluations. The generic price profile is shown in Fig. 2.6 while price levels (A, B, and C) are defined in Table2.13

for three cases (typical price levels in Ontario’s market [65]). Different values of round- trip efficiency for storage between 30% and 70% are considered. The extra revenue of the CAES sized in Section 2.4, is calculated and compared for different cases.

The RTOS algorithm is simulated for a one-year time period considering three dif- ferent modulation factors and different round-trip efficiencies of storage. Annual extra revenue is calculated for the three predefined price profiles and shown in Fig. 2.7in terms of million dollars. As represented in Fig. 2.7, as storage efficiency increases, the revenue increases almost linearly since by increasing the efficiency, the energy loss in storage system decreases. As novel technology materializes, the storage efficiency increases, and thus, storage utilization will become more economical.

Moreover, as represented in Fig. 2.7 (the left-hand and middle columns), the curves at the left side of breakpoints are approximately flat. In this area, storage is not operated since it cannot overcome the OPEX. As expressed in the following, at the left side of the breakpoint efficiency, the arbitrage benefit is less than the OPEX:

X

t∈Ni

(P_tS,Dhg−P_tS,Chg). E_tF M rk.∆T < X t∈Ni

(CS,DhgO. P_tS,Dhg +CS,ChgO. P_tS,Chg).∆T.(2.14)

As represented in Fig. 2.7, there are different breakpoints for Profile 1 (left-hand column) and Profile 2 (middle column), and there is no such a point for Profile 3 (right- hand column) considering storage efficiencies from 30% to 70%. As reported in Table

2.13, each profile has a different High to Low Price Ratio (HLPR) (i.e., C/A ratio) in

weekdays. The larger the HLPR is, the smaller the efficiency breakpoint will be. Since the efficiency at the breakpoint depends on the value of HLPR, and HLPR does not change by price modulation, the breakpoint efficiency does not change at different modulations. The minimum SOC constraint (see (2.6)) forces the storage once a day for compensa- tion of energy dissipation to maintain the SOC above or equal to theSOCS

min. Since any

operation at efficiencies smaller than the breakpoint causes financial loss, as shown in Fig. 2.7 (left-hand column), higher operations of storage results in lower extra revenue.

As the curves of Fig. 2.7(a, d, and, g) represent, in the case of un-modulated prices (i.e., at I = 1), the annual extra revenue is negative for most of the operating points;

negative extra revenue in one operating point means that using the storage is no longer economical. However, by modulating the price profiles, the obtained annual extra revenue increases for the operating points with efficiencies larger than the breakpoint efficiency. If the storage operating point is smaller than the breakpoint efficiency, the price modulation

2.7. Storage Incentivisation 37 30 40 50 60 70 -9 -8 -7 -6 (a): I=1 30 40 50 60 70

Annual Extra Revenue (Million Dollar)

-10 -8 -6 -4 -2 (b): I=2 Round-Trip Efficiency (%) 30 40 50 60 70 -12 -10 -8 -6 -4 -2 0 (c): I=3 30 40 50 60 70 -10 -8 -6 -4 -2 0 (d): I=1 30 40 50 60 70 -10 -5 0 5 10 (e): I=2 Round-Trip Efficiency (%) 30 40 50 60 70 -10 -5 0 5 10 15 20 (f): I=3 30 40 50 60 70 -10 -5 0 5 10 (g): I=1 30 40 50 60 70 -10 0 10 20 30 (h): I=2 Round-Trip Efficiency (%) 30 40 50 60 70 -10 0 10 20 30 40 50 (i): I=3 Break point Break point Break point Break point Break point Break point

Figure 2.7: Annual extra revenue of storage operation vs. round-trip efficiency for three price profiles (see Table 2.13) each with three different price modulation factors. (a), (b), and (c): For price Profile 1; (d), (e), and (f): For price Profile 2; (g), (h), and (i): For price Profile 3.

does not have considerable effect on storage benefit since storage is not operated.

Moreover, comparing the HLPR value of price profiles, it can be observed that the larger the HLPR is, the more extra revenue is obtained (compare Fig. 2.7 (left-hand, middle, and right-hand columns). By increasing the HLPR in Profile 2 compared to Profile 1 and Profile 3 compared to Profile 2, the extra revenue increases.

2.7.2.2 Using Real-world Data

In this section, wholesale electricity prices publicly available in Ontario’s market are used for evaluations. The RTOS algorithm formulated in Section 2.3 (considering the price

Modulation Factor "I" 1 1.5 2 2.5 3 Extra Revenue (M$) -5 0 5 10 15 (a)

Modulation Factor "I"

1 1.5 2 2.5 3 -4 -2 0 2 4 6 (b)

Figure 2.8: Five-year average of storage extra revenue vs. modulation factor I; (a): for the

perfect price forecast and (b): for an imperfect price forecast in Ontario’s electricity market. Table 2.14: Five-year Average of the Extra Revenue in Ontario’s Market (Based on Fig. 2.8)

Perfect Forecast (Fig. 2.8 (a)) Imperfect Forecast (Fig. 2.8(b))

I = 1 I = 1.3 I = 1 I = 1.87

Storage Extra Revenue −$1.94 M $0.00 M −$3.9 M $0.00 M

modulation mechanism as stated by (2.9)) has been executed in a simulation environment for Ontario’s market from 2006 to 2009 and 2011. Two studies have been conducted as follows: In one study, the price forecast is assumed to be perfect; this means that the price forecast is substituted with the actual prices. The second study is conduced using an imperfect forecast of market prices using the back-casting method.

The annual extra revenue of storage operation in Ontario’s market from 2006 to 2009 and 2011 has been calculated and shown in Fig. 2.8 (a) and Fig. 2.8 (b) for perfect and imperfect price forecasts, respectively, at different price modulation factors. Different modulation factors are employed to evaluate the impact of electricity price modulation on storage revenue in case of a real-world market. The five-year average of extra revenue has been reported in Table 2.14 for two important values of modulation factors: I = 1

(pertaining no incentive) and Imin, where Imin is considered as the modulation factor in

which the annual extra revenue of storage operation reaches to zero.

As represented in Fig. 2.8 and Table 2.14, at I = 1, the annual extra revenue is

negative revealing that the storage is not able to return the expected revenue plus OPEX. Moreover, the annual extra revenue increases linearly by increasing the price modulation factor revealing the efficacy and feasibility of the proposed method to incentivize storage owners. As reported in Table 2.14 for the perfect forecast, I = 1.3 is required in order