Distributed generation includes the application of small generators, typically ranging in capacity from 15 to 10,000kW, scattered throughout a power system, to provide the electric power needed by the end-users. Most types of distributed generators utilize traditional power generation paradigms – diesel, combustion turbine, combined cycle turbine, low-head hydro, or other rotating machinery. But in addition, DG also includes fuel cells and renewable power generation methods such as wind, solar, etc. The renewable generators are often lumped into the “DG” category because their small size makes them convenient to connect to the lower voltage (distribution) parts of the electric utility grid. The plant efficiency of most existing large central generation units is in the range of 28 to 35%, meaning that they convert between 28 to 35% of the energy in their fuel into useful electric power. By contrast, efficiencies of 40 to 55% are attributed to small fuel cells and to various “hi-technology” gas turbine and combined cycle units suitable for DG application.
A DG unit does not require transmission and distribution network but provide reliable to the end user as it is located near to electric power demand. In area where incremental expansion cost is high, DG may not only offer a good economic alternative, but appeals on its reliability merits alone. There are many situations where there is no local electric utility grid in an area, and DG of any type is the only possible source of electric power at lower costs. The architecture of modern power systems with distributed generation is shown in Fig. 1. The major turnouts that made electric utilities to interconnect DG into the distribution network are as follows:
- There is growing electricity demand and increase in environmental pollution due to emissions from central power generations which is causing adverse effects to whole ecosystem.
- DG units are closer to customers and T&D system can be expensive to design, build and operate.
- DG is tailorable in both cost and reliability, to a degree than the electric utility often cannot match.
- Usually DG requires shorter installation period and the investment risk is not high.
Distributed generators are generally either utility owned or individual owned. The placement decision is taken by their owners or investors. In most cases, distribution network operators have no control over DG location and size, however, interconnection of DG alters the distribution network operation. These factors drew the attention of distribution network operators for the decision making about the optimal/proper siting and sizing of the DG. The problem of DG placement has attracted many researchers since last decade.
Fig. 1: Architecture of modern power systems with distributed generation
Classification of Distributed Generation
The classification of DGs from their connection & technological points of view is shown in Fig. 2. The different DG technologies that are being deployed into the power systems are Wind Turbine (WT), Micro Turbine (MT), Combined Heat & Power (CHP), Squirrel Cage Induction Generator WT (SCIG WT), Double-Fed Induction Generator WT (DFIG WT), Fuel Cells (FC), Photo Voltaic (PV) and storage devices. Usually DGs are classified according to their different types and operating technologies. However, it is more convenient to classify them from the electric point of view to study their impact on the electric system. Different classifications can be obtained to differentiate between DG types according to their electrical applications, supply duration, generated power types, electric ratings & renewable and non-renewable technologies.
Fig. 2: Connection based classification of DG
Implementation of the different DG technologies is covering a wide range of applications according to the load requirements. The DG type is different for different applications which are discussed below:
- Standby: DG can be considered as a standby to supply the required power for sensitive loads, such as process industries and hospitals, during grid outages.
- Stand-alone: Usually, isolated areas utilize DGs as a power provider instead of connecting to the grid. These areas have geographical obstacles, which make it expensive to be connected to the grid.
- Peak load shaving: The electric power cost varies according to the load demand curves and the corresponding available generation at the same time. Hence, DGs can be used to supply some loads at peak periods, which reduce the electricity cost for large industrial customers who used to pay time-of-use rates (TOU).
- Rural and remote applications: DG can provide required power by the stand-alone remote applications. These applications include lighting, heating, cooling, communication, and small industrial processes. Even more, DGs can support and regulate the system voltage at rural applications (sensitive loads) connected to the grid.
- Base load: Utility owned-DGs are usually used as a base load to provide part of the main required power and support the grid by enhancing the system voltage profile, reducing the power losses and improving the system power quality.
Fig. 3: DG capacities
- DG capacities: DG capacities are not restrictedly defined as they depend on the user type (utility or customer) and/or the used applications. The most commonly used classification is shown in
- Fig. 3. These levels of capacities vary widely from one unit to a large number of units connected in a standard form.
- AC/DC power type: The output electric current can be either direct or alternating. Fuel Cell (FC), PV and batteries produce direct current, which is suitable for dc loads. However, we can convert this current to an alternating one for AC loads and for grid connections. This conversion can be done through a power electronic interface between the DG device and the grid. Other types of DGs like Micro Turbine (MT) and Wind Turbine (WT) provide an alternating current, which for some applications must be controlled using modern power electronic equipment to get regulated voltage.
- Technology: Another attempt for DG classification can be done according to the type of the fuel used. It can be either non-renewable or renewable sources as shown in Fig. 4.
Fig. 4: Technological DG classification
DG Placement
In literature, various objective functions have been considered and optimized, subject to different operating constraints, using conventional methods, intelligent searches and fuzzy set application for the placement of DG. A detailed study of the literature on DG Placement (DGP) is summarized by the objective function model, the constraint model, and the mathematical algorithms to solve these objectives.
Objective and Constraint Functions
In, the DGP deals with the optimal allocation of distributed generation for minimizing the total real power loss in the system using second order method based on Newton’s method. The basic formulation is done with the concept that a sum of all nodal injections of power in a network represents losses. In [5], the impact of DG in power transfer capacity of distribution network and voltage stability has been studied. The overall impact is positive due to the active power injection with objective to minimize the losses. In, problem is formulated using exact loss formula. In, the objective function considered as total power loss in the system to find the optimal DGP. The objective for optimal allocation of Distributed Generation (DG) has been taken as maximization of DG capacity in and with same objective for constant load is developed in, respectively. A method that evaluates the capacity or headroom available on the system and models fixed-power factor distributed generation as negative loads and uses optimal power flow to perform negative load shedding in.
The objective in is to maximize the amount of energy that can be harvested from DG by making best use of the existing assets and available energy resource. To obtain most appropriate DG location, nodal price variation at each bus and line loss sensitivity has been utilized in, as economical and operational criteria. Then mixed-integer non-linear programming (MINLP) approach was used to find the optimal location and the number of DG in appropriate zone. The objective function is to minimize the fuel cost of conventional and DG sources as well as to minimize the line losses in the network. In the maximum DG capacity has been determined by modeling DG as generators with negative cost coefficients. By minimizing the cost of these generators, the DG capacity benefits are maximized. In the problem is formulated with two distinct objective functions, namely, social welfare maximization and profit maximization. In, authors evaluated the impact of DG using multi-objective performance index considering range of technical issues as indices. In, authors have considered the composite technical and economic benefits of DG in multi-objective function and optimized to reduce the voltage and frequency deviation.
Mathematical Algorithms
Analytical Methods
An analytical method, based on the exact loss formula, is proposed for a single DG optimal location & sizing. Analytical expressions for finding optimal size and power factor of different types of DGs are suggested in. An analytical method using a loss sensitivity factor that is based on the equivalent current injection is developed in to find the optimum size and location of a single DG. Two analytical methods for determining the optimal location of a fixed size single DG is proposed in; the first method is applicable to radial and the second one to meshed power systems. An analytical method is proposed in for finding the optimal locations of multiple DGs in combination with the Kalman filter algorithm for determining their optimal size. An analytical method described in computes the optimal location & size of multiple DGs, considering also different types of DGs.
Conventional Optimization Methods
An exhaustive search based method is proposed in evaluating DG placement for optimal power losses and reliability, and a multi-objective performance index, respectively, taking into account the time-varying behavior of demand. A discrete probabilistic generation-load model is reduced into a deterministic model considering all possible operating conditions solved using a Mixed Integer Nonlinear Programming (MINLP) technique for optimally allocating either only wind DG units, or different types of DG units. The optimal DGP is formulated as a multi-period AC Optimal Power Flow (OPF) that is solved using NLP. Optimal DGP of various technologies considering electricity market price fluctuation employing MINLP is proposed. An integrated distribution network planning model, implementing ODGP as an alternative option, is solved by MINLP.
Power electronic devices interfaced DG units are considered with an objective of improving the voltage stability margin for the placement and sized using MINLP. Dynamic programming based optimal DG placement model is proposed which maximizes the profit of the Distribution Network Operator (DNO) considering light, medium, and peak load conditions. The optimal placement and sizing of single and multiple DGs in a distribution level is carried out in, applying sequential quadratic programming utilizing the sensitivity indices and stability.
Intelligent Search Based Methods
The algorithm presented in uses Genetic Algorithm (GA) as a technique to solve the problem of static planning of distribution system expansion considering possible reinforcements or commissioning of new feeders and substations. GA is used to solve an Optimal DG Placement Problem (ODGPP) that considers variable power concentrated load models, distributed loads, & constant power concentrated loads. A GA is employed to solve ODGPP that maximizes the profit of the DNO by the optimal placement of DGs. A GA methodology is implemented to optimally allocate renewable DG units in distribution network to maximize the worth of the connection to the local distribution company as well as the customers connected to the system. A value-based approach considering the benefits and costs of DGs is developed and solved by a GA that computes the optimal number, type, location, and size of DGs. A GA-based method allocates simultaneously DGs and remote controllable switches in distribution networks. Goal programming transforms a multi-objective ODGPP into a single objective ODGPP, which is solved by a GA method. A hybrid GA and fuzzy goal programming is proposed for ODGP. A fuzzy GA is employed to solve a weighted multi-objective ODGPP model. A hybrid GA and immune algorithm solves an ODGPP that maximizes the profit of the DNO.
GA solves a weighted multi-objective ODGP model in. Multi-objective ODGP formulations are solved using a GA and a constrained method. A Non-dominated Sorting GA (NSGA) is used to maximize the distributed wind power integration. NSGA-II (a variant of NSGA) in combination with a max-min approach solves a multi-objective ODGPP. ODGP models with uncertainties are solved by Monte Carlo simulation in conjunction with GA. Placing a single DG based on the ranking of the energy not supplied index or the ranking of the power losses in the network lines. Heuristic methods for sizing wind farms based on modes of voltage instability are proposed. A heuristic cost-benefit approach for optimal DGP to serve peak demands in a competitive electricity market is introduced. A heuristic value-based approach determines the optimum location of a single DG by minimizing the system reliability cost. A heuristic iterative search technique is developed that optimizes the weighting factor of the objective function and maximizes the potential benefit thanks to the optimal DG placement. The ODGP is solved by a heuristic iterative method in two stages, in which clustering techniques and exhaustive search are exploited. A heuristic method calculates the regions of higher probability for location of DG plants. The ODGPP for small distribution networks is solved by a heuristic method.
Problem Formulation
The DG planning is basically a non-linear mixed integer optimization problem which finds the optimal DG siting and sizing that are to be located into the distribution networks subjected to various network operating constraints, DG operating constraints, etc. The objective function may be single or multi-objective in order to maximize the benefit of DG satisfying various network equality and inequality constraints.
Objectives
The main objective functions that are being considered are
Minimization of power loss
where Pi is the power injection at ith node & n is the total number of buses in the system.
Maximizing the reliability
Network reliability assessment contains two types of indices: load point indices and system indices. Load point indices are calculated at each load point connection and are used for the evaluation of system indices. The system indices that can be considered for reliability evaluation are System Average Interruption Frequency Index (SAIFI) and System Average Interruption Duration Index (SAIDI).
Where Ni is the number of customers at the load point i, ui is the outage time and ri is the failure rate. The optimization algorithm is used to minimize the weighted composite index including interruption duration and frequency components. The smaller the value of the defined reliability index (i.e., objective function) is, the higher is the system reliability.
Maximizing the DG capacity
where PDGi is the DG capacity at the ith node & N is the set of all possible DG locations.
Maximizing the profit and social welfare
Social welfare is defined as the difference between total benefit to consumers minus total cost of production. The objective function associated with social welfare has been formulated as quadratic benefit curve submitted by the buyer (DISCO), Bi (PDi) minus quadratic bid curve supplied by seller (GENCO), Ci (PDi) minus the quadratic cost function supplied by DG owner C (PDGi).
The profit maximization formulation is as follows:
where is the total number of nodes in the system, PDGi is the DG size at node i, li is the locational marginal price and C (PDGi) is the cost characteristic of DG at ith node.
Maximizing the voltage stability margin
Where, N is the total number of nodes in the system, Vp with DG, Vp base are voltage profiles of the system with and without DG, prn is the probabilistic nature of DG. The highest value of the voltage index implies the best location of DG in terms of improving the voltage stability of the system.
Constraints
The most commonly used constraints in DG placement (DGP) problem are
Power flow equality constraints
Where, n is the total number of nodes in the system, Pi, Qi are the real and reactive power injections at bus i, Vi is the voltage magnitude at node i, di is the phase angle of complex voltage at node i, qiq is the angle of the i-qth element of the bus admittance matrix & Yiq is i-qth element of the bus admittance matrix.
Bus voltage limitation constraints
where Vimin, Vimax are the lower and upper limits on the voltage.
DG generation limits
where the upper and lower limits on DG real power generation at bus i & are the lower and upper limits on DG reactive power generations at bus i &
Feeder thermal limit
The power carrying capacity of feeders is represented by MVA limits Sk through any feeder k must be well within the maximum thermal capacity Skmax of the lines.
Short circuit level limit
A short circuit calculation is carried out to ensure that fault current with DG, SCLWDG should not increase rated fault current of currently installed protective devices SCLrated as
Design Variables
There are two main design variables, i.e., DG and load variables.
- DG variables that are generally considered are location, size, type, number. In case of renewable generation like wind etc, the location is fixed.
- Load profile is modelled as static load and time-varying load which are considered as load variables.
Solution Techniques
The solution techniques for DGP have been evolving and number of approaches have been developed, each with its particular mathematical and computational characteristics. The most of the techniques discussed are classified into three categories:
- Analytical methods
- Conventional methods,
- Intelligent search based methods
The conventional methods include Linear Programming (LP), Non Linear Programming (NLP) like AC optimal power flow and continuous power flow, Mixed Integer Non-Linear Programming (MINLP), and Analytical approaches. The intelligent search-based methods are Simulated Annealing (SA), Evolutionary Algorithms (EAs), Tabu Search (TS), Particle Swarm Optimization (PSO), GA, etc. have been given wide spread attention as possible techniques to obtain the global optimum for the DGP problem. Fuzzy set approaches has also been applied to DGP to address fuzziness associated with DG generation, demand, etc.
Simulation Results
The most commonly used objectives in the formulation of optimal DG sizing and siting is the power loss reduction and reliability improvement. The simulation results are demonstrated on IEEE 33-node test distribution systems and problem is solved using fminimax nonlinear optimization solver in Matlab. The single-line diagram of the IEEE 33 node test system is shown in Fig. 5. The total real and reactive power load on the system is 3715 kW and 2300 kVar, respectively. At base case condition, the maximum and the minimum bus voltage magnitudes are 1.0 and 0.898 p.u., respectively. The considered DG variables are location and size and fixed variables are type and number. The DG number is fixed to four. The varying load conditions considered, in this work, are normal load, 20% load increase and 20% load decrease. The DG penetration level is considered as 35% of the power supplied from main substation. The objective values are calculated in DIgSILENT programming and transferred into the Matlab and then the optimization tool searches for the optimal size for each DGs configuration. For each DGs configuration, the optimal sizing is found and obtained objective values are given to the fuzzy logic min-max approach to obtain best DG location.
The problem formulation for the optimal DG sizing for all possible DGs configurations is given in (14)-(21) as,
All the components are assumed to have identical reliability data. The failure rate, repair time, maintenance rate and maintenance time are 0.02 outages/year, 30 hours, 0.2 outages/ year and 20 hours, respectively. The upper and lower voltage limits considered are 1.0 & 0.95 p.u., respectively. Three cases are considered in which cases 1-2 represents single objective problems and case 3 represents the multi-objective problem, in which the weights are as follows:
In case-3, reliability and power loss both were given equal weightage (0.5). Table I gives the results of the best DG locations and their optimal sizing for 35% penetration levels. It can be seen that, to minimize the loss and to improve the bus voltages, the optimal places of DGs are the low voltage buses whereas for improving only reliability, end feeder buses are the candidate buses for DGs placements.
Fig. 6: Voltage of IEEE 33 node test distribution system for all the three cases
For meeting all the objectives, the low voltage end feeder buses are the candidate buses for DGs placement. This shows the validity of the approach. It can be seen that these buses are the best choice for DGs placement to improve the voltage profile and reliability of the system. Considering all the objectives together, these buses or nearer buses are selected for the optimal DG locations. It should be noted that the sizes of these DGs are different for different objectives. The voltage profiles with and without DGs corresponding to all the three cases are shown in Fig. 6. In the first two cases, only one objective at a time is emphasized, which makes optimization tool to give more importance to that objective. In the third case, all the objectives are considered with weights assigned to them and so the result obtained is the contribution of all.
Conclusions
The general background, objectives, constraints, and solution algorithms for the optimal allocation of Distributed Generation (DG) have been discussed in this paper. The objectives have been classified as single objective and multi-objective with equality and inequality constraints. In literature, different types of objective functions have been optimized for DGP using various conventional and artificial intelligent methods. In a general optimization formulation, single or multi-objective DG placement with various operational constraints may be solved with conventional optimization algorithms like Linear Programming (LP), Non-linear Programming (NLP), or MINLP. Due to the nonlinear nature of power systems, LP suffers from accuracy limitation to particular operating conditions. Consideration of nonlinear algorithms and integer variables will make the simulation time much longer and the algorithm possibly less robust. The intelligent search based algorithms such as Simulated Annealing (SA), Evolutionary Algorithm (EA), TS and PSO can deal the integer variable very well. However, these are more heuristic than conventional optimization techniques and needs further investigation regarding performance on different larger systems with their improved versions. Another interesting aspect is to include fuzzy set theory to model the uncertainties in objective function, load, generation, electricity price, and constraints for better compromised solution.
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