As for example stated in , the energy system optimization on the generation and distribution side is well recognized and part of many research articles. However, due to an increasing amount of distributed generation and flexibility at the consumer side, the demand side optimization becomes an important field of research within the energy management. Unidirectional and top-down is the traditional way of operation of electrical energy system. For balancing supply and demand, the generation of large power plants is coordinated. That is typically a classic unit commitment problem. However, the achievement of balancing supply and demand is challenged by the increasing number of volatile renewable generation, i.e. wind and solar energy, but also by the increasing amount of electric vehicles (EV) and electro-thermal heating systems, such as heat pumps (HP) or small combined heat and power (CHP) units. 
In other words, the electrical energy grid changes significantly from a demand-side driven to a supply-side driven system due to an increasing amount of distributed energy resources. In this sense a promising approach for the integration of distributed energy resources within the low and medium voltage network can be an efficient and robust demand side response management.
Consequently, the demand side management (DSM) optimization becomes a promising solution for matching demand and supply including volatile generation and flexibility on the demand side. Concepts such as Demand Response (DR) are the main core of many research activities. The analysis and optimization on the demand side focuses on the involvement of the customer and fits to the vision of a customer centric energy grid.
Demand Side Management and Demand Response
We define DR as part of DSM similar to  and , as the “voluntary changes by end-consumers or producers or at storages of their usual electricity/gas flow patterns - in response to market signals such as time-variable prices, incentive payments” or beforehand given agreements between customers and third parties. Such pattern changes are possible due to flexibility on the demand side. Such flexibility might be provided for example through electrical or thermal storages where demand is decoupled from generation, but also from other flexible loads, such as EVs.
Direct Load Control vs. Indirect Load Control
In general DSM and DR concepts can be distinguished between direct and indirect load control. Indirect load control implies an incentive, such as a price signal. Such signal might motivate the consumer to shift its consumption into times of lower prices. Direct load control rather means an agreement between the customer and a third party that allows the party to directly control the loads of the customer based upon the beforehand made agreement .
For field installations the most promising solution which finds well acceptance in research and industry is the automated demand response (OpenADR) protocol which is now a de-facto standard for DR concepts .
Several recent research activities that use mathematical optimization techniques for DR refer both to direct and indirect load control. These research topics are related to the optimization and coordination of the operation supply and demand units throughout a time horizon, e.g. an offline day-ahead scheduling under consideration of flexibility. The flexibility is achieved through temporal shifts over a Horizon T. Such problems are very generally known as the Portfolio Balancing problem.
Demand Side Management in different time horizons (short to long term)
The classic unit commitment problem is mainly short term but can be solved also for medium and long term problems. As shown in fig. 1, similarly as presented in , we can distinguish Demand Side Management according to its time line.
Spinning Reserve in this context refers to primary and secondary and even tertiary control, which is usually done by power plants. However, in DSM, loads can be virtually aggregated and act as negative spinning reserve for frequency control. The time horizon is in between seconds and minutes.
Figure 1: Different time horizon in DSM, based upon 
Next, we refer to market DR, which is based upon market places, where transaction usually happen day-ahead or, depending on the market, intra-day. One exception would be real-time pricing, where wholesale prices, e.g. from the European Energy Exchange (EEX) are directly forwarded to the final customers in real time.
If the DR optimization problem is based upon a static Time-of-use price schedule, the optimization problem is typically shift from short- to medium or long term. Customers reschedule and rearrange their processes and behavior in order to avoid consuming energy during periods of high prices, such as in-between 5pm – 7pm. These periods and the related prices are available for the customer and are typically arranged months before. In other words, a static price schedule is applied, whereby short term DR uses a dynamic (even real-time) price schedule.
Considering further long term DSM, energy efficiency yields on minimizing the energy consumption on the demand side through usage of more efficient components and systems rather than on scheduling processes. Authors in  in particular emphasizes that first motivation should always be on energy efficiency optimization since most of the short- and medium term DR concepts only shift energy in time.
Challenges and Requirements for Demand Side Management and Demand Response in Optimization:
The above mentioned general description of the portfolio balancing problem for city districts and neighborhoods incorporate several challenges both for the mathematical method and the overall approach. First, there is usually a high heterogeneity of participants and devices that must be taken into account. Residential buildings, but also industrial consumers might take part of the portfolio balancing. The load and flexibility of such units diversify within their granularity of time, their amplitude and their criticalness. Second, a city district contains in general a high number of participants and devices which lead to a computational intensive problem with an increasing portfolio size. Consequently, a mathematical optimization must be able to handle a large amount of heterogeneous participants. Third, referring to the concept of demand response and in particular to direct load control, it is an important requirement for the method to ensure data privacy. Fourth, the coordination within city districts usually needs to integrate both local (customer) and global (system) level objectives. In respect to this challenge the method requires an approach for both satisfying global and local objectives. Fifth, depending on the kind of installed devices on the demand side the mathematical optimization method might have to be able to take care of on/off devices leading to an Integer related problem formulation.
Research Paper and Solver
Indirect load control on the demand side is for example studied in  and . In particular  is a very recent example for showing the operation scheduling of Plug-in electric vehicles coordinated by an aggregator agent. The MILP is solved within GAMS Build 21.1.2. using the CPLEX 12.5.1 solver .
This research satisfies all of the mentioned requirements. As mentioned in the challenges above a central optimization becomes hard to solve with an increasing portfolio size. Indirect and direct load control for scheduling loads on the demand side by using a distributed algorithm is hence an active field of research. Consequently many research papers, such as [3, 5, 8–13] propose distributed optimization demand response techniques for (residential) energy demand side management. Decomposition methods such as in  or  use dual decomposition (DD) or the alternating direction method of multipliers (ADMM) such as in [3, 12]. For both DD and ADMM in particular challenges and requirements 1) – 4) are taken into account. 
The residential demand side energy management in  for example used the matlab environment in combination with ILOG CPLEX 12.2 to solve the optimization problems. The ADMM problems were solved using CVX, a package for specifying and solving convex programs , . Looking into integer related problem formulations authors in  propose a column generation approach for direct load control which is solved using the object-oriented Python Interface of Gurobi . Research in  performs a decentralized robust ILP optimization for balancing a portfolio within a microgrid. The optimization uses the CPLEX package within Java. Both  and  are other examples for satisfying all mentioned challenges 1) - 5) and the resulting requirements.  uses a MILP formulation for the optimal control of a residential microgrid using the Gurobi solver as well through the object-oriented interface for Java. Further, authors in  perform a distributed optimization via a multi-agent system using the Java agent development framework (JADE) . However, each local agent solves its own local MILP optimization using MOSEK .
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