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Regulating the proper carbon-aware intervention policy is one of the keys to emission alleviation in the distribution network, whose basis lies in effectively attributing the emission responsibility using emission factors. This paper establishes the distribution locational marginal emission (DLME) to calculate the marginal change of emission from the marginal change of both active and reactive load demand for incentivizing carbon alleviation. It first formulates the day-head distribution network scheduling model based on the second-order cone program (SOCP). The emission propagation and responsibility are analyzed from demand to supply to system emission. Considering the complex and implicit mapping of the SOCP-based scheduling model, the implicit theorem is leveraged to exploit the optimal condition of SOCP. The corresponding SOCP-based implicit derivation approach is proposed to calculate the DLMEs effectively in a model-based way. Comprehensive numerical studies are conducted to verify the superiority of the proposed method by comparing its calculation efficacy to the conventional marginal estimation approach, assessing its effectiveness in carbon alleviation with comparison to the average emission factors, and evaluating its carbon alleviation ability of reactive DLME.

This paper proposes a multiagent based bi-level operation framework for the low-carbon demand management in distribution networks considering the carbon emission allowance on the demand side. In the upper level, the aggregate load agents optimize the control signals for various types of loads to maximize the profits; in the lower level, the distribution network operator makes optimal dispatching decisions to minimize the operational costs and calculates the distribution locational marginal price and carbon intensity. The distributed flexible load agent has only incomplete information of the distribution network and cooperates with other agents using networked communication. Finally, the problem is formulated into a networked multi-agent constrained Markov decision process, which is solved using a safe reinforcement learning algorithm called consensus multi-agent constrained policy optimization considering the carbon emission allowance for each agent. Case studies with the IEEE 33-bus and 123-bus distribution network systems demonstrate the effectiveness of the proposed approach, in terms of satisfying the carbon emission constraint on demand side, ensuring the safe operation of the distribution network and preserving privacy of both sides., Comment: Submitted to IEEE Transactions on Sustainable Energy

Prediction plays a vital role in the active distribution network voltage regulation under the high penetration of photovoltaics. Current prediction models aim at minimizing individual prediction errors but overlook their collective impacts on downstream decision-making. Hence, this paper proposes a safety-aware semi-end-to-end coordinated decision model to bridge the gap from the downstream voltage regulation to the upstream multiple prediction models in a coordinated differential way. The semi-end-to-end model maps the input features to the optimal var decisions via prediction, decision-making, and decision-evaluating layers. It leverages the neural network and the second-order cone program (SOCP) to formulate the stochastic PV/load predictions and the var decision-making/evaluating separately. Then the var decision quality is evaluated via the weighted sum of the power loss for economy and the voltage violation penalty for safety, denoted by regulation loss. Based on the regulation loss and prediction errors, this paper proposes the hybrid loss and hybrid stochastic gradient descent algorithm to back-propagate the gradients of the hybrid loss with respect to multiple predictions for enhancing decision quality. Case studies verify the effectiveness of the proposed model with lower power loss for economy and lower voltage violation rate for safety awareness.

Decarbonizing the energy supply is essential and urgent to mitigate the increasingly visible climate change. Its basis is identifying emission responsibility during power allocation by the carbon emission flow (CEF) model. However, the main challenge of CEF application is the intractable nonlinear relationship between carbon emission and power allocation. So this paper leverages the high approximation capability and the mixed-integer linear programming (MILP) representability of the deep neural networks to tackle the complex CEF model in carbon-electricity coordinated optimization. The compact constraint learning approach is proposed to learn the mapping from power injection to bus emission with sparse neural networks (SNNs). Then the trained SNNs are transformed equivalently as MILP constraints in the downstream optimization. In light of the ``high emission with high price'' principle, the blocked carbon price mechanism is designed to price emissions from the demand side. Based on the constraint learning and mechanism design, this paper proposes the carbon-aware energy management model in the tractable MILP form to unlock the carbon reduction potential from the demand side. The case study verifies the approximation accuracy and sparsity of SNN with fewer parameters for accelerating optimization solution and reduction effectiveness of demand-side capability for mitigating emission.

Electricity price prediction plays a vital role in energy storage system (ESS) management. Current prediction models focus on reducing prediction errors but overlook their impact on downstream decision-making. So this paper proposes a decision-focused electricity price prediction approach for ESS arbitrage to bridge the gap from the downstream optimization model to the prediction model. The decision-focused approach aims at utilizing the downstream arbitrage model for training prediction models. It measures the difference between actual decisions under the predicted price and oracle decisions under the true price, i.e., decision error, by regret, transforms it into the tractable surrogate regret, and then derives the gradients to predicted price for training prediction models. Based on the prediction and decision errors, this paper proposes the hybrid loss and corresponding stochastic gradient descent learning method to learn prediction models for prediction and decision accuracy. The case study verifies that the proposed approach can efficiently bring more economic benefits and reduce decision errors by flattening the time distribution of prediction errors, compared to prediction models for only minimizing prediction errors.

The increasing penetration of distributed energy resources (DERs) will decrease the rotational inertia of the power system and further degrade the system frequency stability. To address the above issues, this paper leverages the advanced neural network (NN) to learn the frequency dynamics and incorporates NN to facilitate system reliable operation. This paper proposes the conservative sparse neural network (CSNN) embedded frequency-constrained unit commitment (FCUC) with converter-based DERs, including the learning and optimization stages. In the learning stage, it samples the inertia parameters, calculates the corresponding frequency, and characterizes the stability region of the sampled parameters using the convex hulls to ensure stability and avoid extrapolation. For conservativeness, the positive prediction error penalty is added to the loss function to prevent possible frequency requirement violation. For the sparsity, the NN topology pruning is employed to eliminate unnecessary connections for solving acceleration. In the optimization stage, the trained CSNN is transformed into mixed-integer linear constraints using the big-M method and then incorporated to establish the data-enhanced model. The case study verifies 1) the effectiveness of the proposed model in terms of high accuracy, fewer parameters, and significant solving acceleration; 2) the stable system operation against frequency violation under contingency.

Power systems are shifted from conventional bulk generation toward renewable generation. This trend leads to the frequency security problem due to the decline of system inertia. On the other hand, natural gas-fired units are frequently scheduled to provide operational flexibility due to their fast adjustment ability. The interdependence between power and natural gas systems is thus intensified. In this paper, we study the frequency constrained scheduling problem from the perspective of an integrated electricity-gas system under variable wind power. We propose a distributionally robust (DR) chance constrained optimization model to co-optimize the unit commitment and virtual inertia provision from wind farm systems. This model incorporates both frequency constraints and natural gas system (NGS) operational constraints and addresses the wind power uncertainty by designing DR joint chance constraints. We show that this model admits a mixed-integer second-order cone programming. Case studies demonstrate that the proposed approach can provide a highly reliable and computationally efficient solution and show the importance of incorporating NGS operational constraints in the frequency constrained scheduling problem., Comment: 11 pages, 5 figures

With more and more distributed energy resources (DERs) deployed in Integrated Energy Systems (IESs), frequency stability challenges the pursuit of reliability and efficiency. This paper proposes a fully-distributed frequency control method for load-side DERs, in which the optimality can be guaranteed in an IES where electricity and heat are coupled. Moreover, the global asymptotic stability of the closed-loop system is proved and the robustness with respect to inaccurate coefficients is shown. Case studies demonstrate the effectiveness of proposed method., Comment: 5 pages

Short term load forecasting has an essential medium for the reliable, economical and efficient operation of the power system. Most of the existing forecasting approaches utilize fixed statistical models with large historical data for training the models. However, due to the recent integration of large distributed generation, the nature of load demand has become dynamic. Thus because of the dynamic nature of the power load demand, the performance of these models may deteriorate over time. To accommodate the dynamic nature of the load demands, we propose a sliding window regression based dynamic model to predict the load demands of the multiarea power system. The proposed algorithm is tested on five zones of New York ISO. Results from our proposed algorithm are compared with four existing techniques to validate the performance superiority of the proposed algorithm.

This paper presents an improved secondary voltage control (SVC) methodology incorporating compressive sensing (CS) for a multi-area power system. SVC minimizes the voltage deviation of the load buses while CS deals with the problem of the limited bandwidth capacity of the communication channel by reducing the size of massive data output from phasor measurement unit (PMU) based monitoring system. The proposed strategy further incorporates the application of a Morphological Median Filter (MMF) to reduce noise from the output of the PMUs. To keep the control area secure and protected locally, Mathematical Singular Entropy (MSE) based fault identification approach is utilized for fast discovery of faults in the control area. Simulation results with 27-bus and 486-bus power systems show that CS can reduce the data size up to 1/10th while the MSE based fault identification technique can accurately distinguish between fault and steady state conditions., Comment: 10 pages, 16 figures

Load management is being recognized as an important option for active user participation in the energy market. Traditional load management methods usually require a centralized powerful control center and a two-way communication network between the system operators and energy end-users. The increasing user participation in smart grids may limit their applications. In this paper, a distributed solution for load management in emerging smart grids is proposed. The load management problem is formulated as a constrained optimization problem aiming at maximizing the overall utility of users while meeting the requirement for load reduction requested by the system operator, and is solved by using a distributed dynamic programming algorithm. The algorithm is implemented via a distributed framework and thus can deliver a highly desired distributed solution. It avoids the required use of a centralized coordinator or control center, and can achieve satisfactory outcomes for load management. Simulation results with various test systems demonstrate its effectiveness., Comment: 12 pages, 18 figures, five tables, accepted by IEEE System Journal, Preprint