Three-phase optimal load flow model and algorithm for active distribution networks

This paper studies the complex energy coupling relationship of unbalanced power distribution network integrated with the natural gas distribution system. An Alternating Direction Method of Multipliers (ADMM) based decentralized solution approach is proposed to achieve the multi-period synergistic operation of the power distribution and natural gas distribution networks. A bi-level solution strategy is used to solve the power distribution subsystem problem, where level-1 is the linearized version of three-phase optimal load flow and level-2 solves the convex nonlinear problem. The level-1 problem helps to determine the status of voltage control devices whereas the level-2 problem obtains the optimal and feasible solution of the optimal load flow problem. The non-convexities present in the integrated energy system are dealt with the Second Order Cone Programming (SOCP) and Quadratic Relaxation (QR). The purposed solution procedure is validated using IEEE 13-bus distribution system integrated with 6-bus natural gas network. The numerical results corroborate the applicability of the proposed approach to minimize the operation cost of the integrated energy system.

The transition from a vertically integrated to a horizontally integrated structure in the electricity system results in an increase in uncertainty at various levels. The new power system topology mandates the inclusion of uncertain behavior in the standard power flow studies, which were previously not necessary. Three-phase load flow has been extensively used for power system analysis in balanced and unbalanced cases. In this paper, an efficient Latin Hypercube Monte-Carlo simulation (LHMCS) approach for a three-phase transmission system load flow has been developed, which can be used for uncertainty quantification and determining the probability distribution of various parameters. The proposed method has been tested using the IEEE-118 bus test system for different cases.

The paper presents grid connected Photovoltaic (PV) models for three-phase distribution load flow analysis. The models comprises of single-diode PV model with and without the effect of the series and parallel resistances, I-V nonlinear question, I-V database and single-phase PV modeled as singlephase real power injection. The three-phase load flow program with Photovoltaic models has been tested using IEEE 13 node feeder. The solution of the base case is compared with the radial distribution analysis package (RDAP) before used to analyze distribution networks. The analysis is carried out with various photovoltaic mathematical models. The simulation results show that the grid-connected three-phase photovoltaic system in distribution network can improve the voltage profile as well as reduce the total system losses. However, single-phase PV DG model does not always guarantee voltage improvements.

Three-phase voltage imbalance occurs by variety of connecting points of single-phase loads. In order to improve three-phase voltage imbalance, connecting points of single-phases loads are exchanged. System planner has to decide how to exchange connection of single-phase loads with the minimum planning cost in order to improve three-phase voltage imbalance. However, since there are many patterns of connection for single-phase loads, it is not easy to determine the optimal connection pattern for single-phase loads with the minimum planning cost under the constraint for improving voltage imbalance. In this paper, authors propose a computational method to support the planner's decision of single-phase loads connection systematically. The proposed method, which is based on effective enumeration algorithm, can obtain the optimal single-phase loads connection pattern, which satisfies with constraint of voltage balance and has the minimum total number of single-phase loads exchanged from previous single-phase loads connection. In the proposed method, three-phase iterative load flow calculation is applied to calculate rate of three-phase voltage imbalance. Three-phase iterative load flow calculation has two simple procedures: (Procedure1) addition of load currents from terminal node of feeder to root one, and (Procedure2) subtraction of voltage drop from root node of feeder to terminal one. In order to check the validity of the proposed method, numerical results are shown for a distribution system model with DG.

An unbalanced electric power system can occur due to unequal lines and/or loads in each phase of the system. For a system with a high level of unbalance, the assumption that the system is balanced becomes incorrect. For a case like this, the system must be analyzed using three-phase approaches because single-phase analysis techniques can no longer be used to obtain accurate results. Therefore, the development of three-phase models of all components of the electric power system, including the wind turbine generating system (WTGS), is very important so that the system can properly be analyzed and its performance can correctly be evaluated. This paper proposes a method to incorporate WTGS in a three-phase load flow analysis of an unbalanced distribution system. The proposed method is based on the previously published single-phase two-port network model. In this paper, the single-phase two-port network model is modified and extended so that it can be applied to unbalanced systems. The model is then included in the three-phase distribution system load flow (DSLF) analysis. The proposed method is validated using 12-node and 19-node distribution systems.

A mixed-integer second order cone program (MISOCP) formulation is proposed for solving Markowitz’s asset portfolio construction problem under a cardinality constraint. Compared with a standard alternative big-M linearly constrained formulation, our reformulation is solved significantly faster using state-of-the-art integer programming solvers. We consider learning methods that are based on the MISCOP formulation: cardinality-constrained Markowitz (CCM) solves the MISCOP for a given cardinality k and training set data of asset returns. We also find reinforcing evidence for factor model theory in the selection of factors to form optimal CCM portfolios. For large datasets in the absence of a hard-cardinality constraint, we propose a method (CCM-R) that is based on the continuous relaxation of our MISCOP, where k selected by rolling time window validation. In predictive performance experiments, based on historical stock exchange data, our learning methods usually outperform a competing extension of the Markowitz model that penalizes the L1 norm of asset weights.

This paper considers the power minimization problem in downlink of cloud radio access networks with limited fronthaul capacity. A joint design of beamforming, remote radio head (RRH) selection and RRH-user association that explicitly takes into account per- fronthaul capacity constraints is considered. The problem of interest is in fact a combinatorial program which is generally NP- hard. We naturally write the considered problem as a mixed integer program by introducing binary selection variables. The challenge is that even if these binary selection variables are relaxed to be continuous, the resulting problem is still nonconvex. For such a problem, finding a high- quality solution, rather than an optimal one, is a more realistic goal. Towards this end we propose two iterative algorithms to deal with combinatorial nature of the joint design problem. In the first method, by novel transformations, we iteratively approximate the continuous nonconvex constraints by convex conic ones using successive convex approximation framework. More explicitly the problem arrived at each iteration of the first method is a mixed-integer second order cone program (MISOCP) for which dedicated solvers are available. The second method is a simplified variant of the first one where we further relax the binary variables in each iteration to be continuous. That is to say, the second method merely requires solving a sequence of SOCPs. After convergence, we then perform a postprocessing procedure on the relaxed selection variables to search for a high-performance solution. Numerical results are presented to demonstrate the superiority of the proposed algorithms over existing methods based on sparse-inducing norm.

This paper presents a novel design of energyoptimal adaptive cruise control (EACC) for internal combustion engine (ICE) vehicles based on hybrid model predictive control (HMPC), which optimally plans the vehicle speed trajectory for higher energy efficiency through taking both traffic and road information ahead into account. HMPC is proposed in this work to cope with the discrete control variable for switching the ICE on and off. HMPC is formulated as a mixed-integer quadratically constrained quadratic programming problem (MIQCQP), which is recast as a mixed-integer second order cone programming (MISOCP) problem. The performance of HMPC-based EACC is evaluated in real driving conditions and compared with linear MPC, as well as with receding horizon dynamic programming (RHDP).

Uncertainties from distributed generations (DGs) make conventional reactive power optimization (RPO) methods difficult to be applied in the distribution network (DN). To settle this issue, a novel two-stage RPO strategy for active distribution network (ADN) based on extreme scenarios is proposed in this paper. Random variables are handled through extreme scenarios, then flexible and inflexible variables are decided in two different stages to adapt to DG’s randomness. Firstly, based on second order cone relaxation (SOCR), power flow equations are convexly relaxed to transform original model into mixed integer second order cone programming (MISOCP). Then, extreme scenario method (ESM) is employed to determine DG’s deployment. Finally, numerical tests are performed on a modified IEEE 33-bus DN to demonstrate the effectiveness and feasibility of the proposed strategy.

Optimal load flow normally considers active and reactive power loads as independent of the voltage level. In the paper the exponential form of a static load model relating the active and reactive power components to the busbar voltage, is considered and the effects of incorporating this load model in the optimal load flow solution of several test systems are studied. The effects of modelling active and reactive powers are considered separately as well as when taken together. The results are compared with the respective standard optimal load flow solutions for a number of standard test systems.The differences in fuel cost, total power loss and voltage values when compared with the standard optimal load flow solution are significant for some systems. The fuel cost and power generation differences are the highest when only the active power variation with the voltage is modelled. The heavier the system loading, the lower the fuel cost difference between conventional OPF, and the OPF incorporating power variations with voltages. The differences in power loss are more pronounced when both active and reactive powers are modelled. The higher the loading, the less pronounced the difference in power loss. More significant deviations in voltage take place when both active and reactive powers are modelled. The modelling of reactive power is more influential on the voltages than is the modelling of active power on the voltage deviations. The contrary is true for the differences in phase angle and incremental cost of power delivered, wherein the main factor is active power modelling. There are no differences in iteration numbers for small-size systems. The larger and more heavily loaded systems exhibit a difference in the required number iterations.

This paper proposes a coordinated active–reactive power optimization model for an active distribution network with energy storage systems, where the active and reactive resources are handled simultaneously. The model aims to minimize the power losses, the operation cost, and the voltage deviation of the distribution network. In particular, the reactive power capabilities of distributed generators and energy storage systems are fully utilized to minimize power losses and improve voltage profiles. The uncertainties pertaining to the forecasted values of renewable energy sources are modelled by scenario-based stochastic programming. The second-order cone programming relaxation method is used to deal with the nonlinear power flow constraints and transform the original mixed integer nonlinear programming problem into a tractable mixed integer second-order cone programming model, thus the difficulty of problem solving is significantly reduced. The 33-bus and 69-bus distribution networks are used to demonstrate the effectiveness of the proposed approach. Simulation results show that the proposed coordinated optimization approach helps improve the economic operation for active distribution network while improving the system security significantly.

PurposeThe purpose of this study is to obtain the optimal frequency for low-frequency transmission lines while minimizing losses and maintaining the voltage stability of low-frequency systems. This study also emphasizes a reduction in calculations based on mathematical approaches.Design/methodology/approachTelegrapher’s method has been used to reduce large calculations in low-frequency high-voltage alternating current (LF-HVac) lines. The static compensator (STATCOM) has been used to maintain voltage stability. For optimal frequency selection, a modified Jaya algorithm (MJAYA) for optimal load flow analysis was implemented.FindingsThe MJAYA algorithm performed better than other conventional algorithms and determined the optimum frequency selection while minimizing losses. Voltage stability was also achieved with the proposed optimal load flow (OLF), and statistical analysis showed that the proposed OLF reduces the frequency deviation and standard error of the LF-HVac lines.Originality/valueThe optimal frequency for LF-HVac lines has been achieved, Telegrapher’s method has been used in OLF, and STATCOM has been used in LF-HVac transmission lines.

Voltage and reactive power control is an important task to ensure the economic and safe operation of the distribution network. Coordinating multiple adjustment methods can improve the operation efficiency of the distribution network. In this paper, voltage and reactive power control devices are considered, such as on load tap changer (OLTC), voltage regulators (VR), capacitor bank (CB) and distributed generation (DG). And the optimization is proposed to solve the meaningless action in existing Volt control. Firstly, the voltage and reactive power optimization model of distribution network is established based on the branch power flow equation, which is relaxed to the mixed integer second-order cone programming (MISOCP). At the same time, considering the action cost of the devices, a rolling optimization mode based on model predictive control (MPC) is proposed. Finally, the effectiveness of the proposed strategy is verified based on the improved IEEE-33 bus test system.

It is an extra heavy burden to maintain the distribution network model since of its frequent changing and large scale. In reality, the network model may involve significant parameter errors, which makes the model not applicable. This paper presents a robust data-driven approach to linearize the three-phase power flow. A three-phase linear power flow (LPF) model for active distribution networks (ADNs) is proposed. To address the issues of measurement outliers and data collinearity, the support vector regression (SVR) algorithm is applied to the linearization regression to obtain the proposed three-phase LPF model. The training process is offline and the obtained LPF model can be used to calculate the power flow online. Numerical tests demonstrate that the proposed approach can achieve satisfactory calculation accuracy with high computational efficiency, even under data collinearity and measurement outliers. Since the proposed LPF has very high accuracy, this model can be incorporated into distribution networks optimization problems.

A direct approach for unbalanced three-phase distribution load flow solutions is proposed in this paper. The special topological characteristics of distribution networks have been fully utilized to make the direct solution possible. Two developed matrices-the bus-injection to branch-current matrix and the branch-current to bus-voltage matrix-and a simple matrix multiplication are used to obtain load flow solutions. Due to the distinctive solution techniques of the proposed method, the time-consuming LU decomposition and forward/backward substitution of the Jacobian matrix or Y admittance matrix required in the traditional load flow methods are no longer necessary. Therefore, the proposed method is robust and time-efficient. Test results demonstrate the validity of the proposed method. The proposed method shows great potential to be used in distribution automation applications.