Smart Grids Optimization & Renewables Energies

SMART GRIDS OPTIMIZATION

https://www.doanalytics.net/Documents/Chapter-V-8-Smart-Grids-Optimization.pdf

INDEX

1. INTRODUCTION

1.1. OPCHAIN-ELE

1.2 OPCHAIN-SGO

1.3. OPCHAIN-SGO integrated with OPCHAIN-E&G

1.4. SMART GRIDS OPTIMIZATION - MATHEMATICAL MODELS

2. FORECAST MODELS

2.1. MATHEMATICAL METHODOLOGIES 

2.2. SHORT/MEDIUM/LONG TERM FORECASTING 

2.3. REAL-TIME/SHORT-TERM FORECASTING (STATE ESTIMATION)

2.4. RENEWABLE ENERGY SOURCES

2.5. MODELING SPOT PRICES IN A FREE MARKET

3. OPTIMIZATION MODELS

3.1. ECONOMIC/REGULATED DISPATCH

3.2. SMART GRID UNIT COMMITMENT

3.3. NETWORK DESIGN OPTIMIZATION

3.4. NETWORK RECONFIGURATION

3.4.1. VOLTAGE CONTROL

3.4.2. FEEDER RECONFIGURATION

3.4.3.   LOCATION/ACTIVATION OF ELECTRICAL ASSETS

3.4.4. PHASE BALANCING

3.5. ETRM: ENERGY TRADING & RISK MANAGEMENT

3.6. DESIGN OF POWER CRITICAL SYSTEMS INCLUDING RELIABILITY

3.7. INDUSTRIAL ENERGY EFFICIENCY

3.8. REAL-TIME DISTRIBUTED OPTIMIZATION

4. TECHNOLOGY PLATFORM

1. INTRODUCTION

1.1. OPCHAIN-ELE (ELEctricity Supply Chain Optimization)

?OPCHAIN-ELE (ELEctricity Supply Chain Optimization) corresponds to a set of mathematical models designed to support the decisions of the various actors involved in the electricity supply chain, in terms of sectoral planning and business generation. According to the structure of modern electricity markets, the support of the business decision-making power generation should be seen from two different points of view.

• Central agents: formed by the regulator, supervisor, planner and market operator
• Generators: agents that operate power plants.

OPCHAIN-GAS corresponds to a mathematical model designed to support the decisions of the various actors involved in the chain of supply of natural gas at the level of sectoral planning. OPCHAIN-ELE and OPCHAIN-GAS together make OPCHAIN-E&G a set of optimization model to dispatch the electricity and gas systems. OPCHAIN-E&G is designed to allow its users to parameterize the model according to the complexity of its supply chain and optimization requirements thereof.

More detailed information of OPCHAIN-E&G

• Electricity & Natural Gas - Advanced Supply Chain & Market Optimization

https://www.dhirubhai.net/pulse/electricity-natural-gas-advanced-supply-chain-jesus-velasquez/ 

1.2 OPCHAIN-SGO: Smart Grids Optimization

OPCHAIN-SGO (Smart Grids Optimization) is a new decision support system that is included in OPCHAIN-E&G. It corresponds to a set of mathematical models designed to support the decisions of the various actors involved in the smart grids supply chain:

1. Electricity Agents Smart Grids Optimization: optimization of the economic and technical aspects related to the “smart grids”.
2. Buildings/Homes Demand Response Optimization: optimization of the management of electrical energy in building assemblies; as:

• Universities
• Malls
• Office buildings
• Urbanizations
• Homes
• Small towns

3. Industrial Energy Efficiency Optimization: optimization of the management of electric power in industrial systems intensive in the consumption of energy.

1.3. OPCHAIN-SGO integrated with OPCHAIN-E&G

The mathematical models of OPCHAIN-SGO integrated with OPCHAIN-E&G cover all electricity supply chain.

The mathematical models of OPCHAIN-SGO may be integrated with OPCHAIN-E&G models sharing the same data-model information system.

1.4. SMART GRIDS OPTIMIZATION - MATHEMATICAL MODELS

OPCHAIN-SGO is integrated by forecast models and optimization models oriented to support the decision making of:

• Electricity Agents Smart Grids: optimization of the economic and technical aspects related to the “smart grids” in electricity companies;
• Buildings/Homes Demand Response: optimization of the management of energy in building assemblies, as: universities, malls, office buildings, homes, urbanizations and/or small towns
• Industrial Energy Efficiency: optimization of the energy management in heavy industries intensive in the consumption of energy.

The forecast models are:  

• FRES - Forecast of Renewable Energy Sources prediction of long (years, months), medium (week, months) and short (days, hours) term availability of renewable energy sources, such as: wind, solar radiation and water inflows.
• FDEM - Forecast of Electricity Demand prediction of long, medium and short term of the of electricity demand.

OPCHAIN-SGO is integrated by the following optimization models: 

• Smart Grid Economic/Regulated Dispatch: optimization of the management of electrical energy in: factories, universities, shopping centers, office buildings, urbanizations.
• Smart Grid Unit Commitment: optimization of the management of the electrical load in real-time.
• Smart Grid Network Reconfiguration: optimization of the topology of the network for: i) voltage control, ii) configuration of feeders, iii) location/activation of electrical assets (transformers, capacitors) and iv) phase balancing.
• Smart Grid Network Design: optimization of design and/or re-design of "smart grids" 
• ETRM - Electricity Trading & Risk Management: decisions to buy/sell electric power one day in advance and on the day of dispatch

2. FORECAST MODELS

The forecast models of OPCHAIN-E&G are required for shaping the future of the following variables: i) energy demand, ii) spot prices, iii) climatological variables and iv) other parameters that may be considered as random variables. These models should support the decision-making processes in: i) real-time/ short and (minutes, hours, days) ii) medium/long term (days, weeks, months,…) 

2.1. MATHEMATICAL METHODOLOGIES 

The methodologies available to deal with the characterization of demand are: i) Advanced Probabilistic Models (APM), ii) Machine Learning (ML), and iii) Artificial Neural Nets (ANN). Any of these methods (or mixes of them) may be the "best"; however, should be considered the integration between forecast models and decision-making optimization models based on Mathematical Programming (MP). In these cases, APM and ML are the simplest way to integrate since they are based on algebraic formulas that can be incorporated in MP optimization models. For the case of APM, the algebraic formulas can be incorporated into the models MP; in the case of ML, the Support Vector Machines (SVM) can be integrated into the MP. 

More information:

• Stochastic Advanced Analytics Modeling - OPCHAIN-SAAM

https://www.dhirubhai.net/pulse/stochastic-advanced-analytics-modeling-opchain-saam-jesus-velasquez/

2.2. SHORT/MEDIUM/LONG TERM FORECASTING 

OPCHAIN-SGO approach is oriented to characterize the forecast using models APM and/or ML that can be formulated as MP optimization models. OPCHAIN-SGO forecast models are based on a simultaneous equations model (linear or non-linear) that is solved with an optimization technology; the objective function may be: i) minimization of the squares of errors (APM), ii) maximization of likelihood function and iii) and minimization of classification errors (ML). This approach facilitates to include restrictions on the parameters to bring coherence to the estimation process. 

2.3. REAL-TIME/SHORT-TERM FORECASTING (STATE ESTIMATION)

 For real-time & short-term forecasting, OPCHAIN-SGO approach is based the concept of State Estimation (SE), specifically the mathematical methodology proposal Kalman (Kalman Filter, KF). 

 SE is supported on a conception of the stochastic processes where the random variable is differentiated of its measures, meaning that the modeler has historic measurements of the random variable and has not the “true” value of the variable; this is the fundamental difference with Classic Statistical approach.

 Therefore, all available observations are considered as random variables, generated by a metering system that is subject of precision errors; moreover, there might be more than one measure, obtained by multiples metering systems. Then two types of noise (errors) are considered in SE modeling:

• e(t), errors due to the modeling of the system, reflecting the uncertainty of knowledge of functions (equations and/or parameters) that determine the behavior of the system that is modeling
• q(t), measurement errors that come from the precision of the metering system.

The classic statistical models only considered a type error, m(t), which integrates modeling errors and measurement errors, m(t) = e(t) + q(t), whereas the SE modeling differs clearly the two types of errors.

KF defines a sequential process of estimation based on the Bayesian combination of a-priori information up to time t-1 with the information obtained at time t.

One of the problems facing in the SE modeling is the definition of the transition state function, Ft[x(t),u(t)], which may be based on: i) the physical process that occurs in the industrial system or ii) statistical parameters identification models. In general terms based on the prediction requires the problem of determining the "true" value of: i) state variables process (i.e precipitation, water inflows, demand, win speed, … ), ii) parameters of the physical models; and iii) parameters of statistical models. Then, SE advantage is possibility of representing the parameters dynamics with equations. This has resulted in creation Dual Kalman Filter () that simultaneously estimates: i) state variables and ii) parameters of the model.

The KF theory can be extended to consider the modeling of systems whose dynamic representation depends on the state system, or regime, in which the system is. The regime/state should be considered as an additional state variable which must be estimated "on line"; it may be associated with Markovian Process that includes a probability of transition between states in each period. The version of KF is called Multi-State Kalman Filter (MS-KF, Velasquez, 1978)

The following table presents the results of the use of the MS-KF in the basin of the Caroni River in Venezuela.

2.4. RENEWABLE ENERGY SOURCES

For the generation of synthetic scenarios of the variable climatic variables, there are two requirements: i) short term (hours, days) and ii) medium/long term (weeks, months). Short-term specific models for each renewable source, should be built, it is not considered in detail in this part.

For medium/long term, there are two alternatives to generate synthetic scenarios:

1.    Statistical synthetic generation model of climatic variables (type Fiering-Matalas),

2.    Generate synthetic series of climatic variables based on mixing of historical series

3.    Generate synthetic series based on the historical series having the ENSO (El Ni?o Southern Oscillation) series as an instrumental variable, this is the standard method in OPCHAIN-SGO.

ENSO events have proven to be determinants of climatological variables (water inflow, wind speed and solar luminosity) mainly in the Pacific Sea area; therefore; ENSO is a main variable to forecast the cost of the energy (via spot price or via marginal cost).

The importance of ENSO events has led to large amount of investigation by multiple organizations, which have multiple models oriented to forecast ENSO events in the short/medium term. Two types of models are used: i) Dynamic: based on the physical modeling of the dynamics of the process; and ii) Statistics: based on empirical evidence of the process adjusted through statistical models.

The International Research Institute for Climate and Society (IRI, https://iri.columbia.edu/, Columbia University) integrates all the predictions based on a Bayesian Ensemble Model that dynamically modifies the a-posteriori probability to be the correct for each of the models.

DW methodology is based on integrating the ENSO forecast of the IRI with the observed historical series of climatological variables. OPCHAIN-ENOS uses an optimization model of which results are the convex combination of historical series that “best” represent a synthetic scenario generated from the statistical characteristics of the IRI forecast.

2.5. MODELING SPOT PRICES IN A FREE MARKET

Prediction spot prices of the energy market is essential for decisions to take an agent that participates in the market, either buyer or seller, either generator, marketer or distributor of energy. Then, the decision-maker requires models that produce spot prices to be used in other mathematical models within the decision-making process.

Mathematical models to be used depend on: i) the planification period (“real-time”/short/medium/long term), and ii) type of the market considering the plant dispatch: by a mathematical model or by offers make by the market agents (“free market”).

 Additionally, two types of mathematical methodologies may be used: i) oriented to forecast based on the historical series” (Advanced Probabilistic Methods (APM), Machine Learning (ML) and Artificial Neural Nets (ANN)) and ii) techno techno-economic models like EDI, ERD, or similar models. This section discusses the case of short/medium/long term forecasting of spot prices using techno-economic models

 In markets dispatched by a mathematical model, the plants are dispatched according to the generation marginal costs that are calculated by a mathematical model that uses the ISO for planning and/or for scheduling (unit commitment); then “best” projection of spot prices, perhaps is that the ISO mathematical model produces.

 In the case of a free market the situation is more complex since the price formation "law" not always can be explained based on mathematical rules (explicit, clear and universal) as that integrates a dispatch mathematical model.

Experience indicates that the relationship of the spot price with marginal costs can be very weak as the graph presents. It was prepared with historical spot prices and the marginal costs of the ISO planning model in the Colombian market.

 Then in a free market the situation is more complex since the "law" of price formation not always can be explained based on mathematical rules (explicit, clear and universal) as traditional economic dispatch model.

The relationship between changes in the market regulation and structural changes in the spot price is evident, at least in the Colombian case. The graph presents two dates that occurred changes in the Colombian regulation, which brought changes in the mean and the standard deviation of the spot price.

Considering the history and experience of DW, OPCHAIN-ELE includes a probabilistic model of the spot price that is linked to variables and parameters of the economic dispatch model (EDI or ERD); it is based the Bayesian combination of several statistical models, that represent different regimes, this approach generates a greater capacity to reflect the tails of the distribution probability function.

3. OPTIMIZATION MODELS

3.1. ECONOMIC/REGULATED DISPATCH

Mathematical model oriented to medium-term planning of the management of electric power in: factories, universities, shopping centers, office buildings, urbanizations, ... . It corresponds to a model of economic dispatch, including constraints associated with the regulation of the electricity market.

 In addition to a planning tool, it is used as a primary information source in other models that are part of the OPCHAIN-SGO and it is based on the concepts of the current OPCHAIN-E&G dispatch model

3.2. SMART GRID UNIT COMMITMENT

 The OPCHAIN-SGO-UC dispatch model includes all the rules that must comply the unit commitment problem. The constraint may be related with: start/stop plants, must run plants, ramps, eolic efficiency, …

3.3. NETWORK DESIGN OPTIMIZATION

Optimal design of radial distribution networks including: power plants with renewable energy, energy storages, sub-stations, transformers, feeders and reliability restrictions. Network Design Optimization is part of the three models required for strategic decision making: 

• NDO - Network Design Optimization: Model of optimization that determines the topology and capabilities of the different types of power technologies that are part of a radial distribution network; 
• ERD – Economic Regulated Dispatch: Model used to determine primary information that is required in the optimal design model, this information may be related to: spot market prices and/or plant clearance. 
• FIN - Financial Evaluation: produces the financial reports required to evaluate the profitability of the financial viability of the projects.

The optimal design of smart grids entails a change in the traditional design modeling approach that assumes that the network topology remains constant once installation has been included in the system.

 New power technologies and the smart metering systems allow on-line, or frequently short (hourly, daily, weekly, monthly), reconfiguration of the system topology, then the optimization model must select the availability of core assets which can be reconfigured over the planning horizon, anticipating the actual operation that will be given in the future.

3.4. NETWORK RECONFIGURATION

Network reconfiguration is the dynamic optimization of the network topology for i) voltage control, ii) feeder configuration, iii) location/activation of electrical assets (transformers, capacitors) and iv) phase balancing.

3.4.1. VOLTAGE CONTROL

 The purpose of voltage control in distribution networks is to change the tap position of transformer regulators in order to achieve the goal of reducing power losses while maintaining satisfactory voltage profiles.

The change of voltage is through several onload tap changers (OLTCs), each capable of regulate the voltage of the secondary side of a transformer at one point in the network.

The purpose of voltage control in distribution networks is to change the tap position of transformer regulators in order to achieve the goal of reducing power losses while maintaining satisfactory voltage profiles.

The change of voltage is through several onload tap changers (OLTCs), each capable of regulate the voltage of the secondary side of a transformer at one point in the network.

 The problem minimizes power losses and switching (tap change) costs; subject to:

• Power flow equations;
• Voltage constraints, both phase to neutral and phase to phase;
• Current constraints, including cables, overhead lines, transformers, neutral and grounding resistance;
• Tap change constraints
• Shunt capacitor change constraints

The voltage control includes the Conservative Voltage Reduction (CVR) that is the concept of lowering the utilization voltage to end-use consumers such that their demands, and energy consumption, decreases. The most prominent benefit of CVR is the peak load reduction, which accordingly reduces the cost of power delivery because it costs more to run peaking generation units; CVR has another benefit of reducing power loss. CVR uses of both capacitors and voltage regulators.

3.4.2. FEEDER RECONFIGURATION

 Feeder reconfiguration is to alter the topological structures of distribution feeders by changing the open/closed states of the sectionalizing or tie switches. The goal is to minimize the total system power loss while keeping the generation cost of distributed generators at minimum.

Benefits of feeder configuration: i) improve network load balancing, i) reduce power losses and iii) prevent service disruption in case of power outage.

3.4.3.   LOCATION/ACTIVATION OF ELECTRICAL ASSETS

Location or relocation of portable assets in accordance with the characteristics of the market based on the periodic review of the operation of the Smart grid whose design can be adapted to changes in demand, seasonal or permanent. An example, the relocation of transformers.

3.4.4. PHASE BALANCING

The goal of phase balancing is to maximize the feeder capacity utilization, to improve power quality, and to reduce energy losses. It is a “combinatorial optimization” problem. The solution is the assignment of customer load to which of the three phases.

3.5. ETRM: ENERGY TRADING & RISK MANAGEMENT

OPCHAIN-ETRM corresponds to a set of mathematical models oriented to support the decisions of the different agents involved in the trade of energy in: i) long-term market, ii) sport market and iii) secondary markets. It is based on a stochastic optimization model that includes equations to risk management. The main input of ETRM is the forecasting of spot prices, two models are available for this:

• E&G-SPOT: Techno-economic (like EDI, ERD, or similar models) that determines spot prices in an energy market economic To be used in medium/large term forecasting. It was presented in a past section.
•  GARCH-SPOT: Spot prices statistical model using S-ARIMAX-GARCH methodologies taking as references historical spot prices series. To be used in real-time or in short-term forecasting. 

The outcome of a risk analysis is the definition of pareto curves risk versus expected income/cost, based on which the decision-maker must define the risk position.

3.6. DESIGN OF POWER CRITICAL SYSTEMS INCLUDING RELIABILITY

A Critical Electrical System (CES) is an electric distribution system, with indicators quality of the provision of transmission, such as the (System Average Interruption Frequency Index) SAIFI and SAIDI (System Average Interruption Duration Index), which they transgressed, or that may violate, their tolerances. The CES is an electrical system with interruptions mainly caused by disconnections (scheduled and unscheduled) on the premises of transmission (transmission lines, substations and transformers) that exceeded, or can be to exceed, the tolerances of rate of failure and unavailability, congestion, overload and other critical parameters, by forming a radial transmission system.

The general objectives are:

• Provide reliability critical electrical systems
• Optimal use of the Energy potential of wind, solar and water resources
• Future scenarios for the exogenous random variables

The reliability of a system may be based on multiple indicators of performance Key Performance Indicator (KPI), one of them, the simplest, it is the probability of correct functioning system. The reliability of distribution systems is a continuous concern for electricity distribution companies and regulators of the electricity sector. Reliability indices used to quantify the quality of the distribution companies’ services correspond to sustained interruptions: SAIDI and SAIFI. Today, the increasing sensitivity of customer to short interruptions has forced agents (companies and regulator) to consider the momentary interruptions that occur in their systems. This has resulted in the interest in reliability indices momentary MAIFI (Momentary Average Interruption Frequency Index) and MAIFIE (Momentary Average Interruption Event Frequency Index).

Reliability can be measured from multiple KPIs, within which it can appoint the commonly used as a reliability indicator by electric power supply companies:

• CIF: Customer Interruption Frequency
• CID: Customer Interruption Duration
• SAIFI: System Average Interruption Frequency Index
• SAIDI: System Average Interruption Duration Index
• CAIDI: Customer Average Interruption Duration Index
• ASAI: Average System Availability Index
• ASUI: Average System Unavailability Index
• AENS: Average Energy Not Supplied
• PENS: Percentage of Energy Not Supplied
• EENS: Expected Energy Not Supplied
• MAIFI: Momentary Average Interruption Frequency Index
• MAIFIE: Momentary Average Interruption Event Frequency Index

 Then the formulas are presented for the most common KPIs.

In mathematical models, KPIs can be: i) measured only, ii.) may be included as part of the objective function, or iii) included as constraints.

 The problem of defining reliability corresponds to a bi-criterium problem, since, if you want to approach the reliability to the optimal theoretical measure, you must incur in higher investment and operating costs. In this case optimization models concentrate on providing to the decision-maker a Pareto curve cost versus reliability who decide the level of reliability that is willing to offer to the users, respecting the minimum reliability (presumably regulated) and the budget available to invest in the system. The following graphic displays the situation, for the case of a KPI whose theoretical maximum value is equal to 1.0

3.7. INDUSTRIAL ENERGY EFFICIENCY

The large-scale industrial production is always tied to heavy use of industrial services (various forms of consumer/producer energy conversion) which make the material conversion process feasible.

The industrial energy efficiency is supported on integration of production processes with energy services oriented to the simultaneous optimization of both industrial production and energy conversion that is related with the contaminant emissions of gas and liquids.

OPCHAIN-SGO can be integrated with models of complex industrial processes, in which is necessary the redesign of the power supply system of in order to optimize it, in accordance with the new power technologies. This type of models includes the handling of polluting processes, i. e. combustion in furnaces, to determine the optimum mix of fuels in accordance with the environmental regulatory taking as a reference the generation of green energy and the sell/buy in the energy markets.

More Information:

• Heavy Industry Energy Efficiency: Optimization, Smart Grids & Process Control

https://www.dhirubhai.net/pulse/heavy-industry-energy-efficiency-optimization-smart-grids-velasquez/ 

• Inland Oil Fields Production & Smart Grids Optimization

https://www.dhirubhai.net/pulse/inland-oil-fields-production-smart-grids-optimization-jesus-velasquez/ 

3.8. REAL-TIME DISTRIBUTED OPTIMIZATION

Real-Time Distributed Optimization is the distribution of the optimization process in many agents that act simultaneous and independently when they received information from the its exogenous environment. The process can be summarized in the following steps:

1.     From a top-down analysis mathematical is possible to construct mathematical or logical rules of interaction between multiple agents (representing each part of the system), which can represent the “state of the reality”,

2.     Starting from the math/logic rules, following an approach bottom-up, is possible to build segmented/atomized models of the real-world.

Using asynchronous optimization processing, it is possible to define the actions of an agent that keep the system on the "optimality path".

An example of the need of RT-DO is the optimization of the performance of actual intelligent power supply networks (smart grids). To achieve the optimality of the new systems of electricity, ideally it is necessary to optimize simultaneously, in an integrate model, all the smart grids that make up the power system. In practice, this is impossible to achieve, the reasons are non-enumerable; however, it is possible, based on the study of the type of power components (smart grids) to establish the communication rules between components to achieve optimality. The next diagram illustrates the concepts.

In public systems, the most complex part of this process may be the agreement between the parties oriented to act cooperatively to maximize the social surplus. In a private company, this may be easier.

 It should be noted that the two previous process cannot implement if the multi-plant, or the smart grid, problem is solved in an integrated model. This is another advantage of LSOM: a better understanding of the functioning of techno-socio-economic systems

More information:

• The Future: Mathematical Programming 4.0

https://www.dhirubhai.net/pulse/future-mathematical-programming-jesus-velasquez/

4. OPCHAIN-SGO - TECHNOLOGY PLATFORM

OPCHAIN-SGO is developed using OPTEX Optimization Expert System, that implies that it inherits all the characteristics of OPTEX.

For more information:

• OPTEX – Optimization Expert System  

https://www.dhirubhai.net/pulse/optex-optimization-expert-system-new-approah-make-models-velasquez/

• Stochastic & Dynamic Benders Theory – Electricity Sector Applications

https://www.dhirubhai.net/pulse/stochastic-dynamic-benders-theory-jesus-velasquez/