Analysis of the Impact of Sub-Hourly Unit Commitment on Power System Dynamics

This paper discusses the impact of the sub-hourly unit commitment problem on power system dynamics. Such an impact is evaluated by means of a cosimulation platform that embeds a sub-hourly stochastic mixed-integer linear programming security constrained unit commitment (sSCUC) into a time domain simulator, as well as includes a rolling planning horizon that accounts for forecast updates. The paper considers different sub-hourly sSCUC resolutions (i.e., 5 and 15 minutes) and different wind penetration levels (i.e., 25 and 50%). The focus is on the transient response of the system and on frequency variations following different sSCUC strategies, and different sSCUC wind power uncertainty and volatility. The case study consists of a comprehensive set of Monte Carlo simulations based on the 39-bus system.

1. Introduction 1 Transmission system operators (TSOs) rely on hourly unit commitment 2 (UC) models to economically operate the system [1]. Since large amounts of 3 stochastic renewable energy sources (RES) can significantly impact on the per-4 formance of the system [2, 3], stochastic programming has been introduced in 5 and demand. Therefore it is of particular importance to model the uncertainty 116 when scheduling the system. There are different methodologies and techniques 117 proposed for optimization under uncertainty, with one of the most popular be- 118 ing the two-stage stochastic programming. In the context of UC, the two-stage 119 stochastic UC makes use of a probabilistic model for the uncertain input param-120 eters, e.g. wind generation, and is usually approximated by a set of scenarios 121 representing the plausible realizations of these random parameters [4]. 122 In this work, a standard MILP sSCUC problem is implemented based on [33], in which wind power production is considered as an uncertain parameter of the system, as follows: (∀g ∈ G, ∀t ∈ {2..., T }) z SU g,t − z SD g,t = z F g,t − IS g (5) (∀g, ∀t ∈ {1}) z SU g,t + z SD g,t ≤ 1 (6) (∀g, ∀t ∈ {1..., T }) z F g,t = IS g (7) (∀g, ∀t > L U P (∀g, ∀t > L U P − f ∈Fn W SP f,t,ω = m∈Mn (δ n,t,ω − δ m,t,ω ) X n,m (∀n, ∀t, ∀ω ∈ Ω) (∀g, ∀t, ∀ω ∈ Ω) p g,t,ω ≥ P min (∀g, ∀t, ∀ω ∈ Ω) p g,t,ω ≤ (P IS g + RU g )z F g,t (∀g, ∀t ∈ {1}, ∀ω ∈ Ω) p g,t,ω ≥ (P IS g − RD g )z F g,t (∀g, ∀t ∈ {1}, ∀ω ∈ Ω) p g,t,ω − p g,t−1,ω ≤ (2 − z F g,t−1 − z F g,t )P SU g (15) + (1 + z F g,t−1 − z F g,t )RU g ) (∀g, ∀t ∈ {2, ..., T }, ∀ω ∈ Ω) p g,t−1,ω − p g,t,ω ≤ (2 − z F g,t−1 − z F g,t )P SD g (16) (∀g, ∀t ∈ {2, ..., T }, ∀ω ∈ Ω) L SH l,t,ω ≤ L l,t (∀l, ∀t, ∀ω ∈ Ω) (∀f, ∀t, ∀ω ∈ Ω) − P max n,m ≤ (δ n,t,ω − δ m,t,ω ) X n,m ≤ P max n,m (∀n, m ∈ M n , ∀t, ∀ω ∈ Ω) p g,t,ω , L SH l,t,ω , W SP f,t,ω ≥ 0 (20) (∀g, ∀l, ∀f, ∀t, ∀ω ∈ Ω) (∀g, ∀t) and the initial state conditions are as follows: (3) represent the total cost to be minimized which includes the fixed, constraints. The power balance constraint is modeled through equations (10). 128 While the capacity limits of generating units are modeled through equations 129 (11)- (12) and their respective ramping limits through (13)-(16 To illustrate the modelling of sSCUC wind uncertainty and volatility, and rolling planning horizon used in this paper, we show below the power balance equations of the sSCUC, as follows: where p g,t,ω is the active power of conventional generating units g, at time 150 period t, and scenario ω (i.e., equivalent of the second-stage variable u f,t,ω in 151 section 2.3); L l,t is the demand for load l at time period t; L SH l,t,ω is the power 152 curtailment from load l, at time period t, and in scenario ω; W k,t,ω and W SP k,t,ω 153 represent the power generation and curtailment, respectively, from wind unit 154 k, in time period t, and scenario ω; X n,m is the reactance of line n − m; δ n,t,ω 155 represent the voltage angle at node n, time period t, and scenario ω; and Ω Kn , 156 Ω Mn are the sets of stochastic power generation (i.e., wind) located at node n, 157 and nodes m ∈ N connected to node n by transmission line, respectively.  high and low wind power scenarios (W H k,t,ω , W L k,t,ω ) are built as percentages of 162 the medium scenario, as follows: where j is the percentage of deviation of the the high and low scenarios with 164 respect to the medium one.

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The consistency of the wind power scenarios with real-world information is 166 compared using wind power data of the   e.g. standard deviation, on top of the wind power forecast [36]. A normal 176 distribution N (µ, σ 2 ) with zero mean and given standard deviation is attached 177 to each wind power scenario, as follows: where W L1 k,t,ω , W M 1 k,t,ω , W H1 k,t,ω are the new low, medium and high wind power 179 scenarios, respectively, after adding the volatility.

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An important aspect to keep in mind when building the scenarios is the 181 relationship between the wind power level and its standard deviation σ. With 182 this aim, two typical days are analysed for two months, namely January (high 183 wind) and July (low wind). The wind power profile for these typical days is 184 shown in Fig. 2. It appears that wind varies more in January than in July.

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More specifically, the standard deviation of wind power generation is found to 186 be 234.78 MW and 68.46 MW, for January and July, respectively, and that high 187 wind leads to higher σ.

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Note that the goal is not to propose new sSCUC models to deal with wind 189 power uncertainty and volatility, but rather to study the impact of a well as-       In order to compare results, a base-case scenario is considered with the   To analyse this relevant case, more scenarios are considered. In Scenarios 326 6 to 9 in Table 1, the probabilities of sSCUC are varied from a sSCUC with 327 100% high wind to a sSCUC with 100% medium, and it can be seen that σ COI To further analyse this, in Table 2    with a significant added value for the operation of the system.

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Finally, Table 3 compares three deterministic cases, namely, low, medium 346 and high sSCUC wind power scenarios. The deterministic low wind power 347 scenario leads to better dynamic behaviour (lower σ COI ).   to the results shown in Fig. 6, this relationship appears to be almost linear 372 within the considered range. As mentioned above, this supports the idea for    (Fig. 1). Next, the base case scenario is depicted in Fig. 8, 9. Compared to 383 the base-case scenario in the 15-minute case study (Fig. 4), frequency variations 384 are lower (Fig. 8)     approaches without compromising the dynamic performance of the system.

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While the sensitivity analysis in case of the perfect forecast is shown in Table   402 5. The deterministic case with low wind gives the better dynamic behaviour, 403 thus confirming the conclusions drawn for the 15-minute sSCUC.  Figure 10 shows σ COI as a function of wind power uncertainty. Again, we 410 can see that such a relationship is almost linear within the used range. This 411 suggests that, even using shorter sSCUC timescales, e.g. 5 minute, higher shares 412 of RES will likely affect the dynamic performance of the system. Following the same procedure as in the 15-minute case study, the standard 415 deviation of wind power scenarios is increased from 10% to 40% with a step of 416 10%. Then, Fig. 10 shows σ COI as a function of wind power volatility. This 417 relationship is almost linear within the considered range, and so these findings 418 just support the conclusions made above. Finally, the impact of wind power 419 volatility on costs is shown in Fig. 11. Results indicate that the higher the wind 420 power volatility, the higher the cost due to more ramping of generating units. parison is performed using scenario 1 (stochastic) and scenario 5 (deterministic) 426 from Table 1.   significantly.
482 Figure 16 shows the trajectories of ω COI for this base case scenario. Com-483 pared to Fig. 4 (3 sSCUC wind power scenarios), there is no significant difference 484 in the dynamic behaviour of the system. To further support this, Table 7 shows 485 some of the relevant results of the sensitivity analysis. As it can be seen, the 486 long-term frequency deviations are similar to those in Table 1 and do not differ 487 Figure 16: 15-minute scheduling -Trajectories of ω COI for 10 sSCUC wind power scenarios. and Ireland, the main concern for TSOs will be on how to cope with 512 high ramp-up and ramp-down of RES rather than the traditional N − 1 513 contingency criteria.

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• In general, higher RES penetration leads to lower costs. However, simu-515 lation results indicate that while the total operating cost will be reduced, 516 the reward of ancillary services will increase due to more ramping of gen-517 erating units.

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• Increasing the number of sSCUC wind power scenarios, namely, from 3 to 519 10, leads to very similar long-term frequency deviations of the system.

541
• Finally, results show that wind power uncertainty has a greater impact 542 than volatility on the dynamic performance of the system, while the other 543 way round is true for the impact on the expected cost. respectively, leads to lower long-term frequency deviations of the system.

579
Future work will focus on designing a feedback control that will take a signal 580 from the system and send it to the sSCUC. Other works will also consider the 581 interaction between sSCUC, microgrids and DAEs. Finally, a study on the 582 impact of sub-hourly UC with inclusion of voltage constraints on long-term 583 dynamic behaviour of the system will be considered.