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Algorithms For Optimal Mode Selection Of Energy Prosumer

Sergiy Denysiuk, Taras Baziuk Institute for Energy saving and energy management of National Technical University of Ukraine "KPI"

IEE NTUU “KPI” Kyiv, Ukraine.

Abstract — Effective use of the potential of EP to regulate the modes of networking and consumption graphs smoothing requires the implementation of an optimization problem. We consider the various components of the overall optimization problem. In each case a set of components of general optimization problem can vary. The algorithm for selecting beneficial treatment that involves obtaining constraints on the parameters of the optimization problem as optimal, acceptable and boundary conditions.

Keywords — energy prosumer, optimization problem, Smart Grid, distributed generation.

I. INTRODUCTION At the request of governmental authorities and the

National Commission in charge of regulation in the electricity sector for achieving effective interaction between participants of the electricity market with energy prosumers a general algorithm that allows the adjustment and balancing of the interests of all stakeholders was developed.

In order to improve the operation of electricity grids in a continuous increase of customers load and increasing share of distributed generation (DG) and implementation of energy prosumers (EP) special methods and tools for creating conditions for optimality of modes were developed. To ensure the profitability of the operation of EP equipment, including DG sources and load management systems, particularly relevant is the issue of planning and operational ("smart") mode control of it’s work. Due to the unstable power generation sources of DG through the stochastic nature of most types of renewable energy sources opportunities for electric adjustment modes of operation that occur on the supply route of the EP and it’s way back are limited.

The use of DG sources and load control systems during their operation provides maximum profit, which is manifested through the sale of electricity generated or saved. Therefore, the adjustment modes of the power system with EP, this becomes the primary problem. However, in some cases, the priority may be given to provide additional services for electricity supplied by the EP, that is, using the potential of EP to regulate the mode of the network to reduce electricity overflows for the consumption schedule alignment and to provide other system services, which involves taking some benefits both for energy companies and for the EP.

One of the challenges of building “Smart” distribution networks is their optimal performance based on new algorithms for the operation and management of the Smart

Grid, new hardware and software and hardware that will perform such control. Characterization of the equipment and Mode Parameters will allow to analyze the main variables evaluated in it, based on the criteria of optimality the comparison of these values allows to select the most appropriate mode of operation of distribution network and consumers equipment with the greatest benefit for each participant.

One of the important trends in the modernization of electricity grid is the system integration of distributed generation sources (DG) of medium and low power at different levels of electricity supply system. The advantage of these sources is the possibility of their placement in close proximity to the consumer that in addition leads to reduction of the load in the grid and also contributes to the reduction of technological losses during transmission from DG source to point of consumption, due to the small distance between them. In addition, properly placed DG sources will reduce the load in the grid and power equipment, which in turn prolongs their operation [5].

Major problems in distribution grid are: 1) high power losses, 2) increased energy loss, 3) excessive (significant, substantial) overloading the network with reactive power flow, 4) reduced level of voltage at the end user. 5) uneven consumption of electricity during the day.

With the further development of electricity sector and the widespread use of power electronics devices, the consumption patterns are gradually changing. They become unbalanced, unstable and include higher harmonics of voltage and current. The consumption of active energy is accompanied not only by reactive power transfer but inactive components of full power (power fluctuation, power distortion) that increase the losses in power systems with DG and internal resistance of the generator system and reduce the capacity of the electrical grid.

The traditional way to assess the consumption of electricity is not forcing consumers and suppliers to make the arrangements on improvement of power quality. We can assume that if further power ripple, distortion and uneven power consumption will remain uncontrolled, the transmission losses of the same amount of active energy will grow, and network capacity will be reduced.

The nature of the consumed active АР and reactive energy АQ for a time T in question may be different. Active АР and reactive АQ energy at the interval T as follows АР=PT; АQ=QT. If energy consumption occurs at a constant value of the

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current I, and lines resistance equals 2RL, the loss of energy in this period will be

Р ( 1 ) Л2Δ А = 2 R I T .

The character of the uneven consumption of active and reactive power at the same values of АР and АQ in the same time interval T, but with distortion pulses = 0.5. Consumption occurs at load current value 2І over the total time T/2.

Energy losses in lines resistances:

,Р(0,5) Л Л P(1)12 2ΔА = 2R (2I) T = 4R I T = 2ΔA2

they’ll be twice higher, though cosϕ will remain the same. This example confirms that the traditional power factor does not account for uneven consumption.

The current value of cosϕ depends on the active and reactive

power cosϕ=Q/P, cosφ= P / S = P / ,2 2(P +Q ) which can continuously vary depending on the mode of the consumer.

Sale of electricity between the power supply organization and the consumer is going in terms of measured active and reactive power at a certain interval of time T:

Р Q

PT Q P T T

P Q

Т TА = Pdt ; A = Qdt.

0 0

A2 -1/2tgj = A / A ; cosj = (1+ tg j ) = ,2 2A + A

∫ ∫

(1)

Depending on the average value of cosϕ, according to (1) tariff premium can be given, it reflects the application of penalties to consumers by reducing network bandwidth and increase losses in it. The current value of active power losses in other similar conditions is inversely proportional to the square of the power factor ΔP-1/cos2ϕ.

The average value of power factor cosϕТ is determined only by the active АР and reactive АQ energy during this period and is not independent of the level of unevenness of consumption.

Uneven electricity consumption can be determined by calculating of the Fryze reactive power QF, defined irregularity in period T: FQ U Iq= ⋅ , where, U– voltage, Iq–

reactive current.

In order to extend the concept of QF as a criterion for assessing the non-optimal consumption for long intervals of time the notion QFτ is in order to calculate this value for certain time intervals τi , where the RMS current i(t) and the voltage u(t) can be considered permanent. Then the whole time interval is divided into n intervals of components for which the RMS voltage and current are constant, and QF has its value:

One way of solving the problems of regulating electricity consumption is to eliminate reactive modes of electrical systems. Let’s consider the method of alignment of load charts in power systems with electricity converters with active variable R(t) and inductive L(t) load, namely compensation of Fryze reactive power QF that occurs during the converting device operation and leads to additional losses in energy transmission and reduces the established generator power to the lowest possible value.

For the systems with voltage value ( ) ,u t U constd t≈ = and

variable load i(t)=var (Fig. 1) let’s calculate active ( )i tAτ and

reactive ( )i tpτ current on the interval [0..4T]. To calculate this

we need to find active ( )i tAτ and reactive ( )i tpτ

current on

the intervals [0…T], [T….3T] and [3T…4], and active ( )i tAτ

and reactive ( )i tpτ current on the interval [0…4T]:

As, ( ) ( )i it tK pτ τ

= − , the compensation current will be as

follows:

Substituting in the above formula the value of resistance

R1(t), R2(t) та R3(t), shown in Fig. 1, frequency f=50 Hz and amplitude of voltage UM, we’ll obtain the graphs of current (Fig. 2).

Knowing the value of active, reactive and compensating currents we can calculate and construct graphs of instantaneous power (Fig. 3).

Let’s determine the reactive power that is required to be compensated in the entire range:

In a purely resistive load can be rewritten as:

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22

,2mi mi

Фi

U IQ

nτ = ∑ ∑∑

where ni – number of intervals.

Fig. 1. Forms of the load on the period [0..4T]

Fig. 2. Charts of the currents under load R(t)

Fig. 3. Charts of the instantaneous power under load R(t)

Determined for different load settings, reactive power of the compensating device allows us to assess the general form of alignment-compensation of the reactive power established by the work of converting devices and to receive information about the actual operation of the device at a given time span.

Connecting DG sources to distribution networks, as well as optimization of operation of modes of the equipment of the

consumer, electricity grid and distributed generators are one of the most promising ways to address these problems.

Power range of different DG sources is very broad currently on the market, allowing you to connect directly to the bus of 0.4 or 6 (10) kV substations [1]. In addition, upgrading the network provides the installation of new metering equipment, devices, remote control, new power equipment , etc. , involving increase of information content in a system that facilitates the selection of more optimal operation mode and network topology. As the source of the initial information for system control and analysis of operational modes, the telemechanics devices can serve and provide the following information: the voltage at the buses, the total active and reactive current load on feeders, etc., as well as new Smart devices [2].

Integration of DG sources and the formation of intelligent power distribution networks, control is carried out by the new efficient algorithms which allow: 1) to connect additional consumers without increasing the capacity of power transformers of substations and lines (now having problems in the large cities); 2) enable consumers to actively participate in the electrical system performance; 3) increase production capacity without increasing consumer consumption from external network; 4) improve the technical and economic efficiency of power supply systems of both the consumers and network companies; 5) improve the stability and reliability of power supply to consumers at lower voltage; 6) create the opportunity to sell excess electricity to consumers and provide additional services for electricity network, which will result in additional profit.

In order to improve the efficiency of operation of the United Energy System of Ukraine (UES) let’s consider methods and tools for creating conditions for optimality of their regimes in continuous growth of consumers load and increasing share of DG sources, including equipment of EP at different levels.

Table 1 shows the benefits received by EP and benefits which interest both EP and system operator, depending on the level at which DG source is integrated or other components of the EP.

The strategy implementation leads to coordination of modes of EP equipment and network. In order to optimize these regimes the pattern of behavior of the EP was established, which highlighted some of the main components of the optimization problem.

The general pattern of behavior involves the formation of an optimization problem components: 1) minimize the cost of electricity; 2) to maximize profits from the sale of electricity and the provision of certain system services; 3) the optimal consumption (selecting and maintaining a schedule of consumption); 4) the optimal network configuration and system settings of electricity; 5) the choice of optimal modes; 6) optimization of the system power supply; 7) the optimal production and use of electric energy generated from their own sources of distributed generation; 8) minimum impact on the environment; 9) other possible benefits.

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TABLE I. ANALYSIS OF THE CONSUMERS AND SYSTEM OPERATOR BENEFITS.

Level The owner of the equipment

Consumer System operator

Equi

pmen

t / d

evic

e The main issues that can be addressed are: 1) improve the reliability of electricity supply of individual equipment, 2) improve the quality of electricity for individual equipment, 3) reduce power costs. Only EP is interested in establishing such equipment.

System operators is not interested to establish their equipment at this level.

Con

sum

er/te

chno

logy

The main issue that can be resolved at this level are: 1) improve the reliability of electricity supply of individual consumers (multiple users), 2) improving the quality of electricity to individual consumers, 3) reduction in energy costs, 4) to avoid exceeding the limit of instantaneous power consumption and volume consumption (as a result - avoidance of penalties), 5) other benefits. Secondary issue is the provision of additional services for the system operator .

The main issues are: 1 ) operation modes control, 2) to provide additional services for modes regulation. Minor in this case will make a profit. This form of ownership will allow the system operator to benefit not only through regulation of the regimes, but also to generate more revenue by electricity production.

Com

pany

/com

mun

ity

The main issue that can be resolved at this level are: 1) improve the reliability of electricity supply of individual consumers (multiple users), 2) improving the quality of electricity to individual consumers, 3) reduction in energy costs, 4) to avoid exceeding the limit of instantaneous power consumption and volume consumption (as a result - avoidance of penalties), 5) other benefits. Secondary issue is the provision of additional services for the system operator .

The main issues are: 1 ) operation modes control, 2) to provide additional services for modes regulation. Minor in this case will make a profit. This form of ownership will allow the system operator to benefit not only through regulation of the regimes, but also to generate more revenue by electricity production.

City

/indu

stria

l hub

The top priority is to maximize profits and create benefits for consumers. Optimization of operating conditions and provision of additional services to the system operator - in second place. And vice versa, if the system operator provides appropriate compensation.

The priority is to regulate the mode settings and extra services, the profit is secondary.

Reg

ion Individual consumers are not

interested in this.

Apart from the use for the purposes of their region, the equipment can be used to adjust the mode of UES of Ukraine.

Depending on the level of EP and features of work of it’s equipment, One need to solve the following components of general optimization problems. Each of the components is provided appropriate model:

1. Costs minimization. The main objective function of this model is to minimize costs:

F1(x) → min

The model described in [3] allows us to identify the main economic factors that influence the behavior of the presumed, helping to assess the order of their value in financial terms and can be used to describe the behavior in the development of

both mechanisms motivating users to participate in the regulation and control mechanisms over the demand.

1

1 1

1

( ( , )), , , , , , )

( , , , ) ( ) ( ( , ), , , )

( , ( ), ( 1), , ) ( , ( ), , )

( , , , ) ( ),

st i eT

a a da it

T T

ga gt t

T

g e g et

C d a g g

P t a a t C d a g

C t g t g t C t g t

P t g g t

θ η θ ξ η

ξ η θ η θ η

θ η θ η

ξ η

=

= =

=

=

= ⋅ + + +

+ − + −

− ⋅

∑

∑ ∑

∑

where t = 1 , ..., T - period of operation (e.g.) T = 14 for hourly planning for the day) ; a(t) – amount of electricity (kW⋅h) consumed from the grid at time t;a=(a(1),…, a(T)) – vector (profile) consumption in all periods of operation; gi(t) – own generation capacity (kW⋅h) for domestic consumption in period t; gе(t) – own generation capacity (kW⋅h) transmitted in the network at time t; gi, gе , g – corresponding vectors of generation; gξ - Option of charging transferred electricity to the grid, for example, the accumulated consumption at cumulative rates depending on the transmitted counting from the beginning of the period of the electricity, including due to a contract with an energy company to generate constraints; aξ - Similar options for billing the electricity consumption, including consumption due to contract restrictions on use;

( , )a gξ ξ ξ= – Vector of parameters for short contracts they refer; η - External conditions on the planning horizon, such as average temperature and length of daylight; θ - The type of customer, the sum of its intrinsic characteristics that affect the cost function; ( , , )a aP t a ξ - The price of electricity consumed, depending on the time period, the volume of consumption and other parameters; ( , , )g aP t a ξ - The price of transmitted electricity to the grid depending on the time period, the volume of outer generation and other parameters;

( , , )gaC t g g′ - The cost of reconfiguration of power generating capacity g to power g ' in period t (major role, for example, can play the costs of starting / stopping power station work);

( , )gC t g - The cost of production of active consumers of the electricity g in period t; ( , , )d t θ η - The need for electricity in period t; ( , )d t η - Appropriate vector (profile) on energy needs. The demand for electricity depends on the type of consumer, and on the prevailing external conditions;

( , )daC d a - Losses due to deviations usage profile on the profile of the need for the entire period of planning.

2. Profit maximization. The main objective function of this model is to maximize profits

F2(x) → max

In order to maximize profits, the interest of the consumer to go to the class of EP can be represented as a function of minimizing the costs for the selected period of time (negative value of this function means profit. Minimizing the costs function on selected time interval can be written as

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maximizing function of profits for both EP (with different share of generation) and generation companies, or virtual power plants):

The main feature of the model is that it allows you to maximize separate consideration of the interaction of the consumer with the power company from its business activities, which is necessary to apply the model in practice. In fact, all the economic activity that is not associated with the generation of electricity is included in the objective function through consumer losses, through diversion of usage profile from the demand on the profile required. The model described in [3] allows us to identify the main economic factors that influence the behavior of the EP, and helps to evaluate the order of magnitude of these factors in financial terms. They, in turn, can determine the order of magnitude of economic incentives that lead consumers to their strategy change. In many cases, to address fundamental issues of appropriateness of various initiatives of the parameters change of the pricing, such rough estimates of factors can be used.

A model of profit maximization of EP suited to describe its behavior as the development of mechanisms to motivate user participation in the regulation and control mechanisms are in demand.

The way consumers interact (normal or EP (various kinds and levels)) network is primarily the result of economic calculation. This calculation should take into account consumer behavior, i.e. the ability to adjust their behavior according to changes of external conditions (control actions), which in turn provides a solution to the minor component of the overall optimization problem (minimize costs).

3. Consumption optimization. Optimization problem of this model is: 1) choosing the optimal consumption schedule, 2) to establish thresholds and optimal consumption and consumption of the schedule within these limits.

In general, the objective function of the optimization schedule of electricity consumption of the network can be written as [4]:

where � – vector of optimized parameters; F(�) – objective function ; ai', bi' – boundary changes of optimized parameters.

For the special case of the optimization of electricity graph objective function can be written as:

Where t – time; u(t)– instantaneous voltage; ( )AC

Hp t− – instantaneous consumption of network capacity; ( )AC

Hp t+ – instantaneous power consumption from other sources (including their own sources of EP); signs "-" and "+" – respectively denote the consumption from the network and consumed with their own sources of DG; ( )AC

Hi t− – current

consumed from the network; ( )ACHi t+ – current consumed from

own DG sources; MB− – the cost of electricity consumed from the grid ; η – efficiency.

In order to select the most optimal consumption schedule, for each parameter of optimization problem constraints must be imposed as conditions that are desirable for the user and the network (optimal conditions), which under certain conditions are acceptable to both parties (acceptable conditions) and conditions, failure of which is unacceptable for one or both sides (limits). These limitations are presented in the form of functions: optimal – G(�) = (g1(�); g2(�);…; gm(�)); permissible – K(�) = (k1(�); g2(�);…; kl(�)); limited – Н(�) =(h1(�); h2(�);…; hp(�)). When solving a specific optimization problem a list should be formed for the above conditions for each of the optimized parameters.

Instantaneous power consumption and current of the prosumers equipment can be written as:

where ( )AC

Hp t – instantaneous load consumed by the prosumer; ( )AC

Hi t – instantaneous power consumed by the load of the prosumer.

When solving a specific optimization problem the list for the above conditions is formed for each of the optimized parameters. For example, the optimization of schedule of electricity consumption can be written as:

Regarding the limits for each parameter of the

optimization problem, the optimal permissible and boundary conditions for the voltage u(t) are determined by the state standard. For instantaneous values of power consumption

4. Optimization of structure, network configuration

and parameters of power supply system.

This model should include: 1) power supply from DG to work with provided efficient operation of the equipment for a minimum specified period of time, 2) the minimum distance from the generator to the consumer, 3) the minimum number of switching 4) the minimum number of transformations, 5) the minimum allowable operation time from one generator, 6) the type and length of power transmission lines, 7) load characteristics, 8) electromagnetic compatibility, 9) energy overflows, 10) energy balance in the control section. F4(�) → opt.

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5. Optimization of EP equipment. Depending on the external conditions and the selected operating mode active consumer equipment must be carried condition: F5(�) → opt.

6. Optimization of the operation modes of electricity grid. This problem is relevant for the case when the owner of the generating and / or regulating equipment EP is the system operator or the consumer is able to provide additional services system operator to adjust the modes of supply. F6(�) → opt.

7. Maximal production of electricity from its own DG sources. Need to ensure maximum power generation and selection of energy produced from own DG sources: F7(�) → max.

8. Reduction of the negative impact on the environment. It is important to reduce the negative environmental impact as taking into account and realizing the potential of DG and renewable sources in order to solve the optimization problem in terms of minimizing the impact on the environment: F8(�) → opt.

Each of the parameters of the general optimization problem has a different degree of importance, depending on the case in question. Therefore, to create the most accurate solution of the optimization problem we suggest using the generalized criteria defined by transformation into scalar:

where Fi(X) – vector of optimized parameters of the system;

1 2,a a – scalar coefficients or criteria of importance (determined by an expert). The dimension of the vectors F1(X),…, F8(X) may be different. Vector coefficients 1 8,...,a a permit to construct a generalized criterion that can be either scalar or vector based on F1(X),…,F8(X) vectors. If F1(X),…,F8(X) is a scalar criterion, then 1 8,...,a a are the weights and the total vector F (X) is a scalar.

For each consumer the number of criteria and the degree of importance of individual components of the overall optimization problem can vary depending on individual circumstances. Therefore, the choice of components and the importance of each of the components should be performed by an expert.

Let’s consider the example. Let’s assume that for a particular prosumer, the following (Table 1) priority components of the optimization problem are selected.

We accept that the function for each of the specified components will take the following values (Table 2). In addition to the selected data let’s consider possible options for combinations of criteria relative importance of each of the values (Table 3). Fig. 4 shows the function of each component of the overall optimization problem graphically.

For each set of importance criteria options under consideration, the general solution of the optimization problem is performed by the expression (2). The results of this calculation are presented in Fig. 5. Comparing these options

can be concluded that the overall benefit of using prosumer will vary depending on the tasks and their priorities.

TABLE II. PRIMARY COMPONENTS OF THE OPTIMIZATION PROBLEM

# Graphic representation Component description

1

Minimizing energy costs. F1(�) → min

2

Maximizing profits from the

sale of electricity

generated from its own sources. F2(�) → max

3

Optimization of consumption. F3(�) → opt

4

Optimization of the electrical

system operation.

F6(�) → opt

TABLE III. POSSIBLE VALUES OF SELECTED FCN-S

Fcn Fcn value

V 1 V 2 V 3 V 4 V 5

F1(X) 1,6 1,55 1,35 1,15 0,88 F2(X) 1 1,25 1,45 1,55 1,6 F3(X) 0,2 0,8 1 1 1,2 F6(X) 1,4 1 1,05 1,2 1

TABLE IV. CRITERIA OF IMPORTANCE TO EACH OF THE OPTIONS VALUE OF THE FUNCTION.

αi The value of the coefficient

V 1 V 2 V 3 V 4 V 5 α1 0,4 0,15 0,2 0,25 0,45 α2 0,25 0,4 0,15 0,2 0,2 α3 0,2 0,25 0,4 0,15 0,3 α4 0,15 0,2 0,25 0,4 0,05 αcn 1 1 1 1 1

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Fig. 4. The functions of the components of general optimization problem

For each set of importance criteria options under consideration, the general solution of the optimization problem is performed by the expression (2). The results of this calculation are presented in Fig. 5. Comparing these options can be concluded that the overall benefit of using prosumer will vary depending on the tasks and their priorities.

Fig. 5. The value of overall optimization function

Algorithm for selecting optimal modes of the prosumer is based on solving the above mentioned general optimization problem, and is as follows:

1) assessment of customer needs;

2) assessing the potential "prosumer behavior" and the feasibility of this potential;

3) determining priorities and the importance of appropriate criteria;

4) formation of the general optimization problem;

5) the formation of a common model of the prosumers of the above components;

6) the general solution of the optimization problem.

The solutions of the general optimization problem (2) are the parameters of the optimal mode of operation for the prosumer. This model allows us to identify priority areas of work for each prosumer, to balance the benefits and consider possible requirements and limitations imposed by the operator of energy system in order to produce the most beneficial effects for all parties. The implementation of the model and algorithm of its use is made by the development of software for optimization of power system with DG and prosumers, as well as the coordination modes of the equipment of the prosumer, the calculation of modes of development of a number of techniques for the design of power systems with prosumer and prosumers, methods for assessing the impact of prosumer to the power supply system.

II. CONCLUSIONS. The restructuration of the power system, system

integration of dg sources, including alternative and renewable energy sources into the electricity grid, and the transition to a smart grid systems, creates new opportunities for further development and electric power in general. Connection of dg sources to the distribution network has a positive impact on its properties, but along with it creates new problems encountered both in connection of dg and management of modes of the electrical system operation. Dg sources can be integrated at various levels of electricity grid, but to ensure the best results, they should be placed optimally. This paper describes the basic optimization problem and in detail, the individual components of the optimization problem.

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