Three-phase Optimal Power Flow Research Articles

Impact of phase selection on accuracy and scalability in calculating distributed energy resources hosting capacity

Hosting capacity (HC) and dynamic operating envelopes (DOEs), defined as dynamic, time-varying HC, are calculated using three-phase optimal power flow (OPF) formulations. Due to the computational complexity of such optimisation problems, HC and DOE are often calculated by introducing certain assumptions and approximations, including the linearised OPF formulation, which we implement in the Python-based tool ppOPF. Furthermore, we investigate how assumptions of the distributed energy resource (DER) connection phase impact the objective function value and computational time in calculating HC and DOE in distribution networks of different sizes. The results are not unambiguous and show that it is not possible to determine the optimal connection phase without introducing binary variables since, no matter the case study, the highest objective function values are calculated with mixed integer OPF formulations. The difference is especially visible in a real-world low-voltage network in which the difference between different scenarios is up to 14 MW in a single day. However, binary variables make the problem computationally complex and increase computational time to several hours in the DOE calculation, even when the optimality gap different from zero is set.

DSO Market for Transactive Scheduling of Electric Vehicle Charging Stations in Constrained Hierarchical Power Distribution and Urban Transportation Networks

The trend toward the deployment of electric vehicle charging stations (EVCSs) equipped with on-site distributed energy resources indicates potential transactive energy market (TEM) operations among EVCSs. However, unlike regular prosumers, EVCS operations are influenced by both the power distribution network (PDN) and the urban transportation network. In this paper, we propose a three-stage approach for solving the hierarchical energy scheduling and trading problem of EVCSs. At the first stage, the day-ahead traffic assignment problem of the transportation system is solved to determine individual EVCSs’ charging load. At the second stage, EVCSs solve their profit maximization problem to determine their energy scheduling and market participation decisions. Lastly, at the third stage, TEM among EVCSs is cleared by the distribution system operator (DSO). With the DSO shouldering both grid operator and market operator functions, the DSO problem is formulated as an unbalanced three-phase optimal power flow (OPF) model integrating a double-sided auction mechanism. To further improve the PDN operation, grid features such as network reconfiguration and tap changers are introduced into the OPF model. The effectiveness of the proposed framework is proved through case studies.

Integration of Centralized and Distributed Methods to Mitigate Voltage Unbalance Using Solar Inverters

Growing penetrations of single-phase distributed generation such as rooftop solar photovoltaic (PV) systems can increase voltage unbalance in distribution grids. However, PV systems are also capable of providing reactive power compensation to reduce unbalance. In this paper, we compare two methods to mitigate voltage unbalance with solar PV inverters: a centralized optimization-based method utilizing a three-phase optimal power flow formulation and a distributed approach based on Steinmetz design. While the Steinmetz-based method is computationally simple and does not require extensive communication or full network data, it generally leads to less unbalance improvement and more voltage constraint violations than the optimization-based method. In order to improve the performance of the Steinmetz-based method without adding the full complexity of the optimization-based method, we propose an integrated method that incorporates design parameters computed from the set-points generated by the optimization-based method into the Steinmetz-based method. We test and compare all methods on a large three-phase distribution feeder with time-varying load and PV data. The simulation results indicate trade-offs between the methods in terms of computation time, voltage unbalance reduction, and constraint violations. We find that the integrated method can provide a good balance between performance and information/communication requirements.

Using OPF-Based Operating Envelopes to Facilitate Residential DER Services

The proliferation of residential distributed energy resources (DER), such as solar PV and batteries, is creating opportunities for DER owners to provide system-level services through aggregators. However, if this aggregated response is not adequately managed by distribution companies, the simultaneous active power exports (or imports) can result in voltages and currents well beyond the limits of their networks. But the big barrier is that, often, distribution companies cannot directly manage DER or aggregators. This work proposes the use of operating envelopes—time-varying, meter-level export/import limits that a distribution company issues to aggregators—to ensure network integrity while facilitating residential DER services. The operating envelopes are calculated using a linearised, three-phase optimal power flow (OPF) technique that also exploits controllable network assets (e.g., on-load tap changers). Using a realistic Australian MV-LV network with 4,600+ residential customers, results show that network integrity can be ensured without the need for distribution companies to directly control DER. Furthermore, existing on-load tap changers create additional voltage headroom and, thus, larger operating envelopes (and potential services). Given that distribution companies do not know the ultimate exports/imports of customers providing services, a probabilistic testing of the operating envelopes confirms that they are adequate for most plausible scenarios.

Three-phase optimal power flow for networked microgrids based on semidefinite programming convex relaxation

Many autonomous microgrids have high penetration of distributed generation (DG) units. Optimal power flow (OPF) is necessary for the optimal dispatch of such networked microgrids (NMGs). Existing convex relaxation methods for three-phase OPF are only applicable to radial networks, not meshed networks. To overcome this limitation, we develop a semidefinite programming (SDP) convex relaxation model, which can be applied to meshed networks and also includes a model of three-phase DG units and on-load voltage regulators with different connection types. The proposed model has higher accuracy than other existing convex relaxation models and the SDP model effectively solves the OPF problem for three-phase meshed networks with satisfactory accuracy, as validated by real 6-bus, 9-bus, and 30-bus NMGs and the IEEE 123-bus test cases. In the SDP model, the convex symmetric-component of the three-phase DG model is shown to be more accurate than three-phase DG that is modelled as three single-phase DG units in three-phase unbalanced OPF. The optimal control variables obtained from the convex relaxation optimization can be used for both the final optimal dispatch strategy and the initial value of non-convex OPF to obtain the globally optimal solution efficiently.

Linearised three‐phase optimal power flow for coordinated optimisation of residential solid‐state power substations

With the increasing integration of single-phase resources, for example, PV, batteries and solid-state power substations (SSPSs), in residential distribution networks, voltage regulation and phase balancing of distribution feeders are facing growing challenges. To solve these challenges, a linearised three-phase optimal power flow (OPF) model is proposed to coordinate the operation of residential solid-state power substations for voltage regulation and phase balancing of distribution feeders. The proposed three-phase OPF model schedules both real and reactive power of each components in the SSPSs with the purpose of minimising the total operating cost as well as improving the grid performance, for example, voltage regulation and phase balancing. Results of case studies validate the accuracy of the proposed three-phase OPF model. In addition, the effectiveness of coordinating multiple SSPSs for voltage regulation and phase balancing has been demonstrated.

Ensuring Distribution Network Integrity Using Dynamic Operating Limits for Prosumers

The number of residential consumers with solar PV and batteries, aka prosumers, has been increasing in recent years. Incentives now exist for prosumers to operate their batteries in more profitable ways than self-consumption mode. However, this can increase prosumer exports or imports, resulting in power flows that can lead to voltage and thermal limit violations in distribution networks. This work proposes a framework for Distribution Network Operators (DNOs) to ensure the integrity of MV-LV networks by using dynamic operating limits for prosumers. Periodically, individual prosumers send their intended operation (net exports/imports) as determined by their local control to the DNO who then assesses network integrity using smart meter data and a power flow engine. If a potential violation is detected, their maximum operating limits are determined based on a three-phase optimal power flow that incorporates network constraints and fairness aspects. A real Australian MV feeder with realistically modelled LV networks and 4,500+ households is studied, where prosumers' local controls operate based on energy prices. Time-series results demonstrate that the proposed framework can help DNOs ensure network integrity and fairness across prosumers. Furthermore, it unlocks larger profitability for prosumers compared with the use the 5kW fixed export limit adopted in Australia.

A Fair Incentive Scheme for Participation of Smart Inverters in Voltage Control

The increasing trend of renewable energy sources integration in the distribution systems may cause voltage fluctuations and voltage limit violations. The smart inverters with reactive power capability and active power curtailment (APC) control can solve the grid voltage issues. In this article, three-phase optimal power flow (TPOPF) is applied to dispatch the APC and reactive power injection (RPI) of inverters. The TPOPF takes smart meter measurements as inputs. The nonproportional APC and proportional APC are examined. In this article, a fair incentive scheme for APC by the inverters is proposed, appropriate for both utility and renewable energy producers. Similarly, unequal RPI and equal RPI by the inverters to maintain the system voltage are studied. The RPI incentive scheme is analyzed by accounting for the costs incurred in overrating of the inverters, power losses, and life reduction due to reactive power supplied by the inverters. The effective location of inverters for APC and RPI in the distribution network is explored. The incentive schemes are implemented in 27-node distribution system and IEEE European low-voltage distribution system.

Uncertainty-Aware Three-Phase Optimal Power Flow Based on Data-Driven Convexification

This paper presents a novel optimization framework of formulating the three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware optimization (UaO) framework is: 1) a deterministic framework that is less complex than the existing optimization frameworks involving uncertainty, and 2) convex such that it admits polynomial-time algorithms and mature distributed optimization methods. To construct this UaO framework, a methodology of learning-aided uncertainty-aware modeling, with prediction errors of stochastic variables as the measurement of uncertainty, and a theory of data-driven convexification are proposed. Theoretically, the UaO framework is applicable for modeling general optimization problems under uncertainty.

Hierarchical coordination strategy for three‐phase MV and LV distribution networks with high‐penetration residential PV units

This paper presents a hierarchical coordination method to improve operation conditions between the medium-voltage distribution network (MVDN) and low-voltage distribution networks (LVDN) considering high-level residential PV units integrating LV distribution networks. It addresses the following issues: (i) rapid power fluctuations and unbalance caused by high-level residential PV units passes to the MV distribution network via the point of common coupling (PCC) and thus increase operation challenges; (ii) power fluctuations, voltage violations and unbalance simultaneously happens in the LVDNs. A hierarchical coordination structure the MVDN and LVDN is proposed. In the MV level, a centralized dispatch method based on three-phase optimal power flow is developed in the timescale of minutes to minimize the power losses, unbalance and PCC adjustments, which are achieved by regulating energy storage systems (ESSs) and PV inverters in the LV level. In the LV level, a distributed control model based on a consensus algorithm is proposed in the timescale of seconds to track the reference active (or reactive) power at the PCC given by the MV level and mitigate its fluctuations. Simulations studies are performed to verify the proposed method.

Conservation voltage reduction (CVR) via two‐timescale control in unbalanced power distribution systems

Voltage control devices are employed in power distribution systems to reduce the power consumption by operating the system closer to the lower acceptable voltage limits; this technique is called conservation voltage reduction (CVR). The different modes of operation for system's legacy devices (with binary control) and new devices (e.g. smart inverters with continuous control) coupled with variable photovoltaic (PV) generation results in voltage fluctuations which makes it challenging to achieve CVR objective. This paper presents a two-timescale control of feeder's voltage control devices to achieve CVR that includes (1) a centralized controller operating in a slower time-scale to coordinate voltage control devices across the feeder and (2) local controllers operating in a faster timescale to mitigate voltage fluctuations due to PV variability. The centralized controller utilizes a three-phase optimal power flow model to obtain the decision variables for both legacy devices and smart inverters. The local controllers operate smart inverters to minimize voltage fluctuations and restore nodal voltages to their reference values by adjusting the reactive power support. The proposed approach is validated using the IEEE-123 bus (medium-size) and R3-12.47-2 (large-size) feeders. It is demonstrated that the proposed approach is effective in achieving the CVR objective for unbalanced distribution systems.

On the Fairness of PV Curtailment Schemes in Residential Distribution Networks

Active power curtailment of residential PV systems is an effective way to mitigate technical issues in distribution networks. However, existing curtailment schemes can treat households unfairly; e.g., Volt-Watt schemes increasingly being adopted worldwide inherently penalize PV systems at remote locations in radial feeders. Nonetheless, whether fairness is improved or not by alternative curtailment schemes depends on how the impacts on households are considered. In this context, household-centric metrics that quantify PV harvesting, energy export and financial benefit are used along with the Jain’s fairness index to assess fairness from different perspectives. To explore the trade-offs brought by schemes that consider fairness differently, four linearized, three-phase Optimal Power Flow (OPF)-based schemes are proposed to determine, periodically, short-term curtailment settings. Using a real Australian 22kV feeder and realistically modelled LV networks with 4,500+ households, a detailed comparison is carried out considering also a Volt-Watt scheme. Results demonstrate tha tall the schemes that consider fairness are effective in removing locational penalizations. However, in terms of fairness, their performance across the adopted metrics reveals noticeable trade-offs. This highlights the need for decision-makers to determine the metric from which fairness can be based upon in a way that aligns with their respective policies.

Distributed multi-period three-phase optimal power flow using temporal neighbors

The penetration of distributed generation in medium (MV) and low (LV) voltage distribution grids has been steadily increasing every year in multiple countries, thus creating new technical challenges in grid operation and motivating developments in distributed optimization for flexibility management. The traditional centralized optimal power flow (OPF) algorithm can solve technical constraints violation. However, computational efficiency, new technologies (e.g., edge computing) and control architectures (e.g., web-of-cells) are demanding for distributed approaches. This work formulates a novel distributed multi-period OPF for three-phase unbalanced grids that is essential when integrating energy storage units in operational planning (e.g., day-ahead) of LV or local energy community grids. The decentralized constrained optimization problem is solved with the alternating direction method of multipliers (ADMM) adapted for unbalanced LV grids and multi-period optimization problems. A 33-bus LV distribution grid is used as a case-study in order to define optimal battery storage scheduling along a finite time horizon that minimizes overall grid operational costs, while complying with technical constraints of the grid (e.g., voltage and current limits) and battery state-of-charge constraints.

Voltage Regulation Planning for Distribution Networks Using Multi-Scenario Three-Phase Optimal Power Flow

Active distribution networks must operate properly for different scenarios of load levels and distributed generation. An important operational requirement is to maintain the voltage profile within standard operating limits. To do this, this paper proposed a Multi-Scenario Three-Phase Optimal Power Flow (MTOPF) that plans the voltage regulation of unbalance and active distribution networks considering typical scenarios of operation. This MTOPF finds viable operation points by the optimal adjustments of voltage regulator taps and distribution transformer taps. The differentiating characteristic of this formulation is that in addition to the traditional tuning of voltage regulator taps of an active network applied for just one scenario of load and generation, it also performs the optimal adjustment of distribution transformer taps, which, once fixed, is able to meet the voltage limits of diverse operating situations. The optimization problem was solved by the primal-dual interior-point method and the formulation was tested using the IEEE 123-bus system.

A Horizon Optimization Control Framework for the Coordinated Operation of Multiple Distributed Energy Resources in Low Voltage Distribution Networks

In recent years, the installation of residential Distributed Energy Resources (DER) that produce (mainly rooftop photovoltaics usually bundled with battery system) or consume (electric heat pumps, controllable loads, electric vehicles) electric power is continuously increasing in Low Voltage (LV) distribution networks. Several technical challenges may arise through the massive integration of DER, which have to be addressed by the distribution grid operator. However, DER can provide certain degree of flexibility to the operation of distribution grids, which is generally performed with temporal shifting of energy to be consumed or injected. This work advances a horizon optimization control framework which aims to efficiently schedule the LV network’s operation in day-ahead scale coordinating multiple DER. The main objectives of the proposed control is to ensure secure LV grid operation in the sense of admissible voltage bounds and rated loading conditions for the secondary transformer. The proposed methodology leans on a multi-period three-phase Optimal Power Flow (OPF) addressed as a nonlinear optimization problem. The resulting horizon control scheme is validated within an LV distribution network through multiple case scenarios with high microgeneration and electric vehicle integration providing admissible voltage limits and avoiding unnecessary active power curtailments.

Robust Energy Management of Isolated Microgrids

This paper presents the mathematical formulation and architecture of a robust energy management system for isolated microgrids featuring renewable energy, energy storage, and interruptible loads. The proposed strategy addresses the challenges of renewable energy variability and forecast uncertainty using a two-stage decision process combined with a receding horizon approach. The first-stage decision variables are determined using a cutting-plane algorithm to solve a robust unit commitment; the second stage solves the final dispatch commands using a three-phase optimal power flow. This novel approach is tested on a modified International Council on Large Electric Systems (CIGRE) test system under different conditions. The proposed algorithm is able to produce reliable dispatch commands without considering probabilistic information from the forecasting system. These results are compared with deterministic and stochastic formulations. The benefits of the proposed control are demonstrated by a reduction in load interruption events and by increasing available reserves without an increase in overall costs.

Three-Phase Optimal Power Flow for Market-Based Control and Optimization of Distributed Generations

The ever-increasing penetration of distributed generation in recent years brings challenges as well as opportunities for distribution companies as the smart grid paradigm evolves. A new three-phase unbalanced optimal power flow algorithm is developed for steady state system analysis to minimize the cost of serving loads in a distribution network. The algorithm is developed based on primal-dual interior point method. Comprehensive system components and constraints are modeled in a generalized fashion. In tests performed on the IEEE test feeder systems, the proposed algorithm is able to solve for optimal solutions under various system conditions and constraints. The potential applications of the program for distribution system design, reconfiguration, and control are also highlighted.

Chordal Conversion Based Convex Iteration Algorithm for Three-Phase Optimal Power Flow Problems

The three-phase optimal power flow (OPF) problem has recently attracted a lot of research interests due to the need to coordinate the operations of large-scale and heterogeneous distributed energy resources in unbalanced electric power distribution systems. The nonconvexity of the three-phase OPF problem is much stronger than that of the single-phase OPF problem. Instead of applying the semidefinite programming relaxation technique, this paper advocates a convex iteration algorithm to solve the nonconvex three-phase OPF problem. To make the convex iteration algorithm computationally efficient for large-scale distribution networks, the chordal conversion based technique is embedded in the convex iteration framework. By synergistically combining the convex iteration method and the chordal based conversion technique, the proposed three-phase OPF algorithm is not only computationally efficient but also guarantees global optimality when the trace of the regularization term becomes zero. At last, to further improve the computational performance, a greedy grid partitioning algorithm is proposed to decompose a single large matrix representing a distribution network to many smaller matrices. The simulation results using standard IEEE test feeders show that the proposed algorithm is computationally efficient, scalable, and yields global optimal solutions while resolving the rank conundrum.

Optimally Allocation of Distributed Generators in Three-Phase Unbalanced Distribution Network

Increasing energy demand can be compensated with integration of distributed energy resources in the three-phase distribution system. Load flow analysis of the unbalanced three-phase distribution system requires a tool and algorithm to manage the multiple sources. In this study, Jaya algorithm is applied and interfaced with open source software openDSS to solve the unbalanced three-phase optimal power flow. Further, co-simulation framework is used to obtain the optimal allocation of two types of multiple distributed generators in unbalanced radial distribution system. The effectiveness of the approach is validated on IEEE 123 node distribution system. For a realistic study, mixes of all type of loads and configuration of the actual distribution system are considered. The results are compared with already published results obtained from established particle swarm optimization.

Research on three‐phase optimal power flow for distribution networks based on constant Hessian matrix

The optimal power flow (OPF) problem for active distribution networks with distributed generation (DG) and a variety of discretely adjustable devices (e.g. on-load tap-changers, OLTCs) is essentially a non-convex, non-linear, mixed-integer optimisation problem. In this study, the quadratic model of three-phase OLTCs is proposed by adding branch currents as unknown variables, which guarantee a constant Hessian matrix throughout iterations. This study proposes a three-phase OPF model for active distribution networks, considering a three-phase DG model. The OPF model is solved by an interior point method incorporating a quadratic penalty function as opposed to a Gaussian penalty function. Furthermore, a voltage regulator is also incorporated into the OPF model to form an integrated regulation strategy. The methodology is tested and validated on the IEEE 13-bus three-phase unbalanced test system.