Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs

Filomena, Tiago Pascoal; Lejeune, Miguel A.

doi:10.1007/s10957-013-0348-y

Cited by 19 publications

(9 citation statements)

References 45 publications

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“…The extra wind capacity in Case 2 displaces over 15% of the conventional generation in Case 1, but at the same time, the combined amounts of capacity needed for up, down and contingency reserves increases by just over 50% from 60 GW/day in Case 1 to 91 GW/day in Case 2. 5 In spite of the increase in total reserves in Case 2, the maximum amount of conventional capacity committed 6 is reduced by more than 5 GW from 63.1 GW in Case 1 to 57.9 GW in Case 2, corresponding to roughly one third of the new wind capacity in Case 2. The importance of this reduction is that although the objective function considers only the costs of operating the system, reducing the maximum capacity committed at the system peak load corresponds to reducing the capital costs of the installed capacity needed to ensure that generation capacity is adequate.…”

Section: The Four Cases Analyzedmentioning

confidence: 98%

“…The main effects of adding deferrable demand in Case 3 compared to Case 2 are 1) slightly less of the PWG is spilled, 2) much less reserve capacity (53 GW/day) is committed because the deferrable demand provides some ramping services, and 3) an additional 3 GW less conventional capacity is needed to maintain adequacy because the deferrable demand shifts some load from the system peak to off-peak hours. 5 The reported amounts of reserves are the sums of the 24 hourly commitments for each type of reserves 6 This maximum is the sum of the maximum commitments for each generating unit over all system states and hours Turning now to the differences in results between the fixed and receding horizons, the differences for Case 1 are trivial because the initial amount of wind capacity is very small, but in Case 2 with 16 GW of additional wind capacity, the receding horizon does lead to lower average costs than the fixed horizon, particularly in the early hours of the morning when most charging occurs (see figure 3). The main reasons, based on the results in table III, are that using the receding horizon leads to 1) slightly less of the PWG is spilled, 2) less up and down reserves for ramping are needed because the updated forecasts of PWG are more accurate, 3) less contingency reserves, and 4) a lower maximum commitment of conventional capacity.…”

Section: The Four Cases Analyzedmentioning

confidence: 99%

“…Stochastic programming has dimensionality issues (e.g., [1], [2]) which are handled using sampling methods to select a subset of possible scenarios by, for example, focusing on the most influential ones [3]. Probabilistic optimization allows violation of some specified network constraints within a threshold [4], [5]. Robust optimization considers a lower bound on the total social benefits by looking at the worst case realizations before the actual system state is realized [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Case for a Simple Two-Sided Electricity Market

Lamadrid

Jeon

Hao

et al. 2017

Proceedings of the 50th Hawaii International Conference on System Sciences (2017)

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Abstract-This paper builds on the results from our earlier research on the design of electricity markets that have to accommodate the uncertainty associated with high penetrations of renewable sources of energy. The key results show that 1) distributed storage (deferrable demand) is an effective way to reduce total system costs, 2) a simple market structure for energy allows aggregators to meet their customers' energy needs and provide ramping services to the system operator, and 3) using a receding-horizon optimization to dispatch units for the next market time-step benefits from the availability of more accurate forecasts of renewable generation and allows market participants to adjust their bids and offers in response to this new information. In our two-sided market, distributed storage in the form of deferrable demand is controlled locally by independent aggregators to minimize their expected payments for energy in the wholesale market, subject to meeting the energy needs of their customers. In addition, these aggregators are responsible for maintaining a stable power factor by installing local capabilities that automatically deal with local power imbalances. Failure to do this triggers penalties paid to the system operator.Our earlier results have shown that it is optimal for an aggregator to submit demand bids into a day-ahead market that include threshold prices for charging and discharging storage and also ensure that the expected amount of stored energy is consistent with the capacity limits of their storage. Because departures from the expected daily pattern of renewable generation are generally persistent (highly positive serial correlated), it is likely that the system operator determines an optimum pattern of demand for the aggregator that violates the capacity limits of storage by the end of the 24-hour period. If the market uses a receding horizon, the results in this paper show that aggregators can modify their bids to ensure that the capacity limits of storage are never violated in the next market time-step.In an empirical application, a stochastic form of multi-period security constrained unit commitment with optimal power flow (the MATPOWER Optimal Scheduling Tool, MOST) using a receding-horizon optimization determines the optimum dispatch and reserves for the next hour and forecasts of the nodal prices for the next 24 hours. The results show that locally controlled deferrable demand is almost as effective as centrally controlled deferrable demand as a way to reduce system costs and mitigate the variability of renewable generation. The additional advantage from using a receding horizon is that the system operator always charges/discharges the storage managed locally by aggregators within the capacity constraints of the storage.

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Section: The Four Cases Analyzedmentioning

confidence: 98%

Section: The Four Cases Analyzedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Case for a Simple Two-Sided Electricity Market

Lamadrid

Jeon

Hao

et al. 2017

Proceedings of the 50th Hawaii International Conference on System Sciences (2017)

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“…Moreover, let

μ \in {double-struckR}^{r}

with

μ = E [ξ]

and

Σ = E [false(ξ - μ false) {(ξ - μ)}^{T}]

be the mean and the covariance matrix for the r ‐variate distribution of ξ, respectively. Formulation

min x^{T} Σ x

s.t. P (ξ^{T} x \geq R) \geq p

e^{T} x = 1

x \geq 0

is usually referred to as the probabilistic Markowitz formulation and its deterministic equivalent defines a nonlinear optimization problem (NLP) (see Bonami and Lejeune, ; Filomena and Lejeune, , ; Lejeune, ). Let

ψ = false(ξ^{T} x - μ^{T} x false) ∕ \sqrt{x^{T} Σ x}

be the standardized random variable representing the normalized portfolio return.…”

Section: Robust and Probabilistic Approachesmentioning

confidence: 99%

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

Mencarelli

d'Ambrosio

2018

Int Trans Operational Res

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In this paper, we review convex mixed-integer quadratic programming approaches to deal with single-objective single-period mean-variance portfolio selection problems under real-world financial constraints. In the first part, after describing the original Markowitz's mean-variance model, we analyze its theoretical and empirical limitations, and summarize the possible improvements by considering robust and probabilistic models, and additional constraints. Moreover, we report some recent theoretical convexity results for the probabilistic portfolio selection problem. In the second part, we overview the exact algorithms proposed to solve the single-objective single-period portfolio selection problem with quadratic risk measure.

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“…is usually referred to as the probabilistic Markowitz formulation and its deterministic equivalent defines a NLP (see [26,89,90,153]). Let ψ = (ξ x − µ x)/ √ x Σx be the standardized random variable representing the normalized portfolio return.…”

Section: Probabilistic Approachmentioning

confidence: 99%

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

Mencarelli

2018

4OR-Q J Oper Res

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Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs

Cited by 19 publications

References 45 publications

The Case for a Simple Two-Sided Electricity Market

The Case for a Simple Two-Sided Electricity Market

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

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