ASSESSMENT OF CONSUMERS POWER CONSUMPTION OPTIMIZATION BASED ON DEMAND SIDE MANAGEMENT

To ensure the functioning of the energy system, coordination and increase the efficiency of its parts need new control mechanisms. Generation, transmission and consumption of electricity needed control mechanisms that include integration of self-organizing power and heat supply systems, built on multi-agent principle. Also they must correspond intellectual basis, monitoring and accumulation. This includes effectiveness assessment of the state and analysis of technical, technological and organizational management mechanisms. One of the main parts is interaction principles of energy systems in accordance with European Community policy at various levels at liberalized electricity market. In most developed countries, demand management programs are widely used as a means of harmonizing the modes of gene ration and consumption in the power supply system. The main direct methods are set in the form of electricity tariffs. Indirect methods are set in the form of programs to manage electricity demand and the possibility of their application to manage electricity demand. Methods for estimating the unevenness of the daily schedule of electricity consumption and the factors influencing the technological environment are presented. The work aims at scientific and applied problem – finding methods of estimation and features of managing the demand for electricity. The use of the proposed estimation methods of electricity consumption influence non-uniformity on the level of power supplies system losses based on Frize QF power and optimization of consumers’ operation modes in the power supply system is considered. Approaches and optimization mechanisms of the daily electricity consumption on the example of a residential complex with the possibility of energy accumulation are offered.


Introduction
The development of modern power systems based on Smart Grid (SG) technologies allows consumers to participate in Demand Side Management (DSM) programs. DSM can solve a number of problems related to covering the unevenness of daily profiles of energy generation and consumption directly on the consumer side, and within the framework of a Virtual Power Plants (VPP) and the global trend of increasing electricity demand.
DSM is about using consumers demand elasticity to keep energy balance or provide additional services [1]. It has become more popular with the new opportunities achieved from SG technologies development [2] Such technologies like 'Internet of Things'(IoT) [3] can provide Energy and agricultural loads. Keeping this in mind the assessment mechanisms for represented systems must take into account peculiarities of operation of all system's elements which in its turn will allow to use DSM mechanisms in the most effective manner.
All this suggests that it is advisable to conduct a study on peculiarities of the structure and operation of the power supply systems with DG sources and Prosumers which are highly affected by DSM mechanisms.
The aim of the study is demand side management components and demand response mechanisms for daily consumption optimization.
To achieve this aim, the following objectives are accomplished: -analyze the optimality of processes in power supply systems with DG sources and Prosumers; -define optimization criteria for power supply systems with DG sources and Prosumers; -define non-sinusoidal impact on the Fryze reactive power Q F change; -optimize electricity consumption profile for household in case of DSM programs implementation.

Materials and methods
The research is based at theoretical methods of uneven consumption influence at power system assessment. As an additional indicator for optimization assessment proposed Fryze reactive power Q F as indicator of optimal schedule deviation. Optimization of household's basic equipment daily consumption schedule with assumption of willingness participation as flexibility coefficient of demand k g was done in MatLab as the goal attainment problem for minimizing a multiobjective optimization problem.

1. Mode optimization features in DG power supply systems with DSM integration
DSM has traditionally been seen as a means of reducing peak demand for electricity in the grid [31]. By reducing the total load on the electrical network, DSM allows to reduce the number of accidents by reducing the number of outages, as well as increase the reliability of the system [32]. The use of DSM programs makes it possible to overcome barriers that prevent the adoption of many related energy efficiency programs and to raise funds for the economic benefits of rational use of electricity and savings from off-peak consumption.
The main mechanism of DSM programs [33] among others, it includes direct control and tools to change peak and off-peak consumption together with energy efficiency programs. Despite global trends, the issue of managing electricity demand in Ukraine remains open [34].
In the general case, the objective function for the organization of the process of solving the mathematical expression of the goal of optimal control of the system is formalized in the form of a function of control quality [33]. For a particular case, the objective function of the optimization problem can be written as: where ΔU -voltage deviation; ΔI -current deviation; Δf -frequency deviation; Δφ -power factor changes; ΔP -power loss; g -other factors, which arise as a result of uneven processes, and which must be considered when optimizing the modes of operation in power supply systems with DG sources and Prosumers.
The general objective function is vector, in some cases in case of its consideration scalarization is necessary, i. e., knowing initial conditions and restrictions, to define such mode of work which maximizes or minimizes the uniform set criterion indicator.

Energy
Consideration and analysis of the operation of the system should be on the time interval T T and distinguish 4 groups of modes of the equation between the graphs of the instantaneous values of the generation power p g (t) and consumption p c (t): 1) p g (t) = p c (t), ∀t, t T T ∈[ , ]; 0 Р g = Р c ; full coordination of generation and load (consumers) operation modes; 2) p g (t) ≠ p c (t); should be provided by the use of technical means, first of all systems of energy storage, reactive power compensation, compensation of non-sinusoidality and asymmetry; 3) p g (t) ≠ p c (t); Р g < Р c ; should be implemented not only through technical means, in particular, given for the second group of modes, but also primarily through the implementation of DSM programs; 4) p g (t) ≠ p c (t); Р g > Р c ; should provide not only to increase the levels of electricity consumption of the existing load, but also the ability to connect additional loads.

2. Demand Side Management optimization features in power supply systems with DG sources and Prosumers
In the case of extending the concept of Fryze reactive power Q F to an arbitrary time interval τ = Т T , the power Q Fτ can be used for retrospective, prospective and real-time analysis. This approach must identify the effects of suboptimal components: voltage deviation ΔU, current deviation ΔI, presence of voltage and current harmonic components k Pu , and k Pi , reactive component (cosφ ≠ 1) [35].
Having identified the indicator of suboptimality, which characterizes the efficiency of regulation and determines the level of suboptimality of energy transfer, let's analyze the available load profiles, in which there are three main options: 1) retrospective with decreasing time interval δ; 2) perspective within the analysis of processes with increasing time interval δ; 3) real-time analysis at δ = 0. The application of Q F to assess the non-uniformity of processes will be shown on the example of a mode characterized by the voltage and current values U i and I i , i n = 1,..., , T i -the duration of the i-th interval, and P U I = 0 0 , where U 0 , I 0 -the average values of voltage and current. If cosϕ = 1 for the interval T T m g > , where T g -the period of the grid, one can write an expression for the power of the Fryze Q F in the form: can be written as: ) . (2) Let's analyze some components of the influence of suboptimal factors on the amount of losses: 1. The effect of voltage deviation ΔU, with ΔІ = 0, I 1 = I 2 ; U 2 = U 1 + ΔU, let's obtain: 2. The effect of current deviation ΔI, with ΔU = 0, U 1 = U 2 , I 2 = I 1 + ΔI, let's obtain: Energy 3. The effect of the time interval increasing (δ 2 = δ 2 +δ * 2 ), let's obtain: In the case of entering relative values for two time intervals δ 1 , δ 2 , the value k Q P opt F ∆ = will be as follows: The optimization of certain types of equipment is based on the consideration of the function:

Methods of power supply system stability assessment
All the elements of aforementioned systems are connected by the continuous processes of generation, transformation, transmission, distribution and storage of electricity. In this stream terms such as «process stability» and «process capability» which are very common can help handling this problem.
A process is said to be stable when all of the response parameters that let's use to measure the process have both constant means and constant variances over time, and also have a constant distribution.
Process capability analysis entails comparing the performance of a process against its specifications. It is possible to say that a process is capable if virtually all of the possible variable values fall within the specification limits.
Using these definitions for power supply systems with DG sources and Prosumers it is possible carefully indicate the variables (indicators of operation) for the assessment.
One of such Process Stability Indicators (PSI) may be the capability of different converters and compensation devices, which are commonly used in the grids with different types of renewables, to influence the grid parameters (e. g. power quality, reliability etc.).
Another indicator may be shown as the sensitivity of the mode parameters to the deviation of the electricity parameters as a converter output signal: where S q ϕ -characterizes the sensitivity of the function φ to change of the parameter q. The control function or energy characteristic can act as a function φ, and the quantity q can characterize both the magnitude of the distortion of the energy characteristic and the output electrical parameter.
In order to ensure the optimal functioning of the power supply systems with DG sources and Prosumers it is important to compare the different conditions of power supply in terms of technical quality, considering their economic importance (cost). This value makes possible to compare technical solutions even if they have different levels of power quality. full paper (2021), «EUREKA: Physics and Engineering» Number 2

Energy
The concept of quality of power supply should be considered for the assessment as a set of properties of the power supply system, which determine the degree of suitability of providing consumers with the specified power quality at the required level of reliability.

4. Methods of reliability evaluation and approach
Nowadays reliability and power quality are the major parts of power supply quality according to EN 50160 standard. Reliability is assessed by the indicators proposed in IEEE 1366 standard in the US and by the indexes SAIDI, SAIFI, MAIFI, ENS which are presented in this standard in Ukraine. Returning to the assessment in power supply systems with DG sources and Prosumers One must consider the problems which different DG sources present to the grid due to the variable behavior of the primary energy source (e. g. solar insulation, wind capacity etc.) and the complexity of the power supply systems with DG sources and Prosumers modes of operation. Due to stochastic behavior of the renewable sources and loads, conventional reliability assessment techniques can't be used in power supply systems with DG sources and Prosumers applications.
For the complex assessment of the power supply systems with DG sources and Prosumers reliability one can use the Normalized Reliability Index -NRI, which should be based on the targeted values of the reliability indexes.
While increasing the reliability in the power supply systems with DG sources and Prosumers one should target to decrease these indexes below the level of the appointed values.
Taking this into account the complexity of the structure and modes of power supply systems with DG sources and Prosumers, described earlier, the reliability index should be normalized for any configuration of DG sources (wind, solar etc.) and diverse modes of power generation.
Depending on the mode of power supply systems with DG sources and Prosumers for the reliability assessment it's proposed to divide all power sources into 3 types: 1. Sources of centralized power generation. 2. Uninterruptible distributed generation sources.

Distributed generation sources with variable output parameters dependent on weather conditions and not regulated by human.
Outages should also be divided into ones caused by weather conditions/absence of primary energy source and ordinary outages.

5. Analysis of the non-sinusoidal impact on the change in the Q F magnitude
The influence of harmonic components on the values i(t) and u(t) is calculated as: When considering electricity processes during the day, the ratio should be approximated by four components Fig. 1 that reflect the average levels of voltage and current. This approach formally reflects electricity consumption in the evening and morning highs and night and day lows [33].
Considering such a case for the day, an expression for the Fryze reactive power, in the case of four time intervals and the theoretical assumption of fully active consumption, knowing the magnitude of the optimum level of voltage and currents for the intervals, it is possible to write the values for voltages and currents as deviations from the optimal level by magnitude ΔІ and ΔU [33].

U U t U t U t U t T I I t I t I t I norm norm
= ∆ + ∆ + ∆ + ∆ = ∆ + ∆ + ∆ + ∆ The closest to the real conditions is the mode of operation of the conditional installation (generator -load). A daily interval of 24 hours was considered [32,35]: The obtained indicator allows to estimate the level of uneven consumption of electricity during the day on the basis of optimal or average values.

6. Optimizing the processes of electricity demand management
Obviously, when DSM mechanisms are implemented, it is necessary to evaluate the demand management performance, which is usually performed on indicators such as [15,16]: - the factor of filling the load schedule k L ; - the total cost of consumed electricity С е . Accordingly, it is necessary to apply two criteria, which are presented in the form of objective functions (OF).
The first OF corresponds to the maximization of the load factor of the load schedule kL [32,34]. where optimization variables are selected by the power consumption values P (i,j) at time interval t j (usually the time interval is 1-2 hours) by consumer groups i. Accordingly, the numerator of the objective function represents the amount of consumed power. The OF is linear with respect to the optimization variables. The dimension of the problem is N × J, where N -number of consumer groups; J -the number of time intervals [32].
The second OF is to minimize the cost С [33]: where the OF by criterion Cе -cost of consumed electricity is also linear and represents a minimization of consumed electricity cost. Optimization variables are selected: power consumption over time interval t j by consumer groups i, electricity tariff Cе, charge for installed capacity сd. The first addition is the charge for the amount of consumed energy, the second addition is the payment for the power.
Optimized schedules of daily electricity consumption are constructed with restrictions in mind [33,34]: that is, the total amount of power consumed Рt the T D time interval remains unchanged and must be constrained at every interval: however, peak consumption from the time interval (t k ; t h ) is evenly transferred to time intervals (t o ; t k ) ∪ (t h ; T D ) (Fig. 2).
where the constraints of the problem relate to the need to save the total power consumption over the billing period: P new,i = P old , and limiting the maximum values of the maximum power consumption: P new,i < P max , arising from network and power system boundary capabilities, such as limited power generation of power system equipment, restrictions on the capacity of the distribution network, transformers, etc.

Fig. 2. Illustration of load transfer while maintaining consumption balance
The above description of the optimization problem is somewhat simplified and does not take into account the ability of the consumer to change consumption profiles in automatic mode for different types of equipment. As an example, it is much easier for a household group user to change their dishwasher consumption profile than a lighting system [33]. To consider the ability of consumers to change the level of their equipment consumption, it is necessary to enter the third criterion and formulate an appropriate optimization problem. Idea is minimization of the initial load schedule irregularity degree after DSМ application -min F g .
The peculiarities of consumers are taken into account by the flexibility coefficient of demand k g , which can take a value from 0 to 1.Value of 0 corresponds to the least flexibility of the equipment, 1 to the maximum flexibility. This coefficient represents the willingness of the consumer to change the consumption profile of specific equipment by shifting consumption to other time intervals [16].

Energy
It is proposed to consider separately the pairs of criteria as being appropriate to the objectives of the consumer and the electricity supply organization [16]: 1) the load factor and the coefficient of irregularity of the graph; 2) reduction of consumed electricity cost and the coefficient of consumption schedule irregularity.
To illustrate the results of the optimization model, a group of one thousand households was selected, with the basic equipment: dishwashers, heating and air conditioning, refrigerators, lighting, cooking equipment and multimedia systems.
In the following, the average power values for typical equipment in this class are discussed. It should be noted that the current two-zone tariff was chosen as the criterion for reducing the consumption of electricity, and the equipment flexibility coefficients were selected from the experience of a number of experts on the use of household appliances. Optimization of the daily schedule was carried out in MatLab.
The resulted optimized curves of consumption graphs for maximization of the fill factor for maintaining the balance of power consumption is shown in Fig. 3.
The resulted optimized curves of consumption graphs for maximization of the fill factor without maintaining the balance, i. e. it is theoretically possible to switch off the devices during peak consumption hours is shown at Fig. 4.

Energy
The resulted optimized curves of consumption graphs for minimizing costs while maintaining the balance of electricity consumption is shown at Fig. 5.

Fig. 5. Minimizing costs while maintaining the balance of consumed electricity
Optimization of the fill factor, which in this case is ideal example of reducing peak consumption, is in practice unattainable, since an important requirement for DSM programs is to balance the benefits gained and the deterioration of consumer comfort. Unlike optimization of the consumption schedule in case of maximization of the fill factor without maintaining the balance (Fig. 3) and minimizing costs while maintaining the balance of consumed electricity (Fig. 5) are the most attractive for consumers of electricity, since they directly benefit from changing their own mode of operation electricity consumption. Table 1 shows the numerical values of the received Q F's on funds and the coefficient of the graph fill before and after optimization, also shows the change in the value of their numerical values. . Table 2 shows that optimization of operation modes on both indicators led to a decrease in the value of the reactive power of the Fryze Q F , which is a characteristic reflection of the decrease in the irregularity of the daily schedule of power consumption.  In conclusion, while constructing the power supply systems with DG sources and Prosumers, one should take into account the generation source types and the variety of their modes of operation.

Discussion of experimental results
Obtained optimization results represent the two main optimization of daily consumption. Optimization of the fill factor, which in this case is ideal example of reducing peak consumption and consumer costs optimization can be used as a part of time-of-use program or demand response programs from utility company. 7.8 % of saved cost can be significant as global economic influence, but growing a fill factor by 29.63 % can influence significant in terms of other important factors. Optimizing the fill factor can influence at CO 2 emission reduction as well as energy savings in terms of reducing losses attached to power balancing. Both optimizations can be used at consumers side with IoT and other appliances that can control its own consumption schedule.
Frize indicator Q F which was used as indicator of «non-optimal» regime while it depends on flat generation-consumption balance, can be used like indicator for local grids operator. The Frize Q F indicator can simplify impact analysis, but every component of electricity quality must be used according to implemented standards.
It must be noted that such optimization is possible only under DSM programs, as its main idea is to prevent additional generation starts to maintain demand by reducing consumers demand by reducing participants cost on electricity.
Today's households can't schedule their home appliances for a day ahead, but liberalized electricity markets and modern control technologies will bring such cases in nearest future. But even now, with the possibilities of two zones tariff system, a lot of consumers prefer to use dishwashers and laundry in night time.

Conclusion
1. Conducted analysis of the processes in power supply systems with DG sources and Prosumers shows that number of different criteria can be united under Q F power indicator.
2. Obtained optimization criteria k Q P opt F ∆ = →min can be used for power supply systems with DG sources and Prosumers uneven regimes optimization.
3. Extended Q F definition to estimate the level of uneven consumption of electricity during the day on the basis of optimal or average values.
4. Presented optimized electricity consumption profiles for household in case of DSM programs implementation shows nice results. There is 29.63 % for fill factor optimization with Q F reduction for 46.1 and 7.8 % for costs saves with 22.25 % in Q F decrease.