Kang Ma

Quantification of Additional Asset Reinforcement Cost From 3-Phase Imbalance

Uneven load distribution leads to a 3-phase imbalance at the low voltage (LV) substation level. This imbalance has distinct impacts on main feeders and LV transformers: for main feeders, it reduces the available capacity as the phase with the least spare capacity determines the usable capacity; for LV transformers, phase imbalance reduces the available capacity due to additional power along the neutral line. To assess the additional reinforcement cost (ARC) arising from a 3-phase imbalance, this paper proposes two novel costing models for main feeders and LV transformers respectively. Each model involves the derivation of an accurate ARC formula based on the degree of three-phase imbalance and a linearized approximation through Taylors expansion to simplify the detailed ARC formula, enabling quantification of future LV investment in scale. The developed models are tested on 4 cases where imbalance ranges from 0 to 10%, and reveals that i) a small imbalance degree may cause a substantial ARC on main feeders; ii) ARC grows exponentially as asset utilization is close to its capacity; and that iii) a main feeder is more sensitive to its respective imbalance degree than an LV transformer under the same condition. The models serve as an effective tool to assist distribution network operators (DNOs) to quantify a key cost (ARC) element from the phase imbalance, allowing DNOs to evaluate their future LV investment in scale.

Quantification of Additional Reinforcement Cost Driven by Voltage Constraint Under Three-Phase Imbalance

Three-phase imbalance causes uneven voltage drops across LV transformers and main feeders. With continuous load growth, the lowest phase voltage at the feeder end determines the voltage spare room, which is lower than if the same power were transmitted through balanced three phases. This imbalance causes additional reinforcement cost (ARC) beyond the balanced case. This paper proposes novel ARC models for a typical LV circuit based on primary-side voltage and current measurements. All models except the accurate model not only enable efficient utility-scale ARC calculations with sufficient accuracy but also remove the need for phasor measurements. The ARC models calculate voltage-driven reinforcement costs for the imbalanced case and the benchmark, i.e., the balanced case, where the ARC is the difference between the above values. The models include: an accurate ARC model considering imbalance in both magnitudes and phase angles; a semi-simplified ARC model assuming balanced phase angles; a fully simplified model assuming a purely resistive LV circuit and a unity power factor; and linearized ARC models considering the imbalance degree for two special cases. Test case proves that: the ARC is a monotonically increasing, convex (concave) but close-to-linear function of current (voltage) imbalance; voltage imbalance has a greater impact on ARCs than current imbalance; a higher degree of current imbalance and/or a deteriorating power factor reduce the accuracy of the fully simplified model; and the accuracy of the semi-simplified model is higher in the case of voltage angle imbalance than in the case of current angle imbalance.

Three-Phase Power Imbalance Decomposition Into Systematic Imbalance and Random Imbalance

Uneven load allocations and random load behaviors are two major causes for three-phase power imbalance. The former mainly cause systematic imbalance, which can be addressed by low-cost phase swapping; the latter contribute to random imbalance, which requires relatively costly demand-side managements. To reveal the maximum potential of phase swapping and the minimum need for demand-side managements, this paper first proposes a novel a priori judgment to classify any set of three-phase power series into one of four scenarios, depending on whether there is a definite maximum phase, a definite minimum phase, or both. Then, this paper proposes a new method to decompose three-phase power series into a systematic imbalance component and a random imbalance component as the closed-form solutions of quadratic optimization models that minimize random imbalance. A degree of power imbalance is calculated based on the systematic imbalance component to guide phase swapping. Case studies demonstrate that 72.8% of 782 low voltage substations have systematic imbalance components. The degree of power imbalance results reveal the maximum need for phase swapping and the random imbalance components reveal the minimum need for demand side management, if the three phases are to be fully rebalanced.

Two-Stage Optimal Scheduling of Electric Vehicle Charging based on Transactive Control

In this paper, a two-stage optimal charging scheme based on transactive control is proposed for the aggregator to manage day-ahead electricity procurement and real-time electric vehicles (EV) charging management in order to minimize its total operating cost. The day-ahead electricity procurement considers both the day-ahead energy cost and expected real-time operation cost. In the real-time charging management, the cost of employing the charging flexibility from the EV owners is explicitly modeled. The aggregator uses a transactive market to manage the real-time charging demand to provide the regulating power. A model predictive control-based method is proposed for the aggregator to clear the transactive market. The real-time charging decisions of the EVs are determined by the clearing of the proposed transactive market according to the real-time requests and preferences of the EV owners. As such, the aggregators decisions in the real-time EV charging management and regulating power markets can be optimized. At the same time, the charging requirements and response preferences of the EV owners are respected. Case studies using real world driving data from the Danish National Travel Surveys were conducted to verify the proposed framework.

Dynamic Game-Based Maintenance Scheduling of Integrated Electric and Natural Gas Grids With a Bilevel Approach

This paper proposes a dynamic game-based maintenance scheduling mechanism for the asset owners of the natural gas grid and the power grid by using a bilevel approach. In the upper level, the asset owners of the natural gas grid and the power grid schedule maintenance to maximize their own revenues. This level is modeled as a dynamic game problem, which is solved by the backward induction algorithm. In the lower level, the independent system operator dispatches the system to minimize the loss of power load and natural gas load in consideration of the system operating conditions under maintenance plans from the asset owners in the upper level. This is modeled as a mixed integer linear programming problem. For the model of the natural gas grid, a piecewise linear approximation associated with the big-M approach is used to transform the original nonlinear model into the mixed integer linear model. Numerical tests on a 6-bus system with a 4-node gas grid and a modified IEEE 118-bus system with a 20-node gas grid show the effectiveness of the proposed model.

Fast decoupled state estimation for distribution networks considering branch ampere measurements

Fast decoupled state estimation (FDSE) is proposed for distribution networks, with fast convergence and high efficiency. Conventionally, branch current magnitude measurements cannot be incorporated into FDSE models; however, in this paper, branch ampere measurements are reformulated as active and reactive branch loss measurements and directly formulated in the proposed FDSE model. Using the complex per unit normalization technique and special chosen state variables, the performance of this FDSE can be guaranteed when it is applied to distribution networks. Numerical tests on seven different distribution networks show that this method outperforms Newton type solutions and is a promising method for practical application.

Utility-Scale Estimation of Additional Reinforcement Cost From Three-Phase Imbalance Considering Thermal Constraints

Widespread three-phase imbalance causes inefficient uses of low voltage (LV) network assets, leading to additional reinforcement costs (ARCs). Previous work that assumed balanced three phases underestimated the reinforcement cost throughout the whole utility by more than 50%. Previous work that quantified the ARCs was limited to individual network components, relying on full sensory data. This paper proposes a novel methodology that will scale the ARC estimation at a utility level, when the data concerning the imbalance of circuits or transformers are scarce. A novel statistical method is developed to estimate the volume of assets that need to be invested by identifying the relationship between the triangular distribution of circuit imbalance and that of circuit utilization. When there are more data available in future, accurate probability distributions can be constructed to reflect the network condition across the whole system. In light of this, two novel generalized ARC estimation formulas are developed that account for generic probability distributions. The developed methodology is applied to a real utility system in the UK, showing that: 1) three-phase imbalance leads to ARCs that are even greater than the reinforcement costs in the balanced case; 2) a 1% increase in the demand growth rate, the maximum degree of imbalance (DIB) and the maximum nominal utilization rate leads to over 10%, approximately 1% and 2% increases in the ARCs, respectively; and 3) the ARC is not sensitive to the minimum DIB values and the minimum nominal utilization rates.

Quantification of Additional Reinforcement Cost From Severe Three-Phase Imbalance

This letter is an enhancement to our previous paper that quantifies additional reinforcement costs (ARCs) for low-voltage assets under moderate degree of three-phase imbalance. The original formulas cause an overestimation of the ARCs under severe imbalance. This letter first quantifies the threshold of the severe degree of imbalance (DIB), below which the original formulas are applicable. Then, the ARC formulas are extended to account for the whole range of DIB. Case studies demonstrate that when the asset loading level is below 33.3% (50%) for a feeder (a transformer), the DIB never exceeds the threshold and the original ARC formulas are applicable; otherwise, the DIB can exceed the threshold and the extended formulas yield correct ARCs.