Microgrid to Provide Ancillary Services by Stochastic Optimization IFAC 2017 World Congress, Toulouse, France The 20th World Congress of the International Federation of Automatic Control, 9-14 July 2017 Microgrid to Provide Ancillary Services by Stochastic Optimization E. Corsetti, A. G. Guagliardi, C. Sandroni Ricerca sul Sistema Energetico – RSE Milan - ITALY

Content The power system transformation microgrid to provide ancillary service Dealing with uncertainties in operational planning Stochastic optimization (stochastic and robust prog.) An example Conclusions Descrizione generale del progetto Definizione dell'obiettivo del progetto Si tratta di un progetto simile a progetti passati o di una nuova impresa? Definizione dell'ambito del progetto Si tratta di un progetto indipendente o correlato ad altri progetti? * Si noti che questa diapositiva non è necessaria per le riunioni settimanali di aggiornamento sullo stato del progetto Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

The power system transformation La trasformazione del sistema elettrico: Agli impianti tradizionali (grandi impianti termici, controllabili centralmente, installati sulle reti di trasmissione), si affiancano Impianti da fonte rinnovabile, solare e eolico, non-programmabili distribuiti e con controllo localizzato decentralizzato installati sulle reti di media e di bassa tensione La rete elettrica è progressivamente accoppiata la rete di trasferimento dati per il monitoraggio il controllo degli impianti. La pianificazione dell’esercizio per includere la maggior parte dei generatori da fonte rinnovabile richiede algoritmi di previsione molto sofisticati e algoritmi di pianificazione che tengano conto delle incertezze legate alla produzione. Le microreti sono piccole reti elettriche accoppiate alla rete principale tramite un solo punto (PCC) e riuniscono al loro interno produzioni da fonte rinnovabile e fossile (gas), carichi di diverso tipo e in alcuni casi sistemi di accumulo. La generazione da fonte rinnovabile deve partecipare sempre di più non solo alla produzione di energia ma anche alla fornitura di servizi per la gestione in sicurezza del sistema elettrico. La fornitura di servizi è il veicolo per espandere la quota di energia rinnovabile e per fornire al sistema la necessaria stabilità Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

The power system transformation Intra-day Day ahead La trasformazione del sistema elettrico: Agli impianti tradizionali (grandi impianti termici, controllabili centralmente, installati sulle reti di trasmissione), si affiancano Impianti da fonte rinnovabile, solare e eolico, non-programmabili distribuiti e con controllo localizzato decentralizzato installati sulle reti di media e di bassa tensione La rete elettrica è progressivamente accoppiata la rete di trasferimento dati per il monitoraggio il controllo degli impianti. La pianificazione dell’esercizio per includere la maggior parte dei generatori da fonte rinnovabile richiede algoritmi di previsione molto sofisticati e algoritmi di pianificazione che tengano conto delle incertezze legate alla produzione. Le microreti sono piccole reti elettriche accoppiate alla rete principale tramite un solo punto (PCC) e riuniscono al loro interno produzioni da fonte rinnovabile e fossile (gas), carichi di diverso tipo e in alcuni casi sistemi di accumulo. La generazione da fonte rinnovabile deve partecipare sempre di più non solo alla produzione di energia ma anche alla fornitura di servizi per la gestione in sicurezza del sistema elettrico. La fornitura di servizi è il veicolo per espandere la quota di energia rinnovabile e per fornire al sistema la necessaria stabilità Operational planning Market results Operation Service provision Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Ancillary Services (AS) Primary – secondary - tertiary control regulation Active power balancing Congestion resolution export active power import active power Day ahead (hours) I servizi al sistema elettrico: I servizi che possono essere offerti alla rete sono diversi da paese a paese, e normalmente sono ancora incentrati sui grandi impianti termoelettrici. Quelli presi in considerazione sono relativi agli scambi di potenza attiva e reattiva per il controllo della frequenza, il bilanciamento della potenza attiva e la risoluzione delle congestioni. La gestione dei servizi è vista sia nelle fasi day-ahead (di pianificazione dell’esercizio) e sia nella fase intra-day (applicazione del programma e controllo dell’andamento) Intra-day (hours – 15-minutes – minutes - seconds) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Microgrid AS provision Microgrid encloses: generators, loads and storages with a PCC; Ancillary Services (AS) planning after energy market result; AS prices uncertainty: what are the best bids to import or export a specific quantity of active power during day hours; Microgrid operator strategy: AS offer to purchase (import) active power: to supply extra loads at cheaper price; AS offer to sell (export) active power: to get revenue; Distribution operator strategy: To maintain grid stability by AS supplied by different users with a high reliability (user extra-capability) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Dealing with uncertainties in OP MODEL Constraints + Objective Function Uncertain Variables UNCERTAINTY MODEL Constraints + Probabilistic Objective Function Decision Variables MODEL: è la optimization planning deterministica UNCERTAIN identifica i parametri(le variabili) che sono soggette a incertezza OP>TIMIZATION: è la fase di elaborazione e soluzione del modello ottenuto dai passi precedenti, il suo output consiste del valore delle variabili di decisione e del modello ottimo OPTIMIZATION Optimal Design Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Stochastic optimization - algorithms Linear Programming (deterministic model) min 𝑥,𝑦 𝑐∙𝑥+𝑑∙𝑦 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: 𝐴𝑥=𝑏, 𝐵𝑥+𝐶𝑦=𝑒, 𝑥, 𝑦≥0 Stochastic Optimization Problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Stochastic programming: x : decision variables not conditioned by uncertainty DESIGN VARIABLES y : decision variables influenced by uncertainty CONTROL (DECISION) VARIABLES Robust Programming : z : error vectors to measure INFEASIBILITY of control constraints under scenario s. mean moment (other moments can be introduced in order to qualify robust program) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Stochastic optimization - algorithms Stochastic programming optimization problems with uncertainty (two stages) min 𝑥 𝑡,𝑠 ( 𝑡 ( 𝑐 𝑡 ∙ 𝑥 𝑡 ) + 𝑠 𝑝 𝑠 ∙ 𝑡 (𝑑 𝑡,𝑠 ∙ 𝑦 𝑡,𝑠 ) ) , 𝑡∈𝑇, 𝑠∈𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜𝑠 Stochastic Optimization Problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Stochastic programming: x : decision variables not conditioned by uncertainty DESIGN VARIABLES y : decision variables influenced by uncertainty CONTROL (DECISION) VARIABLES Robust Programming : z : error vectors to measure INFEASIBILITY of control constraints under scenario s. mean moment (other moments can be introduced in order to qualify robust program) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Stochastic optimization - algorithms Robust programming (some) robustness measures are dealt with uncertainty min 𝑥 𝑡,𝑠  ( 𝑥 𝑡 , 𝑦 𝑡 )+∙(𝑧) mean moment + feasibility penalty min 𝑥 𝑡,𝑠 𝑡,𝑠 𝑝 𝑠 ∙( ( 𝑐 𝑡,𝑠 ∙ 𝑥 𝑡 )(𝑑 𝑡,𝑠 ∙ 𝑦 𝑡,𝑠 ) )+∙(𝑧) 𝑡∈𝑇, 𝑠∈𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜𝑠 : tradeoff between feasibility robustness and costs. Stochastic Optimization Problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Stochastic programming: x : decision variables not conditioned by uncertainty DESIGN VARIABLES y : decision variables influenced by uncertainty CONTROL (DECISION) VARIABLES Robust Programming : z : error vectors to measure INFEASIBILITY of control constraints under scenario s. mean moment (other moments can be introduced in order to qualify robust program) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Stochastic optimization – scenarios & risk Uncertain parameters and associated values identify the possible scenarios of the problem N-parameters each one with m-values give rise to a huge number of scenarios (#𝑆= 𝑚 𝑛 ), limit the number of scenarios to confine the complexity of the evaluation: 1 m 2 n … Stochastic Optimization Problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Stochastic programming: x : decision variables not conditioned by uncertainty DESIGN VARIABLES y : decision variables influenced by uncertainty CONTROL (DECISION) VARIABLES Robust Programming : z : error vectors to measure INFEASIBILITY of control constraints under scenario s. mean moment (other moments can be introduced in order to qualify robust program) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Stochastic optimization – scenarios & risk risk evaluation criteria to select the best result from the optimization: ℛ 𝑠 𝑡 = 𝒫 𝑠 ⋅ℐ(𝑠) ( 𝒫 𝑠 is the probability of a fault event, and ℐ(𝑠) is the impact, that is the cost, associated to the event occurrence;) Risk is an index about the possibility to really provide the service offered. Services are offered according to capability, that is: the availability of generation (sell energy), or absorption (purchase energy). Impact associated to risk to not-provide the service: it is defined by some penalty cost; Stochastic Optimization Problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Stochastic programming: x : decision variables not conditioned by uncertainty DESIGN VARIABLES y : decision variables influenced by uncertainty CONTROL (DECISION) VARIABLES Robust Programming : z : error vectors to measure INFEASIBILITY of control constraints under scenario s. mean moment (other moments can be introduced in order to qualify robust program) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Microgrid resources: Generator (CHP gas engine) Different electrical loads (inelastic, flexible and cumulative) and thermal load; Electrical storage system; PV field; PCC (Point of Common Coupling). Microgrid input data forecasts (typical winter day): Microgrid characteristics Input for the experimentation Elastic load (not necessarily supplied) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Energy price results and AS prices forecast for the day-ahead market; Scenario definition: AS prices variability and associated probability; To buy To sell Prob.[%] 5 40 10 30 variability 0.6 1 1.4 0.2 1.7 scenarios S1 S2 S3 S4 S5 S6 Descrizione generale del progetto Definizione dell'obiettivo del progetto Si tratta di un progetto simile a progetti passati o di una nuova impresa? Definizione dell'ambito del progetto Si tratta di un progetto indipendente o correlato ad altri progetti? * Si noti che questa diapositiva non è necessaria per le riunioni settimanali di aggiornamento sullo stato del progetto Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision The set of constraints Power balance 𝑃 𝐺𝑟𝑖𝑑 𝐼𝑛 𝑡 − 𝑃 𝐺𝑟𝑖𝑑 𝑂𝑢𝑡 𝑡 + 𝑃 𝐺𝑒𝑛 𝑠 𝑡 + 𝑃 𝐵𝑎𝑡 𝑑𝑐ℎ,𝑠 𝑡 + 𝑃 𝑝𝑣 𝑡 + 𝑃 𝐺𝑟𝑖𝑑,𝐴𝑆 𝐼𝑛,𝑠 𝑡 − 𝑃 𝐺𝑟𝑖𝑑,𝐴𝑆 𝑂𝑢𝑡,𝑠 𝑡 + 𝑃 𝐵𝑎𝑡 𝑐ℎ,𝑠 𝑡 = 𝑃 𝐿𝑜𝑎𝑑 𝑇𝑂𝑇,𝑠 𝑡 , 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑡𝑇, 𝑠𝑆 Storage system state of energy 𝑆𝑜𝑒 𝐵𝑎𝑡 𝑠 𝑡+1 = 𝑆𝑜𝑒 𝐵𝑎𝑡 𝑠 𝑡 − 𝑃 𝐵𝑎𝑡 𝑑𝑐ℎ,𝑠 𝑡 ∙ 1 𝐸 𝐵𝑎𝑡 𝑚𝑎𝑥 ∙ η dch ∙𝜏+ 𝑃 𝐵𝑎𝑡 𝑐ℎ,𝑠 𝑡 ∙ 𝜂 𝑐ℎ 𝐸 𝐵𝑎𝑡 𝑚𝑎𝑥 ∙𝜏 Cumulative loads 𝑙 𝐶,𝑠 𝑖 𝜏 = 𝑡∈𝜏 𝑙 𝐶,𝑠 𝑖 (t)∙𝜏 , 𝜏⊆𝑇 & 𝑠∈𝑆 … Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Stochastic programming (SLP) Objective Function (two-stage) min 𝑃 (𝑐(𝑡) 𝑃 𝐺𝑟𝑖𝑑 𝐼𝑛 𝑡 −𝑟(𝑡) 𝑃 𝐺𝑟𝑖𝑑 𝑂𝑢𝑡 𝑡 + 𝑠∈𝑆 𝑝 𝑠 𝑡∈𝑇 𝑟 𝐴𝑠𝐺𝑟𝑖𝑑,𝑠 𝐼𝑛 𝑡 𝑃 𝐴𝑠𝐺𝑟,𝑠 𝑂𝑢𝑡 𝑡 + 𝑐 𝐴𝑠𝐺𝑟𝑖𝑑,𝑠 𝐼𝑛 ∙ 𝑡 + 𝑃 𝐺𝐸𝑁 𝑠 𝑡 ∙ 𝑐 𝑆 𝐺𝐸𝑁 𝑡 − 𝑙 𝐴,𝑆 𝑒𝑙 (𝑡)∙𝛿 𝑡∈𝑇 𝑟 𝐴𝑠𝐺𝑟𝑖𝑑,𝑠 𝐼𝑛 𝑡 𝑃 𝐴𝑠𝐺𝑟,𝑠 𝑂𝑢𝑡 𝑡 + 𝑐 𝐴𝑠𝐺𝑟𝑖𝑑,𝑠 𝐼𝑛 ∙ 𝑡 + 𝑃 𝐺𝐸𝑁 𝑠 𝑡 ∙ 𝑐 𝑆 𝐺𝐸𝑁 𝑡 − 𝑙 𝐴,𝑆 𝑒𝑙 (𝑡)∙𝛿 , where #T=24h Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Robust (Ro) programming Objective Function. Generator operating costs are the limit of service provision selling energy: min 𝑃  𝑠∈𝑆 𝑝 𝑠 𝑡∈𝑇 𝑃 𝐺𝐸𝑁 𝑠 𝑡 ∙ 𝑐 𝑆 𝐺𝐸𝑁 𝑡 −𝑟 𝐴𝑠𝐺𝑟𝑖𝑑,𝑠 𝐼𝑛 𝑡 𝑃 𝐴𝑠𝐺𝑟,𝑠 𝑂𝑢𝑡 𝑡 2 Tests with different weights  to highlight different models: Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Ro15 Ro10 Ro5 Ro1  15 10 5 1 Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Stochastic optimization –microgrid AS provision Practical risk index definition: Probability to not-provide the service is computed by (relative) extra-capability (EC). EC to provide energy generation or absorption is in per unit. Impact associated to risk to not-provide the service: it is the double fare associated to the service; EC>2 2> EC >1 1> EC> 0.5 0.5>EC>0.1 0.1>EC>0 Probability 0.01 0.05 0.2 0.3 0.5 Stochastic Optimization Problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Stochastic programming: x : decision variables not conditioned by uncertainty DESIGN VARIABLES y : decision variables influenced by uncertainty CONTROL (DECISION) VARIABLES Robust Programming : z : error vectors to measure INFEASIBILITY of control constraints under scenario s. mean moment (other moments can be introduced in order to qualify robust program) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: Total costs Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Costs shown by all models have the same trend, SLP in S3 shows a light minimum; Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: Elastic load supplied Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) All models have the same behaviour, unless SLP which in S1 and S2 completely supply the elastic load; this impact very little on costs as the AC price to purchase Energy is very low compared with the operation costs of the gas engine. Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: Service provision – purchase and sell energy Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Diagrams show just scenarios compatible with the service; Costs to purchase energy (left) are comparable, a little difference for SLP in S2 and S3 due to extra-cost to supply the whole set of elastic loads. Revenues to sell energy (right) do not show relevant differences; Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: Service provision – relative extra capability Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) These graphs are built for those scenarios to provide a (coherent) service, and express a relative extra-capability; Absorption capability is greater for robust methods; Generation capability is quite homogenous; Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: Service provision – risk evaluation Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Risk associated to the different methods are quite homogenous. Differences can be neglected. Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: Summary Among the different robust algorithms (R1, R5, R10 and R15) there are no relevant differences to justify their distinction; Really, for the data proposed and the robust penalty function, even between stochastic and robust appear very light differences. The most relevant one concerns the ability of stochastic algorithm to supply the whole elastic load, at least in the absorption scenarios. The robust methods are limited by the penalty function that fosters energy export, rather than energy import to supply extra loads; Risk: the greater risk to absorb energy shown by stochastic method is justified by the huge quantity of extra load that reduce the extra-absorption, while for the robust method holds the opposite; The best bid exhausts the extra load of the microgrid. Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

An example – microgrid AS provision Results of experimentation: The plan of stochastic method for Scenario2 Stochastic optimization problems: The nature of decisions (discrete – continuous – scalar – vector) Uncertainties (binomial failure – gaussian noise in weather – loads and generation – heavily tailed electricity prices) The dynamics (…) Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.

Conclusions and future work Work proposed Stochastic and robust programming algorithms was proposed to set the best bid for microgrid provision of ancillary service with prices uncertainty to the problem for the AS market for a microgrid; The proposed mathematical models integrates elastic and cumulative loads in order to increase the absorption capability of the microgrid. It also provides specific index to evaluate the service provision reliability (risk and capability); Stochastic programming and robust optimization shown very light differences; Future work Consider extra uncertainty parameters (e.g., renewable power production, load forecasts, ecc.) at the same time; Enable the switch between scenarios during program application (deal with storage complexity). Descrizione generale del progetto Definizione dell'obiettivo del progetto Si tratta di un progetto simile a progetti passati o di una nuova impresa? Definizione dell'ambito del progetto Si tratta di un progetto indipendente o correlato ad altri progetti? * Si noti che questa diapositiva non è necessaria per le riunioni settimanali di aggiornamento sullo stato del progetto Microgrid to Provide Ancillary Services by Stochastic Optimization - E. Corsetti et Al.