Load increase response window identification and low-carbon regulation for grid-interactive salt lake chemical parks under process feasibility constraints

Abstract

The increasing penetration of renewable energy has intensified the pressure on power grids to accommodate renewable generation, while the production processes of energy intensive loads are subject to stringent process rigidity constraints, posing substantial challenges to source–load interactive scheduling. To address this issue, this paper investigates typical energy intensive loads in a salt lake chemical park and proposes a method for load increase response window identification and low-carbon regulation under process feasibility constraints. First, based on the material transfer relationships in potassium, lithium, and magnesium coproduction, a load increase potential assessment model is developed to characterize the formation and interprocess transfer of adjustable load potential by jointly considering process feasibility and distribution network access margins. Second, a feasibility discrimination model for load increase response windows is established, in which shift rhythm adaptation, material buffer consistency, and renewable power matching are incorporated into a unified evaluation framework. An improved method integrating the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and multi-criteria optimization and compromise solution (VIKOR) is then used to identify suitable response windows under surplus renewable power conditions. Finally, a low-carbon regulation model is formulated to coordinate renewable energy accommodation with coproduction process constraints, and an adaptive large neighborhood search (ALNS) algorithm embedded with process feasibility reconstruction is designed to solve the model. In three representative seasonal scenarios, each spanning 24 h and based on case inputs jointly constructed from archived desensitized operating sequences, engineering constraints, and standardized scenario parameters, the proposed method achieved renewable energy accommodation of 10.9–14.0 MWh, incremental net benefits of CNY 66,400–89,100, and net carbon reductions of approximately 3.0–3.2 tCO₂, while satisfying all process and distribution network constraints. Tests using 30 paired random seeds further showed that the improved ALNS converged faster and exhibited lower variability than Basic ALNS. An extended analysis over 7 days further revealed the tradeoff among renewable energy accommodation, inventory accumulation, and economic returns. These results indicate that, under the operating conditions and parameter ranges considered for the park, the proposed method can coordinate renewable energy accommodation, production feasibility, economic performance, and carbon mitigation.

1 Introduction

With the large-scale integration of volatile renewable energy sources such as wind and photovoltaic power, the operational objective of distribution networks has gradually expanded from secure power supply alone to the coordinated pursuit of secure operation and local renewable energy accommodation (IEA, 2024; Liu et al., 2018a). The randomness and temporal variability of renewable generation intensify net load fluctuations, increasing the demand for short-term flexibility resources. Existing studies have shown that the stable operation of power systems with high renewable energy penetration depends on the coordinated support of flexibility resources such as demand response, energy storage, and grid interconnection (Khalili et al., 2025; Mohseni and Brent, 2022; Zhang et al., 2024a). Among these resources, demand response can mitigate source-load mismatch by adjusting electricity consumption periods and load intensity, and can improve low-carbon operational performance (Ding et al., 2023; Yang et al., 2025). In renewable-rich regions, relying only on source-side regulation or energy storage configuration is often insufficient to fully absorb local surplus renewable power during certain periods. Therefore, transforming energy-intensive industrial loads into low-carbon response resources callable by distribution networks has become an important approach for improving local renewable energy accommodation (Dao, 2026; Ranaboldo et al., 2024).

Existing demand response studies have mainly focused on peak shaving, load shifting, and load reduction, whereas load increase response is also of great importance under high renewable energy penetration. Load increase response refers to actively increasing executable load during periods of surplus renewable power, thereby reducing wind and photovoltaic curtailment and improving green electricity utilization. Existing studies have shown that industrial loads can participate in peak shaving and valley filling as well as coordinated renewable energy accommodation, but their response capability is constrained by production continuity, equipment status, and safety boundaries (Golmohamadi, 2022; Yasmin et al., 2024). For continuous production processes, load regulation capability is not equivalent to residual equipment capacity and cannot be simply determined by power upper and lower limits. A scheduling instruction can be truly executed in the production process only when material balance, inventory buffering, equipment operation, and product quality constraints are satisfied (Leinauer et al., 2022).

Industrial demand response has been investigated from the perspectives of production scheduling, electricity price response, and industrial flexibility modeling. Related studies have embedded energy-intensive processes such as metal casting, steelmaking, and electrofused magnesium production into power system scheduling models, demonstrating that process-level production constraints significantly affect demand response capability (Gómez et al., 2026; Li et al., 2025; Ramin et al., 2018). Coordinated electricity-carbon demand response studies have also incorporated dynamic carbon emission factors and industrial load regulation into optimization models, providing a methodological basis for low-carbon dispatch of energy-intensive industries (Cao et al., 2023). However, most existing models focus on a single production process or an equivalent load unit, and the characterization of load increase boundaries jointly formed by material reflux, intermediate inventory, and upstream and downstream receiving capability in multi-product coproduction processes remains insufficient.

Salt lake chemical parks exhibit significant process coupling characteristics. The coproduction of potassium, lithium, and magnesium usually depends on the coordinated operation of brine input, mother liquor reflux, and intermediate inventory. Studies on salt lake brine resource utilization have shown that lithium extraction and magnesium-lithium separation often rely on multi-stage coupled processes rather than isolated unit processes (Zhang et al., 2023; Zhu et al., 2023). Studies on adsorption and membrane-based lithium extraction have also shown that component concentration, separation conditions, and industrial operating states jointly affect process stability (Xu et al., 2021; Zhang et al., 2024b). Therefore, a change in the treatment intensity of one branch not only changes the load of the current process, but also affects downstream material composition, inventory states, and product output rhythms. The load increase capability of salt lake chemical loads is not the margin of a single device, but the process receiving capability jointly determined by material transfer, inventory buffering, and quality boundaries.

Response window identification provides an effective method for connecting renewable energy accommodation demand with industrial process executability. Existing studies usually select response periods based on electricity prices, load forecasts, equipment states, or surplus renewable power, and use multi-criteria evaluation methods for ranking (Meng et al., 2023; Zhang et al., 2025b). Studies on production sequence constraints have shown that the production sequence of industrial loads directly affects the execution effect of demand response instructions (Wang X. et al., 2024). Studies on industrial load flexibility enhancement have also indicated that regulation potential assessment should be considered together with production constraints and source-load interaction mechanisms (Zhang J. et al., 2025). TOPSIS, VIKOR, and Criteria Importance Through Intercriteria Correlation (CRITIC) methods have been widely used for candidate scheme evaluation and weight determination (Hwang and Yoon, 1981; Opricovic and Tzeng, 2004; Diakoulaki et al., 1995). However, for salt lake chemical parks, a period with high surplus renewable power does not necessarily constitute an executable load increase response window. Shift rhythm, material buffering, response delay, and distribution network access boundaries all affect whether a load increase instruction can actually be received by the production process. Therefore, the core of response window identification should shift from determining whether surplus renewable power exists to determining whether surplus renewable power can be safely absorbed by the production process.

Low-carbon regulation studies have incorporated demand response, carbon emission constraints, and source-load interaction into integrated energy systems or distribution network optimization, demonstrating the role of flexible loads in improving renewable energy utilization and reducing carbon emissions (Tan et al., 2023). Low-carbon optimal dispatch studies for distribution networks have further shown that industrial flexible loads can improve renewable energy accommodation while satisfying network operation constraints (Wang W. et al., 2024). However, for salt lake chemical parks, low-carbon regulation cannot only pursue renewable curtailment reduction or carbon reduction maximization; it must also guarantee material balance, inventory safety, product quality, and distribution network operating boundaries. Therefore, the load increase regulation model should first use process-feasible response windows to define the regulation space, and then coordinate renewable energy accommodation, carbon emissions, and distribution network operation constraints within this space.

2 Materials and methods

2.1 Flexible load modeling for a salt lake chemical park under process feasibility constraints

2.1.1 Load composition and process material transfer relationships in the salt lake chemical park

The potassium, lithium, and magnesium coproduction process in a salt lake chemical park relies on cascade brine utilization and mother liquor recycling. It includes brine transport, main product branches, and public utility units for mother liquor reflux, compressed air, and circulating cooling. These branches are coupled through mother liquor circulation and intermediate inventory buffering. Accordingly, branch throughput changes affect component concentrations, product output rhythms, and utility loads, thereby shaping park-level load increase capability. The corresponding production process flow of potassium, lithium, and magnesium coproduction loads in the salt lake chemical park is illustrated in Figure 1.

FIGURE 1

In potassium, lithium, and magnesium coproduction, the process load of each production branch is jointly determined by the material processing state and equipment operating conditions, while the total park load also includes electricity consumption by the utility systems. The corresponding load relationships are expressed by Equations 1 and 2. In the coproduction chain, mother liquor from the potassium branch enters the lithium salt production process, and the tail liquor from lithium extraction is further transferred to the magnesium salt branch, causing branch inventories to vary continuously with material transfer. The inventory recursion in Equation 3 is established on the basis of material conservation, while Equation 4 describes the evolution of composition states and product outputs. Because load increase response mainly arises from adjustments to process treatment intensity, Equations 1, 2 are locally linearized around the current operating point to obtain the park load increase power decomposition in Equation 5, with the load sensitivity coefficients calculated according to Equation 6.where each load sensitivity coefficient is identified from historical operating data and local perturbation tests near the current operating point, with the resulting power–throughput mapping constrained by the rated process power. The expanded equipment load expressions for each production branch and the utility system are provided in Supplementary Equations S1, 2 of Supplementary Section S1, and the composition state and product output relationships are provided in Supplementary Equations S3, 4 of Supplementary Section S2.1, 2.1.

2.1.2 Effect of production shift rhythm and response delay on load increase capability

Although potassium, lithium, and magnesium coproduction is primarily continuous, shift handover inspections and concentrated operations can still reduce the execution stability of load increase commands during local periods. Such effects generally peak near the operation time and gradually decay as the temporal distance increases. Therefore, the periodic Gaussian kernel in Equation 7 is used to characterize production rhythm disturbances. On this basis, because intermediate inventory can absorb short term material fluctuations, inventory sufficiency is further used to correct the disturbance amplitude. A load increase command can be converted into an actual process load only after material transfer and equipment state adjustment, and its effect is jointly influenced by process inertia and material residence time. The branch load increment is described by Equation 8. Feed changes caused by operations also continue to affect branch states through subsequent processing stages. Equation 9 is therefore used to recursively update the process disturbance residual:where and are determined from the maximum normalized decrease in actual load increase power during the corresponding operating periods relative to the steady operating baseline; and are converted from the full width at half maximum of the operation influence curve; is identified by nonlinear least squares using the logistic relationship between inventory level and disturbance amplitude; is identified using a first order autoregressive model based on the historical load increase response sequence; and are determined from the material residence time distribution or step response data, and the delay weights are normalized according to Supplementary Equation S5 of Supplementary Section S2.3; is the disturbance decay time constant, which is determined by exponential regression of the decay sequence after the operation ends.

2.1.3 Assessment of load increase potential under process buffer margin constraints

The load increase capability of a continuous chemical branch is not equivalent to its residual equipment capacity and is also jointly constrained by inventory states and product quality boundaries. Equation 10 constructs the comprehensive branch buffer margin from the normalized distances between each state variable and its allowable boundary, and uses the minimum value to represent the dominant bottleneck limiting load increase capability. Further considering current treatment headroom, available inventory accommodation space, and upstream material supply, Equation 11 gives the maximum material increment that can be transferred by branch r during period t, ensuring that the load increase process remains constrained by the actual material accommodation capability:

Combining process-side potential, utility margin, grid access capacity, rhythm disturbance, and response delay yields the total plant load increase potential (Equation 12):

The equipment level mapping and process accommodation boundaries of the branch load increase potentials are given in Supplementary Equation S6 of Supplementary Section S2.4.

2.1.4 Flexible load interface considering process feasibility and distribution network access boundaries

The preceding model provides the process side load increase potential, but the executable load increase amount of the park remains limited by distribution network access capability. In this study, distributed renewable generation within the park is included inside the accounting boundary at the point of common coupling (PCC). Both the baseline self-consumption of renewable energy and the additional renewable energy accommodated by load increase reduce the active power exchange at the PCC, whereas the reactive power change caused by the load increase is still determined by the load power factor. Equation 13 first derives the baseline PCC exchange power from the park production load and baseline renewable self-consumption, and then calculates the net exchange power and equivalent transformer apparent power after load increase. Because the load increase process causes a concurrent change in reactive power when the load power factor is assumed approximately constant, and because reactive power variation and voltage constraints are important factors in the secure integration of renewable energy (Abaza et al., 2021), Equation 14 uses the voltage sensitivities to active and reactive power to estimate the voltage deviation at each node, thereby jointly describing process feasibility and distribution network security boundaries:

The above sensitivity model is used to rapidly assess the grid state after load increase, but errors from the linear approximation may accumulate as the load increase magnitude grows. To verify the accuracy of the resulting access boundary, Equation 15 uses the alternating current (AC) power flow equations to recalculate the active power, reactive power, and voltage states at each node. Equation 16 jointly maps the net PCC active power exchange from Equation 13 and the load reactive power to the access node, from which the actual transformer apparent power is obtained. Equation 17 then compares the AC power flow results with the approximate results from Equations 13, 14, and evaluates the validity of the linear boundary using the maximum nodal voltage deviation and transformer loading deviation:

The grid-side accessible load increase limit is jointly determined by PCC capacity, transformer capacity, and voltage margin (Equation 18):

2.2 Load increase response window identification integrating process response margin and renewable power matching

2.2.1 Feature construction for process-power coupled load increase response windows

Whether a candidate period can form an executable load increase response window first depends on whether the dispatch command can be stably converted into an actual process load. Equation 19 therefore defines production rhythm adaptability, using the reciprocal of the production rhythm disturbance to characterize response stability during operating periods and the geometric mean of the disturbance residuals and effective delays of the three branches to reflect weak links in the coproduction process. Equation 20 further defines material buffer consistency, using branch buffer margins and material residence times to characterize the accommodation capability for additional throughput, while correcting the feasibility loss caused by material mismatch using inventory differences between adjacent branches. A response window must also be consistent with surplus renewable energy in both power magnitude and temporal variation. Therefore, Equation 21 uses the common lower bound of surplus renewable power, process load increase potential, and grid side access capability as the effective matching power, while accounting for adjacent period fluctuations and the minimum effective load increase threshold. These indicators are expressed as:

2.2.2 Feasibility discrimination model considering coproduction material flow constraints and process safety margin

After the process load increase potential and grid access margin are obtained for each period, response intervals with continuous execution conditions must be further identified. Equation 22 restricts the window duration to the allowable range and requires every period within the window to retain positive joint load increase space. The surplus renewable power corrected by the production rhythm and buffer state must also remain positive, thereby forming the candidate window set. For an activated window, Equation 23 generates the target load increase trajectory according to the temporal distribution of corrected surplus renewable power within the window, allowing load increase power to preferentially follow renewable power variations while keeping the total response energy of the window unchanged:

After the candidate windows are determined, the target load increase trajectory must be allocated among the production branches while ensuring that the regulation result does not exceed the joint accommodation capability of the process and grid sides. Equation 24 uses to denote the actual process load increase power within the window, constrains it to follow the target trajectory, and limits both the total park load increase power and the branch material adjustments. The material flow changes induced by load increase further alter branch inventory and composition states. Accordingly, Equation 25 updates the effective inventory according to material conservation and verifies the regulated composition evolution using the process state mapping:

The expanded recursions for inventory and composition states after load increase execution are provided in Supplementary Equations S7, 8 of Supplementary Section S3.1, 3.2.

As the window activation amount increases, branch inventories gradually approach their operating boundaries, process disturbances accumulate, and the remaining load increase space is compressed. To prevent a high margin in a local period or a single branch from masking a potential bottleneck, Equation 26 uses the most adverse period and the weakest branch within the window as the criterion and takes the minimum after normalizing the inventory boundary margin, disturbance tolerance, and remaining load increase ratio. The resulting characterizes the overall feasibility of the window at a given activation level. On this basis, Equation 27 constrains the minimum feasibility score and AC validation errors and requires Equations 24–26 to hold throughout the window, thereby determining the maximum activation amount that the candidate window can safely accommodate:

2.2.3 Improved TOPSIS-VIKOR method for extracting optimal load increase response windows

After the candidate windows pass the feasibility check, they must be comprehensively compared in terms of load increase capability, renewable energy accommodation performance, and operational stability. Equation 28 constructs the window evaluation vector. The activated power per unit duration, renewable energy accommodation ratio, and carbon reduction benefit reflect response effectiveness; buffer consistency and production rhythm adaptability characterize process executability; and the disturbance residual and power fluctuation are treated as cost indicators. Because the indicators differ in dimension and preference direction, Equation 29 normalizes benefit and cost indicators separately. Equation 30 further integrates the TOPSIS relative closeness and VIKOR compromise ranking results, thereby evaluating the overall performance of each window while retaining constraints on weak indicators and determining the comprehensive priority of the candidate windows. Finally, Equation 31 selects a set of nonoverlapping response windows with the optimal comprehensive score from the candidate windows satisfying the activation and feasibility thresholds:

2.3 Low-carbon load increase regulation model considering renewable accommodation and coproduction process coordination

2.3.1 Decision variables and window activation constraints

After the preferred response windows are determined, low-carbon regulation is further transformed into a problem of window activation and process quantity allocation. Equation 32 incorporates the window activation amount and the key adjustment quantities of each branch into a unified decision space to coordinate the accommodation of the target load increase power among different processes. Based on this decision scheme, Equation 33 generates the park load increase trajectory according to the distribution of surplus renewable power within each window after correction by production rhythm and buffer state, and simultaneously calculates the actual renewable energy accommodation and curtailment reduction:

2.3.2 Objective function for low-carbon regulation

Although sustained production increases within response windows can improve renewable energy accommodation, their economic viability depends on whether the revenue from additional products can cover electricity, operating, and inventory costs. Accordingly, Equation 34 constructs a technoeconomic objective function that accounts for the value of incremental potassium, lithium, and magnesium products, deducts the costs of renewable electricity and grid electricity purchases, and includes production adjustment and inventory holding costs. The terminal inventory term constrains the cumulative effect of overproduction over multiple days. During scheduling, the terminal inventory of the current day becomes the initial state of the following day, thereby preventing short term renewable energy accommodation from being achieved through persistent inventory accumulation. On this basis, the change in carbon emissions is converted into carbon trading revenue and incorporated into the objective function together with penalties for production plan deviation, process disturbance, and load fluctuation. This study adopts a park level gate-to-gate incremental carbon accounting boundary to quantify changes in purchased electricity emissions, renewable energy life cycle emissions, incremental product production emissions, and emissions from carbon-containing material processing under the regulation scenario relative to baseline production. The main results use hourly marginal grid emission factors, with a carbon price of 80 CNY/tCO₂ as the baseline scenario. The carbon reduction before and after load increase is calculated by Equation 35, which simultaneously considers purchased electricity emissions, emissions from incremental process production, and emission changes caused by carbon-containing material processing:

2.3.3 Process feasibility, distribution network, and carbon accounting constraints

To ensure that the low-carbon regulation scheme is practically executable within each preferred window, the window activation amount is first limited by the maximum accommodable level, as shown in Equation 36. The total park load increase power must not exceed the common upper bound of the process potential and distribution network access margin, as specified by Equation 37. Equation 38 directly uses the complete AC power flow results to verify PCC exchange power, transformer apparent power, nodal voltages, and line thermal stability limits, while also constraining the errors between the local linear screening results and the AC power flow results. Equation 39 limits load increase ramping between adjacent periods. The material increments of each process are constrained by the transmissible boundaries in Equation 40, while the product inventories generated by increased production are recursively updated according to Equation 41, with delivery capacity and terminal inventory ranges imposed:

Detailed forms of the inventory recursion, product output and quality boundaries, and robust safety margin constraints are provided in Supplementary Equations S9-17 of Supplementary Section S4.1-4.3.

2.4 Solution method based on adaptive large neighborhood search with process feasibility reconstruction

To address the coupling among window combinations, activation amounts, and process adjustment quantities, this study proposes an adaptive large neighborhood search algorithm embedded with process feasibility reconstruction. ALNS reconstructs candidate solutions within large neighborhoods using destroy and repair operators and adaptively updates operator selection weights according to historical search performance (Ropke and Pisinger, 2006). Candidate schemes are encoded uniformly according to Equation 42, in which only window selection, window activation amount, and adjustment quantities of key accommodation processes are treated as independent search variables. The remaining branch flows, thermal states, and product increments are recursively determined by the process feasibility reconstruction operator. The set operations in Equations 43, 44 act on the set of activated windows contained in the current solution rather than on the complete solution vector. During the destroy stage, window scores, feasibility gaps, and interval overlaps are jointly evaluated. During the repair stage, candidate schemes are generated according to the marginal insertion gain. Process states are then recursively updated along the time axis, followed by AC power flow validation. Equation 45 permits only schemes satisfying the hard constraints to enter the simulated annealing acceptance process, while Equation 46 updates the operator weights and annealing temperature. The specific recursions for process feasibility reconstruction and power consistency repair are provided in Supplementary Section S4.4, 4.5.

The solution procedure of the adaptive large neighborhood search algorithm embedded with process feasibility reconstruction is presented below:

3 Results

3.1 Case scenario and parameter settings

To validate the proposed method, a representative scheduling case with a 24 h horizon and 15 min resolution was developed for a potassium, lithium, and magnesium coproduction salt lake chemical park in Qinghai, China. Three seasonal renewable energy scenarios, four production operating states, and a continuous 7 d extension analysis were considered. The case inputs were jointly constructed from archived desensitized operating sequences, equipment rated parameters, process safety boundaries, and network operating constraints. Time series parameters were unified at a 15 min resolution, the mechanism mappings were constrained by material conservation and equipment capacity, and the economic and carbon parameters were configured under a consistent scenario setting. The identified parameters were fixed before multi-condition assessment. The AVEVA platform performed dynamic state recursion in a separate software environment to assess the cross-platform execution consistency of the final regulation commands. The case framework is shown in Figure 2, the representative source–load scenarios are shown in Figure 3, the parameter sources, preprocessing procedures, calibration or identification methods, and validation pathways are provided in Supplementary Section S5, 6.11 and Supplementary Table 11, and the AVEVA platform implementation relationship is described separately in Supplementary Section S6.7.

FIGURE 2

FIGURE 3

To avoid selecting representative curves directly on the basis of experience, the archived desensitized candidate-day source–load curves were standardized and hierarchically clustered. The candidate day closest to the center of its cluster was then selected as the representative day, thereby preserving intraday temporal characteristics and differences in source–load variability among scenarios (Liu Y. et al., 2018).

The left column of Figure 3 presents the S1–S3 candidate curves and representative-day sequences, which respectively characterize concentrated photovoltaic output in summer, wind power fluctuations in winter, and mixed wind and photovoltaic characteristics during transitional seasons. The middle column presents four production operating states: LT1, high-load stable operation; LT2, rated continuous operation; LT3, low-load constrained operation; and LT4, frequent state transitions. The representative load sequence adopted for each scenario is indicated by the black dashed line. The right column presents the time-of-use electricity price, marginal grid emission factor, and renewable electricity emission factor as exogenous inputs for response window identification and economic low-carbon regulation. The continuous 7 d source–load sequences for the three scenarios, together with the renewable power surplus and regulated accommodation results under different production states, are provided in Supplementary Section S6.1 and Supplementary Figures S1, 2.

3.2 Load increase response window identification results

To compare the dispatch capability and executability of candidate response windows across scenarios, the window ranking, dispatch energy, activation rate, renewable power overlap, and post-regulation process and network margins are evaluated, as shown in Table 1.

A total of seven feasible response windows are identified in Table 1. Scenario S1 forms a continuous primary window from 09:00 to 16:15 and achieves the highest dispatch energy. Owing to renewable power fluctuations and production rhythm effects, S2 and S3 exhibit dispersed responses over multiple periods. All windows retain sufficient post-regulation network margin, whereas the minimum normalized process margin is 0.036, indicating that load increase capability is mainly constrained by the production process.

To examine the robustness of window ranking to the weighting method, the analytic hierarchy process (AHP; Saaty, 1986), game theory combination weighting (Tang et al., 2024), and the method based on the removal effects of criteria (MEREC; Keshavarz−Ghorabaee et al., 2021) are selected as comparison methods while the candidate windows, indicator normalization method, and TOPSIS–VIKOR parameters are kept unchanged. Only the method used to determine the indicator weights is varied.

Figure 4 further illustrates the joint screening of response windows by renewable energy conditions and process executability. The left column shows that the final load increase command is always jointly constrained by the renewable power surplus, process capability, and network boundaries. The middle column shows that a period is identified as an effective window only when the comprehensive criterion jointly formed by renewable energy availability and process executability exceeds the threshold. Scenario S1 forms a continuous primary window around noon, whereas S2 and S3 exhibit multiple discrete windows because of renewable power fluctuations and changes in process states. The right column compares different weighting methods. The proposed method and game theory combination weighting produce exactly the same window rankings in S2 and S3, with both the mean Kendall τ and the preferred window agreement rate equal to 1.00. AHP changes the preferred window in both scenarios, whereas MEREC changes the preferred window in S2 and the local ranking in S3. The inset shows that the score gaps between the first and second ranked windows obtained by the proposed method are 0.13 and 0.39 in S2 and S3, respectively, close to the corresponding values of 0.15 and 0.39 obtained by the game theory method. These results show that, with fixed fusion weights, the proposed method still yields ranking results and decision discrimination similar to those of game theory combination weighting, while avoiding the additional procedure required to solve combination coefficients.

FIGURE 4

The park load, branch material flows, and product output trajectories before and after regulation within representative response windows are provided in Supplementary Section S6.2 and Supplementary Figure S3.

3.3 Low-carbon regulation results of the proposed method

Based on the window identification and ranking results for each scenario, the improved ALNS is used to optimize window activation energy and process adjustment variables. The resulting technical, economic, and carbon indicators are shown in Table 2.

Table 2 shows that S1 achieves the highest renewable energy accommodation and net benefit, but its maximum branch utilization reaches 95.0%, indicating that its load increase capability is close to the local equipment capacity boundary. Scenario S2 is constrained by process states and temporal matching, resulting in relatively lower renewable energy accommodation and net benefit, with a minimum normalized process margin of 0.036. Although S3 accommodates less renewable energy than S1, it achieves the greatest net carbon reduction, indicating better alignment between its load increase periods and periods with high marginal emission factors. All process and network constraints are satisfied in the three scenarios. Renewable energy accommodation ranges from 10.88 to 13.98 MWh, net benefit ranges from 6.64 × 10⁴ to 8.91 × 10⁴ CNY, and net carbon reduction ranges from 3.01 to 3.23 tCO₂.

Figure 5 compares the temporal evolution of renewable energy disposition, incremental economic balance, and carbon balance in scenarios S1–S3. Load growth is concentrated in periods with surplus renewable power and process feasibility, resulting in renewable energy accommodation of 13.98, 10.88, and 12.55 MWh in the three scenarios, respectively. The response in S1 is relatively concentrated, whereas S2 and S3 exhibit dispersed responses across multiple windows. Although the regulation process introduces incremental electricity, operating, and inventory costs, product revenue and carbon reduction revenue keep the cumulative net benefit positive. Avoided emissions are substantially greater than incremental emissions in all scenarios, yielding final net carbon reductions of 3.17, 3.01, and 3.23 tCO₂, respectively. These results indicate that the proposed method can jointly achieve renewable energy accommodation, economic benefits, and carbon reduction while maintaining process executability.

FIGURE 5

Figure 6 shows that, after regulation, the material flows of all branches vary coordinately with the response windows, and all rigid constraint margins remain positive. The peak incremental production rates in S1, S2, and S3 are approximately 4.8, 1.7, and 2.1 t/h, respectively, and are generally matched with the delivery process. This indicates that the proposed method can realize executable load growth regulation without violating inventory, quality, or equipment capacity boundaries.

FIGURE 6

Figure 7 shows that the minimum voltage curves obtained from the local linear model and AC power flow calculations nearly coincide. The voltage root mean square errors in S1–S3 are only 2.9, 0.8, and 3.5 μp.u., respectively. Line and transformer loading rates remain below the 100% limit in all scenarios, and the minimum voltage remains within the allowable range, indicating that the regulation schemes satisfy the AC executability requirements of the distribution network.

FIGURE 7

Beyond the representative scenarios, four operating conditions, namely, high-load stable operation, rated continuous operation, low-load constrained operation, and frequent state transitions, were further established and tested at load increase levels of 25%, 50%, 75%, and 100%, yielding 16 combinations. Detailed results are provided in Supplementary Figure S12 and Supplementary Table 12. Across these combinations, the load tracking root mean square error (RMSE) ranged from 0.016 to 0.063 MW, the mean normalized root mean square error (NRMSE) of material flows ranged from 1.58% to 5.62%, the mean inventory NRMSE ranged from 0.074% to 0.150%, and the maximum absolute composition error did not exceed 0.00534. Relative to complete alternating current (AC) power flow, the voltage RMSE of the linear network model ranged from 0.026 to 3.465 μp.u., and the maximum absolute error ranged from 0.059 to 31.969 μp.u. AC power flow converged for all 1,536 periods, the minimum nodal voltage was 0.981 p.u., and no case was falsely classified as feasible by the linear model. These results indicate that the linear model can be used for rapid screening of candidate schemes, whereas final network feasibility remains subject to confirmation by complete AC power flow.

The joint distributions of renewable energy accommodation, incremental net benefit, and minimum AC voltage, together with the process feasibility boundary, are provided in Supplementary Section S6.3 and Supplementary Figure S4. The economic sensitivity results under variations in carbon price, electricity price, and product price are provided in Supplementary Section S6.4 and Supplementary Figure 5.

3.4 Comparative analysis of different regulation methods

Four benchmark implementations were constructed. PS-MILP was developed with reference to the production–electricity coupled mixed integer framework reported in the literature (Kelley et al., 2018) and was configured using the process variables and boundaries of the park. RO-MPS was developed with reference to the multiprocess robust scheduling framework reported in the literature (Lv et al., 2025) and used the uncertainty set of the present case. Green-peak preferentially increased load during periods of peak renewable power surplus, whereas Without-shift-buffer removed the shift rhythm and process buffer constraints. All comparisons followed a unified protocol of “native solution–common evaluation–conditional repair–metric recalculation.” Under identical source–load, process, network, and ramping boundaries, the common evaluator performed 96-period forward recursion and complete AC power flow validation on each native command and recorded only the constraint status. Common repair was activated only for schemes with rigid constraint violations, after which all objective and constraint-related metrics were recalculated from the same resulting schedule. Process feasibility prescreening belongs exclusively to the native structure of the proposed method, and the common repair procedure does not use response window rankings or ALNS search information. Table 3 reports native, post-evaluation or post-repair values and signed changes; Supplementary Table 10 gives full results.

Changes in Table 3 are calculated as the post-common-step value minus the native value. The proposed method retained its original command after common evaluation, achieving 13.98 MWh of renewable energy accommodation, a net benefit of 8.91 × 10⁴ CNY, and a net carbon reduction of 3.17 tCO₂. After common repair, the renewable energy accommodation values of PS-MILP and RO-MPS were 15.75 and 15.63 MWh, respectively, with absolute command adjustments of 2.94 and 2.22 MWh. The corresponding adjustments for Green-peak and Without-shift-buffer were 1.78 and 6.87 MWh, respectively. Positive changes in net benefit reflect reductions in electricity purchase, inventory, or disposal costs after excessive load increase commands were curtailed. All post-repair metrics were recalculated under the same constraint system and are explicitly labeled using the “method → common repair” workflow. The complete constraint states before and after repair are provided in Supplementary Table 10.

Figure 8 compares native commands, post-common-step outcomes, and native-scheme constraint status. The proposed method retains its commands after common evaluation; the other methods are labeled “method → common repair.” Objective and constraint changes are listed in Supplementary Table 10.

FIGURE 8

The numerical differences between each ablation configuration and the continuous relaxation reference are provided in Supplementary Section S6.5 and Supplementary Figure 6. Under joint perturbations, the ex ante direct feasibility rate of the frozen nominal commands ranged from 19.5% to 44.2%. With a maximum of 12 iterations and a tolerance of 1 × 10⁻⁸, feasibility was restored for all 3,000 samples, with a median absolute adjustment of 0.090–0.135 MWh. The violation categories, adjustment components, and changes in the windows and objective values are provided in Supplementary Section S6.6 and Supplementary Figure 7.

3.5 Algorithm performance comparison

To evaluate the search performance of the improved ALNS, it was compared with Basic ALNS, a Gurobi linearized model, and a sequential least squares programming (SLSQP) continuous relaxation model. In this study, the SLSQP solution serves as a common numerical reference for the continuous relaxation, and the proximity of each method to this reference is expressed by the relative difference. In S1–S3, Basic ALNS and the improved ALNS used 30 fully paired random seeds per scenario, the same budget of 700 evaluations, and the same final rigid constraint evaluator, with 10 runs for each of the three initial solution types. Each algorithm retained its own search and repair structures. Complete statistics, stratified results, and convergence trajectories recorded at fixed evaluation intervals are provided in Supplementary Table 9 and Supplementary Figure 11.

Table 4 shows that, under the same candidate response window set and final rigid constraint evaluation criteria, the improved ALNS achieved a mean feasible renewable energy accommodation of 13.982 MWh, approximately 0.034 MWh higher than that of Basic ALNS. The standard deviation decreased from 0.024 MWh to less than 0.001 MWh, and the median number of iterations required to reach 99% of the terminal value decreased from 605 to 320. Under a unified computing environment and an evaluation procedure comprising complete mechanism recursion and AC power flow validation over 96 periods, the total runtime decreased from 5.72 to 4.10 min. The mean relative difference between the improved ALNS and the SLSQP continuous relaxation reference was below 0.001%, indicating their numerical proximity for the same case. The SLSQP termination status, iteration count, tolerance, and maximum variable bound residual are provided in Supplementary Table 5, and the paired statistics for S1–S3 are provided in Supplementary Table 9.

Figure 9 further shows that the improved ALNS achieved faster objective value improvement and more concentrated terminal value distributions in all three scenarios. Under the same budget of 700 evaluations, the median number of iterations required to reach 99% of the terminal value was lower than that of Basic ALNS in each scenario. The runtimes shown in the lower panels are the total runtimes of the unified complete evaluation procedure and are used to compare, on a consistent basis, the computational burdens of Basic ALNS, the improved ALNS, the Gurobi linearized implementation, and the SLSQP continuous relaxation reference. Supplementary Figure 11 reports the convergence trajectories and terminal value distributions for the three initial solution types: ranking-greedy, MILP-guided, and random-repaired.

FIGURE 9

3.6 Cross-platform intermodel consistency assessment using a digital twin platform

To examine the dynamic execution consistency of the regulation commands in a separate software environment, the 96-period commands for S1–S3 were input into a digital twin platform developed in AVEVA. Within the same project technical framework, the optimization model and the platform separately implemented the optimization calculation chain and the dynamic state recursion chain. They shared source–load inputs, engineering boundaries, and initial states, and the final commands were transmitted unidirectionally from the optimization side to the platform side. The platform applied dynamic limit projection according to its safety logic, and all errors, margins, and constraint states were calculated from the final executed trajectories. Figure 10 and Supplementary Figures 8, 9 present the cross-platform intermodel consistency assessment under the shared engineering boundaries.

FIGURE 10

Figure 10 uses the platform export results for 96 periods of 15 min in each scenario. The command tracking RMSE values for S1–S3 were 0.039, 0.047, and 0.063 MW, respectively. Dynamic limit projection was triggered in 0, 9, and five periods, respectively, and the reported errors, margins, and zero residual violations all correspond to the final executed trajectories. The implementation relationship and the comparisons of inventory, material flow, composition, incremental product output, and network margin are provided in Supplementary Section S6.7 and Supplementary Figures 8, 9. The results demonstrate good dynamic execution consistency between the two implementations under shared engineering boundaries.

4 Discussion

4.1 Formation mechanism of executable load increase capability under process constraints

The case results show that the load increase capability of the salt lake chemical park is not the static difference between equipment rated capacity and current load, but a time varying executable region jointly formed by surplus renewable power, process accommodation capability, and distribution network access boundaries. In S1, the midday photovoltaic surplus continuously aligns well with the process margin, thereby forming the primary response window from 09:00 to 16:15. In S2 and S3, wind power fluctuations, shift disturbances, and changes in inventory states produce clearly segmented response windows.

The normalized process margins are closer to zero in all scenarios, while the distribution network retains relatively sufficient access space, indicating that the load increase upper limit in this case is mainly determined by inventory, quality, material transfer, and equipment treatment capacity. Identifying response periods solely from renewable power peaks or residual equipment capacity tends to overestimate the actual flexibility of continuous production loads. Potential load increase space can be converted into executable regulation capability only when renewable energy demand and process accommodation capability overlap in time.

4.2 Integrated regulation benefits under process and network safety constraints

The 24 h scheduling results show that S1 achieves the highest renewable energy accommodation and net benefit, at 13.98 MWh and 8.91 × 10⁴ CNY, respectively. Although the renewable energy accommodation in S3 is slightly lower than that in S1, its net carbon reduction reaches 3.23 tCO₂, the highest among the three scenarios. This indicates that renewable energy accommodation and carbon reduction do not have a simple linear relationship, because their relationship is also jointly affected by time varying marginal emission factors, renewable energy life cycle emissions, and incremental process emissions.

The method comparison indicates that the native schemes of PS-MILP, RO-MPS, Green-peak, and Without-shift-buffer became feasible schedules after the unified common repair, whereas the proposed method retained its original commands during common evaluation. In the cross-platform assessment, the RMSE of the final executed trajectories in S1–S3 ranged from 0.039 to 0.063 MW, with no residual process or network violations, indicating good consistency between the optimization calculation chain and the platform dynamic execution chain under the current scenarios and shared engineering boundaries.

4.3 Role of process feasibility reconstruction in discrete scheduling

Activating and adjusting response windows changes branch flows, inventory, and quality states in subsequent periods. The problem therefore exhibits clear coupling between discrete decisions and continuous state recursion. After each window destroy and repair operation, the improved ALNS reallocates branch treatment quantities along the time axis and recursively updates inventory and process states, thereby avoiding the state inconsistencies that arise when constraints are repaired only once at the end of the search.

In representative scenario S1, the improved ALNS achieved a mean feasible renewable energy accommodation of 13.98 MWh. The standard deviation decreased from 0.024 MWh for Basic ALNS to less than 0.001 MWh, and the median number of iterations required to reach 99% of the terminal value decreased from 605 to 320. The 30 paired random seed tests in each of the three scenarios used the same budget of 700 evaluations and the same final feasibility evaluator. The Holm-adjusted p values indicated statistically significant paired improvements, with positive paired differences maintained across all three initial solution types. The Gurobi linearized model used conservative process boundaries, whereas the SLSQP result served as a numerical reference for the continuous relaxation and was used to report relative differences. These results verify the search stability and feasible solution quality of the improved ALNS under the current case, initialization design, and evaluation budget.

4.4 Economic and operational sustainability of sustained overproduction for renewable energy accommodation

Figure 11 shows a pronounced nonmonotonic relationship between renewable energy accommodation and incremental net benefit over a continuous 7 d operating horizon. During the initial stage, additional electricity consumption can be converted into deliverable products, and renewable energy accommodation and net benefit increase simultaneously. Once accommodation exceeds product delivery capacity, additional output is gradually converted into terminal inventory, inventory holding and disposal costs increase, and net benefit begins to decline.

FIGURE 11

For S1, the economic optimum corresponds to approximately 56.4 MWh of renewable energy accommodation and a net benefit of 34.5 × 10⁴ CNY. When accommodation increases to the compromise knee point of approximately 84.6 MWh, terminal unsold inventory has increased to 21.9 t. If the maximum accommodation of 110.3 MWh is pursued, terminal inventory increases to 62.6 t and net benefit decreases to −32.2 × 10⁴ CNY. S2 and S3 similarly exhibit diminishing returns and rapid inventory accumulation beyond the economic optimum, although their maximum accommodation points remain close to break-even.

Multiday inventory therefore constitutes an intertemporal state variable linking adjacent scheduling days. Overproduction in the current period not only incurs holding costs but also compresses the inventory accommodation space in subsequent periods, thereby reducing the adjustable capability available during future renewable power surplus periods. Repeated implementation of the single-day maximum accommodation strategy is therefore unsustainable both economically and operationally. Compared with the maximum accommodation point, the economic optimum or Pareto knee point provides a more appropriate operational reference for balancing renewable energy utilization, product delivery, and inventory risk. The daily trajectories in Supplementary Figure 10 correspond to the economic optimum for each scenario. The daily evolution of incremental output, product delivery, and terminal inventory in each scenario is provided in Supplementary Section S6.8 and Supplementary Figure 10

4.5 Limitations and future work

The empirical scope is defined by a Qinghai salt lake chemical park and a 24 h primary horizon, supplemented by a continuous 7 d analysis, four operating states, and four load increase levels. The cross-platform assessment additionally examines command consistency in a separate software environment. Subsequent research will extend this framework to longer operating records, additional coproduction structures, and cross-park cases for online parameter updating and model transfer.

From the perspective of methodological structure, the transferable layer includes a networked process representation based on material conservation, modeling of intermediate inventory and response delay, shift and ramping constraints, response window generation and ranking, joint technoeconomic and carbon optimization, final AC power flow validation, and process feasibility reconstruction embedded in the search. This layer is applicable to processes with continuous material flow, intermediate inventory, and process–electricity coupling, including steel, chlor-alkali, papermaking, cement, and air separation. The industry specific layer includes potassium salt evaporation and flotation, lithium adsorption and concentration, magnesium salt precipitation and dehydration, the mother liquor transfer topology, transfer coefficients, recovery rates, and quality boundaries. When the method is transferred to other industries, the equipment and state equations in this layer must be replaced and recalibrated using the corresponding operating data, while the basic structures of the window identification, regulation optimization, and network validation layers can be retained.

The framework can be extended with longer operating and historical dispatch records to update load sensitivities, response delays, and material transfer parameters, and with cross-case applications in other parks and continuous energy intensive industries. Renewable energy forecast errors, product demand uncertainty, bidirectional demand response, and market incentives can be incorporated into day ahead–intraday rolling coordination to enhance adaptability across multiple time scales.

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